Fundamentals of C++ Programming

Richard L. Halterman

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Contents

1 The Context of Software Development

IPO Software I .

1.2 Development Tools.

1.3 Learning Programming with C++ .

11.4 Exercisesl .

2 Writing a C++ Program

2.1 General Structure of a Simple C++Program .

2.2 Editing, Compiling, and Running the Program

2.3 Variations of our simple program.

2.4 Template for simple C++ programs.

1275 Exercisesl .

13 Values and Variables I

3.1 Integer Values.

3.2 Variables and Assignment.

13.3 Identifiers! .

|3.4 Additional Integer Types) .

3.5 Floating-point Types .

1376 Constants! .

3.7 Other Numeric Types.

13.8 Characters! .

3.9 Enumerated Types.

3.10 Type Inference with auto.

13.11 Exercisesl .

|4 Expressions and Arithmetic!

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4.1 Expressions.

|4.2 Mixed Type Expressions) .

4.3 Operator Precedence and Associativity

14.4 Comments! .

4.5 Formatting.

4.6 Errors and Warnings .

4.6.1 Compile-time Errors.

14.6.2 Run-time Errorsl .

4.6.3 Logic Errors .

4.6.4 Compiler Warnings.

4.7 Arithmetic Examples.

4.8 Integers vs. Floating-point Numbers .

4.8.1 Integer Implementation . . . .

4.8.2 Floating-point Implementation

4.9 More Arithmetic Operators.

4.10 Bitwise Operators.

4.11 Algorithms .

14.12 Exercises! .

|5 ConditionarExecutionl

5.1 Type bool.

5.2 Boolean Expressions.

5.3 The Simple if Statement .

5.4 Compound Statements .

1575 The if/else Statement ].

5.6 Compound Boolean Expressions . . .

15.7 Nested Conditionalsl .

5.8 Multi-way if/else Statements.

15.9 Errors in Conditional Statements! . . .

15.10 Exercisesl .

|6 Iteration!

16.1 The while Statement! .

[672 Nested Loops) .

6.3 Abnormal Loop Termination.

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16.3.1 The break statement! .

6.3.2 The goto Statement.

16.3.3 The continue Statement! .

6.4 Infinite Loops.

6.5 Iteration Examples .

6.5.1 Drawing a Tree.

6.5.2 Printing Prime Numbers ....

1676 Exercisesl .

17 OtherConditional and Iterative Statements!

1771 The switch Statement! .

7.2 The Conditional Operator.

17.3 The do/while Statement! .

17.4 The for Statement! .

17.5 Exercisesl .

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|8 Using Function?]

8.1 Introduction to Using Functions

8.2

Standard Math Functions

8.3

Maximum and Minimum

Table caption18.4 clockFunctionll

18.5 Character Functions!

18.6 Random Numbers I .

1877 Exercisesl .

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|9 Writing Functions)

119.1 Function Basicsl .

9.2 Using Functions.

9.3 Pass by Value.

9.4 Function Examples.

9.4.1 Better Organized Prime Generator

9.4.2 Command Interpreter.

9.4.3 Restricted Input ....

9.4.4 Better Die Rolling Simulator

9.4.5 Tree Drawing Function

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Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

9.4.6 Floating-point Equality.

9.4.7 Multiplication Table with Functions

9.5 Organizing Functions.

9.6 Commenting Functions.

9.7 Custom Functions vs. Standard Functions .

19.8 Exercisesl .

10 Managing Functions and Data

110.1 GlobalVariablesI .

110.2 Static Variables .

110.3 Overloaded Function^ .

10.4 Default Arguments.

110.5 Recursion .

[10.6 Making Functions Reusable) .

110.7 Pointersl .

riO.8 Reference Variables I.

[10.9 Pass by Reference) .

10.9.1 Pass by Reference via Pointers .

10.9.2 Pass by Reference via References

10.1 OHigher-order Functions.

110.11 Exercisesl .

11 Sequences

111.1 Vectorsl .

11.1.1 Declaring and Using Vectors

11.1.2 Traversing a Vector.

111.1.3 Vector Methodsl .

111.1.4 Vectors and Functions I . . .

111.1.5 Multidimensional Vectors I .

11.2 Arrays|.

11.2.1 Static Arrays.

11.2.2 Pointers and Arrays.

11.2.3 Dynamic Arrays.

j 11.2.4 Copying an Array) .

11.2.5 Multidimensional Arrays . .

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11.2.6 C Strings.

11.2.7 Command-line Arguments

|11.3 Vectors vs. Arrays] .

111 A Prime Generation with a Vector! . .

111.5 Exercisesl .

|12 Sorting and Searching)

12.1 Sorting .

112,2 Flexible Sorting) .

12.3 Search .

(12.3.1 Linear Search! .

[12.3.2 Binary Search] .

112.4 Vector Permutations! .

12.5 Randomly Permuting a Vector.

112,6 Exercisesl .

113 Standard C++ Classes!

13.1 String Objects .

13.2 Input/Output Streams.

113.3 File Streams! .

13.4 Complex Numbers .

13.5 Better Pseudorandom Number Generation

Il3.6~Exercisesl .

14 Custom Objects

15 Fine Tuning Objects

15.1 Passing Object Parameters.

15.2 Pointers to Objects and Object Arrays]

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115.3 The thi s Pointerl .442

115.4 const Methods 1 .445

15.5 Separating Method Declarations and Definitions.446

15.6 Preventing Multiple Inclusion . 453

15.7 Overloaded Operators.456

15.7.1 Operator Functions.456

15.7.2 Operator Methods . 459

115.8 stati c Membersl .460

115.9 Classes vs. structsl .464

lll5.10Friendsl .465

H5.11Exercisesl .470

[16 Building some Useful Classes)

116.1 A Better Rational NumberClassI .

16.2 Stopwatch.

16.3 Sorting with Logging.

16.4 Automating Testing.

16.5 Convenient High-quality Pseudorandom Numbers

116.6 Exercises! .

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17 Inheritance and Polymorphism!

117.1 I/O Stream Inheritance! .

117.2 Inheritance Mechanics! .

117.3 Uses of Inheritance! .

[17.4 Polymorphism] .

17.5 Alternative to Inheritance and Polymorphism

17.6 Adapter Design Pattern].

117.7 Protected Membersl .

17.8 Fine Tuning Inheritance.

17.9 Exercises! .

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[18 Memory Management! 543

|| 18.1 Memory Available to C++Programs! . 543

18.2 Manual Memory Management. 544

118.3 Linked Lists! . 549

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18.4 Resource Management 118.5 Rvalue References! . . 18.6 Smart Pointers] .

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19 Generic Programming

19.1 Function Templates

19.2 Class Templates . .

19.3 Exercises! .

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20 The Standard Template Library

12071 Containers! .

120.2 Iterators! .

20.3 Iterator Ranges.

1120.4 Lambda Functions! .

20.5 Algorithms in the Standard Library|

20.6 Namespaces.

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121 Associative Containers!

121.1 Associative Containers! . .

21.2 The std : : set Data Type

21.3 Tuples.

Table caption21.4 The std : : map Data Type

21.5 The std :: unordered map Data Type

21.6 Counting with Associative Containers

21.7 Grouping with Associative Containers

Table caption121.8 Memoizationl

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22 Handling Exceptions

122.1 Motivation! .

22.2 Exception Examples .

22.3 Custom Exceptions.

||2274 CatchingMultipleExceptions||

|22.5 Exception Mechanics! . . . . 22.6 Using Exceptions.

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©2018 Richard L. Halterman

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A Using Visual Studio 2015 to Develop C++ Programs

|B Command Line Development!

IB .0.1 Visual Studio Command Line Toolsl .

|B.0.2 Developing C++ Programs with the GNU Toolj|

[Bibliography!

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Preface

Legal Notices and Information

Permission is hereby granted to make hardcopies and freely distribute the material herein under the following conditions:

• The copyright and this legal notice must appear in any copies of this document made in whole or in part.

• None of material herein can be sold or otherwise distributed for commercial purposes without written permission of the copyright holder.

• Instructors at any educational institution may freely use this document in their classes as a primary or optional textbook under the conditions specified above.

A local electronic copy of this document may be made under the terms specified for hard copies:

• The copyright and these terms of use must appear in any electronic representation of this document made in whole or in part.

• None of material herein can be sold or otherwise distributed in an electronic form for commercial purposes without written permission of the copyright holder.

• Instructors at any educational institution may freely store this document in electronic form on a local server as a primary or optional textbook under the conditions specified above.

Additionally, a hardcopy or a local electronic copy must contain the uniform resource locator (URL) providing a link to the original content so the reader can check for updated and corrected content. The current standard URL is http: //python .cs.southern.edu/cppbook/progcpp.pdf

If you are an instructor using this book in one or more of your courses, please let me know. Keeping track of how and where this book is used helps me justify to my employer that it is providing a useful service to the community and worthy of the time I spend working on it. Simply send a message to halterman@southern. edu with your name, your institution, and the course(s) in which you use it.

The source code for all labeled listings is available at

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Chapter 1

The Context of Software Development

A computer program, from one perspective, is a sequence of instructions that dictate the flow of electrical impulses within a computer system. These impulses affect the computer’s memory and interact with the display screen, keyboard, mouse, and perhaps even other computers across a network in such a way as to produce the “magic” that permits humans to perform useful tasks, solve high-level problems, and play games. One program allows a computer to assume the role of a financial calculator, while another transforms the machine into a worthy chess opponent. Note the two extremes here:

• at the lower, more concrete level electrical impulses alter the internal state of the computer, while

• at the higher, more abstract level computer users accomplish real-world work or derive actual pleasure.

So well is the higher-level illusion achieved that most computer users are oblivious to the lower-level activity (the machinery under the hood, so to speak). Surprisingly, perhaps, most programmers today write software at this higher, more abstract level also. An accomplished computer programmer can develop sophisticated software with little or no interest or knowledge of the actual computer system upon which it runs. Powerful software construction tools hide the lower-level details from programmers, allowing them to solve problems in higher-level terms.

The concepts of computer programming are logical and mathematical in nature. In theory, computer programs can be developed without the use of a computer. Programmers can discuss the viability of a program and reason about its correctness and efficiency by examining abstract symbols that correspond to the features of real-world programming languages but appear in no real-world programming language. While such exercises can be very valuable, in practice computer programmers are not isolated from their machines. Software is written to be used on real computer systems. Computing professionals known as software engineers develop software to drive particular systems. These systems are defined by their underlying hardware and operating system. Developers use concrete tools like compilers, debuggers, and profilers. This chapter examines the context of software development, including computer systems and tools.

©2018 Richard L. Halterman

Draft date: September 25, 2018

1.1 Software

A computer program is an example of computer software. Software makes a computer a truly universal machine transforming it into the proper tool for the task at hand. One can refer to a program as a piece of software as if it were a tangible object, but software is actually quite intangible. It is stored on a medium. A hard drive, a CD, a DVD, and a USB pen drive are all examples of media upon which software can reside. The CD is not the software; the software is a pattern on the CD. In order to be used, software must be stored in the computer’s memory. Typically computer programs are loaded into memory from a medium like the computer’s hard disk. An electromagnetic pattern representing the program is stored on the computer’s hard drive. This pattern of electronic symbols must be transferred to the computer’s memory before the program can be executed. The program may have been installed on the hard disk from a CD or from the Internet. In any case, the essence that was transferred from medium to medium was a pattern of electronic symbols that direct the work of the computer system.

These patterns of electronic symbols are best represented as a sequence of zeroes and ones, digits from the binary (base 2) number system. An example of a binary program sequence is

10001011011000010001000001001110

To the underlying computer hardware, specifically the processor, a zero here and three ones there might mean that certain electrical signals should be sent to the graphics device so that it makes a certain part of the display screen red. Unfortunately, only a minuscule number of people in the world would be able to produce, by hand, the complete sequence of zeroes and ones that represent the program Microsoft Word for an Intel-based computer running the Windows 8 operating system. Further, almost none of those who could produce the binary sequence would claim to enjoy the task.

The Word program for older Mac OS X computers using a PowerPC processor works similarly to the Windows version and indeed is produced by the same company, but the program is expressed in a completely different sequence of zeroes and ones! The Intel Core i7 processor in the Windows machine accepts a completely different binary language than the PowerPC processor in the Mac. We say the processors have their own machine language.

1.2 Development Tools

If very few humans can (or want) to speak the machine language of the computers’ processors and software is expressed in this language, how has so much software been developed over the years?

Software can be represented by printed words and symbols that are easier for humans to manage than binary sequences. Tools exist that automatically convert a higher-level description of what is to be done into the required lower-level code. Higher-level programming languages like C++ allow programmers to express solutions to programming problems in terms that are much closer to a natural language like English. Some examples of the more popular of the hundreds of higher-level programming languages that have been devised over the past 60 years include FORTRAN, COBOL, Lisp, Haskell, C, Perl, Python, Java, and C#. Most programmers today, especially those concerned with high-level applications, usually do not worry about the details of underlying hardware platform and its machine language.

One might think that ideally such a conversion tool would accept a description in a natural language, such as English, and produce the desired executable code. This is not possible today because natural languages are quite complex compared to computer programming languages. Programs called compilers that translate one computer language into another have been around for over 60 years, but natural language

©2018 Richard L. Halterman

Draft date: September 25, 2018

processing is still an active area of artificial intelligence research. Natural languages, as they are used by most humans, are inherently ambiguous. To understand properly all but a very limited subset of a natural language, a human (or artificially intelligent computer system) requires a vast amount of background knowledge that is beyond the capabilities of today’s software. Fortunately, programming languages provide a relatively simple structure with very strict rules for forming statements that can express a solution to any problem that can be solved by a computer.

Consider the following program fragment written in the C++ programming language:

subtotal = 25;

tax = 3;

total = subtotal + tax;

These three lines do not make up a complete C++ program; they are merely a piece of a program. The statements in this program fragment look similar to expressions in algebra. We see no sequence of binary digits. Three words, subtotal, tax, and total, called variables, are used to hold information. Mathematicians have used variables for hundreds of years before the first digital computer was built. In programming, a variable represents a value stored in the computer’s memory. Familiar operators (= and +) are used instead of some cryptic binary digit sequence that instructs the processor to perform the operation. Since this program is expressed in the C++ language, not machine language, it cannot be executed directly on any processor. A C++ compiler is used to translate the C++ code into machine code.

The higher-level language code is called source code. The compiled machine language code is called the target code. The compiler translates the source code into the target machine language.

The beauty of higher-level languages is this: the same C++ source code can be compiled to different target platforms. The target platform must have a C++ compiler available. Minor changes in the source code may be required because of architectural differences in the platforms, but the work to move the program from one platform to another is far less than would be necessary if the program for the new platform had to be rewritten by hand in the new machine language. Just as importantly, when writing the program the human programmer is free to think about writing the solution to the problem in C++, not in a specific machine language.

Programmers have a variety of tools available to enhance the software development process. Some common tools include:

• Editors. An editor allows the user to enter the program source code and save it to files. Most programming editors increase programmer productivity by using colors to highlight language features. The syntax of a language refers to the way pieces of the language are arranged to make well-formed sentences. To illustrate, the sentence

The tall boy runs quickly to the door.

uses proper English syntax. By comparison, the sentence

Boy the tall runs door to quickly the.

is not correct syntactically. It uses the same words as the original sentence, but their arrangement does not follow the rules of English.

Similarly, programmers must follow strict syntax rules to create well-formed computer programs. Only well-formed programs are acceptable and can be compiled and executed. Some syntax-aware editors can use colors or other special annotations to alert programmers of syntax errors before the program is compiled.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 1.1 Source code to target code sequence

Executable

program

©2018 Richard L. Halterman

Draft date: September 25, 2018

• Compilers. A compiler translates the source code to target code. The target code may be the machine language for a particular platform or embedded device. The target code could be another source language; for example, the earliest C++ compiler translated C++ into C, another higher-level language. The resulting C code was then processed by a C compiler to produce an executable program. C++ compilers today translate C++ directly into machine language.

The complete set of build tools for C++ includes a preprocessor, compiler, and linker:

- Preprocessor —adds to or modifies the contents of the source file before the compiler begins processing the code. We use the services of the preprocessor mainly to #i nclude information about library routines our programs use.

- Compiler —translates C++ source code to machine code.

- Linker —combines the compiler-generated machine code with precompiled library code or compiled code from other sources to make a complete executable program. Most compiled C++ code is incapable of running by itself and needs some additional machine code to make a complete executable program. The missing machine code has been precompiled and stored in a repository of code called a library. A program called a linker combines the programmer’s compiled code and the library code to make a complete program.

We generally do not think about the preprocessor, compiler, and linker working as three separate programs (although they do); the tools we use make it appear as only one process is taking place: translating our source code to an executable program.

• Debuggers. A debugger allows a programmer to more easily trace a program’s execution in order to locate and correct errors in the program’s implementation. With a debugger, a developer can simultaneously run a program and see which line in the source code is responsible for the program’s current actions. The programmer can watch the values of variables and other program elements to see if their values change as expected. Debuggers are valuable for locating errors (also called bags ) and repairing programs that contain errors. (See Section j4.6jfor more information about programming errors.)

• Profilers. A profiler collects statistics about a program’s execution allowing developers to tune appropriate parts of the program to improve its overall performance. A profiler indicates how many times a portion of a program is executed during a particular run, and how long that portion takes to execute. Profilers also can be used for testing purposes to ensure all the code in a program is actually being used somewhere during testing. This is known as coverage. It is common for software to fail after its release because users exercise some part of the program that was not executed anytime during testing. The main purpose of profiling is to find the parts of a program that can be improved to make the program run faster.

The programming components of the development process are illustrated in Figure j 1,11

Many developers use integrated development environments (IDEs). An IDE includes editors, debuggers, and other programming aids in one comprehensive program. Examples of IDEs for C++ include Microsoft’s Visual Studio 2015, the Eclipse Foundation’s Eclipse CDT, and Apple’s XCode.

Despite the plethora of tools (and tool vendors’ claims), the programming process for all but trivial programs is not automatic. Good tools are valuable and certainly increase the productivity of developers, but they cannot write software. There are no substitutes for sound logical thinking, creativity, common sense, and, of course, programming experience.

©2018 Richard L. Halterman

Draft date: September 25, 2018

1.3 Learning Programming with C++

Bjarne Stroustrup of AT&T Bell Labs created C++ in the mid 1980s. C++ is an extension of the programming language C, a product of AT&T Bell Labs from the early 1970s. C was developed to write the Unix operating system, and C is widely used for systems-level software and embedded systems development. C++ initially provided object-oriented programming features (see Chapter jT3] and Chapter [T?) and later added generic programming capabilities. C++’s close relationship to C allows C++ programs to utilize a large collection of code developed in C.

C++ is widely used in industry for commercial software development. It is an industrial strength programming language used for developing complex systems in business, science, and engineering. Examples of software written in C++ include Microsoft Windows 8, Microsoft Office, macOS, and Adobe Creative Suite.

In order to meet the needs of commercial software development and accomplish all that it does, C++ itself is complex. While experienced programmers can accomplish great things with C++, beginners sometimes have a difficult time with it. Professional software developers enjoy the flexible design options that C++ permits, but beginners need more structure and fewer options so they can master simpler concepts before moving on to more complex ones.

This book does not attempt to cover all the facets of the C++ programming language. Experienced programmers should look elsewhere for books that cover C++ in much more detail. The focus here is on introducing programming techniques and developing good habits. To that end, our approach avoids some of the more esoteric features of C++ and concentrates on the programming basics that transfer directly to other imperative programming languages such as Java, C#, and Python. We stick with the basics and explore more advanced features of C++ only when necessary to handle the problem at hand.

1.4 Exercises

1. What is a compiler?

2. How is compiled code different from source code?

3. What tool does a programmer use to produce C++ source code?

4. What tool(s) does a programmer use to convert C++ source code into executable machine code?

5. What does the linker do?

6. Does the linker deal with files containing source code or machine language code?

7. What does the preprocessor do to source code?

8. List several advantages developing software in a higher-level language has over developing software in machine language.

9. How can an IDE improve a programmer’s productivity?

10. Name a popular C++ IDE is used by programmers developing for Microsoft Windows.

11. Name a popular C++ IDE is used by programmers developing for Apple macOS.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 2

Writing a C++ Program

Properly written C++ programs have a particular structure. The syntax must be correct, or the compiler will generate error messages and not produce executable machine language. This chapter introduces C++ by providing some simple example programs and associated fundamental concepts. Most of the concepts presented in this chapter are valid in many other programming languages as well. While other languages may implement the concepts using slightly different syntax, the ideas are directly transferable to other languages like C, Java, C#, and Ada.

2.1 General Structure of a Simple C++ Program

Listing [XT] (simple.cpp) is one of the simplest C++ programs that does something:

You can type the text as shown in Listing |271|| (simple.cpp) into an editor and save it to a file named simple.cpp. The actual name of the file is irrelevant, but the name “simple” accurately describes the nature of this program. The extension .cpp is a common extension used for C++ source code.

After creating this file with a text editor and compiling it, you can run the program. The program prints the message

This is a simple C++ program!

Listing [2T| (simple.cpp) contains four non-blank lines of code:

• #include <iostream>

This line is a preprocessing directive. All preprocessing directives within C++ source code begin with a # symbol. This one directs the preprocessor to add some predefined source code to our existing

©2018 Richard L. Halterman

Draft date: September 25, 2018

source code before the compiler begins to process it. This process is done automatically and is invisible to us.

Here we want to use an object from the i ostream library, a collection precompiled C++ code that C++ programs (like ours) can use. The iostream library contains elements that handle input and output (I/O)—printing to the display, getting user input from the keyboard, and dealing with files.

One of the items used in Listing 2.1 (simple.cpp), std : : cout, is not part of the C++ language itself. This item, along with other things related to input and output, were developed in C++, compiled, and stored in the i ostream library. The compiler needs to be aware of these i ostream items so it can compile our program. The #i nclude directive specifies a file, called a header , that contains the specifications for the library code. The compiler checks how we use std : : cout within our code against its specification in the <iostream> header to ensure that we are using the library code correctly.

Most of the programs we write use this #i nclude <iostream> directive, and some programs we will write in the future will # include other headers as well.

• int main() {

This specifies the real beginning of our program. Here we are declaring a function named main. All C++ programs must contain this function to be executable. Details about the meaning of i nt and the parentheses will appear in later chapters. More general information about functions appear in Chapter Sjand Chapter 9’

The opening curly brace at the end of the line marks the beginning of the body of a function. The body of a function contains the statements the function is to execute.

• std::cout << "This is a simple C++ program!\n";

The body of our mai n function contains only one statement. This statement directs the executing program to print the message This is a simple C+ + program! on the screen. A statement is the fundamental unit of execution in a C++ program. Functions contain statements that the compiler translates into executable machine language instructions. C++ has a variety of different kinds of statements, and the chapters that follow explore these various kinds of statements. All statements in C++ end with a semicolon (;). A more detailed explanation of this statement appears below.

• }

The closing curly brace marks the end of the body of a function. Both the open curly brace and close curly brace are required for every function definition.

Note which lines in the program end with a semicolon (;) and which do not. Do not put a semicolon after the #include preprocessor directive. Do not put a semicolon on the line containing mai n, and do not put semicolons after the curly braces.

2.2 Editing, Compiling, and Running the Program

C++ programmers have two options for C++ development environments. One option involves a commandline environment with a collection of independent tools. The other option is to use an IDE (see Section [172) which combines all the tools into a convenient package. Visual Studio is the dominant IDE on the Microsoft

©2018 Richard L. Halterman

Draft date: September 25, 2018

Windows platform, and Apple Mac developers often use the XCode IDE. AppendixJA provides an overview of how to use the Visual Studio 2015 IDE to develop a simple C++ program.

The myriad of features and configuration options in these powerful IDEs can be bewildering to those learning how to program. In a command-line environment the programmer needs only type a few simple commands into a console window to edit, compile, and execute programs. Some developers prefer the simplicity and flexibility of command-line build environments, especially for less complex projects.

One prominent command-line build system is the GNU Compiler Collection (http : //gcc . gnu . org), or GCC for short. The GCC C++ compiler, called g++, is one of most C++ standards conforming compilers available. The GCC C++ compiler toolset is available for the Microsoft Windows, Apple Mac, and Linux platforms, and it is a free, open-source software project with a world-wide development team. Appendix [Bjprovides an overview of how to use the GCC C++ compiler.

Visual Studio and XCode offer command line development options as well. Appendix [Bjprovides an overview of the Visual Studio command line development process.

2.3 Variations of our simple program

Listing |2T2) (simple2.cpp) shows an alternative way of writing Listing |271 [ (simple.cpp).

printing object. We can omit the std : : prefix and use the shorter name, cout. This directive is optional, but if we omit it, we must use the longer name. The name std stands for “standard,” and the std prefix indicates that cout is part of a collection of names called the standard namespace. The std namespace holds names for all the standard C++ types and functions that must be available to all standards-conforming C++ development environments. Components outside the standard library provided by third-party developers reside in their own separately-named namespaces. These include open-source projects and commercial libraries.

Listing |2.3|| (simple3.cpp) shows another way to use the shorter name for cout within a C++ program.

While Listing 2.2 (simple2.cpp) made the name cout known to the compiler via its focused usi ng directive, Listing 2.3 (simple3.cpp) provides a blanket using directive that makes all names in the std

©2018 Richard L. Halterman

Draft date: September 25, 2018

namespace available to the compiler. This approach offers some advantages for smaller programs, such as examples in books and online tutorials. This blanket usi ng directive allows programmers to use shorter names as in the more more focused using directives, and it also can use fewer lines of code than the more focused usi ng directives, especially when the program uses multiple elements from the std namespace.

Our choice of usi ng directives (or not) makes no difference in our final product, the executable program. The compiler generates the same machine language code for all three versions—no using, focused usi ng, and blanket usi ng. We thus must select an approach that enhances our ability to write and manage our software projects.

It is important to note that while this blanket usi ng approach has its place, its use generally is discouraged for more complex software projects. At this point we cannot fully appreciate the rationale for avoiding the usi ng namespace std directive, but later, in Section 20.6 we will have enough experience to understand the disadvantages of the blanket usi ng namespace std directive. We will strive for best practices from the start and avoid the blanket usi ng statement. We generally will use the full names of the elements in the std namespace and use the more focused using directives in our code when it makes sense to do so.

The statement in the mai n function in any of the three versions of our program uses the services of an object called std : : cout. The std : : cout object prints text on the computer’s screen. The text of the message as it appears in the C++ source code is called a string, for string of characters. Strings are enclosed within quotation marks ("). The symbols << make up the insertion operator. You can think of the message to be printed as being “inserted” into the cout object. The cout object represents the output stream; that is, text that the program prints to the console window. The end of the message contains the symbol sequence \n. This known as a character escape sequence, and this combination of backslash and the letter n represents the newline character. It indicates that the printing on that line is complete, and any subsequent printing should occur on the next line. This newline character effectively causes the cursor to move down to the next line. If you read the statement from left to right, the cout object, which is responsible for displaying text on the screen, receives the text to print terminated with the newline character to move to the next line.

For simplicity, we’ll refer to this type of statement as a print statement, even though the word print does not appear anywhere in the statement.

With minor exceptions, any statement in C++ must appear within a function definition. Our single print statement appears within the function named main.

Any function, including mai n, may contain multiple statements. In Listing 2.4 (arrow.cpp), six print statements draw an arrow on the screen:

Listing2.4: arrow.cpp

Table captionftinclude <iostream> int main() {

std:

: cout

<< "

*

\n" ;

std:

: cout

<< "

***

\n" ;

std:

: cout

<< "

•k-k-k-k k

\n" ;

std:

: cout

<< "

k

\n" ;

std:

: cout

<< "

k

\n" ;

std:

: cout

<< "

k

\n" ;

}

The output of Listing ph4| (arrow.cpp) is

©2018 Richard L. Halterman

Draft date: September 25, 2018

Each print statement “draws” a horizontal slice of the arrow. The six statements

std:

: cout

<< "

\n

std:

: cout

<< "

~k

\n

std:

: cout

<< "

\n

std:

: cout

<< "

\n

std:

: cout

<< "

\n

std:

: cout

<< "

\n

constitute the body of the main function. The body consists of all the statements between the open curly brace ({) and close curly brace (}). We say that the curly braces delimit the body of the function. The word delimit means to determine the boundaries or limits of something. The { symbol determines the beginning of the function’s body, and the } symbol specifies the end of the function’s body.

We can rewrite Listing ||2.4| (arrow.cpp) to achieve the same effect with only one long print statement as Listing |2.5[(arrow2.cpp) shows.

Listing2.5: arrow2.cpp

#include <iostream>

int main() {

std::cout <<

<<

<<

<<

<<

<<

}

" * \n"

" *** \n"

" ***** \n"

" * \n"

" * \n"

" * \n" ;

At first. Listing pL4] (arrow.cpp) and Listing |2T5| (arrow2.cpp) may appear to be identical, but upon closer inspection of this new program we see that std : : cout appears only once within mai n, and only one semicolon (;) appears within mai n. Since semicolons in C++ terminate statements, there really is only one statement. Notice that a single statement can be spread out over several lines. The statement within mai n appearing as

std::cout << "

*

\n"

<< "

\n"

<< "

~k~k

\n"

<< "

\n"

<< "

\n"

<< "

\n" ;

have just as easily been written as

std::cout << "

\n"

<< "

~k

\n"

<< "

'k'k ~k

\n"

<< "

\n"

<< "

\n"

<< "

★

\n";

Table caption©2018 Richard L. Halterman

Draft date: September 25, 2018

but the first way of expressing it better portrays how the output will appear. Read this second version carefully to convince yourself that the printed pieces will indeed flow to the std : : cout printing object in the proper sequence to produce the same picture of the arrow.

Consider the mistake of putting semicolons at the end of each of the lines in the “one statement” version:

<< "

k

\n

<< "

k k k

\n

<< "

kk k k k

\n

<< "

k

\n

<< "

k

\n

<< "

k

\n

If we put this code fragment in mai n, the program will not compile. The reason

is simple—the semicolon at the end of the first line terminates the statement on that line. The compiler expects a new statement on the next line, but

<< " *** \n";

is not a complete legal C++ statement since the << operator is missing the std : : cout object. The string " *** \n" has nothing to “flow into.”

Listing |2j6| (empty.cpp) is even simpler than Listing [XT] (simple.cpp).

Since Listing |X6| (empty.cpp) does not use the std : : cout object and so does not need the #i nclude and usi ng directives. While it is legal and sometimes even useful in C++ to write functions with empty bodies, such functions will do nothing when they execute. Listing 2.6 (empty.cpp) with its empty mai n function is, therefore, truly the simplest executable C++ program we can write, but it does nothing when we runs it!

In general, a C++ program may contain multiple functions, but we defer such generality until Chapter|9j For now, we will restrict our attention to programs with only amain function.

2.4 Template for simple C++ programs

For our immediate purposes all the programs we write will have the form shown in Figure [271 [

Our programs generally will print something, so we need the # include directive that brings the std : : cout definition from <i ostream> into our program. Depending on what we need our program to do, we may need additional #i nclude directives. The mai n function definition is required for an executable program, and we will fill its body with statements that make our program do as we wish. Later, our programs will become more sophisticated, and we will need to augment this simple template.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 2.1 The general structure of a very simple C++ program.

include directives

nt main () {

program statements

}

2.5 Exercises

1. What preprocessor directive is necessary to use statements with the std: :cout printing stream object?

2. What statement allows the short name cout to be used instead of std : : cout?

3. What does the name std stand for?

4. All C++ programs must have a function named what?

5. The body of mai n is enclosed within what symbols?

6. What operator directs information to the std : : cout output stream?

7. Write a C++ program that prints your name in the console window.

8. Write a C++ program that prints your first and last name in the console window. Your first name should appear on one line, and your last name appear on the next line.

9. What other files must you distribute with your executable file so that your program will run on a Windows PC without Visual Studio installed?

10. Can a single statement in C++ span multiple lines in the source code?

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 3

Values and Variables

In this chapter we explore some building blocks that are used to develop C++ programs. We experiment with the following concepts:

• numeric values

• variables

• declarations

• assignment

• identifiers

• reserved words

In the next chapter we will revisit some of these concepts in the context of other data types.

3.1 Integer Values

The number four (4) is an example of a numeric value. In mathematics, 4 is an integer value. Integers are whole numbers, which means they have no fractional parts, and an integer can be positive, negative, or zero. Examples of integers include 4, —19, 0, and —1005. In contrast, 4.5 is not an integer, since it is not a whole number.

C++ supports a number of numeric and non-numeric values. In particular, C++ programs can use integer values. It is easy to write a C++ program that prints the number four, as Listing|3J^(number4.cpp) shows.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Notice that unlike the programs we saw earlier. Listing |3T| (number4.cpp) does not use quotation marks ("). The number 4 appears unadorned with no quotes. The expression ' \ n ' represents a single newline character. Multiple characters comprising a string appear in double quotes ("), but, in C++, a single character represents a distinct type of data and is enclosed within single quotes ('). (Section [378] provides more information about C++ characters.) Compare Listing |3.1| (number4.cpp) to Listing f3L2| (number4-alt.cpp).

Both programs behave identically, but Listing |3T| (number4.cpp) prints the value of the number four, while Listing|3.2|(number4-alt.cpp) prints a message containing the digit four. The distinction here seems unimportant, but we will see in Section [372] that the presence or absence of the quotes can make a big difference in the output.

The statement

std::cout << "4\n" ;

sends one thing to the output stream, the string "4\n". The statement

std::cout << 4 << '\n' ;

sends two things to the output stream, the integer value 4 and the newline character ' \ n ' .

©2018 Richard L. Halterman

Draft date: September 25, 2018

In published C++ code you sometimes will see a statement such as the following: std::cout << 4 << std::endl;

This statement on the surface behaves exactly like the following statement: std::cout << 4 << '\n' ;

but the two expressions std : : endl and ' \n ' do not mean exactly the same thing. The std : : endl expression does involve a newline character, but it also performs some additional work that normally is not necessary.

Programs that do significant printing may execute faster if they terminate their output lines with ' \ n ' instead of std: :endl. The difference in speed is negligible when printing to the console, but the different can be great when printing to hies or other output streams. For most of the programs we consider, the difference in program execution speed between the two is imperceptible; nonetheless, we will prefer ' \ n ' for printing newlines because it is a good habit to form (and it requires five fewer keystrokes when editing code).

The three major modern computing platforms are Microsoft Windows, Apple macOS, and Linux. Windows handles newlines differently from macOS and Linux. Historically, the character ' \ n' represents a new line, usually known as a line feed or LF for short, and the character 1 \ r ' means carriage return, or CR for short. The terminology comes from old-fashioned typewriters which feed a piece of paper into a roller on a carriage that moves to the left as the user types (so the imprinted symbols form left to right). At the end of a line, the user must advance the roller so as to move the paper up by one line (LF) and move the carriage back all the way to its left (CR). Windows uses the character sequence CR LF for newlines, while macOS and Linux use LF. This can be an issue when attempting to edit text hies written with an editor on one platform with an editor on a different platform.

The good news is that the C++ standard guarantees that the std : : cout output stream translates the ' \ n' character as it appears in C++ source code into the correct character sequence for the target platform. This means you can print ' \ n 1 via std : : cout, and it will behave identically on all the major platforms.

In C++ source code, integers may not contain commas. This means we must write the number two thousand, four hundred sixty-eight as 2468, not 2,468. Modern C++ does support single quotes ( ' ) as digit separators, as in 2 ' 468. Using digit separators can improve the human comprehension reading large numbers in C++ source code.

In mathematics, integers are unbounded; said another way, the set of mathematical integers is infinite. In C++ the range of integers is limited because all computers have a finite amount of memory. The exact range of integers supported depends on the computer system and particular C++ compiler. C++ on most 32-bit computer systems can represent integers in the range —2,147,483,648 to +2,147,483,647.

What happens if you exceed the range of C++ integers? Try Listing |33j (exceed.cpp) on your system.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Negative three billion is too large for 32-bit integers, however, and the program’s output is obviously wrong:

1294967296

The number printed was not even negative! Most C++ compilers will issue a warning about this statement. Section |4~6| explores errors vs. warnings in more detail. If the compiler finds an error in the source, it will not generate the executable code. A warning indicates a potential problem and does not stop the compiler from producing an executable program. Here we see that the programmer should heed this warning because the program’s execution produces meaningless output.

This limited range of values is common among programming languages since each number is stored in a fixed amount of memory. Larger numbers require more storage in memory. In order to model the infinite set of mathematical integers an infinite amount of memory would be needed! As we will see later, C++ supports an integer type with a greater range. Section 4,8.1 ' provides some details about the implementation of C++ integers.

3.2 Variables and Assignment

In algebra, variables are used to represent numbers. The same is true in C++, except C++ variables also can represent values other than numbers. Listing |T4] (variable.cpp) uses a variable to store an integer value and then prints the value of the variable.

The mai n function in Listing 3.4 (variable.cpp) contains three statements:

• i nt x;

This is a declaration statement. All variables in a C++ program must be declared. A declaration specifies the type of a variable. The word i nt indicates that the variable is an integer. The name of the integer variable is x. We say that variable x has type i nt. C++ supports types other than integers, and some types require more or less space in the computer’s memory. The compiler uses the declaration to reserve the proper amount of memory to store the variable’s value. The declaration enables the compiler to verify the programmer is using the variable properly within the program; for example, we will see that integers can be added together just like in mathematics. For some other data types, however, addition is not possible and so is not allowed. The compiler can ensure that a variable involved in an addition operation is compatible with addition. It can report an error if it is not.

The compiler will issue an error if a programmer attempts to use an undeclared variable. The compiler cannot deduce the storage requirements and cannot verify the variable’s proper usage if it not declared. Once declared, a particular variable cannot be redeclared in the same context. A variable may not change its type during its lifetime.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• x = 10;

This is an assignment statement. An assignment statement associates a value with a variable. The key to an assignment statement is the symbol = which is known as the assignment operator. Here the value 10 is being assigned to the variable x. This means the value 10 will be stored in the memory location the compiler has reserved for the variable named x. We need not be concerned about where the variable is stored in memory; the compiler takes care of that detail.

After we declare a variable we may assign and reassign it as often as necessary.

• std::cout << x << ' \n ' ;

This statement prints the variable x’s current value.

Note that the lack of quotation marks here is very important. If x has the value 10, the statement

std::cout << x << '\ n ' ;

prints 10, the value of the variable x, but the statement

std::cout << "x" << '\n';

prints x, the message containing the single letter x.

The meaning of the assignment operator (=) is different from equality in mathematics. In mathematics, = asserts that the expression on its left is equal to the expression on its right. In C++, = makes the variable on its left take on the value of the expression on its right. It is best to read x = 5 as “x is assigned the value 5,” or “x gets the value 5.” This distinction is important since in mathematics equality is symmetric: if x = 5, we know 5 = x. In C++, this symmetry does not exist; the statement

5 = x;

attempts to reassign the value of the literal integer value 5, but this cannot be done, because 5 is always 5 and cannot be changed. Such a statement will produce a compiler error:

error C2106: ’= ’: left operand must be l-value

Variables can be reassigned different values as needed, as Listing|T5j(multipleassignrnent.cpp) shows.

Listing 3.5: multi pleassi gnment. cpp

#include <iostream>

int main() { i nt x; x = 10;

std:

: :cout

<<

X

<<

' \n

x =

20;

std:

: :cout

<<

X

<<

' \n

x =

30;

std:

: :cout

<<

X

<<

' \n

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

Observe the each print statement in Listing [33| (multipleassignment.cpp) is identical, but when the program runs the print statements produce different results.

A variable may be given a value at the time of its declaration; for example, Listing |3T6j (variable-init.cpp) is a variation of Listing|3.4|(variable.cpp).

Notice that in Listing f3(6| |(variable-init.cpp) the declaration and assignment of the variable x is performed in one statement instead of two. This combined declaration and immediate assignment is called initialization.

C++ supports another syntax for initializing variables as shown in ListingJ3T7]falt-variable-init.cpp).

This alternate form is not commonly used for simple variables, but it necessary for initializing more complicated kinds of variables called objects. We introduce objects in Chapter[13]and Chapter|T4|

Multiple variables of the same type can be declared and, if desired, initialized in a single statement. The following statements declare three variables in one declaration statement:

int x, y, z;

The following statement declares three integer variables and initializes two of them: int x = 0, y, z = 5;

Here y’s value is undefined. The declarations may be split up into multiple declaration statements:

int x = 0; int y; int z = 5;

In the case of multiple declaration statements the type name (here i nt) must appear in each statement.

The compiler maps a variable to a location in the computer’s memory. We can visualize a variable and its corresponding memory location as a box as shown in Figure |3.1|

We name the box with the variable’s name. Figure [3.2[ shows how the following sequence of C++ code affects memory.

int a, b; a = 2;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 3.1 Representing a variable and its memory location as a box

a

5

b = 5; a = b; b = 4;

Importantly, the statement a = b;

does not mean a and b refer to the same box (memory location). After this statement a and b still refer to separate boxes (memory locations). It simply means the value stored in b’s box (memory location) has been copied to a’s box (memory location), a and b remain distinct boxes (memory locations). The original value found in a’s box is overwritten when the contents of b’s box are copied into a. After the assignment of b to a, the reassignment of b to 4 does not affect a.

3.3 Identifiers

While mathematicians are content with giving their variables one-letter names like x, programmers should use longer, more descriptive variable names. Names such as alti tude, sum, and user_name are much better than the equally permissible a, s, and u. A variable’s name should be related to its purpose within the program. Good variable names make programs more readable by humans. Since programs often contain many variables, well-chosen variable names can render an otherwise obscure collection of symbols more understandable.

C++ has strict rules for variable names. A variable name is one example of an identifier. An identifier is a word used to name things. One of the things an identifier can name is a variable. We will see in later chapters that identifiers name other things such as functions and classes. Identifiers have the following form:

• Identifiers must contain at least one character.

• The first character must be an alphabetic letter (upper or lower case) or the underscore

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghij klmnopqrstuvwxyz_

• The remaining characters (if any) may be alphabetic characters (upper or lower case), the underscore, or a digit

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghij klmnopqrstuvwxyz_0123456789

• No other characters (including spaces) are permitted in identifiers.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 3.2 How memory changes during variable assignment

a b

int a, b; ? ?

a b

a = 2; 2 ?

a b

b = 5; 25

a b

a = b; 5 5

a b

b = 4; 54

• A reserved word cannot be used as an identifier (see Table |3.l) .

Here are some examples of valid and invalid identifiers:

• All of the following words are valid identifiers and so qualify as variable names: x, x2, total, port_22, and FLAG.

• None of the following words are valid identifiers: sub-total (dash is not a legal symbol in an identifier), first entry (space is not a legal symbol in an identifier), 4all (begins with a digit), #2 (pound sign is not a legal symbol in an identifier), and class (class is a reserved word).

C++ reserves a number of words for special use that could otherwise be used as identifiers. Called reserved words or keywords , these words are special and are used to define the structure of C++ programs and statements. Table 13.1 [ lists all the C++ reserved words.

The purposes of many of these reserved words are revealed throughout this book.

You may not use any of the reserved words in Table [3711| as identifiers. Fortunately, if you accidentally attempt to use one of the reserved words in a program as a variable name, the compiler will issue an error (see Section |4.6| for more on compiler errors).

In Listing 2.1 (simple.cpp) we used several reserved words: usi ng, namespace, and i nt. Notice that i nclude, cout, and mai n are not reserved words.

Some programming languages do not require programmers to declare variables before they are used; the type of a variable is determined by how the variable is used. Some languages allow the same variable

©2018 Richard L. Halterman

Draft date: September 25, 2018

alignas

decltype

namespace

struct

alignof

default

new

switch

and

delete

noexcept

template

and_eq

double

not

thi s

asm

do

not_eq

thread_local

auto

dynamic_cast

nullptr

throw

bitand

else

operator

true

bi tor

enum

or

try

bool

explicit

or_eq

typedef

break

export

private

typeid

case

extern

protected

typename

catch

false

public

uni on

char

float

register

unsigned

charl6_t

for

reinterpret_cast

usi ng

char32_t

f riend

return

virtual

class

goto

short

voi d

compl

if

signed

volatile

const

inline

sizeof

wchar_t

constexpr

int

static

whi le

const_cast

long

static_assert

xor

continue

mutable

static_cast

xor_eq

Table captionTable 3.1: C++ reserved words. C++ reserves these words for specific purposes in program construction. None of the words in this list may be used as an identifier; thus, you may not use any of these words to name a variable.

to assume different types as its use differs in different parts of a program. Such languages are known as dynamically-typed languages. C++ is a statically-typed language. In a statically-typed language, the type of a variable must be explicitly specified before it is used by statements in a program. While the requirement to declare all variables may initially seem like a minor annoyance, it offers several advantages:

• When variables must be declared, the compiler can catch typographical errors that dynamically-typed languages cannot detect. For example, consider the following section of code:

int ZERO;

ZERO = 1;

The identifier in the first line ends with a capital “Oh.” In the second line, the identifier ends with the digit zero. The distinction may be difficult or impossible to see in a particular editor or printout of the code. A C++ compiler would immediately detect the typo in the second statement, since ZERO (last letter a zero) has not been declared. A dynamically-typed language would create two variables: ZERO and ZERO.

• When variables must be declared, the compiler can catch invalid operations. For example, a variable may be declared to be of type i nt, but the programmer may accidentally assign a non-numeric value to the variable. In a dynamically-typed language, the variable would silently change its type introducing an error into the program. In C++, the compiler would report the improper assignment as error, since once declared a C++ variable cannot change its type.

• Ideally, requiring the programmer to declare variables forces the programmer to plan ahead and think more carefully about the variables a program might require. The purpose of a variable is tied to its type, so the programmer must have a clear notion of the variable’s purpose before declaring it. When

©2018 Richard L. Halterman

Draft date: September 25, 2018

variable declarations are not required, a programmer can “make up” variables as needed as the code is written. The programmer need not do the simple double check of the variable’s purpose that writing the variable’s declaration requires. While declaring the type of a variable specifies its purpose in only a very limited way, any opportunity to catch such errors is beneficial.

• Statically-typed languages are generally more efficient than dynamically-typed languages. The compiler knows how much storage a variable requires based on its type. The space for that variable’s value will not change over the life of the variable, since its type cannot change. In a dynamically typed language that allows a variable to change its type, if a variable’s type changes during program execution, the storage it requires may change also, so memory for that variable must be allocated elsewhere to hold the different type. This memory reallocation at run time slows down the program’s execution.

C++ is a case-sensitive language. This means that capitalization matters, i f is a reserved word, but none of If, IF, or i F are reserved words. Identifiers are case sensitive also; the variable called Name is different from the variable called name.

Since it can be confusing to human readers, you should not distinguish variables merely by names that differ in capitalization. For the same reason, it is considered poor practice to give a variable the same name as a reserved word with one or more of its letters capitalized.

3.4 Additional Integer Types

C++ supports several other integer types. The type short i nt, which may be written as just short, represents integers that may occupy fewer bytes of memory than the i nt type. If the short type occupies less memory, it necessarily must represent a smaller range of integer values than the i nt type. The C++ standard does not require the short type to be smaller than the i nt type; in fact, they may represent the same set of integer values. The Tong i nt type, which may be written as just long, may occupy more storage than the i nt type and thus be able to represent a larger range of values. Again, the standard does not require the long type to be bigger then the i nt type. Finally, the long long int type, or just long long, may be larger than a long. The C++ standard guarantees the following relative ranges of values hold:

short int < int < long int < long long int

On a small embedded device, for example, all of these types may occupy the exact same amount of memory and, thus, there would be no advantage of using one type over another. On most systems, however, there will some differences in the ranges.

C++ provides integer-like types that exclude negative numbers. These types include the word unsigned in their names, meaning they do not allow a negative sign. The unsigned types come in various potential sizes in the same manner as the signed types. The C++ standard guarantees the following relative ranges of unsigned values:

unsigned short < unsigned < unsigned long < unsigned long long

Table |3.2| lists the differences among the signed and unsigned integer types in Visual C++. Notice that the corresponding signed and unsigned integer times occupy the same amount of memory. As a result, the unsigned types provide twice the range of positive values available to their signed counterparts. For applications that do not require negative numbers, the unsigned type may be a more appropriate option.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Type Name

Short Name

Storage

Smallest Magnitude

Largest Magnitude

short int

short

2 bytes

-32,768

32,767

int

int

4 bytes

-2,147,483,648

2,147,483,647

long int

long

4 bytes

-2,147,483,648

2,147,483,647

long long int

long long

8 bytes

-9,223,372,036,854,775,808

9,223,372,036,854,775,807

unsigned short

unsigned short

2 bytes

0

65,535

unsigned int

unsigned

4 bytes

0

4,294,967,295

unsigned long int

unsigned long

4 bytes

0

4,294,967,295

unsigned long long int

unsigned long long

8 bytes

0

18,446,744,073,709,551,615

Table captionTable 3.2: Characteristics of Visual C++ Integer Types

Within the source code, any unadorned numerical literal without a decimal point is interpreted as an i nt literal; for example, in the statement

int x = 4456;

the literal value 4456 is an i nt. In order to represent 4456 as an long, append an L, as in long x = 4456L;

C++ also permits the lower-case l ( elle ), as in long x = 44561;

but you should avoid it since on many display and printer fonts it looks too much like the digit 1 (one). Use the LL suffix for long long literals. The suffixes for the unsigned integers are u (unsi gned), us (unsigned short), uL (unsigned long), and uLL (unsi gned long long). The capitalization is unimportant, although capital Ls are preferred.

Within C++ source code all integer literals are int values unless an L or 1 is appended to the end of the number; for example, 2 is an i nt literal, while 2L is along literal.

3.5 Floating-point Types

Many computational tasks require numbers that have fractional parts. For example, the formula from mathematics to compute the area of a circle given the circle’s radius, involves the value 7t, which is approximately 3.14159. C++ supports such non-integer numbers, and they are called floating-point numbers. The name comes from the fact that during mathematical calculations the decimal point can move or “float” to various positions within the number to maintain the proper number of significant digits. The types float and double represent different types of floating-point numbers. The type double is used more often, since it stands for “double-precision floating-point,” and it can represent a wider range of values with more digits of

precision. The float type represents single-precision floating-point values that are less precise. Table 3.3

provides some information about floating-point values as commonly implemented on 32-bit computer systems. Floating point numbers can be both positive and negative.

As you can see from Table 3.3, doubles provide more precision at the cost of using more memory. Listing |3.8) (pi-print.cpp) prints an approximation of the mathematical value n.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Type

Storage

Smallest Magnitude

Largest Magnitude

Minimum Precision

float

4 bytes

1.17549 x 10~ 38

3.40282 x 10+ 38

6 digits

double

8 bytes

2.22507 x 10- 308

1.79769 x 10+ 308

15 digits

long double

8 bytes

2.22507 x 10- 308

1.79769 x 10+ 308

15 digits

Table captionTable 3.3: Characteristics of Floating-point Numbers on 32-bit Computer Systems

Listing3.8: pi-print.cpp

#include <iostream>

int main() {

double pi = 3.14159; std::cout << "Pi = " << pi << std::cout << "or " << 3.14 <<

}

' \n ' ;

" for short" << '\n' ;

The first line in Listing 3.8 (pi-print.cpp) declares a variable named pi and assigns it a value. The second line in Listing 3.8 (pi-print.cpp) prints the value of the variable pi, and the third line prints a literal value. Any literal numeric value with a decimal point in a C++ program automatically has the type double, so

3.14

has type double. To make a literal floating-point value a float, you must append an f or F to the number, as in

3.14f

(The f or F suffix is used with literal values only; you cannot change a double variable into a float variable by appending an f. Attempting to do so would change the name of the variable!)

All floating-point literals are double values unless an f or F is appended to the end of the number; for example, 2.0isadouble literal, while 2. Qf is a float literal.

Floating-point numbers are an approximation of mathematical real numbers. As in the case of the i nt data type, the range of floating-point numbers is limited, since each value requires a fixed amount of memory. In some ways, though, i nts are very different from doubles. Any integer within the range of the i nt data type can be represented exactly. This is not true for the floating-point types. Consider the real number K. Since 7t contains an infinite number of digits, a floating-point number with finite precision can only approximate its value. Since the number of digits available is limited, even numbers with a finite number of digits have no exact representation; for example, the number 23.3123400654033989 contains too many digits for the double type and must be approximated as 23.3023498654034. Section 4.8.2 contains more information about the consequences of the inexact nature of floating-point numbers.

We can express floating-point numbers in scientific notation. Since most programming editors do not provide superscripting and special symbols like x, C++ slightly alters the normal scientific notation. The number 6.022 x 10 23 is written 6.022e23. The number to the left of the e (we can use capital E as well) is

©2018 Richard L. Halterman

Draft date: September 25, 2018

the mantissa, and the number to the right of the e is the exponent of 10. As another example, —5.1 x 10 4 is expressed in C++ as -5 . le-4. Listing T9| (scientificnotation.cpp) prints some scientific constants using scientific notation.

Listing 3.9: sc-ient-ificnotation. cpp

#include <iostream> int main() {

double avogadros_number = 6.022e23, std::cout << "Avogadro's number = " std::cout << "Speed of light = " <<

}

c = 2.998e8;

<< avogadros_number << 1 \n' c << 1 \n 1 ;

Section 4.8.2 provides some insight into the implementation of C++ floating-point values and explains how

internally all floating-point numbers are stored in exponential notation with a mantissa and exponent.

3.6 Constants

In Listing |3.9| (scientificnotation.cpp), Avogadro’s number and the speed of light are scientific constants; that is, to the degree of precision to which they have been measured and/or calculated, they do not vary. C++ supports named constants. Constants are declared like variables with the addition of the const keyword:

const double PI = 3.14159;

Once declared and initialized, a constant can be used like a variable in all but one way—a constant may not be reassigned. It is illegal for a constant to appear on the left side of the assignment operator (=) outside its declaration statement. A subsequent statement like

PI = 2.5;

would cause the compiler to issue an error message:

error C3892: ’PI’: you cannot assign to a variable that is const

and fail to compile the program. Since the scientific constants do not change, Listing pTlOj (const.cpp) is a better version of Listing jL9| (scientificnotation.cpp).

Since it is illegal to assign a constant outside of its declaration statement, all constants must initialized where they are declared.

By convention, C++ programmers generally express constant names in all capital letters; in this way, within the source code a human reader can distinguish a constant quickly from a variable.

©2018 Richard L. Halterman

Draft date: September 25, 2018

3.7 Other Numeric Types

C++ supports several other numeric data types:

• long int — typically provides integers with a greater range than the i nt type; its abbreviated name is long. It is guaranteed to provide a range of integer values at least as large as the i nt type.

An integer literal with a L suffix, as in 19L, has type long. A lower case elle (1) is allowed as a suffix as well, but you should not use it because it is difficult for human readers to distinguish between 1 (lower case elle) and 1 (digit one). (The L suffix is used with literal values only; you cannot change an i nt variable into a long by appending an L. Attempting to do so would change the name of the variable!)

• short i nt —typically provides integers with a smaller range than the i nt type; its abbreviated name is short. It is guaranteed that the range of i nts is at least as big as the range of shorts.

• unsi gned i nt —is restricted to nonnegative integers; its abbreviated name is unsi gned. While the unsigned type is limited in nonnegative values, it can represent twice as many positive values as the i nt type. (The name i nt is actually the short name for si gned i nt and i nt can be written as si gned.)

• long double — can extend the range and precision of the double type.

While the C++ language standard specifies minimum ranges and precision for all the numeric data types, a particular C++ compiler may exceed the specified minimums.

C++ provides such a variety of numeric types for specialized purposes usually related to building highly efficient programs. We will have little need to use many of these types. Our examples will use mainly the numeric types i nt for integers, double for an approximation of real numbers, and, less frequently, unsi gned when nonnegative integral values are needed.

3.8 Characters

The char data type is used to represent single characters: letters of the alphabet (both upper and lower case), digits, punctuation, and control characters (like newline and tab characters). Most systems support the American Standard Code for Information Interchange (ASCII) character set. Standard ASCII can represent 128 different characters. Table 13.41 lists the ASCII codes for various characters.

In C++ source code, characters are enclosed by single quotes ( ' ), as in

char ch = 'A' ;

Standard (double) quotes (") are reserved for strings, which are composed of characters, but strings and chars are very different. C++ strings are covered in Section 11.2.6 The following statement would produce a compiler error message:

ch = "A";

since a string cannot be assigned to a character variable.

Internally, chars are stored as integer values, and C++ permits assigning numeric values to char variables and assigning characters to numeric variables. The statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

0

null

16

32

space

48

0

64

e

80

P

96

112

P

1

17

33

1

49

1

65

A

81

Q

97

a

113

q

2

18

34

ii

50

2

66

B

82

R

98

b

114

r

3

19

35

#

51

3

67

C

83

S

99

c

115

s

4

20

36

$

52

4

68

D

84

T

100

d

116

t

5

21

37

%

53

5

69

E

85

U

101

e

117

u

6

22

38

&

54

6

70

F

86

V

102

f

118

V

7

bell

23

39

i

55

7

71

G

87

w

103

g

119

w

8

backspace

24

40

(

56

8

72

H

88

X

104

h

120

X

9

tab

25

41

)

57

9

73

I

89

Y

105

i

121

y

10

newline

26

42

~k

58

:

74

3

90

z

106

j

122

Z

11

27

43

+

59

>

75

K

91

[

107

k

123

{

12

formfeed

28

44

>

60

<

76

L

92

\

108

1

124

1

13

return

29

45

61

=

77

M

93

]

109

m

125

}

14

30

46

.

62

>

78

N

94

A

110

n

126

~

15

31

47

/

63

?

79

0

95

111

0

127

Table captionTable 3.4: ASCII codes for characters

ch = 65;

assigns a number to a cha r variable to show that this perfectly legal. The value 65 is the ASCII code for the character A. If ch is printed, as in

ch = 65;

std::cout << ch;

the corresponding character. A, would be printed because ch’s declared type is char, not i nt or some other numeric type.

Listing |3.1 l|[ (charexample.cpp) shows how characters can be used within a program.

The program displays A, A, A

The first A is printed because the statement chi = 65;

assigns the ASCII code for A to chi. The second A is printed because the statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

ch2 = 'A' ;

assigns the literal character A to ch2. The third A is printed because the literal character ' A' is sent directly to the output stream.

Integers and characters can be freely assigned to each other, but the range of chars is much smaller than the range of i nts, so care must be taken when assigning an i nt value to a cha r variable.

Some characters are non-printable characters. The ASCII chart lists several common non-printable characters:

1 \ n ' —the newline character 1 \ r ' —the carriage return character 1 \ b ' —the backspace character

1 \ a ' —the “alert” character (causes a “beep” sound or other tone on some systems) 1 \ t' —the tab character 1 \ f' —the formfeed character

1 \ 0 ' —the null character (used in C strings, see Section 11.2.6)

These special non-printable characters begin with a backslash (\) symbol. The backslash is called an escape symbol, and it signifies that the symbol that follows has a special meaning and should not be interpreted literally. This means the literal backslash character must be represented as two backslashes:

'W.

These special non-printable character codes can be embedded within strings. To embed a backslash within a string, you must escape it; for example, the statement

std::cout << "C:\\Dev\\cppcode" << ' \n ' ;

would print

C:\Dev\cppcode

See what this statement prints:

std::cout << "AB\bCD\aEF" << '\n' ;

The following two statements behave identically:

std::cout << "End of line" << '\n' ; std::cout << "End of line\n";

On the Microsoft Windows platform, the character sequence "\r\n" (carriage return, line feed) appears at the end of lines in text files. Under Unix and Linux, lines in text files end with ' \ n ' (line feed). On Apple Macintosh systems, text file lines end with the ' \ r ' (carriage return) character. The compilers that adhere to the C++ standard will ensure that the ' \ n ' character in a C++ program when sent to the output stream will produce the correct end-of-line character sequence for the given platform.

©2018 Richard L. Halterman

Draft date: September 25, 2018

3.9 Enumerated Types

C++ allows a programmer to create a new, very simple type and list all the possible values of that type. Such a type is called an enumerated type , or an enumeration type. The enum keyword introduces an enumerated type. The following shows the simplest way to define an enumerated type:

enum Color { Red, Orange, Yellow, Green, Blue, Violet };

Here, the new type is named Color, and a variable of type Color may assume one of the values that appears in the list of values within the curly braces. The semicolon following the close curly brace is required. Sometimes the enumerated type definition is formatted as

enum Color {

Red,

Orange,

Yellow,

Green,

Blue,

Violet

};

but the formatting makes no different to the compiler.

The values listed with the curly braces constitute all the values that a variable of the enumerated type can attain. The name of each value of an enumerated type must be a valid C++ identifier (see Section [|3.3| .

Given the Color type defined as above, we can declare and use variables of the enum type as shown by the following code fragment:

Color myColor; myColor = Orange;

Here the variable myColor has our custom type Color, and its value is Orange.

When declaring enumerated types in this manner it is illegal to reuse an enumerated value name within another enumerated type within the same program. In the following code, the enumerated value Light appears in both the Shade type and Wei ght type:

enum Shade { Dark, Dim, Light, Bright }; enum Weight { Light, Medium, Heavy };

These two enumerated types are incompatible because they share the value Light, and so the compiler will issue an error.

This style of enumerated type definition is known as an unscoped enumeration. C++ inherits this unscoped enumeration style from the C programming language. The C++ standards committee introduced relatively recently an enhanced way of defining enumerated types known as scoped enumerations, also known as enumeration classes. Scoped enumerations solve the problem of duplicate enumeration values in different types. The following definitions are legal within the same program:

enum class Shade { Dark, Dim, Light, Bright }; enum class Weight { Light, Medium, Heavy };

When referring to a value from a scoped enumeration we must prepend the name of its type (class), as in

©2018 Richard L. Halterman

Draft date: September 25, 2018

Shade color = Shade::Light;

Weight mass = Weight::Light;

In this case Shade and Wei ght are the scoped enumeration types defined above. Prefixing the type name to the value with the : : operator enables the compiler to distinguish between the two different values. Scoped enumerations require the type name prefix even if the program contains no other enumerated types. In modern C++ development, scoped enumerations are preferable to unscoped enumerations. You should be familiar with unscoped enumerations, though, as a lot of published C++ code and older C++ books use unscoped enumerations.

Whether scoped or unscoped, the value names within an enum type must be unique. The convention in C++ is to captialize the first letter of an enum type and its associated values, although the language does not enforce this convention.

An enum type is handy for representing a small number of discrete, non-numeric options. For example, consider a program that controls the movements made by a small robot. The allowed orientations are forward, backward, left, right, up, and down. The program could encode these movements as integers, where 0 means left, 1 means backward, etc. While that implementation will work, it is not ideal. Integers may assume many more values than just the six values expected. The compiler cannot ensure that an integer variable representing a robot move will stay in the range 0...5. What if the programmer makes a mistake and under certain rare circumstances assigns a value outside of the range 0...5? The program then will contain an error that may result in erratic behavior by the robot. With enum types, if the programmer uses only the named values of the enum type, the compiler will ensure that such a mistake cannot happen.

A particular enumerated type necessarily has far fewer values than a type such as i nt. Imagine making an integer enum type and having to list all of its values! (The standard 32-bit i nt type represents over four billion values.) Enumerated types, therefore, are practical only for types that have a relatively small range of values.

3.10 Type Inference with auto

C++ requires that a variable be declared before it is used. Ordinarily this means specifying the variable’s type, as in

int count; char ch; double limit;

A variable may be initialized when it is declared:

int count = 0; char ch = 'Z ' ; double limit = 100.0;

Each of the values has a type: 0 is an i nt, ' Z ' is a char, and 0.0 is a double. The auto keyword allows the compiler to automatically deduce the type of a variable if it is initialized when it is declared:

auto count = 0; auto ch = 'Z' ; auto limit = 100.0;

The auto keyword may not be used without an accompanying initialization; for example, the following declaration is illegal:

©2018 Richard L. Halterman

Draft date: September 25, 2018

auto x;

because the compiler cannot deduce x’s type.

Automatic type inference is supported only by compilers that comply with the latest C++11 standard. Programmers using older compilers must specify a variable’s exact type during the variable’s declaration.

Automatic type deduction with auto is not useful to beginning C++ programmers. It is just as easy to specify the variable’s type. The value of auto will become clearer when we consider some of the more advanced features of C++ (see Section f20T2| .

3.11 Exercises

1. Will the following lines of code print the same thing? Explain why or why not.

std::cout << 6 << '\n' ; std::cout << "6" << '\n' ;

2. Will the following lines of code print the same thing? Explain why or why not.

std::cout << x << '\ n ' ; std::cout << "x" << '\ n ' ;

3. What is the largest i nt available on your system?

4. What is the smallest i nt available on your system?

5. What is the largest double available on your system?

6. What is the smallest double available on your system?

7. What C++ data type represents nonnegative integers?

8. What happens if you attempt to use a variable within a program, and that variable is not declared?

9. What is wrong with the following statement that attempts to assign the value ten to variable x?

10 = x;

10. Once a variable has been properly declared and initialized can its value be changed?

11. What is another way to write the following declaration and initialization?

int x = 10;

12. In C++ can you declare more than variable in the same declaration statement? If so, how?

13. In the declaration

int a; int b;

©2018 Richard L. Halterman

Draft date: September 25, 2018

do a and b represent the same memory location?

14. Classify each of the following as either a legal or illegal C++ identifier:

(a) fred

(b) if

(c) 2x

(d) -4

(e) sum_total

(f) sumTotal

(g) sum-total

(h) sum total

(i) sumtotal

(j) While

(k) x2

(l) Private

(m) public

(n) $16

(o) xTwo

(p) _static

(q) _4

(r) _

(s) 10%

(t) a27834

(u) wilma ' s

15. What can you do if a variable name you would like to use is the same as a reserved word?

16. Why does C++ require programmers to declare a variable before using it? What are the advantages of declaring variables?

17. What is the difference between float and double?

18. How can a programmer force a floating-point literal to be a float instead of a double?

19. How is the value 2.45 x 10~ 5 expressed as a C++ literal?

20. How can you ensure that a variable’s value can never be changed after its initialization?

21. How can you extend the range of i nt on some systems?

22. How can you extend the range and precision of double on some systems?

23. Write a program that prints the ASCII chart for all the values from 0 to 127.

24. Is " i " a string literal or character literal?

25. Is ' i ' a string literal or character literal?

©2018 Richard L. Halterman

Draft date: September 25, 2018

26. Is it legal to assign a cha r value to an i nt variable?

27. Is it legal to assign an i nt value to a cha r variable?

28. What is printed by the following code fragment?

i nt x; x = ' A ' ;

std::cout << x << '\n' ;

29. What is the difference between the character ' n ' and the character 1 \n ' ?

30. Write a C++ program that simply emits a beep sound when run.

31. Create an unscoped enumeration type that represents the days of the week.

32. Create a scoped enumeration type that represents the days of the week.

33. Create an unscoped enumeration type that represents the months of the year.

34. Create a scoped enumeration type that represents the months of the year.

35. Determine the exact type of each of the following variables:

(a)

auto

a = 5;

(b)

auto

b = false;

(c)

auto

c = 9.3;

(d)

auto

d = 5.If;

(e)

auto

e - 5L;

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 4

Expressions and Arithmetic

This chapter uses the C++ numeric types introduced in Chapter [3] to build expressions and perform arithmetic. Some other important concepts are covered—user input, source formatting, comments, and dealing with errors.

4.1 Expressions

A literal value like 34 and a properly declared variable like x are examples of simple expressions. We can use operators to combine values and variables and form more complex expressions. Listing [4T| (adder.cpp) shows how the addition operator (+) is used to add two integers.

In Listing [[4l| (adder.cpp):

• int valuel, value2, sum;

This statement declares three integer variables, but it does not initialize them. As we examine the rest of the program we will see that it would be superfluous to assign values to the variables here.

• std::cout << "Please enter two integer values:

This statement prompts the user to enter some information. This statement is our usual print statement, but it is not terminated with the end-of-line marker ' \ n '. This is because we want the cursor to remain at the end of the printed line so when the user types in values they appear on the same line as the message prompting for the values. When the user presses the enter key to complete the input, the cursor will automatically move down to the next line.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• std::cin >> valuel >> value2;

This statement causes the program’s execution to stop until the user types two numbers on the keyboard and then presses enter. The first number entered will be assigned to valuel, and the second number entered will be assigned to value2. Once the user presses the enter key, the value entered is assigned to the variable. The user may choose to type one number, press enter, type the second number, and press enter again. Instead, the user may enter both numbers separated by one of more spaces and then press enter only once. The program will not proceed until the user enters two numbers.

The std : : ci n input stream object can assign values to multiple variables in one statement, as shown here:

int numl, num2, num3;

std::cin >> numl >> num2 >> num3;

A common beginner’s mistake is use commas to separate the variables, as in

int numl std::cin

num2, num3;

>> numl, num2,

num3;

The compiler will not generate an error message, because it is legal C++ code. The statement, however, will not assign the three variables from user input as desired. The comma operator in C++ has different meanings in different contexts, and here it is treated like a statement separator; thus, the variables num2 and num3 are not involved with the std : : ci n input stream object. We will have no need to use the comma operator in this way, but you should be aware of this potential pitfall.

std : : ci n is a object that can be used to read input from the user. The >> operator—as used here in the context of the std : : ci n object—is known as the extraction operator. Notice that it is “backwards” from the << operator used with the std : : cout object. The std : : ci n object represents the input stream—information flowing into the program from user input from the keyboard. The > > operator extracts the data from the input stream std : : ci n and assigns the pieces of the data, in order, to the various variables on its right.

• sum = valuel + value2;

This is an assignment statement because it contains the assignment operator (=). The variable sum appears to the left of the assignment operator, so sum will receive a value when this statement executes. To the right of the assignment operator is an arithmetic expression involving two variables and the addition operator. The expression is evaluated by adding together the values of the two variables. Once the expression’s value has been determined, that value can be assigned to the sum variable.

All expressions have a value. The process of determining the expression’s value is called evaluation. Evaluating simple expressions is easy. The literal value 54 evaluates to 54. The value of a variable named x is the value stored in the memory location reserved for x. The value of a more complex expression is found by evaluating the smaller expressions that make it up and combining them with operators to form potentially new values.

Table 4.1 lists the main C++ arithmetic operators. Table 4.1 The common arithmetic operations, ad

dition, subtraction, and multiplication, behave in the expected way. All these operators are classified as binary operators because they operate on two operands. In the statement

x = y + z;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Operator

Meaning

+

addition

subtraction

■k

multiplication

/

division

%

modulus

Table captionTable 4.1: The simple C++ arithmetic operators

the right side is an addition expression y + z. The two operands of the + operator are y and z.

Two of the operators above, + and serve also as unary operators. A unary operator has only one operand. The - unary operator expects a single numeric expression (literal number, variable, or complex numeric expression within parentheses) immediately to its right; it computes the additive inverse of its operand. If the operand is positive (greater than zero), the result is a negative value of the same magnitude; if the operand is negative (less than zero), the result is a positive value of the same magnitude. Zero is unaffected. For example, the following code sequence

i nt x = 3; int y = -4; i nt z = 0;

std::cout << -x << " " << -y << " " -z << ' \ n' ; within a program would print

-3 4 0

The following statement

std::cout << -(4 - 5) << '\n' ; within a program would print

The unary + operator is present only for completeness; when applied to a numeric value, variable, or expression, the resulting value is no different from the original value of its operand. Omitting the unary + operator from the following statement

x = +y;

does not change the statement’s behavior.

All the arithmetic operators are subject to the limitations of the data types on which they operate; for example, on a system in which the largest i nt is 2,147,483,647, the expression

2147483647 + 1

will not evaluate to the correct answer since the correct answer falls outside the range of i nts.

If you add, subtract, multiply, is divide two i nts, the result is an integer. As long as the operation does not exceed the range of i nts, the arithmetic works as expected. Division, however, is another matter. The statement

std::cout << 10/3 << " " << 3/10 << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 4.1 Integer division vs. integer modulus. Integer division produces the quotient, and modulus produces the remainder. In this example, 25/3 is 8, and 25963 is 1.

8 ---=/ 25/3

3)~25

-24

]_ - 25%3

prints

3 0

because in the first case 10 divided by 3 is 3 with a remainder of 1, and in the second case 3 divided by 10 is 0 with a remainder of 3. Since integers are whole numbers, any fractional part of the answer must be discarded. The process of discarding the fractional part leaving only the whole number part is called truncation. 10 divided by 3 should be 3.3333..., but that value is truncated to 3. Truncation is not rounding; for example, 11 divided by 3 is 3.6666..., but it also truncates to 3.

Truncation simply removes any fractional part of the value. Both 10.01 and 10.999 truncate to 10.

It does not round.

The modulus operator (96) computes the remainder of integer division; thus, std: : cout << 10963 << " " << 39610 << ' \n' ;

prints

3

since 10 divided by 3 is 3 with a remainder of 1, and 3 divided by 10 is 0 with a remainder of 3. Figure [4~T| uses long division for a more hands on illustration of how the integer division and modulus operators work.

The modulus operator is more useful than it may first appear. Listing |471T| (tirneconv.cpp) shows how we can use it to convert a given number of seconds to hours, minutes, and seconds.

In contrast to integer arithmetic, floating-point arithmetic with doubles behaves as expected:

std::cout << 10.0/3.0 << " " << 3.0/10.0 << '\n' ;

prints

3.33333 0.3

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Figure 4.2 Range of ints vs. range of doubles

<

Range of double

^ Range of int ^

<■

WV

■>

+1.8 x 10

308

-2.1 x 10 y

+2.1 x 10 a

+1.8 x 10

308

Since a cha r is stored internally as a number (see Section 3.8), we can perform arithmetic on characters. We will have little need to apply mathematics to characters, but sometimes it is useful. As an example, the lower-case letters of the alphabet a-z occupy ASCII values 97-123, with a = 97, b = 98, etc. The uppercase letters A-Z are coded as 65-91, with A = 65, B = 66, etc. To capitalize any lower-case letter, you need only subtract 32, as in

char lower = 'd' , upper = lower - 32; std::cout << upper << '\n' ;

This section of code would print D. If you do not remember the offset of 32 between upper- and lower-case letter, you can compute it with the letters themselves:

upper = lower - ('a' - 'A');

In this case, if lower has been assigned any value in the range ' a ' to ' z ' , the statement will assign to upper the capitalized version of lower. On the other hand, if lower’s value is outside of that range, upper will not receive a meaningful value.

4.2 Mixed Type Expressions

Expressions may contain mixed elements; for example, the following program fragment int x = 4;

double y = 10.2, sum; sum = x + y;

adds an i nt to a double, and the result is being assigned to a double. How is the arithmetic performed?

As shown in Figure 4.2, the range of i nts falls completely within the range of doubles; thus, any i nt value can represented by a double. The i nt 4 also can be expressed as the double 4.0. In fact, since the largest i nt on most systems is 2,147,483,647, the minimum 15 digits of double precision are more than adequate to represent all integers exactly. This means that any i nt value can be represented by a double. The converse is not true, however. 2,200,000,000 can be represented by a double but it is too big for the i nt type. We say that the double type is wider than the i nt type and that the i nt type is narrower than the double type.

It would be reasonable, then, to be able to assign i nt values to double variables. The process is called widening, and it is always safe to widen an i nt to a double. The following code fragment

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double dl; int il = 500; d 1 = i 1;

std::cout << "dl = " << dl << '\n' ; is legal C++ code, and when part of a complete program it would display

= 500

Assigning adoubletoanint variable is not always possible, however, since the double value may not be in the range of i nts. Furthermore, if the double variable falls within the range of i nts but is not a whole number, the int variable is unable to the manage fractional part. Consider the following code fragment:

double d = 1.6; int i = d;

The second line assigns 1 to i. Truncation loses the 0.6 fractional part (see Section 4.1). Note that proper rounding is not done. The Visual C++ compiler will warn us of a potential problem:

warning C4244: '= ': conversion from ’double’ to ’int’, possible loss of data

This warning reminds us that some information may be lost in the assignment. While the compiler and linker will generate an executable program when warnings are present, you should carefully scrutinize all warnings. This warning is particularly useful, since it is easy for errors due to the truncation of floatingpoint numbers to creep into calculations.

Converting from a wider type to a narrower type (like double to i nt) is called narrowing. It often is necessary to assign a floating-point value to an integer variable. If we know the value to assign is within the range of i nts, and the value has no fractional parts or its truncation would do no harm, the assignment is safe. To perform the assignment without a warning from the compiler, we use a procedure called a cast, also called a type cast. The cast forces the compiler to accept the assignment without a issuing a warning. The following statement convinces the compiler to accept the double-to-i nt assignment without a warning:

i = static_cast<int> (d) ;

The reserved word stati c_cast performs the narrowing conversion and silences the compiler warning. The item to convert (in this case the variable d) is placed in the parentheses, and the desired type (in this case the type i nt) appears in the angle brackets. The statement

i = static_cast<int> (d) ;

does not change the type of the variable d; d is declared to be a double and so must remain a double variable. The statement makes a copy of d’s value in a temporary memory location, converting it to its integer representation during the process.

We also can cast literal values and expressions:

i = static_cast<int> (1.6); i = static_cast<int> (x + 2.1);

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Narrowing a floating-point value to an integer discards any fractional part. Narrowing truncates; it does not round. For example, the double value 1.7 narrows to the i nt value 1.

The widening conversion is always safe, so a type cast is not required. Narrowing is a potentially dangerous operation, and using an explicit cast does not remove the danger—it simply silences the compiler. For example, consider Listing |42| (badnarrow.cpp).

The Visual C++ compiler issues a warning about the possible loss of precision when assigning d to i. Silencing the warning with a type cast in this case is a bad idea; the program’s output indicates that the warning should be heeded:

= 2.2e+009, i = -2147483648

The printed values of i and d are not even close, nor can they be because it is impossible to represent the value 2,200,000,000 as an i nt on a system that uses 32-bit integers. When assigning a value of a wider type to a variable of a narrower type, the programmer must assume the responsibility to ensure that the actual value to be narrowed is indeed within the range of the narrower type. The compiler cannot ensure the safety of the assignment.

Casts should be used sparingly and with great care because a cast creates a spot in the program that is immune to the compiler’s type checking. A careless assignment can produce a garbage result introducing an error into the program.

When we must perform mixed arithmetic—such as adding an i nt to a double — the compiler automatically produces machine language code that copies the i nt value to a temporary memory location and transforms it into its double equivalent. It then performs double-precision floating-point arithmetic to compute the result.

Integer arithmetic occurs only when both operands are i nts. 1/3 thus evaluates to 0, but 1.0/3.0, 1/3.0, and 1.0/3 all evaluate to 0.33333.

Since double is wider than i nt, we say that double dominates i nt. In a mixed type arithmetic expression, the less dominant type is coerced into the more dominant type in order to perform the arithmetic operation.

Section|3.9|introduced enumerated types. Behind the scenes, the compiler translates enumerated values into integers. The first value in the enumeration is 0, the second value is 1, etc. Even though the underlying implementation of enumerated types is integer, the compiler does not allow the free exchange between integers and enumerated types. The following code will not compile:

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enum class Color { Red, Orange, Yellow, Green, Blue, Violet }; std::cout << Color::Orange << " " << Color::Green << '\n' ;

The std: : cout printing object knows how to print integers, but it does not know anything about our Color class and its values. If we really want to treat an enumerated type value as its underlying integer, we must use a type cast. Listing |473| (enumcast.cpp) shows how to extract the underlying integer value from an enumerated type.

Listing |43](enumcast.cpp) prints prints

3

This is the expected output because Color: : Red is 0, Color: : Orange is 1, Color: : Yellow is 2, Color: : Green is 3, etc.

Even though enumerated types are encoded as integers internally, programmers may not perform arithmetic on enumerated types without involving casts. Such opportunities should be very rare; if you need to perform arithmetic on a variable, it really should be a numerical type, not an enumerated type.

4.3 Operator Precedence and Associativity

When different operators are used in the same expression, the normal rules of arithmetic apply. All C++

operators have a precedence and associativity.

• Precedence —when an expression contains two different kinds of operators, which should be applied first?

• Associativity —when an expression contains two operators with the same precedence, which should be applied first?

To see how precedence works, consider the expression 2 + 3*4

Should it be interpreted as (2 + 3) * 4

(that is, 20), or rather is 2 + (3 * 4)

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(that is, 14) the correct interpretation? As in normal arithmetic, in C++ multiplication and division have equal importance and are performed before addition and subtraction. We say multiplication and division have precedence over addition and subtraction. In the expression

2 + 3*4

the multiplication is performed before addition, since multiplication has precedence over addition. The result is 14. The multiplicative operators (*, /, and %) have equal precedence with each other, and the additive operators (binary + and -) have equal precedence with each other. The multiplicative operators have precedence over the additive operators.

As in standard arithmetic, in C++ if the addition is to be performed first, parentheses can override the precedence rules. The expression

(2 + 3) * 4

evaluates to 20. Multiple sets of parentheses can be arranged and nested in any ways that are acceptable in standard arithmetic.

To see how associativity works, consider the expression 2-3-4

The two operators are the same, so they have equal precedence. Should the first subtraction operator be applied before the second, as in

(2 - 3) - 4

(that is, —5), or rather is 2 - (3 - 4)

(that is, 3) the correct interpretation? The former (—5) is the correct interpretation. We say that the subtraction operator is left associative, and the evaluation is left to right. This interpretation agrees with standard arithmetic rules. All binary operators except assignment are left associative. Assignment is an exception; it is right associative. To see why associativity is an issue with assignment, consider the statement

w = x = y = z;

This is legal C++ and is called chained assignment. Assignment can be used as both a statement and an expression. The statement

x = 2 ;

assigns the value 2 to the variable x. The expression x = 2

assigns the value 2 to the variable x and evaluates to the value that was assigned; that is, 2. Since assignment is right associative, the compiler would interpret the chained assignment example as if it were written as

w = (x = (y = z)) ; which behaves as follows:

• The expression y = z is evaluated first, z’s value is assigned to y, and the value of the expression y = z is z’s value.

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Arity

Operators

Associativity

Unary

+,

Binary

*, /, °o

Left

Binary

+,

Left

Binary

=

Right

Table 4.2: Operator precedence and associativity. The operators in each row have a higher precedence than the operators below it. Operators within a row have the same precedence.

• The expression x = (y = z)is evaluated. The value of y = z, that is z, is assigned to x. The overall value of the expression x = y = z is thus the value of z. Now the values of x, y, and z are all equal (to z).

• The expression w = (x = y = z)is evaluated. The value of the expression x = y = z is equal to z’s value, so z’s value is assigned to w. The overall value of the expression w = x = y = z is equal to z, and the variables w, x, y, and z are all equal (to z).

As in the case of precedence, we can use parentheses to override the natural associativity within an expression.

The unary operators have a higher precedence than the binary operators, and the unary operators are right associative. This means the statements

std::cout << -3 + 2 << '\n' ; std::cout << -(3 + 2) << '\n' ;

which display

-1

-5

behave as expected.

Table |4.2| shows the precedence and associativity rules for some C++ operators. The * operator also has a unary form that has nothing to do with mathematics; it is covered in SectionjT0.7[

4.4 Comments

Good programmers annotate their code by inserting remarks that explain the purpose of a section of code or why they chose to write a section of code the way they did. These notes are meant for human readers, not the compiler. It is common in industry for programs to be reviewed for correctness by other programmers

or technical managers. Well-chosen identifiers (see Section 3.31 and comments can aid this assessment process. Also, in practice, teams of programmers develop software. A different programmer may be required to finish or fix a part of the program written by someone else. Well-written comments can help others understand new code quicker and increase their productivity modifying old or unfinished code. While it may seem difficult to believe, even the same programmer working on her own code months later can have a difficult time remembering what various parts do. Comments can help greatly.

Any text contained within comments is ignored by the compiler. C++ supports two types of comments: single line comments and block comments:

Single line comment —the first type of comment is useful for writing a single line remark:

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// Compute the average of the values avg = sum / number;

The first line here is a comment that comment explains what the statement that follows it is supposed to do. The comment begins with the double forward slash symbols (/ /) and continues until the end of that line. The compiler will ignore the / / symbols and the contents of the rest of the line. This type of comment is also useful for appending a short comment to the end of a statement:

avg = sum / number; // Compute the average of the values

Here, an executable statement and the comment appear on the same line. The compiler will read the assignment statement here, but it will ignore the comment. The compiler generates the same machine code for this example as it does for the preceding example, but this example uses one line of source code instead of two.

• Block comment —the second type of comment begins with the symbols /* and is in effect until the */ symbols are encountered. The /* . . . */ symbols delimit the comment like parentheses

delimit a parenthetical expression. Unlike parentheses, however, these block comments cannot be nested within other block comments.

The block comment is handy for multi-line comments:

/* After the computation is completed the result is displayed. */ std::cout << result << '\n' ;

What should be commented? Avoid making a remark about the obvious; for example:

result = 0; // Assign the value zero to the variable named result

The effect of this statement is clear to anyone with even minimal C++ programming experience. Thus, the audience of the comments should be taken into account; generally, “routine” activities require no remarks. Even though the effect of the above statement is clear, its purpose may need a comment. For example:

result = 0; // Ensures 'result' has a well-defined minimum value

This remark may be crucial for readers to completely understand how a particular part of a program works. In general, programmers are not prone to providing too many comments. When in doubt, add a remark. The extra time it takes to write good comments is well worth the effort.

4.5 Formatting

Program comments are helpful to human readers but ignored by the compiler. Another aspect of source code that is largely irrelevant to the compiler but that people find valuable is its formatting. Imagine the difficulty of reading a book in which its text has no indentation or spacing to separate one paragraph from another. In comparison to the source code for a computer program, a book’s organization is quite simple. Over decades of software construction programmers have established a small collection of source code formatting styles that the industry finds acceptable.

The compiler allows a lot of leeway for source code formatting. Consider Listing |4.4j (reformattedvariable.cpp) which is a reformatted version of Listingj!3.4 (variable.cpp).

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Listing [43|(reformattedvariable2.cpp) is another reformatted version of Listing|3.4||(variable.cpp).

Both reformatted programs are valid C++ and compile to the same machine language code as the original version. Most would argue that the original version is easier to read and understand more quickly than either of the reformatted versions. The elements in Listing ||3.4|| (variable.cpp) are organized better. Experienced C++ programmers would find both Listing |4.4| ( reformattedvariable.cpp) and Listing |43] (reformattedvariable2.cpp) visually painful.

What are some distinguishing characteristics of Listing |3.4| (variable.cpp)?

• Each statement appears on its own line. A statement is not unnecessarily split between two lines of text. Visually, one line of text implies one action (statement) to perform.

• The close curly brace aligns vertically with the line above that contains the corresponding open curly brace. This makes it easier to determine if the curly braces match and nest properly. It also better portrays the logical structure of the program. The ability to accurately communicate the logical structure of a program becomes very important as write more complex programs. Programs with complex logic frequently use multiple nested curly braces (for example, see Listing |57Ll [ (troubleshoot, cpp)). Without a consistent, organized arrangement of curly braces it can difficult to determine which opening brace goes with a particular closing brace.

• The statements that constitute the body of main are indented several spaces. This visually emphasizes the fact that the elements are indeed logically enclosed. As with curly brace alignment, indentation to emphasize logical enclosure becomes more important as more complex programs are considered.

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• Spaces are used to spread out statements and group pieces of the statement. Space around the operators (=) makes it easier to visually separate the operands from the operators and comprehend the details of the expression. Most people find the statement

total_sale = subtotal + tax;

much easier to read than total_sale=subtotal+tax;

since the lack of space in the second version makes it more difficult to pick out the individual pieces of the statement. In the first version with extra space, it is clearer where operators and variable names begin and end.

In a natural language like English, a book is divided into distinct chapters, and chapters are composed of paragraphs. One paragraph can be distinguished from another because the first line is indented or an extra space appears between two paragraphs. Space is used to separate words in each sentence. Consider how hard it would be to read a book if all the sentences were printed like this one:

Theboyranquicklytothetreetoseethestrandedcat.

Judiciously placed open space in a C++ program can greatly enhance its readability.

C++ gives the programmer a large amount of freedom in formatting source code. The compiler reads the characters that make up the source code one symbol at a time left to right within a line before moving to the next line. While extra space helps readability, spaces are not allowed in some places:

- Variable names and reserved words must appear as unbroken units.

- Multi-symbol operators like < < cannot be separated (< < is illegal).

One common coding convention that is universal in C++ programming is demonstrated in Listing |3T10|| (const.cpp). While programmers usually use lower-case letters in variable names, they usually express constant names with all capital letters; for example, PI is used for the mathematical constant 7Z instead of pi. C++ does not require constants to be capitalized, but capitalizing them aids humans reading the source code so they can quickly distinguish between variables and constants.

Figure {43) shows the four most common ways programmers use indentation and place curly braces in C++ source code.

The K&R and ANSI styles are the most popular in published C++ source code. The Whitesmith and Banner styles appear much less frequently, http://en.wi kipedia.org/wiki/Indent_style reviews the various ways to format C++ code. Observe that all the accepted formatting styles indent the block of statements contained in the mai n function.

Most software development organizations adopt a set of style guidelines, sometimes called code conventions. These guidelines dictate where to indent and by how many spaces, where to place curly braces, how to assign names to identifiers, etc. Programmers working for the organization are required to follow these style guidelines for the code they produce. This better enables any member of the development team to read and understand more quickly code written by someone else. This is necessary when code is reviewed for correctness or when code must be repaired or extended, and the original programmer is no longer with the development team.

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Figure 4.3 The most common C++ coding styles.

K & R Style

int

{

main()

}

Body

ANSI Style

Table captionint main() {

Body

Whitesmith Style

Even if you are not forced to use a particular style, it is important to use a consistent style throughout the code you write. As our programs become more complex we will need to use additional curly braces and various levels of indentation to organize the code we write. A consistent style (especially one of the standard styles shown in Figure |4.3| makes it easier to read and verify that the code actually expresses our intent. It also makes it easier to find and fix errors. Said another way, haphazard formatting increases the time it takes to develop correct software because programmer’s mistakes hide better in poorly formatted code.

Good software development tools can boost programmer productivity, and many programming editors have the ability to automatically format source code according to a standard style. Some of these editors can correct the code’s style as the programmer types in the text. A standalone program known as a pretty printer can transform an arbitrarily formatted C++ source file into a properly formatted one.

4.6 Errors and Warnings

Beginning programmers make mistakes writing programs because of inexperience in programming in general or because of unfamiliarity with a programming language. Seasoned programmers make mistakes due to carelessness or because the proposed solution to a problem is faulty and the correct implementation of an incorrect solution will not produce a correct program. Regardless of the reason, a programming error falls under one of three categories:

• compile-time error

• run-time error

• logic error

4.6.1 Compile-time Errors

A compile-time error results from the programmer’s misuse of the language. A syntax error is a common compile-time error. For example, in English one can say

The boy walks quickly.

This sentence uses correct syntax. However, the sentence

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The boy walk quickly.

is not correct syntactically: the number of the subject (singular form) disagrees with the number of the verb (plural form). It contains a syntax error. It violates a grammatical rule of the English language. Similarly, the C++ statement

x = y + 2;

is syntactically correct because it obeys the rules for the structure of an assignment statement described in Section 3.2 However, consider replacing this assignment statement with a slightly modified version:

Y + 2 = x;

If a statement like this one appears in a program and the variables x and y have been properly declared, the compiler will issue an error message; for example, the Visual C++ compiler reports (among other things):

error C2106: ’= ’: left operand must be l-value

The syntax of C++ does not allow an expression like y + 2 to appear on the left side of the assignment operator.

(The term l-value in the error message refers to the left side of the assignment operator; the 1 is an “elle,” not a “one.”.)

The compiler may generate an error for a syntactically correct statement like

x = y + 2;

if either of the variables x or y has not been declared; for example, if y has not been declared. Visual C++ reports:

error C2065: ’y’: undeclared identifier

Other common compile-time errors include missing semicolons at the end of statements, mismatched curly braces and parentheses, and simple typographical errors.

Compile-time errors usually are the easiest to repair. The compiler pinpoints the exact location of the problem, and the error does not depend on the circumstances under which the program executes. The exact error can be reproduced by simply recompiling the same source code.

Compilers have the reputation for generating cryptic error messages. They seem to provide little help as far as novice programmers are concerned. Sometimes a combination of errors can lead to messages that indicate errors on lines that follow the line that contains the actual error. Once you encounter the same error several times and the compiler messages become more familiar, you become better able to deduce the actual problem from the reported message. Unfortunately C++ is such a complex language that sometimes a simple compile-time error can result in a message that is incomprehensible to beginning C++ programmers.

4.6.2 Run-time Errors

The compiler ensures that the structural rules of the C++ language are not violated. It can detect, for example, the malformed assignment statement and the use of a variable before its declaration. Some violations of the language cannot be detected at compile time, however. A program may not run to completion but instead terminate with an error. We commonly say the program “crashed.” Consider Listing [46] (dividedanger.cpp) which under certain circumstances will crash.

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The expression dividend/divisor

is potentially dangerous. If the user enters, for example, 32 and 4, the program works nicely

Please enter two integers to divide: 32 4 32/4 = 8

and displays the answer of 8. If the user instead types the numbers 32 and 0, the program reports an error and terminates. Division by zero is undefined in mathematics, and integer division by zero in C++ is illegal. When the program attempts the division at run time, the system detects the attempt and terminates the program.

This particular program can fail in other ways as well; for example, outside of the C++ world, 32.0 looks like a respectable integer. If the user types in 32.0 and 8, however, the program crashes because 32.0 is not a valid way to represent an integer in C++. When the compiler compiles the source line

std::cin >> dividend >> divisor;

given that dividend has been declared to be an i nt, it generates slightly different machine language code than it would if dividend has been declared to be a double instead. The compiled code expects the text entered by the user to be digits with no extra decoration. Any deviation from this expectation results in a run-time error. Similar results occur if the user enters text that does not represent an integer, like fred.

Observe that in either case—entry of a valid but inappropriate integer (zero) or entry of a non-integer (32.0 or fred )—it is impossible for the compiler to check for these problems at compile time. The compiler cannot predict what the user will enter when the program is run. This means it is up to the programmer to write code that can handle bad input that the user may provide. As we continue our exploration of programming in C++, we will discover ways to make our programs more robust against user input (see Listing |5.2| (betterdivision.cpp) in Chapter[5j for example). The solution involves changing the way the program runs depending on the actual input provided by the user.

4.6.3 Logic Errors

Consider the effects of replacing the expression

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dividend/divisor;

in Listing|4.6|(dividedanger.cpp) with the expression: divisor/dividend;

The program compiles with no errors. It runs, and unless a value of zero is entered for the dividend, no run-time errors arise. However, the answer it computes is not correct in general. The only time the correct answer is printed is when dividend = d i visor. The program contains an error, but neither the compiler nor the run-time system is able detect the problem. An error of this type is known as a logic error.

Listing {47iT0| (faultytempconv.cpp) is an example of a program that contains a logic error. Listing [4720j (faultytempconv.cpp) compiles and does not generate any run-time errors, but it produces incorrect results.

Beginning programmers tend to struggle early on with compile-time errors due to their unfamiliarity with the language. The compiler and its error messages are actually the programmer’s best friend. As the programmer gains experience with the language and the programs written become more complicated, the number of compile-time errors decrease or are trivially fixed and the number of logic errors increase. Unfortunately, both the compiler and run-time environment are powerless to provide any insight into the nature and sometimes location of logic errors. Logic errors, therefore, tend to be the most difficult to find and repair. Tools such as debuggers are frequently used to help locate and fix logic errors, but these tools are far from automatic in their operation.

Errors that escape compiler detection (run-time errors and logic errors) are commonly called bugs. Since the compiler is unable to detect these problems, such bugs are the major source of frustration for developers. The frustration often arises because in complex programs the bugs sometimes only reveal themselves in certain situations that are difficult to reproduce exactly during testing. You will discover this frustration as your programs become more complicated. The good news is that programming experience and the disciplined application of good programming techniques can help reduce the number logic errors. The bad news is that since software development in an inherently human intellectual pursuit, logic errors are inevitable. Accidentally introducing and later finding and eliminating logic errors is an integral part of the programming process.

4.6.4 Compiler Warnings

A warning issued by the compiler does mark a violation of the rules in the C++ language, but it is an notification to the programmer that the program contains a construct that is a potential problem. In Listing |4T0| (tempconv.cpp) the programmer is attempting to print the value of a variable before it has been given a known value.

An attempt to build Listing [4?7| (uninitialized.cpp) yields the following message from the Visual C++ compiler:

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warning C4700: uninitialized local variable ’n’ used

The compiler issued a warning but still generated the executable file. When run, the program produces a random result because it prints the value in memory associated with the variable, but the program does not initialize that memory location.

Listing 4.8 (narrow.cpp) assigns a double value to an i nt variable, which we know from Section 4.1 truncates the result.

When compiled we see

warning C4244: ’= ': conversion from ’double’ to ’int’, possible loss of data

Since it is a warning and not an error, the compiler generates the executable, but the warning should prompt us to stop and reflect about the correctness of the code. The enhanced warning level prevents the programmer from being oblivious to the situation.

The default Visual C++ warning level is 3 when compiling in the IDE and level 1 on the command line (that is why we use the /W3 option on the command line); the highest warning level is 4. You can reduce the level to 1 or 2 or disable warnings altogether, but that is not recommended. The only reason you might want to reduce the warning level is to compile older existing C++ source code that does meet newer C++ standards. When developing new code, higher warning levels are preferred since they provide more help to the programmer. Unless otherwise noted, all the complete program examples in this book compile cleanly under Visual C++ set at warning level 3. Level 3 is helpful for detecting many common logic errors.

We can avoid most warnings by a simple addition to the code. Section 4.2 showed how we can use stati c_cast to coerce a wider type to a narrower type. At Visual C++ warning Level 3, the compiler issues a warning if the cast is not used. The little code that must be added should cause the programmer to stop and reflect about the correctness of the construct. The enhanced warning level prevents the programmer from being oblivious to the situation.

Use the strongest level of warnings available to your compiler. Treat all warnings as problems that must be corrected. Do not accept as completed a program that compiles with warnings.

We may assign a double literal to a float variable without any special type casting. The compiler automatically narrows the double to a float as Listing 4.9 (assignfloat.cpp) shows:

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The statement

number = 10.0;

assigns a double literal (10.0) to a float variable. You instead may explicitly use a float literal as: number = 10.0 f;

4.7 Arithmetic Examples

The kind of arithmetic to perform in a complex expression is determined on an operator by operator basis. For example, consider Listing |4.10| (tempconv.cpp) that attempts to convert a temperature from degrees Fahrenheit to degrees Celsius using the formula

°C= - x (IF-32)

Listing j4. 10j| (tempconv.cpp) contains comments that document each step explaining the code’s purpose. An initial test is promising:

Enter the temperature in degrees F: 32 Degrees C = 0

Water freezes at 32 degrees Fahrenheit and 0 degrees Celsius, so the program’s behavior is correct for this test. Several other attempts are less favorable—consider

©2018 Richard L. Halterman

Draft date: September 25, 2018

Enter the temperature in degrees F: 212 Degrees C = 0

Water boils at 212 degrees Fahrenheit which is 100 degrees Celsius, so this answer is not correct.

Enter the temperature in degrees F: -40 Degrees C = 0

The value —40 is the point where the Fahrenheit and Celsius curves cross, so the result should be —40, not zero. The first test was only coincidentally correct.

Unfortunately, the printed result is always zero regardless of the input. The problem is the division 5/9 in the statement

degreesC = 5/9* (degreesF - 32);

Division and multiplication have equal precedence, and both are left associative; therefore, the division is performed first. Since both operands are integers, integer division is performed and the quotient is zero (5 divided by 9 is 0, remainder 5). Of course zero times any number is zero, thus the result. The fact that a floating-point value is involved in the expression (degreesF) and the overall result is being assigned to a floating-point variable, is irrelevant. The decision about the exact type of operation to perform is made on an operator-by-operator basis, not globally over the entire expression. Since the division is performed first and it involves two integer values, integer division is used before the other floating-point pieces become involved.

One solution simply uses a floating-point literal for either the five or the nine, as in degreesC = 5.0/9* (degreesF - 32);

This forces a double-precision floating-point division (recall that the literal 5.0 is a double). The correct result, subject to rounding instead of truncation, is finally computed.

Listing j4TT|(timeconv.cpp) uses integer division and modulus to split up a given number of seconds to hours, minutes, and seconds.

Listing 4.11: timeconv.cpp

// File timeconv.cpp

#include <iostream> int main() {

int hours, minutes, seconds;

std::cout << "Please enter the number of seconds:"; std::cin >> seconds;

// First, compute the number of hours in the given number // of seconds

hours = seconds / 3600; // 3600 seconds = 1 hours

// Compute the remaining seconds after the hours are // accounted for seconds = seconds % 3600;

// Next, compute the number of minutes in the remaining // number of seconds

minutes = seconds / 60; // 60 seconds = 1 minute

// Compute the remaining seconds after the minutes are

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

// accounted for seconds = seconds 96 60;

// Report the results

std::cout << hours << " hr, " << minutes << " min, << seconds << " sec\n";

If the user enters 10000, the program prints 2 hr , 46 mi n, 40 sec. Notice the assignments to the seconds variable, such as

seconds = seconds % 3600

The right side of the assignment operator (=) is first evaluated. The remainder of seconds divided by 3,600 is assigned back to seconds. This statement can alter the value of seconds if the current value of seconds is greater than 3,600. A similar statement that occurs frequently in programs is one like

x = x + 1;

This statement increments the variable x to make it one bigger. A statement like this one provides further evidence that the C++ assignment operator does not mean mathematical equality. The following statement from mathematics

x = x+ 1

is surely never true; a number cannot be equal to one more than itself. If that were the case, I would deposit one dollar in the bank and then insist that I really had two dollars in the bank, since a number is equal to one more than itself. That two dollars would become 3.00, then 4.00, etc., and soon I would be rich. In C++, however, this statement simply means “add one to x and assign the result back to x.”

A variation on Listing |4.111| (timeconv.cpp). Listing |4.12 (enhancedtimeconv.cpp) performs the same logic to compute the time pieces (hours, minutes, and seconds), but it uses more simple arithmetic to produce a slightly different output—instead of printing 11,045 seconds as 3 hr, 4 min, 5 sec, Listing |4.12|| (enhancedtimeconv.cpp) displays it as 3:04:05. It is trivial to modify Listing |4.11 || (timeconv.cpp) so that it would print 3:4:5, but Listing |4TT2| (enhancedtimeconv.cpp) includes some extra arithmetic to put leading zeroes in front of single-digit values for minutes and seconds as is done on digital clock displays.

Listing 4.12: enhancedti meconv. cpp

// File enhancedtimeconv.cpp

#include <iostream> int main() {

int hours, minutes, seconds;

std::cout << "Please enter the number of seconds:"; std::cin >> seconds;

// First, compute the number of hours in the given number // of seconds

hours = seconds / 3600; // 3600 seconds = 1 hours

// Compute the remaining seconds after the hours are // accounted for seconds = seconds 96 3600;

// Next, compute the number of minutes in the remaining // number of seconds

minutes = seconds / 60; // 60 seconds = 1 minute

// Compute the remaining seconds after the minutes are

©2018 Richard L. Halterman

Draft date: September 25, 2018

// accounted for seconds = seconds % 60;

// Report the results std::cout << hours <<

// Compute tens digit of minutes int tens = minutes / 10; std: :cout << tens;

// Compute ones digit of minutes int ones = minutes % 10; std::cout << ones <<

// Compute tens digit of seconds tens = seconds / 10; std::cout << tens;

// Compute ones digit of seconds ones = seconds % 10; std::cout << ones << '\n ' ;

Listing 4.12 (enhancedtimeconv.cpp) uses the fact that if x is a one- or two-digit number, x / 10 is the tens digit of x. If x / 10 is zero, x is necessarily a one-digit number.

4.8 Integers vs. Floating-point Numbers

Floating-point numbers offer some distinct advantages over integers. Floating-point numbers, especially doubles have a much greater range of values than any integer type. Floating-point numbers can have fractional parts and integers cannot. Integers, however, offer one big advantage that floating-point numbers cannot—exactness. To see why integers are exact and floating-point numbers are not, we will explore the way computers store and manipulate the integer and floating-point types.

Computers store all data internally in binary form. The binary (base 2) number system is much simpler than the familiar decimal (base 10) number system because it uses only two digits: 0 and 1. The decimal system uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Despite the lack of digits, every decimal integer has an equivalent binary representation. Binary numbers use a place value system not unlike the decimal system. Figure}4.4(shows how the familiar base 10 place value system works.

Figure 4.4 The base 10 place value system

100,000 10,000 1,000 100 10 1

473,406 = 4 x 10 5 + 7 x 10 4 + 3 x 10 3 + 4 x 10 2 + 0 x 10 1 +6 x 10° = 400,000 + 70,000 + 3,000 + 400 + 0 + 6 = 473,406

With 10 digits to work with, the decimal number system distinguishes place values with powers of 10. Compare the base 10 system to the base 2 place value system shown in Figure[4.5|

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 4.5 The base 2 place value system

32 16 8 4 2 1

100111 2 = 1 x2 5 + 0x2 4 + 0x2 3 + 1 x2 2 + 1 x 2 ! + 1 x 2°

= 32+0+0+4+2+1 = 39

With only two digits to work with, the binary number system distinguishes place values by powers of two. Since both binary and decimal numbers share the digits 0 and 1, we will use the subscript 2 to indicate a binary number; therefore, 100 represents the decimal value one hundred, while IOO 2 is the binary number four. Sometimes to be very clear we will attach a subscript of 10 to a decimal number, as in 100io

In the decimal system, it is easy to add 3+5:

3

H - 5 8 ”

The sum 3 + 9 is a little more complicated, as early elementary students soon discover:

3

+ 9

The answer, of course, is 12, but there is no single digit that means 12—it takes two digits, 1 and 2. The sum is

1

03 + 09 12

We can say 3 + 9 is 2, carry the 1. The rules for adding binary numbers are shorter and simpler than decimal numbers:

O2 + O2 = O2

O2 + I2 = I2

I2+O2 = I2 I2 + I2 = IO2

We can say the sum I 2 + I 2 is 0 2 , carry the I 2 . A typical larger sum would be

11

9 io = IOOI2 + 3 10 = H2

12 10 = HOO2

4.8.1 Integer Implementation

Mathematical integers are whole numbers (no fractional parts), both positive and negative. Standard C++ supports multiple integer types: i nt, short, long, and long long, unsi gned, unsi gned short.

©2018 Richard L. Halterman

Draft date: September 25, 2018

unsigned long, and unsi gned long long. These are distinguished by the number of bits required to store the type, and, consequently, the range of values they can represent. Mathematical integers are infinite, but all of C++’s integer types correspond to finite subsets of the mathematical integers. The most commonly used integer type in C++ is i nt. All i nts, regardless of their values, occupy the same amount of memory and, therefore use the same number of bits. The exact number of bits in an i nt is processor specific. A 32-bit processor, for example, is built to manipulate 32-bit integers very efficiently. A C++ compiler for such a system most likely would use 32-bit i nts, while a compiler for a 64-bit machine might represent i nts with 64 bits. On a 32-bit computer, the numbers 4 and 1,320,002,912 both occupy 32 bits of memory.

For simplicity, we will focus on unsigned integers, particularly the unsi gned type. The unsi gned type in Visual C++ occupies 32 bits. With 32 bits we can represent 4,294,967,296 different values, and so Visual C++’s unsi gned type represents the integers 0.. .4,294,967,295. The hardware in many computer systems in the 1990s provided only 16-bit integer types, so it was common then for C++ compilers to support 16-bit unsi gned values with a range 0.. .65,535. To simplify our exploration into the properties of computer-based integers, we will consider an even smaller, mythical unsigned integer type that we will call unsigned ti ny. C++ has no such unsigned ti ny type as it has a very small range of values— too small to be useful as an actual type in real programs. Our unsigned ti ny type uses only five bits of storage, and Table 4.3 shows all the values that a variable of type unsigned tiny can assume.

Binary Bit String

Decimal Value

00000

0

00001

1

00010

2

00011

3

00100

4

00101

5

00110

6

00111

7

01000

8

01001

9

01010

10

01011

11

01100

12

01101

13

01110

14

01111

15

10000

16

10001

17

10010

18

10011

19

10100

20

10101

21

10110

22

10111

23

11000

24

11001

25

11010

26

11011

27

11100

28

11101

29

11110

30

11111

31

Table captionTable 4.3: The unsigned tiny values

Table 4.3 shows that the unsigned ti ny type uses all the combinations of 0s and Is in five bits. We can derive the decimal number 6 directly from its bit pattern:

0 0 110

00110 =>

16 8 42 1

Ox 16 + 0x8 + 1x4+lx2 + 0x1=6

©2018 Richard L. Halterman

Draft date: September 25, 2018

To see that arithmetic works, try adding 4 + 3:

4 10 = 00100 2 + 310 = 000112 7 10 = OOIII2

That was easy since involved no carries. Next we will try 3 + 1:

11

310 = 00011 2

+ 1 10 = OOOOI2 4 io = OOIOO2

In the ones column (rightmost column), I 2 + I 2 = IO 2 , so write a 0 and carry the 1 to the top of the next column to the left (that is, the twos column). In the twos column, I 2 + I 2 + O 2 = IO 2 , so we must carry a 1 into the fours column as well.

The next example illustrates a limitation of our finite representation. Consider the sum 8 + 28:

11

810 = OIOOO2 + 28 io = IHOO2 4 10 = 1 OOIOO2

In the this sum we have a carry of 1 from the eights column to the 16s column, and we have a carry from the 16s column to nowhere. We need a sixth column (a 32s column), another place value, but our unsigned ti ny type is limited to five bits. That carry out from the 16s place is lost. The largest unsi gned ti ny value is 31, but 28 + 8 = 36. It is not possible to store the value 36 in an unsigned tiny just as it is impossible to store the value 5,000,000,000 in a C++ unsi gned variable.

Consider exceeding the capacity of the unsigned ti ny type by just one:

11111

31 io = IIIH2

+ 110 = 000012

O10 = 1 OOOOO2

Adding one to the largest possible unsigned ti ny, 31, results in the smallest possible value, 0! This mirrors the behavior of the actual C++ unsigned type, as Listing 4.13 (unsignedoverflow.cpp) demonstrates.

Listing 4.13: unsignedoverflow. cpp

#include <iostream> int main() {

unsigned x = 4294967293; // Almost the largest possible unsigned value

std :

: cout

<<

X

<<

" +

1 = " <<

X

+

1

<<

' \n

std:

: cout

<<

X

<<

" +

2 = " <<

X

+

2

<<

' \n

std :

: cout

<<

X

<<

" +

3 = " <<

X

+

3

<<

' \n

Listing [4~T3| (unsignedoverflow.cpp) prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 4.6 The cyclic nature of 32-bit unsigned integers. Adding 1 to 4,294,967,295 produces 0, one position clockwise from 4,294,967295. Subtracting 4 from 2 yields 4,294,967,294, four places counterclockwise from 2.

4294967293

+

1 = 4294967294

4294967293

+

2 = 4294967295

4294967293

+

3 = 0

In fact, Visual C++’s 32-bit unsi gneds follow the cyclic pattern shown in Figure 4.6

In the figure, an addition moves a value clockwise around the circle, while a subtraction moves a value counterclockwise around the circle. When the numeric limit is reached, the value rolls over like an automobile odometer. Signed integers exibit a similar cyclic pattern as shown in Figure |4.7| l

In the case of signed integers, as Figure 14.71 shows, adding one to the largest representable value produces the smallest negative value. Listing 37l4[(integeroverflow.cpp) demonstrates.

Listing4.14: integeroverflow.cpp

Table captionftinclude <iostream> int main() {

Table captionint x = 2147483645; // Almost the largest possible int value

std:

: cout

<<

X

<<

" +

1 = " <<

X

+

1

<<

' \n

std:

: cout

<<

X

<<

" +

2 = " <<

X

+

2

<<

' \n

std:

: cout

<<

X

<<

" +

3 = " <<

X

+

3

<<

' \n

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 4.7 The cyclic nature of 32-bit signed integers. Adding 1 to 2,147,483,647 produces —2,147,483,648, one position clockwise from 2,147,483,647. Subtracting 5 from —2,147,483,645 yields 2,147,483,646, five places counterclockwise from —2,147,483,645.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table captionListing |47l4|(integeroverflow.cpp) prints

2147483645

+

1 = 2147483646

2147483645

+

2 = 2147483647

2147483645

+

3 = -2147483648

Attempting to exceed the maximum limit of a numeric type results in overflow, and attempting to exceed the minimum limit is called underflow. Integer arithmetic that overflow or underflow produces a valid, yet incorrect integer result. The compiler does not check that a computation will result in exceeding the limit of a type because it is impossible to do so in general (consider adding two integer variables whose values are determined at run time). Also significantly, an overflow or underflow situation does not generate a run-time error. It is, therefore, a logic error if a program performs an integral computation that, either as a final result or an intermediate value, is outside the range of the integer type being used.

4.8.2 Floating-point Implementation

The standard C++ floating point types consist of float, double, and long double. Floating point numbers can have fractional parts (decimal places), and the term floating point refers to the fact the decimal point in a number can float left or right as necessary as the result of a calculation (for example, 2.5 x 3.3 = 8.25, two one-decimal place values produce a two-decimal place result). As with the integer types, the different floating-point types may be distinguished by the number of bits of storage required and corresponding range of values. The type float stands for single-precision floating-point, and double stands for double-precision floating-point. Floating point numbers serve as rough approximations of mathematical real numbers, but as we shall see, they have some severe limitations compared to actual real numbers.

On most modern computer systems floating-point numbers are stored internally in exponential form according to the standard adopted by the Institute for Electrical and Electronic Engineers (IEEE 754). In the decimal system, scientific notation is the most familiar form of exponential notation:

One mole contains 6.023 x 10 23 molecules.

Here 6.023 is called the mantissa, and 23 is the exponent.

The IEEE 754 standard uses binary exponential notation; that is, the mantissa and exponent are binary numbers. Single-precision floating-point numbers (type float) occupy 32 bits, distributed as follows:

Mantissa 24 bits

Exponent 7 bits

Sign 1 bit

Total 32 bits

Double-precision floating-point numbers (type double) require 64 bits:

Mantissa 52 bits

Exponent 11 bits

Sign 1 bit

Total 64 bits

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 4.8 A ti ny float simplified binary exponential value

1

ol/lx?

-2 o-3

2 2

The details of the IEEE 754 implementation are beyond the scope of this book, but a simplified example serves to highlight the limitations of floating-point types in general. Recall the fractional place values in the decimal system. The place values, from left to right, are

10,000

1,000

100

10

1

•

I

10

I

100

I

1000

I

10,000

To 4

10 2

10 2

10 1

“ io 0

•

10- 1

10~ 2

10~ 2

10~ 4

Each place value is one-tenth the place value to its left. Move to the right, divide by ten; move to the left, multiply by ten. In the binary system, the factor is two instead of ten:

16

8

4

2

1

•

1

2

I

4

I

8

1

16

2 4

2 i

2 1

2 l

2 U

•

2~ 1

2~ 2

2~ J

2~ 4

As in our unsigned tiny example (see Section 4.8.1), consider a a binary exponential number that

consists of only five bits—far fewer bits than either floats or doubles in C++. We will call our mythical floating-point type tiny float. The first three bits of our 5-bit tiny float type will represent the mantissa, and the remaining two bits store the exponent. The three bits of the mantissa all appear to the right of the binary point. The base of the 2-bit exponent is, of course, two. Figure ]4.8|j illustrates such a value.

To simplify matters even more, neither the mantissa nor the exponent can be negative. Thus, with three bits, the mantissa may assume one of eight possible values. Since two bits constitute the exponent of ti ny floats, the exponent may assume one of four possible values. Table 4.4 lists all the possible values that ti ny float mantissas and exponents may assume. The number shown in Figure 4.8 is thus

(Ix2~'+0x2^ + lx 2" 3 ) x 2( lx2l + 0x2 °)

2.5

x 2

2

Table 4.5 combines the mantissas and exponents to reveal all possible ti ny float values that we can represent with the 32 different bit strings made up of five bits. The results are interesting.

The range of our tiny float numbers is 0.. .7. Just stating the range is misleading, however, since

1

it might give the impression that we may represent any value in between 0 and 7 down to the -th place.

8

This, in fact, is not true. We can represent 2.5 with this scheme, but we have no way of expressing 2.25. Figure 4.9 plots all the possible ti ny float values on the real number line.

©2018 Richard L. Halterman

Draft date: September 25, 2018

3-bit Mantissas

Bit String

Binary Value

Decimal Value

000

o.ooo 2

000

2+4+8

=

0.000

001

o.ooh

0 0 1 2+4+8

=

0.125

010

0.0102

0 1 0

7+4+8

=

0.250

011

0.0112

0 1 1

2+4+8

=

0.375

100

0.1002

1 0 0 2+4+8

=

0.500

101

o.ioh

1 0 1

7+4+8

=

0.625

110

0.1 to 2

1 1 0

2+4+8

=

0.750

111

0.1112

1 1 1 2+4+8

=

0.875

Bit String

2-bit Exponents

Binary Value Decimal Value

00

2 UU 2

~1P = 1

01

2 U1 2

= 2

10

2 1U 2

7F = 4

11

2 ll 2

"I? = 8

Table captionTable 4.4: The eight possible mantissas and four possible exponents that make up all ti ny float values

Figure 4.9 A plot of all the possible ti ny float numbers on the real number line. Note that the numbers are more dense near zero and become more sparse moving to the right. The precision in the range 0... 1 is one-eighth. The precision in the range 1... 2 is only one-fourth, and over the range 2... 4 it drops to one-half. In the range 4...7 our tiny float type can represent only whole numbers.

0

1 1 3 1 5 3 7 8 4 8 2 8 4 8

1 I 1 I 1

1 A 'O

%

5

+

5

6

+

6

7

7

Table 4.5 and Figure 4.9 reveal several troubling issues about our ti ny float type:

1. There are many gaps; for example, the value 2.4 is missing and thus cannot be represented exactly (2.5 is the closest approximation). As another example, 0.75 and 1.75 both appear, but 2.75 is missing.

2. The scheme duplicates some numbers; for example, three different bit patterns represent the decimal value 0.5:

0.100 x2°° = 0.010 x2 01 = 0.001 x2 10 = 0.5io

This duplication limits the number of different values that can be represented by a given number of bits. In our ti ny float example 12 of the 32 bit strings (37.5%) are redundant.

3. The numbers are not uniformly dense. There are more values nearer to zero, and the numbers become more sparse farther away from zero.

Our unsigned tiny type discussed in Section 4.8.1 exhibits none of these weaknesses. All integers in a given range (0...31) are present, no two bit strings represent the same value, and the integers are uniformly distributed across their specified range. While the standard integer types provided by C++ have much greater ranges than our unsigned tiny type, they all share these same qualities: all values in their ranges are present, and all bit strings represent unique integer values. The standard floating-point types provided by C++ use many more bits than our tiny float type, yet they exhibit the same problems

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table captionBit String Interpretation Decimal Equivalent Value

00000

,000 2 x 2™2

0.000 x 1

0.000

00001

,000 2 x 2 01 2

0.000 x 2

0.000

00010

,000 2 x 2'°2

0.000 x 4

0.000

00011

,000 2 x 2 n 2

0.000 x 8

0.000

00100

,001 2 x 2 00 2

0.125 x 1

0.125

00101

,001 2 x 2 01 2

0.125 x 2

0.250

00110

,001 2 x 2 i0 2

0.125 x 4

0.500

00111

,001 2 x 2 n 2

0.125 x 8

1.000

01000

.010 2 x 2°°2

0.250 x 1

0.250

01001

,010 2 x 2 01 2

0.250 x 2

0.500

01010

.010 2 x 2 10 2

0.250 x 4

1.000

01011

,010 2 x 2 n 2

0.250 x 8

2.000

01100

.011 2 x 2°°2

0.375 x 1

0.375

01101

.011 2 x 2 01 2

0.375 x 2

0.750

01110

.011 2 x 2‘°2

0.375 x 4

1.500

01111

.011 2 x 2 n 2

0.375 x 8

3.000

10000

,100 2 x 2°°2

0.500 x 1

0.500

10001

,100 2 x 2 01 2

0.500 x 2

1.000

10010

o

o

X

to

o

0.500 x 4

2.000

10011

,100 2 x 2 n 2

0.500 x 8

4.000

10100

.101 2 x 2°°2

0.625 x 1

0.625

10101

,101 2 x 2 01 2

0.625 x 2

1.250

10110

.101 2 x 2'°2

0.625 x 4

2.500

10111

O

X

to

0.625 x 8

5.000

11000

,110 2 x 2 00 2

0.750 x 1

0.750

11001

,110 2 x 2 01 2

0.750 x 2

1.500

11010

.110 2 x 2'°2

0.750 x 4

3.000

11011

.110 2 x 2 n 2

0.750 x 8

6.000

11100

,111 2 x 2°°2

0.875 x 1

0.875

11101

,m 2 x 2 01 2

0.875 x 2

1.750

11110

,111 2 x 2 10 2

0.875 x 4

3.500

11111

.111 2 x 2 n 2

0.875 x 8

7.000

Table captionTable 4.5: The tiny float values. The first three bits of the bit string constitute the mantissa, and the last two bits represent the exponent. Given five bits we can produce 32 different bit strings. Notice that due to the ways different mantissas and exponents can combine to produce identical values, the 32 different bit strings yield only 20 unique

Table captiontiny float values.

shown to a much smaller degree: missing values, multiple bit patterns representing the same values, and uneven distribution of values across their ranges. This is not solely a problem of C++’s implementation of floating-point numbers; all computer languages and hardware that adhere to the IEEE 754 standard exhibit these problems. To overcome these problems and truly represent and compute with mathematical real numbers we would need a computer with an infinite amount of memory along with an infinitely fast processor.

Listing |4.15|(imprecisedifference.cpp) demonstrates the inexactness of floating-point arithmetic.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The output of Listingj4.15||(imprecisedifference.cpp) is:

0.5

0.5799999999999272

The program uses an additional #i nclude directive: ttinclude <iomanip>

This preprocessor directive allows us to use the std : : setp reci si on output stream manipulator that directs the std : : cout output stream object to print more decimal places in floating-point values. During the program’s execution, the first subtraction yields the correct answer. We now know that some floatingpoint numbers (like 0.5) have exact internal representations while others are only approximations. The exact answer for the second subtraction should be 0.58, and if we round the reported result to 12 decimal places, the answer matches. Floating-point arithmetic often produces results that are close approximations of the true answer.

Listing ; 4.16| (precise8th.cpp) computes zero in a roundabout way:

1_I_I_I_I_I_I_I_I =0

88888888

Listing4.16: precise8th.cpp

ffinclude <iostream>

int main() {

double one = 1.0,

one_eighth = 1.0/8.0,

zero = one - one_eighth - one_eighth - one_eighth

- one_eighth - one_eighth - one_eighth

- one_eighth - one_eighth;

std::cout << "one = " << one << ", one_eighth = " << one_eighth << ", zero = " << zero << '\n';

Listing |4~T6| (precise8th.cpp) prints

u

, one_eighth = 0.125, zero = 0

The number - has an exact decimal representation, 0.625. It also has an exact binary representation, 0.001 2 . 1 1

Consider, however, -. While - = 0.2 has a finite representation in base 10, it has no finite representation in base 2:

- = 0.2 = 0 . 0011001100110011 2 5

In the binary representation the 0011 2 bit sequence repeats without end. This means - does not have an

exact floating-point representation. Listing

4.17

(imprecise5th.cpp) illustrates with arithmetic involving -.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 4.17:

■impreciseSth.

cpp

#include <

iostream>

int

main()

{

double

one = 1.0,

one_fifth = 1

.0/5

. 0 ,

zero = one

one_

fifth

one_fifth - one_fifth

one_

fifth

one_fifth;

std::cout << "one =

" <<

one <<

", one_fifth = " << one_fifth

<< ", zero

— M

<< zero

A

A

:T

}

Table captionone = 1, one_fifth = 0.2, zero = 5.55112e-017

Surely the reported answer (5.551122 x 10 “ 17 = 0.00000000000000005551122) is close to the correct answer (zero). If you round it to the one-quadrillionth place (15 places behind the decimal point), it is correct.

What are the ramifications for programmers of this inexactness of floating-point numbers? Section j9.4.6| shows how the misuse of floating-point values can lead to logic errors in programs.

Being careful to avoid overflow and underflow, integer arithmetic is exact and, on most computer systems, faster than floating-point arithmetic. If an application demands the absolute correct answer and integers are appropriate for the computation, you should choose integers. For example, in financial calculations it is important to keep track of every cent. The exact nature of integer arithmetic makes integers an attractive option. When dealing with numbers, an integer type should be the first choice of programmers.

The limitations of floating-point numbers are unavoidable since computers have finite resources. Compromise is inevitable even when we do our best to approximate values with infinite characteristics in a finite way. Despite their inexactness, double-precision floating-point numbers are used every day throughout the world to solve sophisticated scientific and engineering problems; for example, the appropriate use of floating-point numbers have enabled space probes to reach distant planets. In the example C++ programs above that demonstrate the inexactness of floating-point numbers, the problems largely go away if we agree that we must compute with the most digits possible and then round the result to fewer digits. Floating-point numbers provide a good trade-off of precision for practicality.

4.9 More Arithmetic Operators

As Listing }4.12[ (enhancedtimeconv.cpp) demonstrates, an executing program can alter a variable’s value by performing some arithmetic on its current value. A variable may increase by one or decrease by five. The statement

x = x + 1 ;

increments x by one, making it one bigger than it was before this statement was executed. C++ has a shorter statement that accomplishes the same effect:

x++ 5

This is the increment statement. A similar decrement statement is available:

©2018 Richard L. Halterman

Draft date: September 25, 2018

x--; // Same as x = x - 1;

These statements are more precisely post-increment and post-decrement operators. There are also preincrement and pre-decrement forms, as in

—x; // Same as x = x - 1;

++y; // Same as y = y + 1;

When they appear alone in a statement, the pre- and post- versions of the increment and decrement operators work identically. Their behavior is different when they are embedded within a more complex statement. Listing 4.18 (prevspost.cpp) demonstrates how the pre- and post- increment operators work slightly differently.

Table captionListing |4.18[ (prevspost.cpp) prints

xl=l,

yl=10

, x2=100

, y2=1000

xl=2,

yi=i,

x2=100,

y2=1000

xl=2,

yi=i,

x2=101,

y2=101

If xl has the value 1 just before the statement yl = xl++;

then immediately after the statement executes xl is 2 and yl is 1.

If xl has the value 1 just before the statement yl = ++xl;

then immediately after the statement executes xl is 2 and yl is also 2.

As you can see, the pre-increment operator uses the new value of the incremented variable when evaluating the overall expression. In contrast, the post-increment operator uses the original value of the incremented variable when evaluating the overall expression. The pre- and post-decrement operator behaves similarly.

For beginning programmers it is best to avoid using the increment and decrement operators within more complex expressions. We will use them frequently as standalone statements since there is no danger of misinterpreting their behavior when they are not part of a more complex expression.

©2018 Richard L. Halterman

Draft date: September 25, 2018

C++ provides a more general way of simplifying a statement that modifies a variable through simple arithmetic. For example, the statement

x = x + 5;

can be shorted to x += 5;

This statement means “increase x by five.” Any statement of the form

x op- exp-.

where

• x is a variable.

• op- is an arithmetic operator combined with the assignment operator; for our purposes, the ones most useful to us are +=, -=, *=, /=, and

• exp is an expression compatible with the variable x.

Arithmetic reassignment statements of this form are equivalent to

x = x op exp\

This means the statement x *= y + z;

is equivalent to

x = x * (y + z) ;

The version using the arithmetic assignment does not require parentheses. The arithmetic assignment is especially handy if a variable with a long name is to be modified; consider

temporary_filename_length = temporary_filename_length / (y + z); versus

temporary_filename_length /= y + z;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 4.10 The bit positions of a 32-bit C++ unsigned integer

31 30292827 2625 2423 2221 20 19 18 17 16 15 14 13 12 11 10 9 87654321 0

Do not accidentally reverse the order of the symbols for the arithmetic assignment operators, like in the statement

x =+ 5;

Notice that the + and = symbols have been reversed. The compiler interprets this statement as if it had been written

x = +5;

that is, assignment and the unary operator. This assigns x to exactly five instead of increasing it by five.

Similarly,

x =- 3;

would assign —3 to x instead of decreasing x by three.

Section|4.10)examines some additional operators available in C++.

4.10 Bitwise Operators

In addition to the common arithmetic operators introduced in Section [471] C++ provides a few other specialpurpose arithmetic operators. These special operators allow programmers to examine or manipulate the individual bits that make up data values. They are known as the bitwise operators. These operators consist of &, |, A , ~ , >>, and <<. Applications programmers generally do not need to use bitwise operators very often, but bit manipulation is essential in many systems programming tasks.

Consider 32-bit unsigned integers. The bit positions usually are numbered right to left, starting with zero. Figure )4.1~0| shows how the individual bit positions often are numbered.

The bitwise and operator, &, takes two integer subexpressions and computes an integer result. The expression e\ & <?2 is evaluated as follows:

If bit 0 in both e\ and ei is 1, then bit 0 in the result is 1; otherwise, bit 0 in the result is 0.

If bit 1 in both e\ and e 2 is 1, then bit 1 in the result is 1; otherwise, bit 1 in the result is 0.

If bit 2 in both e\ and ei is 1, then bit 2 in the result is 1; otherwise, bit 2 in the result is 0.

©2018 Richard L. Halterman

Draft date: September 25, 2018

If bit 31 in both e\ and e 2 is 1, then bit 31 in the result is 1; otherwise, bit 31 in the result is 0.

For example, the expression 13 & 14 evaluates to 12, since:

13 io = 00000000000000000000000000001101 2

& 14io = 00000000000000000000000000001110 2 12 10 = 00000000000000000000000000001100 2

Bits 2 and 3 are one for both 13 and 14; thus, bits 2 and 3 in the result must be one.

The bitwise or operator, |, takes two integer subexpressions and computes an integer result. The expression e\ | ei is evaluated as follows:

If bit 0 in both e\ and e 2 is 0, then bit 0 in the result is 0; otherwise, bit 0 in the result is 1.

If bit 1 in both e\ and e 2 is 0, then bit 1 in the result is 0; otherwise, bit 1 in the result is 1.

If bit 2 in both e\ and e 2 is 0, then bit 2 in the result is 0; otherwise, bit 2 in the result is 1.

If bit 31 in both e\ and <? 2 is 0, then bit 31 in the result is 0; otherwise, bit 31 in the result is 1.

For example, the expression 13 ] 14 evaluates to 15, since:

13io = 00000000000000000000000000001101 2 | 14 10 = 00000000000000000000000000001110 2 15 10 = 00000000000000000000000000001111 2

Bits 4-31 are zero in both 13 and 14. In bits 0-3 either 13 has a one or 14 has a one; therefore, the result has ones in bits 0-3 and zeroes everywhere else.

The bitwise exclusive or (often refered to as xor ) operator ( A ) takes two integer subexpressions and computes an integer result. The expression e\ A e 2 is evaluated as follows:

If bit 0 in e\ is the same as bit 0 in <? 2 , then bit 0 in the result is 0; otherwise, bit 0 in the result is 1.

If bit 1 in ej is the same as bit 1 in e 2 , then bit 1 in the result is 0; otherwise, bit 1 in the result is 1.

If bit 2 in e\ is the same as bit 2 in <? 2 , then bit 2 in the result is 0; otherwise, bit 2 in the result is 1.

If bit 31 in e\ is the same as bit 31 in e 2 , then bit 31 in the result is 0; otherwise, bit 31 in the result is 1.

For example, the expression 13 A 14 evaluates to 3, since:

13io = 00000000000000000000000000001101 2

" 14io = 00000000000000000000000000001110 2

3 10 = 00000000000000000000000000000011 2

Bits 0 and 1 differ in 13 and 14, so these bits are one in the result. The bits match in all the other positions, so these positions must be set to zero in the result.

The bitwise negation operator ( ~ ) is a unary operator that inverts all the bits of its expression. The expression ~ e is evaluated as follows:

©2018 Richard L. Halterman

Draft date: September 25, 2018

If bit 0 in e is 0, then bit 0 in the result is 1; otherwise, bit 0 in the result is 0.

If bit 1 in e is 0, then bit 1 in the result is 1; otherwise, bit 1 in the result is 0.

If bit 2 in e is 0, then bit 2 in the result is 1; otherwise, bit 2 in the result is 0.

If bit 31 in e is 0, then bit 31 in the result is 1; otherwise, bit 31 in the result is 0.

For example, the unsigned expression ~ 13u evaluates to 4,294,967,282, since

13i 0 = 00000000000000000000000000001101 2

negate |

—14 10 = 11111111111111111111111111110010 2

For signed integers the 31st bit stores the number’s sign. Signed integers use a representation called two’s complement binary, a slight variation of the standard binary layout. Suffice it to say that the i nt expression ~ 13 evaluates to the same bit pattern as ~ 13u, but as a signed integer it represents —14.

The shift operators move all the bits in an integer to the left or right:

• Shift left (<<). The expression x < < y, where x and y are integer types, shifts all the bits in x to the left y places. Zeros fill vacated positions. The bits shifted off the left side are discarded. The expression 5 << 2 evaluates to 20, since 5io = 1012 shifted two places to the left yields IOIOO2 = 20io- Observe that x < < y is equal to x x 2 y .

• Shift right (>>). The expression x >> y, where x and y are integer types, shifts all the bits in x to the right y places. What fills the vacated bits on the left depends on whether the integer is signed or unsigned (for example, i nt vs. unsi gned):

- For signed values the vacated bit positions are filled with the sign bit (the original leftmost bit).

- For unsigned values the vacated bit positions are filled with zeros.

The bits shifted off the right side are discarded. The expression 5 >> 2 evaluates to 1, since 510 = 10O shifted two places to the left yields OOI2 = 2010 (the original bits in positions 1 and 0 are shifted off the end and lost). Observe that x > > y is equal to x-tr2 y .

Do not confuse the left shift operator (<<) with the output stream insertion operator (< <). The operators are identical, but the context differentiates them. If the left operand is an integer type, < < means left shift; if the left operand is a stream output object like std: :cout, << means send the right-hand operand to the output stream object for display.

Similarly, the input stream object std : : ci n uses the >> for a different purpose from the right shift operator used with integers.

Listing |4T9) (bitwiseoperators.cpp) experiments with bitwise operators.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 4.19: bitwiseoperators. cpp

Table caption#include <iostream> int main() {

int

x. y;

std:

: cout

<<

"Please

enter two integers:

II .

5

std:

: ci n :

>>

X

V

V

std:

: cout

<<

x << "

& "

A

A

A

A

II

A

A

(x &

V)

A

A

'd

std:

: cout

<<

x << "

1 "

<< y << " = " <<

(x |

y)

c

V

V

std:

: cout

<<

x << "

A "

<< y << " = " <<

(x A

y)

c

V

V

std:

: cout

<<

<<

X

A

A

" = " << ~x << 1

\n' ;

std:

: cout

<<

x << "

<< "

<< 2 << " = " <<

(x

<<

2 ) << 1 \n

std :

: cout

<<

x << "

>> "

<< 2 << " = " <<

(x

>>

2 ) << 1 \n

}

Developers use bitwise operations for a variety of systems-level programming tasks. For example, in a graphical user interface (GUI), the user generates events by interacting with an application using the mouse and a keyboard. One event might be clicking a mouse button over a particular graphical element (like a button) within a window. Multiple pieces of information about this event can be stored in a single integer. For example, bit 0 may indicate whether or not the key was held down when the mouse button

was clicked. Bit 1 may be responsible for the Rjn key, bit 3 for the ■tiQB key, etc. Thus the integer value 5, which in binary is

00000000000000000000000000000101

means that when the mouse button was clicked both the ■TCffltia and keys were being held down. This might require a different action on the part of the program than if some other combination of keys (or none) were being pressed. For example, suppose the i nt variable key_status holds information about which keys the user was depressing during the most recent mouse click. Consider the expression key_status & 1. The bit string

00000000000000000000000000000001

represents the expression 1 , and the value of key_status is unknown, so key_status & 1 is

&

key_status = ???????????????????????????????? 2

1 IQ = 00000000000000000000000000000001 2

0 10 or Uo = 0000000000000000000000000000000?2

If the answer is zero, this means bit 0 is 0 in key_status, and so the |

the other hand, if the answer is one, this means bit 0 is 1 , and so the | expression

key_status & 1

t Shift

t Shift

key is not depressed. On key is depressed. In the

the 1 is called a mask , since it serves to mask off, or “remove” the first 31 bits of key_status.

Usually the GUI library will define constants that help programmers examine or modify particular bits; for example, given the following constants:

const int SHIFT_DOWN = 1; // This is 0...0001

const int CTRL_D0WN = SHIFT_DOWN << 1; // This is 0...0010

const int ALT_D0WN = CTRL_D0WN << 1; // This is 0...0100

©2018 Richard L. Halterman

Draft date: September 25, 2018

the expression

key_status & 1

is better written

key_status & SHIFT_DOWN The expression

key_status & SHIFT_DOWN | ALT_DOWN

can test for both the ■Kjntn and keys being down during the mouse event. Do you see how the expression SHIFT_DOWN | ALT_DOWN means both keys are down simultaneously?

We can use masks to ensure that certain bits are on or off. To see how, consider the mask 5, which is 00000000000000000000000000000101

If x is a 32-bit integer variable, we can selectively turn on its bits 0 and 2 with the statement x = x | 5;

Next, consider the unsigned value 4294967290U, which is ~ 5u, or

11111111111111111111111111111010

If x is a 32-bit integer variable, we can selectively turn off its bits 0 and 2 with the statement x = x & 4294967290U;

We cannot fully appreciate the utility of using bitwise operators for masking purposes until we consider conditional execution in Chapter|||5^j Even then, since we concentrate on applications programming instead of systems programming in this book, we will have little use for the bitwise operators except for a few isolated situations. It is good to be aware of their presence, though, since their accidental use may lead to difficult to diagnose compiler messages and logic errors.

Like the other C++ arithmetic operators that work on two operands, we may combine the bitwise binary operators &, |, A , <<, and >> with assignment to simplify the modification of a variable; for example, the following statement

x = x | y; // Turn on bits in x determined by

may be written as

x | = y; // Turn on bits in x determined by

Table |4i6| lists the possibilities.

4.11 Algorithms

An algorithm is a finite sequence of steps, each step taking a finite length of time, that solves a problem or computes a result. A computer program is one example of an algorithm, as is a recipe to make lasagna. In

©2018 Richard L. Halterman

Draft date: September 25, 2018

Assignment

Short Cut

x = x & y;

X

II

<

x = x 1 y;

x |= y;

X

II

X

>

X

>

II

<

X

II

X

A

A

X

A

A

II

X

II

X

V

V

X

V

V

II

Table captionTable 4.6: The bitwise assignment operators

both of these examples, the order of the steps matter. In the case of lasagna, the noodles must be cooked in boiling water before they are layered into the filling to be baked. It would be inappropriate to place the raw noodles into the pan with all the other ingredients, bake it, and then later remove the already baked noodles to cook them in boiling water separately. In the same way, the ordering of steps is very important in a computer program. While this point may be obvious, consider the following sound argument:

1. The relationship between degrees Celsius and degrees Fahrenheit can be expressed as

°C= ^ x (°F — 32)

2. Given a temperature in degrees Fahrenheit, the corresponding temperature in degrees Celsius can be computed.

Armed with this knowledge. Listing |420j(faultytempconv.cpp) follows directly.

Unfortunately, the executing program always displays

-17.7778

regardless of the input provided. The English description provided above is correct. No integer division problems lurk, as in Listing |4.10| (tempconv.cpp). The problem lies simply in statement ordering. The statement

degreesC = 5.0/9*(degreesF - 32);

©2018 Richard L. Halterman

Draft date: September 25, 2018

is an assignment statement, not a definition of a relationship that exists throughout the program. At the point of the assignment, degreesF has the value of zero. The executing program computes and assigns the degreesC variable before receiving degreesF’s value from the user.

As another example, suppose x and y are two integer variables in some program. How would we interchange the values of the two variables? We want x to have y’s original value and y to have x’s original value. This code may seem reasonable:

x = y;

y = x;

The problem with this section of code is that after the first statement is executed, x and y both have the same value (y’s original value). The second assignment is superfluous and does nothing to change the values of x or y. The solution requires a third variable to remember the original value of one the variables before it is reassigned. The correct code to swap the values is

temp = x;

x = y;

y = temp;

This small example emphasizes the fact that algorithms must be specified precisely. Informal notions about how to solve a problem can be valuable in the early stages of program design, but the coded program requires a correct detailed description of the solution.

The algorithms we have seen so far have been simple. Statement 1, followed by Statement 2, etc. until every statement in the program has been executed. Chapter [5j and Chapter |6| introduce some language constructs that permit optional and repetitive execution of some statements. These constructs allow us to build programs that do much more interesting things, but more complex algorithms are required to make it happen. We must not lose sight of the fact that a complicated algorithm that is 99% correct is not correct. An algorithm’s design and implementation can be derailed by inattention to the smallest of details.

4.12 Exercises

1. Is the literal 4 a valid C++ expression?

2. Is the variable x a valid C++ expression?

3. Is x + 4 a valid C++expression?

4. What affect does the unary + operator have when applied to a numeric expression?

5. Sort the following binary operators in order of high to low precedence: +, 96, =.

6 . Write a C++ program that receives two integer values from the user. The program then should print the sum (addition), difference (subtraction), product (multiplication), quotient (division), and remainder after division (modulus). Your program must use only integers.

A sample program run would look like (the user enters the 10 and the 2 after the colons, and the program prints the rest):

Please

enter

the

first number: 10

Please

enter

the

second number: 2

10 + 2

= 12

10-2

= 8

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

10

*

2 = 20

10

/

2 = 5

10

O'

'0

2 = 0

Can you explain the results it produces for all of these operations?

7. Write a C++ program that receives two double-precision floating-point values from the user. The program then should print the sum (addition), difference (subtraction), product (multiplication), and quotient (division). Your program should use only integers.

A sample program run would look like (the user enters the 10 and the 2.5 after the colons, and the program prints the rest):

Please enter the first number: 10 Please enter the second number: 2.5 10 + 2.5 = 12.5

10 - 2.5 = 7.5

10 * 2.5 = 25

10 / 2.5 = 4

Can you explain the results it produces for all these operations? What happens if you attempt to compute the remainder after division (modulus) with double-precision floating-point values?

8 . Given the following declaration:

i nt x = 2;

Indicate what each of the following C++ statements would print.

(a)

std:

: cout

<<

"x"« ' \n'

3

(b)

std:

: cout

<<

C

V

V

X

3

(C)

std:

: cout

<<

c

V

V

X

(d)

std:

: cout

<<

V

V

1—1

+

X

' \n' ;

(e)

std:

: cout

<<

X

+

1-*

A

A

' \n' ;

(f)

std:

: cout

<<

x + 1 << '

\n' ;

9. Sort the following types in order from narrowest to widest: i nt, double, float, long, char.

10. Given the following declarations:

int il =2, i2 = 5, i3 = -3;

double dl = 2.0, d2 = 5.0, d3 = -0.5;

Evaluate each of the following C++ expressions.

(a)

il

+

i 2

(b)

il

/

i 2

(c)

i 2

/

il

(d)

il

i3

(e)

dl

+

d2

(f)

dl

/

d2

(g)

d2

/

dl

Table caption©2018 Richard L. Halterman

Draft date: September 25, 2018

(h) d3 * dl

(i) d 1 + i 2

(j) 'll / d2

(k) d2 / il

(l) -12 / dl

(m) il/i2*dl

(n) dl*il/i2

(o) dl/d2*i 1

(p) i l*dl/d2

(q) i2/il*dl

(r) dl*i2/i 1

(s) d2/dl*i 1

(t) i l*d2/dl

11. What is printed by the following statement:

std::cout << /* 5 */ 3 << '\n' ;

12. Given the following declarations:

int il = 2, i2 = 5, i3 = -3;

double dl = 2.0, d2 - 5.0, d3 = -0.5;

Evaluate each of the following C++ expressions.

(a)

il +

("i 2

* i3)

(b)

i 1 *

("i 2

+ "i 3)

(c)

-il /

("i 2

+ i3)

(d)

-il /

i 2 +

i3

(e)

3 + ■

4 + 5

/ 3

(f)

(3 +

4 +

5) / 3

(g)

dl +

( d 2

* d3)

(h)

dl +

d2 *

d3

(i)

dl /

d2

d3

(1)

dl /

( d 2

- d3)

(k)

dl +

d2 +

d3 / 3

0 )

(dl

+ d2

+ d3 ) /

3

(m)

dl +

d2 +

(d3 /

3)

(n)

3 *

(dl +

d2) *

(dl - d3)

13. How are single-line comments different from block comments?

14. Can block comments be nested?

15. Which is better, too many comments or too few comments?

©2018 Richard L. Halterman

Draft date: September 25, 2018

16. What is the purpose of comments?

17. The programs in Listing j|3.4|j (variable.cpp), Listing [44] (reformattedvariable.cpp), and Listing [43| (reformattedvariable2.cpp) compile to the same machine code and behave exactly the same. What makes one of the programs clearly better than the others?

18. Why is human readability such an important consideration?

19. Consider the following program which contains some errors. You may assume that the comments within the program accurately describe the program’s intended behavior.

ttinclude <iostream>

Table captionint main() {

int nl, n2, dl;

//

// Get two numbers from the user

cin << nl << n2;

//

// Compute sum of the two

numbers

std::cout << nl + n2 << '

\n' ;

//

// Compute average of the

two numbers

std::cout << nl+n2/2 << '

\n' ;

//

// Assign some variables dl = d2 = 0;

//

// Compute a quotient

std::cout << nl/dl << '\n

1 .

3

//

// Compute a product nl*n2 = dl;

//

// Print result

std::cout << dl << '\n ' ;

//

1

2

3

4

5

6

7

8

For each line listed in the comments, indicate whether or not a compile-time, run-time, or logic error is present. Not all lines contain an error.

20. What distinguishes a compiler warning from a compiler error? Should you be concerned about warnings? Why or why not?

21. What are the advantages to enhancing the warning reporting capabilities of the compiler?

22. Write the shortest way to express each of the following statements.

(a) x = x + 1;

(b) x = x / 2;

(c) x = x - 1;

(d) x = x + y;

(e) x = x - (y + 7) ;

(f) x = 2*x;

(g) number_of_cLosed_cases = number_of_closed_cases + 2*ncc;

23. What is printed by the following code fragment?

©2018 Richard L. Halterman

Draft date: September 25, 2018

int xl = 2, yl, x2 = 2, y2; yl = ++xl; y2 = x2++;

std::cout << xl << " " << x2 << '\n' ; std::cout << yl << " " << y2 << '\n' ;

Why does the output appear as it does?

24. Consider the following program that attempts to compute the circumference of a circle given the radius entered by the user. Given a circle’s radius, r, the circle’s circumference, C is given by the formula:

C = 2nr

ttinclude <iostream>

int main() {

double C, r;

const double PI = 3.14159;

// Formula for the area of a circle given its radius C = 2*PI*r;

// Get the radius from the user

cout >> "Please enter the circle's radius: cin << r;

// Print the circumference

std::cout << "Circumference is " << C << '\n' ;

(a) The compiler issues a warning. What is the warning?

(b) The program does not produce the intended result. Why?

(c) How can it be repaired so that it not only eliminates the warning but also removes the logic error?

25. In mathematics, the midpoint between the two points {xi,y \) and (xj■ yi) is computed by the formula

f x i +x 2 yi +12

V 2 ’ 2 )

Write a C++ program that receives two mathematical points from the user and computes and prints their midpoint.

A sample run of the program produces

Please enter the first point: (0,0)

Please enter the second point: (1,1)

The midpoint of (0,0) and (1,1) is (0.5,0.5)

The user literally enters "(0,0)" and "(1,1)" with the parentheses and commas as shown. To see how to do this, suppose you want to allow a user to enter the point (2.3,9), assigning the x component of the point to a variable named x and the y component to a variable named y. You can add the following code fragment to your program to achieve the desired effect:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Food

Calories

Bean burrito

357

Salad w/dressing

185

Milkshake

388

Table captionTable 4.7: Calorie content of several fast food items

double x, y;

char left_paren, comma, right_paren;

std::cin >> left_paren >> x >> comma >> y >> right_paren;

If the user literally types (2.3,9), the std : : ci n statement will assign the ( character to the variable left_paren. It next will assign 2.3 to the variable x. It assigns the , character to the variable named comma, the value 9 to the y variable, and the ) character to the ri ght_paren variable. The left_paren, comma, and right_paren variables are just placeholders for the user’s input and are not used elsewhere within the program. In reality, the user can type in other characters in place of the parentheses and comma as long as the numbers are in the proper location relative to the characters; for example, the user can type *2.3: 9#, and the program will interpret the input as the point (2.3,9).

26. Table |4.7|| lists the Calorie contents of several foods. Running or walking burns off about 100 Calories per mile. Write a C++ program that requests three values from the user: the number of bean burritos, salads, and shakes consumed (in that order). The program should then display the number of miles that must be run or walked to burn off the Calories represented in that food. The program should run as follows (the user types in the 3 2 1):

Number of bean burritos, bowls of salad, and milkshakes eaten? 321 You ingested 1829 Calories

You will have to run 18.29 miles to expend that much energy

Observe that the result is a floating-point value, so you should use floating-point arithmetic to compute the answers for this problem.

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 5

Conditional Execution

All the programs in the preceding chapters execute exactly the same statements regardless of the input, if any, provided to them. They follow a linear sequence: Statement 1, Statement 2, etc. until the last statement is executed and the program terminates. Linear programs like these are very limited in the problems they can solve. This chapter introduces constructs that allow program statements to be optionally executed, depending on the context (input) of the program’s execution.

5.1 Type bool

Arithmetic expressions evaluate to numeric values; a Boolean expression, evaluates to true or false. While Boolean expressions may appear very limited on the surface, they are essential for building more interesting and useful programs.

C++ supports the non-numeric data type bool, which stands for Boolean. The term Boolean comes from the name of the British mathematician George Boole. A branch of discrete mathematics called Boolean algebra is dedicated to the study of the properties and the manipulation of logical expressions. Compared to the numeric types, the bool type is very simple in that it can represent only two values: true or false. Listing 5.1 (boolvars.cpp) is a simple program demonstrating the use of Boolean variables.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Operator

Meaning

==

Equal to

<

Less than

>

Greater than

< =

Less than or equal to

> =

Greater than or equal to

i

Not equal to

Table captionTable 5.1: C++ Relational operators

int x = a, y = true;

std::cout << "a = " << a << ", b = " << b

<< ", x = " << x << ", y = " << y << ' \n 1 ; // More mixing

a = 1725; // Warning issued b = -19; // Warning issued

std::cout << "a = " << a << ", b = " << b << 1 \ n' ;

As you can see from running Listing 5.1 (boolvars.cpp), the Boolean values false and true are represented as integer 0 and integer 1. More precisely, zero represents the bool value false, and any non-zero integer (positive or negative) means true. The direct assignment to a bool variable of an integer other than 0 or 1 may result in a warning (Visual C++ reports truncation of ’int’ to ’bool’), but the variable is still interpreted as true. The data type bool is basically a convenience for programmers; any C++ program that uses bool variables can be rewritten using integers instead to achieve the same results. While Boolean values and variables are freely compatible and interchangeable with integers, the bool type is convenient and should be used when the context involves truth values instead of numbers.

It is important to note that the Visual C++ compiler issues warnings for the last two assignment statements in Listing j5TT| (boolvars.cpp). Even though any non-zero value is considered true, 1 is the preferred integer equivalent to true (as you can see when you attempt to print the literal value true). Since the need to assign to a Boolean variable a value other than true or false or the equivalent 1 or 0 should be extremely rare, the compiler’s message alerts the programmer to check to make sure the assignment is not a mistake.

5.2 Boolean Expressions

The simplest Boolean expressions are false and true, the Boolean literals. A Boolean variable is also a Boolean expression. An expression comparing numeric expressions for equality or inequality is also a Boolean expression. The simplest kinds of Boolean expressions use relational operators to compare two expressions. Table |5TT| lists the relational operators available in C++.

Table (5T2( shows some simple Boolean expressions with their associated values. An expression like 10 < 20 is legal but of little use, since the expression true is equivalent, simpler, and less likely to confuse human readers. Boolean expressions are extremely useful when their truth values depend on the values of one or more variables.

The relational operators are binary operators and are all left associative. They all have a lower precedence than any of the arithmetic operators; therefore, the expression

©2018 Richard L. Halterman

Draft date: September 25, 2018

Expression

Value

10 < 20

always true

10 >= 20

always false

x == 10

true only if x has the value 10

X != y

true unless x and y have the same values

Table captionTable 5.2: Relational operator examples

X + 2 < y / 10

is evaluated as if parentheses were placed as so: (x + 2) < (y / 10)

C++ allows statements to be simple expressions; for example, the statement x == 15;

may look like an attempt to assign the value 15 to the variable x, but it is not. The = operator performs assignment, but the == operator checks for relational equality. If you make a mistake and use == as shown here. Visual C++ will issue a warning that includes the message

warning C4553: '==' : operator has no effect; did you intend ’= ’?

Recall from Section 'A.6 A that a compiler warning does not indicate a violation of the rules of the language; rather it alerts the programmer to a possible trouble spot in the code.

Another example of an expression used as a statement is x + 15;

This statement is a legal (but useless) C++ statement, and the compiler notifies us accordingly:

warning C4552: ’+ ’: operator has no effect; expected operator with side-effect

Why are expressions allowed as statements? Some simple expressions have side effects that do alter the behavior of the program. One example of such an expression is x + + . Listing 4.18j|(prevspost.cpp) showed how x + + behaves both as a standalone statement and as an expression within a larger statement. A more common example is the use of a function call (which is an expression) as standalone a statement. (We introduce functions in Chapter||8|) In order to keep the structure of the language as uniform as possible, C++ tolerates useless expressions as statements to enable programmers to use the more useful expression-statements. Fortunately, most compilers issue informative warnings about the useless expressionstatements to keep developers on track.

©2018 Richard L. Halterman

Draft date: September 25, 2018

5.3 The Simple if Statement

The Boolean expressions described in Section 5.2| at first may seem arcane and of little use in practical programs. In reality. Boolean expressions are essential for a program to be able to adapt its behavior at run time. Most truly useful and practical programs would be impossible without the availability of Boolean expressions.

The run-time exceptions mentioned in Section 4.6 arise from logic errors. One way that Listing |46| (dividedanger.cpp) can fail is when the user enters a zero for the divisor. Fortunately, programmers can take steps to ensure that division by zero does not occur. Listing |5.2| (betterdivision.cpp) shows how it might be done.

The second std : : cout statement may not always be executed. In the following run

Please enter two integers to divide: 32 8 32/8 = 4

it is executed, but if the user enters a zero as the second number:

Please enter two integers to divide: 32 0

the program prints nothing after the user enters the values.

The last statement in Listing 5.2 (betterdivision.cpp) begins with the reserved word i f. The i f statement allows code to be optionally executed. In this case, the printing statement is executed only if the variable di vi sor’s value is not zero.

The Boolean expression divisor != 0

determines if the single statement that follows the right parenthesis is executed. If divisor is not zero, the message is printed; otherwise, the program prints nothing.

Figure 5.1 shows how program execution flows through the i f statement, of Listing 5.2 (betterdivision.cpp).

The general form of a simple i f statement is

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 5.1 if flowchart

©2018 Richard L. Halterman

Draft date: September 25, 2018

if

( condition

)

statement

• The reserved word i f begins the i f statement.

• The Boolean expression condition determines whether or not the body will be executed. The Boolean expression must be enclosed within parentheses as shown.

The statement is the statement to be executed if the Boolean expression is true. The statement makes up the body of the i f statement. Section 5.4 shows how the body can be composed of multiple statements.

Good coding style dictates we should indent the body to emphasize the optional execution and improve the program’s readability. The compiler does not require the indentation. Sometimes programmers will place a one-statement body on the same line as the i f ; for example, the following i f statement optionally assigns y:

if (x < 10)

y = x;

and could be written as

if (x < 10) y = x;

but should not be written as

if (x < 10)

y = x;

because the lack of indentation hides the fact that the program optionally executes the assignment statement. The compiler will accept it, but it is misleading to human readers accustomed to the indentation convention. The compiler, of course, will accept the code written as

if (x<10)y=x;

but the lack of spaces makes it difficult for humans to read.

©2018 Richard L. Halterman

Draft date: September 25, 2018

When the i f statement is written the preferred way using two lines of source code, it is important not to put a semicolon at the end of the first line:

if (x < 10); // No! Don't do this!

Y = x;

Here, the semicolon terminates the i f statement, but the indentation implies that the second line is intended to be the body of the i f statement. The compiler, however, interprets the badly formatted i f statement as if it were written as

if (x

< 10 )

; // This

x:

is what is really going on.

This is legal in C++; it means the i f statement has an empty body. In which case the assignment is not part of the body. The assignment statement is after the body and always will be executed regardless of the truth value of the Boolean expression.

When checking for equality, as in

if (x == 10)

std::cout << "ten" ;

be sure to use the relational equality operator (==), not the assignment operator (=). Since an assignment statement has a value (the value that is assigned, see Section 4.3). C++ allows = within the conditional expression. It is, however, almost always a mistake when beginning programmers use = in this context. Visual C++ at warning Level 4 checks for the use of assignment within a conditional expression; the default Level 3 does not.

5.4 Compound Statements

Sometimes you need to optionally execute more than one statement based on a particular condition. Listing [5.3| (alternatedivision.cpp) shows how you must use curly braces to group multiple statements together into one compound statement.

©2018 Richard L. Halterman

Draft date: September 25, 2018

quotient = dividend / divisor;

std::cout << dividend << " divided by " << divisor << << quotient << '\n' ;

i s

The assignment statement and printing statement are both a part of the body of the i f statement. Given the truth value of the Boolean expression divisor != 0 during a particular program run, either both statements will be executed or neither statement will be executed.

A compound statement consists of zero or more statements grouped within curly braces. We say the curly braces define a block of statements. As a matter of style many programmers always use curly braces to delimit the body of an i f statement even if the body contains only one statement:

if (x < 10) {

y = x;

}

They do this because it is easy to introduce a logic error if additional statements are added to the body later and the programmer forgets to add then required curly braces.

The format of the following code if (x < 10)

y = x;

z = x + 5;

implies that both assignments are part of the body of the i f statement. Since multiple statements making up the body must be in a compound statement within curly braces, the compiler interprets the code fragment as if it had been written

if (x < 10)

Such code will optionally execute the first assignment statement and always execute the second assignment statement.

The programmer probably meant to write it as if (x < 10) {

y = x;

z = x + 5;

}

The curly braces are optional if the body consists of a single statement. If the body consists of only one statement and curly braces are not used, then the semicolon that terminates the statement in the body also terminates the i f statement. If curly braces are used to delimit the body, a semicolon is not required after the body’s close curly brace.

An empty pair of curly braces represents an empty block. An empty block is a valid compound statement.

©2018 Richard L. Halterman

Draft date: September 25, 2018

5.5 The if/else Statement

One undesirable aspect of Listing |5.2[ (betterdivision.cpp) is if the user enters a zero divisor, the program prints nothing. It may be better to provide some feedback to the user to indicate that the divisor provided cannot be used. The i f statement has an optional else clause that is executed only if the Boolean expression is false. Listing 5.4 (betterfeedback.cpp) uses the i f/else statement to provide the desired effect.

A given program run will execute exactly one of either the i f body or the else body. Unlike in Listing [572|(betterdivision.cpp), a message is always displayed.

Please enter two integers to divide: 32 0 Division by zero is not allowed

The else clause contains an alternate body that is executed if the condition is false. The program’s flow of execution is shown in Figure [5l2]

Listing |5l4| (betterfeedback.cpp) avoids the division by zero run-time error that causes the program to terminate prematurely, but it still alerts the user that there is a problem. Another application may handle the situation in a different way; for example, it may substitute some default value for di vi sor instead of zero.

The general form of an i f /else statement is

if (

condition

)

statement 1

else

statement 2

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 5.2 if/else flowchart

©2018 Richard L. Halterman

Draft date: September 25, 2018

• The reserved word i f begins the i f /else statement.

• The condition is a Boolean expression that determines whether the running program will execute statement 1 or statement 2. As with the simple i f statement, the condition must appear within parentheses.

• The program executes statement 1 if the condition is true. To make the i f/else statement more readable, indent statement 1 more spaces than the i f line. This part of the i f statement is sometimes called the body of the i f .

• The reserved word else begins the second part of the i f /else statement.

• The program executes statement 2 if the condition is false. To make the i f/else statement more readable, indent statement 2 more spaces than the else line. This part of the i f/else statement is sometimes called the body of the else.

The body of the else clause of an i f/else statement may be a compound statement:

if (x == y)

std::cout << x; else {

x = 0;

std::cout << y;

}

or the i f body alone may be a compound statement:

if (x == y) {

std::cout << x; x = 0;

}

else

std::cout << y;

or both parts may be compound:

if (x == y) {

std::cout << x; x = 0;

}

else {

std::cout << y;

y = Q;

}

or, as in Listing 5.4 (betterfeedback.cpp), both the i f body and the else body can be simple statements.

Remember, if you wish to associate more than one statement with the body of the i f or else, you must use a compound statement. Compound statements are enclosed within curly braces ({}).

©2018 Richard L. Halterman

Draft date: September 25, 2018

If you ever attempt to use an i f /else statement and discover that you need to leave the else clause empty, as in

if (x == 2)

std::cout << "x = " << x << '\n' ;

else

; // Nothing to do otherwise

or, using a slightly different syntax, as if (x == 2)

std::cout << "x = " << x << '\n' ;

else {

} // Nothing to do otherwise

you instead should use a simple i f statement: if (x == 2)

std::cout << "x = " << x << '\n' ;

The empty else clauses shown above do work, but they complicate the code and make it more difficult for humans to read.

Due to the imprecise representation of floating-point numbers (see Listing ||4T17[ (imprecise5th.cpp) in Section |4.1| , programmers must use caution when using the equality operator (==) by itself to compare floating-point expressions. Listing 5.5 (samedifferent.cpp) uses an i f /else statement to demonstrate the perils of using the equality operator with floating-point quantities.

Listing 5.5: samedifferent.cpp

ffinclude <iostream> #include <iomanip>

int main() {

double dl = 1.11 d2 = 2.11 std::cout << "dl std::cout << "d2 if (dl == d2)

std::cout <<

else

std::cout << std::cout << "dl std::cout << "d2

- 1 . 10 ,

- 2 . 10 ;

= " << dl << '\n 1 ;

= " << d2 << '\n 1 ;

"Same\n" ;

"Different\n" ;

= " << std::setprecisi on(20) = " << std::setprecisi on(20)

<< dl << << d2 <<

' \n' ; ' \n' ;

In Listing 5.5 (samedifferent.cpp) the displayed values of dl and d2 are rounded so they appear equivalent, but internally the exact representations are slightly different. By including the header i omani p we can use the std: :setprecision stream manipulator to force std::coutto display more decimal places in the floating-point number it prints. Observe from the output of Listing |5.5|| (samedifferent.cpp) that the two quantities that should be identically 0.01 are actually slightly different.

dl = 0.01 d2 = 0.01 Different

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table captione\ e 2 e\ && <?2 e\ \ \ e 2 \e\

false

false

false

false

true

false

true

false

true

true

true

false

false

true

false

true

true

true

true

false

Table captionTable 5.3: Logical operators— e\ and «2 are Boolean expressions

dl = 0.010000000000000009 d2 = 0.0099999999999997868

This result should not discourage you from using floating-point numbers where they truly are needed. In Section [9.4.6|| we will see how to handle floating-point comparisons properly.

5.6 Compound Boolean Expressions

Simple Boolean expressions, each involving one relational operator, can be combined into more complex Boolean expressions using the logical operators && (and), | | (or), and ! (not). A combination of two or more Boolean expressions using logical operators is called a compound Boolean expression.

To introduce compound Boolean expressions, consider a computer science degree that requires, among other computing courses. Operating Systems and Programming Languages. If we isolate those two courses, we can say a student must successfully complete both Operating Systems and Programming Languages to qualify for the degree. A student that passes Operating Systems but not Programming Languages will not have met the requirements. Similarly, Programming Languages without Operating Systems is insufficient, and a student completing neither Operating Systems nor Programming Languages surely does not qualify.

Logical AND works in exactly the same way. If e\ and ei are two Boolean expressions, e\ && e 2 is true only if e\ and ei are both true; if either one is false or both are false, the compound expression is false.

To illustrate logical OR, consider two mathematics courses. Differential Equations and Linear Algebra. A computer science degree requires one of those two courses. A student who successfully completes Differential Equations but does not take Linear Algebra meets the requirement. Similarly, a student may take Linear Algebra but not Differential Equations. It is important to note the a student may elect to take both Differential Equations and Linear Algebra (perhaps on the way to a mathematics minor), but the requirement is no less fulfilled.

Logical OR works in a similar fashion. Given our Boolean expressions e\ and c j 2 , the compound expression e\ | | e 2 is false only if e\ and e 2 are both false; if either one is true or both are true, the compound expression is true. Note that logical OR is an inclusive or, not an exclusive or. In informal conversion we often imply exclusive or in a statement like “Would you like cake or ice cream for dessert?” The implication is one or the other, not both. In computer programming the or is inclusive; if both subexpressions in an or expression are true, the or expression is true.

Logical NOT simply reverses the truth value of the expression to which it is applied. If e is a true Boolean expression, ! e is false; if e is false, ! e is true.

is called a truth table. It shows all the combinations of truth values for two simple expressions and the values of compound Boolean expressions built from applying the &&, | |, and ! C++ logical operators.

Table 5.3

Both && and | | are binary operators; that is, they require two operands, both of which must be Boolean

©2018 Richard L. Halterman

Draft date: September 25, 2018

expressions. Logical not (!) is a unary operator (see Section ||4.1| ; it requires a single Boolean operand immediately to its right.

Operator ! has higher precedence than both && and | ). && has higher precedence than | |. && and | j are left associative; ! is right associative. && and | | have lower precedence than any other binary operator except assignment. This means the expression

x <= y && x <= z is evaluated

(x <= y) && (x <= z)

Some programmers prefer to use the parentheses as shown here even though they are not required. The parentheses improve the readability of complex expressions, and the compiled code is no less efficient.

The relational operators such as < compare two operands. The result of the comparison is a Boolean value, which is freely convertible to an integer. The misapplication of relational operators can lead to surprising results; consider, for example, the expression

1 <= x <= 10

This expression is always true, regardless of the value of x! If the programmer’s intent is to represent the mathematical notion of x falling within the range 1... 10 inclusive, as in 1 < x < 10, the above C++ expression is not equivalent.

The expression

1 <= x <= 10 is evaluated as

(1 <= x) <= 10

If x is greater than or equal to one, the subexpression 1 ~ <= ~ x evaluates to true, or integer 1. Integer 1, however, is always less than 10, so the overall expression is true. If instead x is less than one, the subexpression 1 ~ <= ~ x evaluates to false, or integer 0. Integer 0 is always less than 10, so the overall expression is true. The problem is due to the fact that C++ does not strictly distinguish between Boolean and integer values.

A correct way to represent the mathematical notion of 1 < x < 10 is 1 <= x && x <= 10

In this case x must simultaneously be greater than or equal to 1 and less than or equal to 10. The revised Boolean expression is a little more verbose than the mathematical representation, but it is the correct formulation for C++.

The following section of code assigns the indicated values to a bool:

bool b; int x = 10; int y = 20;

©2018 Richard L. Halterman

Draft date: September 25, 2018

b

=

(x

==

10)

3

//

assigns

true to b

b

=

(x

! =

10)

3

//

assigns

false to b

b

=

(X

==

10

&&

y

== 20);

//

assigns

true to b

b

=

(X

! =

10

&&

y

== 20);

//

assigns

false to b

b

=

(X

==

10

&&

y

!= 20);

//

assigns

false to b

b

=

(X

! =

10

&&

y

!= 20);

//

assigns

false to b

b

=

(X

==

10

1 1

y

== 20);

//

assigns

true to b

b

=

(X

! =

10

y

== 20);

//

assigns

true to b

b

=

(X

= =

10

y

!= 20);

//

assigns

true to b

b

=

(X

! =

10

y

!= 20);

//

assigns

false to b

Convince yourself that the following expressions are equivalent:

(x ! = y)

! (x == y)

(x < y || x > y)

In the expression e\ && ej both subexpressions e\ and ej must be true for the overall expression to be true. Since the && operator evaluates left to right, this means that if e\ is false, there is no need to evaluate ei- If e\ is false, no value of e 2 can make the expression e\ && ei true. The logical and operator first tests the expression to its left. If it finds the expression to be false, it does not bother to check the right expression. This approach is called short-circuit evaluation. In a similar fashion, in the expression e\ | | ej, if e\ is true, then it does not matter what value ei has—a logical or expression is true unless both subexpressions are false. The | | operator uses short-circuit evaluation also.

Why is short-circuit evaluation important? Two situations show why it is important to consider:

• The order of the subexpressions can affect performance. When a program is running, complex expressions require more time for the computer to evaluate than simpler expressions. We classify an expression that takes a relatively long time to evaluate as an expensive expression. If a compound Boolean expression is made up of an expensive Boolean subexpression and an less expensive Boolean subexpression, and the order of evaluation of the two expressions does not affect the behavior of the program, then place the more expensive Boolean expression second. If the first subexpression is false and && is being used, then the expensive second subexpression is not evaluated; if the first subexpression is true and | | is being used, then, again, the expensive second subexpression is avoided.

• Subexpressions can be ordered to prevent run-time errors. This is especially true when one of the subexpressions depends on the other in some way. Consider the following expression:

(x != 0) && (z/x > 1)

Here, if x is zero, the division by zero is avoided. If the subexpressions were switched, a run-time error would result if x is zero.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Arity

Operators

Associativity

unary

(post) ++, (post) —, static_cast

unary

(pre)++, (pre) —, !,+,

binary

*, /, °0

left

binary

+,

left

binary

A

A

V

V

left

binary

V

A

V

II

A

II

left

binary

==, ! =

left

binary

&&

left

binary

11

left

binary

=. +=, -=, *=, /=,%=

right

Table captionTable 5.4: Precedence of C++ Operators (High to Low)

Suppose you wish to print the word “OK” if a variable x is 1, 2, or 3. An informal translation from English might yield:

if (x == 1 || 2 || 3)

std::cout << "0K\n";

Unfortunately, x’s value is irrelevant; the code always prints the word “OK.” Since the == operator has lower precedence than | (, the expression

x == 1 || 2 || 3

(x == 1)

2

3

The expression x == 1 is either true or false, but integer 2 is always interpreted as true, and integer 3 is interpreted as true is as well.

The correct statement would be

if (x == 1 || x == 2 || x == 3) std::cout << "0K\n";

The revised Boolean expression is more verbose and less similar to the English rendition, but it is the correct formulation for C++.

Our current list of C++ operators is shown in Table [5i4 |

5.7 Nested Conditionals

The statements in the body of the i f or the else may be any C++ statements, including other i f /else statements. We can use nested i f statements to build arbitrarily complex control flow logic. Consider Listing |5.6|| (checkrange.cpp) that determines if a number is between 0 and 10, inclusive.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int main() { int value;

std::cout << "Please enter an integer value in the range 0...10:

std::cin >> value;

if (value >= 0) // First check

if (value <= 10) // Second check

std::cout << "In range"; std::cout << "Done\n";

Listing |5.6|| (checkrange.cpp) behaves as follows:

• The program checks the value >= 0 condition first. If value is less than zero, the executing program does not evaluate the second condition and does not print In range, but it immediately executes the print statement following the outer i f statement which prints Done.

• If the executing program finds value to be greater than or equal to zero, it checks the second condition. If the second condition is met, it displays the In range message; otherwise, it is not. Regardless, the program prints Done before it terminates.

For the program to display the message In range both conditions of this nested i f must be met. Said another way, the first condition and the second condition must be met for the In range message to be printed. From this perspective, we can rewrite the program to behave the same way with only one i f statement, as Listing |5?7](newcheckrange.cpp) shows.

Listing 5.7: newcheckrange. cpp

ftinclude <iostream>

int main() { int value;

std::cout << "Please enter an integer value in the range 0.. std::cin >> value; if (value >= 0 && value <= 10) std::cout << "In range\n";

}

,.10: ";

Listing |5.7[ (newcheckrange.cpp) uses a logical && to check both conditions at the same time. Its logic is simpler, using only one i f statement, at the expense of a slightly more complex Boolean expression in its condition. The second version is preferable here because simpler logic is usually a desirable goal.

Sometimes a program’s logic cannot be simplified as in Listing [577[ (newcheckrange.cpp). In Listing |5.8| (enhancedcheckrange.cpp) one i f statement alone is insufficient to implement the necessary behavior.

Listing 5.8: enhancedcheckrange. cpp

ftinclude <iostream>

int main() { int value;

std::cout << "Please enter an integer value in the range 0...10: "

std::cin >> value;

if (value >= 0) // First check

if (value <= 10) // Second check

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Draft date: September 25, 2018

std::cout << value << " is acceptable\n" ;

else

std::cout << value << " is too large\n";

else

std::cout << value << " is too small\n";

Listing |5/8| (enhancedcheckrange.cpp) provides a more specific message instead of a simple notification of acceptance. The program prints exactly one of three messages based on the value of the variable. A single i f or i f /else statement cannot choose from among more than two different execution paths.

Listing 5.9 (binaryconversion.cpp) uses a series of i f statements to print a 10-bit binary string representing the binary equivalent of a decimal integer supplied by the user. (Section |4r8| provides some background information about the binary number system.) We use i f /else statements to print the individual digits left to right, essentially assembling the sequence of bits that represents the binary number.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << 0; if (value >= 16) {

std::cout << 1; value °o= 16;

}

else

std::cout << 0; if (value >= 8) {

std::cout << 1; value °o= 8;

}

else

std::cout << 0; if (value >= 4) {

std::cout << 1; value °o= 4;

}

else

std::cout << 0; if (value >= 2) {

std::cout << 1; value °o= 2;

}

else

std::cout << 0; std::cout << value << '\n';

}

}

In Listing |5^9| (binaryconversion.cpp):

• The outer i f checks to see if the value the use provides is in the proper range. The program works only for nonnegative integer values less than 1,024, so the range is 0-1023.

• Each inner i f compares the user-supplied entered integer against decreasing powers of two. If the number is large enough, the program:

- prints the digit 1 to the console, and

- removes via the remainder operator that power of two’s contribution to the value.

If the number is not at least as big as the given power of two, the program prints a 0 instead and moves on without modifying the input value.

• For the ones place at the end no check is necessary—the remaining value will be 0 or 1 and so the program prints whatever remains.

The following shows a sample run of Listing [5T9j (binaryconversion.cpp):

Please enter an integer value in the range 0...1023: 805 1100100101

Figure [53] illustrates the execution of Listing |5.9| (binaryconversion.cpp) when the user enters 805.

Listing |5T0| (simplerbinaryconversion.cpp) simplifies the logic of Listing {5T9| (binaryconversion.cpp) at the expense of some additional arithmetic. It uses only one i f statement.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 5.3 The process of the binary number conversion program when the user supplies 805 as the input value.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The sole i f statement in Listing 5.10 (simplerbinaryconversion.cpp) ensures that the user provides an integer in the proper range. The other i f statements that originally appeared in Listing 5.9 (binaryconversion.cpp) are gone. A clever sequence of integer arithmetic operations replace the original conditional logic. The two programs— binaryconversion.cpp and simplerbinaryconversion.cpp —behave identically but simplerbinaryconversion.cpp’s logic is simpler.

Listing |5.11 1 (troubleshoot. cpp) implements a very simple troubleshooting program that (an equally simple) computer technician might use to diagnose an ailing computer.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

if (choice == 'n' ) { // It is not plugged in, plug it in std::cout << "Plug it in. If the problem persists, " << "please run this program again. \n";

}

else { // It is plugged in

std::cout << "Is the switch in the \"on\" position? (y/n):"; std::cin >> choice;

if (choice == 'n') { // The switch is off, turn it on!

std::cout << "Turn it on. If the problem persists, "

<< "please run this program again. \n";

}

else { // The switch is on

std::cout << "Does the computer have a fuse? (y/n):";

std::cin >> choice;

if (choice == 'n') { // No fuse

std::cout << "Is the outlet OK? (y/n):";

std::cin >> choice;

if (choice == 'n') { // Fix outlet

std::cout << "Check the outlet's circuit "

<< "breaker or fuse. Move to a "

<< "new outlet, if necessary. "

<< "If the problem persists, "

<< "please run this program again. \n";

}

else { // Beats me!

std::cout << "Please consult a service << "technician.\n" ;

}

}

else { // Check fuse

std::cout << "Check the fuse. Replace if "

<< "necessary. If the problem "

<< "persists, then "

<< "please run this program again. \n";

}

}

}

}

else { // The computer has power

std::cout << "Please consult a service technician.\n" ;

}

This very simple troubleshooting program attempts to diagnose why a computer does not work. The potential for enhancement is unlimited, but this version only deals with power issues that have simple fixes. Notice that if the computer has power (fan or disk drive makes sounds or lights are visible), the program directs the user to seek help elsewhere! The decision tree capturing the basic logic of the program is shown in Figure ||5/4j

The steps performed are:

1. Is it plugged in? This simple fix is sometimes overlooked.

2. Is the switch in the on position? This is another simple fix.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 5.4 Decision tree for troubleshooting a computer system

Has power?

No I Yes

l ^

Is plugged in?

No I Yes

Plug it in. Is the switch on?

No I Yes

Turn switch on. Fuse OK?

No | Ye s

Check fuse. Seek other help.

3. If applicable, is the fuse blown? Some computer systems have a user-serviceable fuse that can blow out during a power surge. (Most newer computers have power supplies that can handle power surges and have no user-serviceable fuses.)

4. Is there power at the receptacle? Perhaps the outlet’s circuit breaker or fuse has a problem.

The program directs the user to make the easier checks first. It progressively introduces more difficult checks as it continues. Based on your experience with troubleshooting computers that do not run properly, you may be able to think of many enhancements to this simple program.

Note that in Listing |5.111| (troubleshoot.cpp) curly braces are used in many places where they strictly are not necessary. Their inclusion in Listing |5TT](troubleshoot.cpp) improves the readability of the program and makes the logic easier to understand. Even if you do not subscribe to the philosophy of using curly braces for every i f/else body, it is a good idea to use them in situations that improve the code’s readability.

Recall the time conversion program in Listing |4.11 1 | (timeconv.cpp). If the user enters 10000, the program runs as follows:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Suppose we wish to improve the English presentation by not using abbreviations. If we spell out hours, minutes, and seconds, we must be careful to use the singular form hour, minute, or second when the corresponding value is one. Listing 5.12 (timeconvcondl.cpp) uses if /else statements to express to time units with the correct number.

The i f/else statements within Listing 5.12 (timeconvcondl .cpp) are responsible for printing the correct version—singular or plural—for each time unit. One run of Listing |5.12[(timeconvcond1 .cpp) produces

©2018 Richard L. Halterman

Draft date: September 25, 2018

Please enter the number of seconds:10000 2 hours 46 minutes 40 seconds

All the words are plural since all the value are greater than one. Another run produces

Please enter the number of seconds:9961 2 hours 46 minutes 1 second

Note the word second is singular as it should be.

Please enter the number of seconds:3601 1 hour 0 minutes 1 second

Here again the printed words agree with the number of the value they represent.

An improvement to Listing unit if the value is zero. Listing

5.12| (timeconvcond1 .cpp) would not print a value and its associated time

5.13 (timeconvcond2.cpp) adds this feature.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

if (minutes == 1)

std::cout << " minute

else

std::cout << " minutes

}

// Print seconds at all?

if (seconds > 0 || (hours == 0 && minutes std::cout << seconds;

// Decide between singular and plural if (seconds == 1)

std:

:cout <<

" second";

std:

:cout <<

" seconds"

}

std::cout << '\n 1 ;

== 0 && seconds

form of seconds

0 )) {

In Listing 5.13 (timeconvcond2.cpp) each code segment responsible for printing a time value and its English word unit is protected by an i f statement that only allows the code to execute if the time value is greater than zero. The exception is in the processing of seconds: if all time values are zero, the program should print 0 seconds. Note that each of the i f /else statements responsible for determining the singular or plural form is nested within the i f statement that determines whether or not the value will be printed at all.

One run of Listing l5.13|(timeconvcond2.cpp) produces

Please enter the number of seconds:10000 2 hours 46 minutes 40 seconds

All the words are plural since all the value are greater than one. Another run produces

Please enter the number of seconds:9961 2 hours 46 minutes 1 second

Note the word second is singular as it should be.

Please enter the number of seconds:3601 1 hour 1 second

Here again the printed words agree with the number of the value they represent.

Please enter the number of seconds:7200 2 hours

Another run produces:

Please enter the number of seconds:60 1 minute

Finally, the following run shows that the program handles zero seconds properly:

Please enter the number of seconds:© 0 seconds

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 5.5 Flowchart with multiple optional execution pathways

1

5.8 Multi-way if/else Statements

A simple i f/else statement can select from between two execution paths. Suppose we wish to choose one execution path from among several possible paths, as shown in Figure |53f ?

Listing |5i8| (enhancedcheckrange.cpp) showed how to select from among three options. What if exactly one of many actions should be taken? Nested i f/else statements are required, and the form of these nested i f/else statements is shown in Listing 5.14 (digittoword.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

if (value == 4)

std::cout << "four";

else

if (value == 5)

std::cout << "five";

else

std::cout << "Too large";

std::cout << '\n 1 ;

}

Observe the following about Listing |f5T4| (digittoword.cpp):

• It prints exactly one of eight messages depending on the user’s input.

• Notice that each i f body contains a single printing statement and each else body, except the last one, contains an i f statement. The control logic forces the program execution to check each condition in turn. The first condition that matches wins, and its corresponding i f body will be executed. If none of the conditions are true, the last else’s Too large message will be printed.

• No curly braces are necessary to delimit the if or else bodies since each body contains only a single statement (although a single deeply nested i f/else statement is a mighty big statement).

Listing |5.14j| (digittoword.cpp) is formatted according to the conventions used in earlier examples. As a consequence, the mass of text drifts to the right as more conditions are checked. A commonly used alternative style, shown in Listingij5.15||(restyleddigittoword.cpp), avoids this rightward drift.

Listing 5.15: restyleddi gi ttoword. cpp

#include <iostream>

int main() { int value;

std::cout << "Please enter an integer in the range 0..

5 . ii .

std :: cin >> value

5

if (value < 0) std :: cout <<

"Too small";

else if (value ==

0)

std::cout <<

"zero" ;

else if (value ==

1)

std: : cout <<

"one" ;

else if (value ==

2)

std :: cout <<

"two" ;

else if (value ==

3)

std :: cout <<

"three" ;

else if (value ==

4)

std :: cout <<

"four";

else if (value ==

5)

std :: cout <<

"fi ve" ;

else

std :: cout <<

"Too large";

std :: cout << 1 \n 1

5

}

Based on our experience so far, the formatting of Listing |5.15[ (restyleddigittoword.cpp) somewhat hides the true structure of the program’s logic, but this style of formatting multi-way i f/else statements is

©2018 Richard L. Halterman

Draft date: September 25, 2018

so common that it is regarded as acceptable by most programmers. The sequence of else i f lines all indented to the same level identifies this construct as a multi-way i f /else statement.

Listing 5.16 (datetransformer.cpp) uses a multi-way i f/else to transform a numeric date in month/day format to an expanded US English form and an international Spanish form; for example, 2/14 would be converted to February 14 and 14 febrero.

Listing 5.16: datetransformer.cpp

ffinclude <iostream> int main() {

std::cout << "Please enter the month and day as numbers:

int month, day;

std::cin >> month >> day;

// Translate month into English if (month == 1)

std::cout << "January"; else if (month == 2)

std::cout << "February"; else if (month == 3)

std::cout << "March"; else if (month == 4)

std::cout << "April"; else if (month == 5)

std::cout << "May" ; else if (month == 6)

std::cout << "June"; else if (month == 7)

std::cout << "July"; else if (month == 8)

std::cout << "August"; else if (month == 9)

std::cout << "September"; else if (month == 10)

std::cout << "October"; else if (month == 11)

std::cout << "November";

else

std::cout << "December";

// Add the day

std::cout << " " << day << " or " << day << " de ";

// Translate month into Spanish if (month == 1)

std::cout << "enero"; else if (month == 2)

std::cout << "febrero"; else if (month == 3)

std::cout << "marzo"; else if (month == 4)

std::cout << "abril"; else if (month == 5)

std::cout << "mayo"; else if (month == 6)

std::cout << "junio"; else if (month == 7)

©2018 Richard L. Halterman

Draft date: September 25, 2018

std:

:cout <<

"j ulio" ;

else if (month ==

8)

std:

:cout <<

"agosto" ;

else if (month ==

9)

std:

:cout <<

"septiembre"

else if (month ==

10)

std:

:cout <<

"octubre" ;

else if (month ==

11)

std::cout <<

else

"noviembre" ;

std:

:cout <<

"diciembre" ;

Table captionstd::cout << 1 \n 1 ;

A sample run of Listing[5.16|(datetransformer.cpp) is shown here:

Please enter the month and day as numbers: 5 20 May 20 or 20 de mayo

Figure 5.6 compares the structure of the if/else statements in a program such as Listing 5.15 (restyleddigittoword.cpp) to those in a program like Listing [5l9| (binaryconversion.cpp).

In a program like Listing 5.15 (restyleddigittoword.cpp), the i f/else statements are nested, while in a program like Listing 5.9 (binaryconversion.cpp) the i f/else statements are sequential.

C++ provides the tools to construct some very complicated conditional statements. It is important to resist the urge to make things overly complex. Consider the problem of computing the maximum of five integer values provided by the user. The complete solution is left as an exercise in Section J57TO} but here we will outline an appropriate strategy.

Suppose you allow the user to enter all the values at once; for example, for integer variables nl, n2, n3, n4, and n5:

std::cout << "Please enter five integer values: " std::cin >> nl >> n2 >> n3 >> n4 >> n5;

Now, allow yourself one extra variable called max. All variables have a meaning, and their names should reflect their meaning in some way. Well let our additional max variable mean "maximum I have determined so far." The following is one approach to the solution:

1. Set max equal to nl. This means as far as we know at the moment, nl is the biggest number because max and nl have the same value.

2. Compare max to n2. If n2 is larger than max, change max to have n2’s value to reflect the fact that we determined n2 is larger; if n2 is not larger than max, we have no reason to change max, so do not change it.

3. Compare max to n3. If n3 is larger than max, change max to have n3’s value to reflect the fact that we determined n3 is larger; if n3 is not larger than max, we have no reason to change max, so do not change it.

4. Follow the same process for n4 and n5.

In the end the meaning of the max variable remains the same-"maximum I have determined so far," but, after comparing max to all the input variables, we now know that it is the maximum value of all five input

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 5.6 The structure of the i f statements in a program such as Listing 5.15 (restyleddigittoword.cpp) (left) vs. those in a program like Listing|5.9j|(binaryconversion.cpp) (right)

1

I

I

I

©2018 Richard L. Halterman

Draft date: September 25, 2018

numbers. The extra variable max is not strictly necessary, but it makes thinking about the problem and its solution easier.

Something to think about: Do you want a series of i f statements or one large multiway i f /else construct?

Also, you may be tempted to write logic such as

if (nl >= n2 && nl >= n3 && nl >= n4 && nl >=n5) std::cout << "The maximum is " << nl << ' \n' ; else if ( n2 >= nl && n2 >= n3 && // the rest omitted . . .

This will work, but this logic is much more complicated and less efficient (every >= and && operation requires a few machine cycles to execute). Since it is more complicated, it is more difficult to write correctly, in addition to being more code to type in. It is easy to use > by mistake instead of > =, which will not produce the correct results. Also, if you use this more complicated logic and decide later to add more variables, you will need to change all of the i f conditions in your code and, of course, make sure to modify each one of the conditions correctly. If you implement the simpler strategy outlined before, you need only add one simple i f statement for each additional variable.

Chapter |6j introduces loops, the ability to execute statements repeatedly. You easily can adapt the first approach to allow the user to type in as many numbers as they like and then have the program report the maximum number the user entered. The second approach with the more complex logic cannot be adapted in this manner. With the first approach you end up with cleaner, simpler logic, a more efficient program, and code that is easier to extend.

5.9 Errors in Conditional Statements

Consider Listing pT7| (badequality.cpp).

Listing [5.17| (badequality.cpp) demonstrates a common mistake—using the assignment operator where the equality operator is intended. This program, when run, always prints the message “two” and insists the user entered 2 regardless of the actual input. Recall from Section |43| that the assignment expression has a value. The value of an assignment expression is same as the value that is assigned; thus, the expression

input = 2

has the value 2. When you consider also that every integer can be treated as a Boolean value (see Section 5.1) and any non-zero value is interpreted as true, you can see that the condition of i f statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

if (input = 2)

std::cout << "two\n";

is always true. Additionally, the variable i nput is always assigned the value 2.

Since it is such a common coding error, most C++ compilers can check for such misuse of assignment. At warning Level 4, for example. Visual C++ will issue a warning when assignment appears where a conditional expression is expected:

warning C4706: assignment within conditional expression

Occasionally the use of assignment within a conditional expression is warranted, so the compiler does not perform this check by default. For our purposes it is good idea to direct the compiler to perform this extra check.

Carefully consider each compound conditional used, such as value >0 && value <= 10

found in Listing| [5?7j| (newcheckrange.cpp). Confusing logical and and logical or is a common programming error. If you substitute | | for &&, the expression

x > 0 || x <— 10

is always true, no matter what value is assigned to the variable x. A Boolean expression that is always true is known as a tautology. Think about it. If x is an i nt, what value could the variable x assume that would make

x > 0 || x <— 10

false? Regardless of its value, one or both of the subexpressions will be true, so this compound logical or expression is always true. This particular or expression is just a complicated way of expressing the value true.

Another common error is contriving compound Boolean expressions that are always false, known as contradictions. Suppose you wish to exclude values from a given range; for example, reject values in the range 0...10 and accept all other numbers. Is the Boolean expression in the following code fragment up to the task?

// I want to use all but 0, 1, 2, 10

if (value <0 && value > 10)

/* Code to execute goes here . . . */

A closer look at the condition reveals it can never be true. What number can be both less than zero and greater than ten at the same timel None can, of course, so the expression is a contradiction and a complicated way of expressing false. To correct this code fragment, replace the && operator with | |.

5.10 Exercises

1. What values can a variable of type bool assume?

2. Where does the term bool originate?

©2018 Richard L. Halterman

Draft date: September 25, 2018

3. What is the integer equivalent to t rue in C++?

4. What is the integer equivalent to false in C++?

5. Is the value -16 interpreted as true or false?

6. May an integer value be assigned to a bool variable?

7. Can true be assigned to an i nt variable?

8. Given the following declarations:

int x = 3, y = 5, z = 7;

bool bl = true, b2 = false, b3 = x == 3, b4 = y < 3; evaluate the following Boolean expressions:

(a)

x =

= 3

(b)

X <

y

(c)

X >

= y

(d)

X <

= y

(e)

x !

= y

- 2

(f)

x <

10

(g)

x >

= 0

&& X

< 10

(h)

X <

0 .

&& X

<

10

(i)

X >

- 0

&& X

< 2

(j)

X <

0

1 1 x

<

10

00

X >

0

1 x

<

10

(1)

X <

0

1 1 x

>

10

(m)

bl

(n)

i—1

_Q

(o)

!b2

(P)

bl

&&

b2

9. Express the following Boolean expressions in simpler form; that is, use fewer operators, x is an i nt.

(a) ! (x == 2)

(b) x < 2 || x == 2

(c) ! (x < y)

(d) ! (x <= y)

(e) x < 10 && x > 20

(f) x > 10 || x < 20

(g) x != 0

(h) x —— 0

10. What is the simplest tautology?

11. What is the simplest contradiction?

©2018 Richard L. Halterman

Draft date: September 25, 2018

12. Write a C++ program that requests an integer value from the user. If the value is between 1 and 100 inclusive, print “OK;” otherwise, do not print anything.

13. Write a C++ program that requests an integer value from the user. If the value is between 1 and 100 inclusive, print “OK;” otherwise, print “Out of range.”

14. The following program attempts to print a message containing the English word corresponding to a given integer input. For example, if the user enters the value 3, the program should print "You entered a three". In its current state, the program contains logic errors. Locate the problems and repair them so the program will work as expected.

#include <iostream> int main() {

std::cout << "Please in value in the range 1...5:

int value;

std::cin >> value;

// Translate number into its English word

if (month == 1)

std::cout << "You entered a"; std::cout << "one" ; std::cout << '\n' ; else if (month == 2)

std::cout << "You entered a"; std::cout << "two" ; std::cout << '\n' ; else if (month == 3)

std::cout << "You entered a"; std::cout << "three"; std::cout << '\n' ; else if (month == 4)

std::cout << "You entered a"; std::cout << "four"; std::cout << '\n' ; else if (month == 5)

std::cout << "You entered a"; std::cout << "five"; std::cout << '\n' ; else // Value out of range

std::cout << "You entered a"; std::cout << "value out of range"; std::cout << '\n' ;

15. Consider the following section of C++ code: // i , j , and k are ints

if (i < j) {

if (j < k)

i = j;

else

j = k;

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

else {

if (j > k)

j = i;

else

i = k;

}

std::cout << "i = " << i << " j = " << j << " k = " << k << ' \n' ; What will the code print if the variables i , j , and k have the following values?

(a) i is 3, j is 5, and k is 7

(b) i is 3, j is 7, and k is 5

(c) i is 5, j is 3, and k is 7

(d) i is 5, j is 7, and k is 3

(e) i is 7, j is 3, and k is 5

(f) i is 7, j is 5, and k is 3

16. Consider the following C++ program that prints one line of text:

ttinclude <iostream>

int main() { int input; std::cin >> input; if (input < 10) { if (input != 5)

std::cout << "wow " ;

else

input++;

}

else {

if (input == 17) input += 10;

else

std::cout << "whoa ";

}

std::cout << input << ' \n' ;

}

What will the program print if the user provides the following input?

(a) 3

(b) 21

(c) 5

(d) 17

(e) -5

17. Why does the following section of code always print " ByeHi "?

©2018 Richard L. Halterman

Draft date: September 25, 2018

i nt x;

std::cin >> x;

if (x < 0) ;

std::cout << "Bye" ; std::cout << "Hi\n" ;

18. Write a C++ program that requests five integer values from the user. It then prints the maximum and minimum values entered. If the user enters the values 3, 2, 5, 0, and 1, the program would indicate that 5 is the maximum and 0 is the minimum. Your program should handle ties properly; for example, if the user enters 2, 4, 2, 3, and 3, the program should report 2 as the minimum and 4 as maximum.

19. Write a C++ program that requests five integer values from the user. It then prints one of two things: if any of the values entered are duplicates, it prints "DUPLICATES"; otherwise, it prints "ALL UNIQUE".

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 6 Iteration

Iteration repeats the execution of a sequence of code. Iteration is useful for solving many programming problems. Iteration and conditional execution are key components of algorithm construction.

6.1 The while Statement

Listing |6T|(counttofive.cpp) counts to five by printing a number on each output line.

Listing 6.1: counttofive. cpp

Table caption#include <iostream>

int main() { std::cout

<<

1

<<

' \n

5

std:

: cout

<<

2

<<

' \n

5

std:

: cout

<<

3

<<

' \n

5

std:

: cout

<<

4

<<

' \n

5

std:

: cout

<<

5

<<

' \n

5

}

When compiled and run, this program displays

1

2

3

4

5

How would you write the code to count to 10,000? Would you copy, paste, and modify 10,000 printing statements? You could, but that would be impractical! Counting is such a common activity, and computers routinely count up to very large values, so there must be a better way. What we really would like to do is print the value of a variable (call it count), then increment the variable (count++), and repeat this process until the variable is large enough (count == 5 or perhaps count == 10000). This process of executing the same section of code over and over is known as iteration, or looping , and in C++ we can implement loops in several different ways.

Table captionListing 6.2 (iterativecounttofive.cpp) uses a whi le statement to count to five:

Listing 6.2: iterativecounttofive

•cpp

ftinclude <iostream>

int main() {

int count = 1; while (count <= 5) {

//

Initialize counter

std::cout << count <<

'In';

// Display counter, then

count++;

}

}

//

Increment counter

Listing 6.2 (iterativecounttofive.cpp) uses a while statement to display a variable that is counting up to five. Unlike the approach taken in Listing [6T| (counttofive.cpp), it is trivial to modify Listing [672] (iterativecounttofive.cpp) to count up to 10,000—-just change the literal value 5 to 10000.

The line

while (count <= 5)

begins the whi le statement. The expression within the parentheses must be a Boolean expression. If the Boolean expression is true when the the program’s execution reaches the whi le statement, the program executes the body of the whi le statement and then checks the condition again. The program repeatedly executes the statement(s) within the body of the whi le as long as the Boolean expression remains true.

If the Boolean expression is true when the whi le statement is executed, the body of the whi le statement is executed, and the body is executed repeatedly as long as the Boolean expression remains true.

The statements

std::cout << count << '\n' ; count++;

constitute the body of the whi le statement. The curly braces are necessary since more than one statement makes up the body.

The while statement has the general form:

whi le

( condition )

statement

• The reserved word whi le begins the whi le statement.

• The Boolean expression condition determines whether the body will be (or will continue to be) executed. The expression must be enclosed within parentheses as shown.

• The statement is the statement to be executed while the Boolean expression is true. The statement makes up the body of the whi le statement. The statement may be a compound statement (multiple statements enclosed within curly braces, see Section|!5.4|.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 6.1 while flowchart for Listing 6.2 (iterativecounttofive.cpp)

Start

Except for using the reserved word while instead of i f, a whi le statement looks identical to an i f statement. Sometimes beginning programmers confuse the two or accidentally type i f when they mean whi le or vice-versa. Usually the very different behavior of the two statements reveals the problem immediately; however, sometimes, especially in nested complex logic, this mistake can be hard to detect.

Figure [6.1 1 shows how program execution flows through Listing |6.2|| (iterativecounttofive.cpp).

The program checks the whi le’s condition before executing the body, and then re-checks the condition each time after it executes the body. If the condition is initially false the program’s execution skips the body completely and continues executing the statements that follow the whi le’s body. If the condition is initially true, the program repeatedly executes the body until the condition becomes false, at which point the loop terminates. Program execution then continues with the statements that follow the loop’s body, if any. Observe that the body may never be executed if the Boolean expression in the condition is initially false.

Listing j6.3| (countup.cpp) counts up from zero as long as the user wishes to do so.

Listing6.3: countup.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

/*

* Counts up from zero. The user continues the count by entering

* 1 Y 1 . The user discontinues the count by entering 'N 1 .

*/

#include <iostream>

int main() {

char input; int count = 0; bool done = false;

while (Idone) {

// Print the current value of count std::cout << count << '\n';

std::cout << "Please enter \"Y\" to continue or \"N\" to quit: "; std::cin >> input;

// Check for "bad" input

if (input != 1 Y 1 && input != 'y' && input != 'N' && input != 'n') std::cout << << input <<

<< " is not a valid choice" << '\n'; else if (input == 'Y' || input == 1 y' ) count++; // Keep counting else if (input == 'N' [| input == 'n') done = true; // Quit the loop

}

}

// The users choice // The current count // We are not done

A sample run of Listing |673| (countup.cpp) produces

Table caption0

Please

1

enter

ii Y"

to

continue

or

"N"

to

qui t:

y

±

Please

enter

ii Y"

to

continue

or

"N"

to

qui t:

y

z

Please

O

enter

ii Y"

to

continue

or

"N"

to

qui t:

y

J

Please

enter

ii Y"

to

continue

or

"N"

to

qui t:

q

"q" is

o

not a

valid

choice

J

Please

enter

ii Y "

to

continue

or

"N"

to

qui t:

r

"r" is

o

not a

valid

choice

J

Please

enter

IIY"

to

continue

or

"N"

to

qui t:

W

"W" is

not a

valid

choice

o

Please

enter

ii Y"

to

continue

or

"N"

to

qui t:

Y

4

Please

C

enter

ii Y"

to

continue

or

"N"

to

qui t:

y

3

Please

enter

ii Y”

to

continue

or

"N"

to

qui t:

n

Table captionIn ListingfOi|(countup.cpp) the expression

©2018 Richard L. Halterman

Draft date: September 25, 2018

input != 'Y' && input != 'y' && input != 'N' && input != 'n'

is true if the character variable input is not equal to one of the listed character literals. The Boolean variable done controls the loop’s execution. It is important to note that the expression

! done

inside the while’s condition evaluates to the opposite truth value of the variable done; the expression does not affect the value of done. In other words, the ! operator applied to a variable does not modify the variable’s value. In order to actually change the variable done, you would need to reassign it, as in

done = !done; // Invert the truth value

For Listing 6.3 fcountup.cpp) we have no need to invert its value. We ensure that its value is false initially and then make it t rue when the user enters a capital or lower-case N.

Listing [6T4] (addnonnegatives.cpp) is a program that allows a user to enter any number of nonnegative integers. When the user enters a negative value, the program no longer accepts input, and it displays the sum of all the nonnegative values. If a negative number is the first entry, the sum is zero.

The initialization of i nput to zero coupled with the condition i nput >= 0 of the whi le guarantees that program will execute the body of the while loop at least once. The if statement ensures that a negative entry will not be added to sum. (Could the condition have used > instead of >= and achieved the same results?) When the user enters a negative integer the program will not update sum, and the condition of the while will no longer be true. The program’s execution then leaves the loop and executes the print statement at the end.

Listing 6.4 (addnonnegatives.cpp) shows that a whi le loop can be used for more than simple counting. The program does not keep track of the number of values entered. The program simply accumulates the

©2018 Richard L. Halterman

Draft date: September 25, 2018

entered values in the variable named sum.

It is a little awkward in Listing |6~4| (addnonnegatives.cpp) that the same condition appears twice, once in the whi le and again in the i f. Furthermore, what if the user wishes to enter negative values along with nonnegative values? We can simplify the code with a common C++ idiom that uses std : : ci n and the extraction operator as a condition within a whi le statement.

If x is an integer, the expression

std::cin >> x

evaluates to false if the user does not enter a valid integer literal. Armed with this knowledge we can simplify and enhance Listing [6l4j (addnonnegatives.cpp) as shown in Listing|6T5|(addnumbers.cpp).

The condition reads a value from the input stream and, if it is successful, it is interpreted as true. When the user enters ' q ' , the loop is terminated. If the user types ' q ' at the beginning, the loop is not entered. The i f statement is no longer necessary, since the statement

sum += input;

can be executed only if i nput has been legitimately assigned. Also, the variable i nput no longer needs to initialized with a value simply so the loop is entered the first time; now it is assigned and then checked within the condition of the whi le.

In Listing ||6.5|(addnumbers.cpp), the program’s execution will terminate with any letter the user types; an entry of ' x ' or Ctrl-Z will terminate the sequence just as well as ' q ' .

If you use the

while (std::cin >> x) {

// Do something . . .

}

idiom, be aware that when the loop is exited due to the input stream being unable to read a value of the type of variable x, the std : : ci n input stream object is left in an error state and cannot be used for the rest of the program’s execution. It you wish to use this technique and reuse std : : ci n later, you must reset std : : ci n and extract and discard keystrokes entered since the last valid use of the extractor operator. This recovery process is covered in Section [13l2| but, for now, use this idiom to control a loop only if the program does not require additional user input later during its execution.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing |6)6j| (powersof10.cpp) prints the powers of 10 from 1 to 1,000,000,000 (the next power of ten, 10,000,000,000, is outside the range of the i nt type).

Listing (6)6] (powersofl0.cpp) produces

1

10

100

1000

10000

100000

1000000

10000000

100000000

1000000000

It is customary to right justify a column of numbers, but Listing j6.6|| (powersofl O.cpp) prints the powers of ten with their most-significant digit left aligned. We can right align the numbers using a stream object called a steam manipulator. The specific stream manipulator we need is named std : : setw. setw means “set width.” It can be used as

std::cout << std::setw(3) << x << '\n' ;

This statement prints the value of x right justified within a three character horizontal space on the screen. Listing 1577] (powersofl Ojustified.cpp) shows the affects of setw.

Listing [6J](powersof10justified.cpp) prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

1

10

100

1000

10000

100000

1000000

10000000

100000000

1000000000

Observe that in order to use setw the compiler needs to be made aware of it. The needed information about std : : setw is not found in the i ostream header file, so an additional preprocessor include directive is required:

ttinclude <iomanip>

The std: : setw manipulator “conditions” the output stream for the next item to be printed. The values passed to the “conditioned” stream are all right justified within the number of spaces specified by std: : setw.

As an aside, this is good place to reveal another trick to improve the output of a C++ program. Listing |6l|(powersof10withcommas.cpp) enhances Listing |6.7||(powersof1 Ojustified.cpp) by adding commas in the appropriate places in the displayed numbers.

Listing |6.8|(powersof1 Owithcommas.cpp) prints

1

10

100

1,000

10,000

100,000

1 , 000,000

10 , 000,000

100 , 000,000

1 , 000 , 000,000

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 6.2 Decision tree for troubleshooting a computer system Listing 6.9 (troubleshootloop.cpp)

-► Has power?

No I Yes

Is plugged in?

No I Yes

Plug it in. Is the switch on?

No I Yes

i ^

- Turn switch on. Fuse OK?

No | Ye s

i } I

- Check fuse. Seek other help.

The statement

std::cout.imbue(std::locale ("") ) ;

adjusts the std : : cout object to print number with digit separators appropriate for the current country. If you replace the statement with

std::cout. i mbue(std::locale ("german" )) ;

the output becomes

1

10

100

1.000

10.000

100.000

1 . 000.000

10 . 000.000

100 . 000.000

1 . 000 . 000.000

because the German language uses periods in place of commas for digit separators. The "german" locale also would display a comma where the decimal point would appear in an English floating-point number.

We can use a whi le statement to make Listing 5.11 (troubleshoot. cpp) more convenient for the user. Recall that the computer troubleshooting program forces the user to rerun the program once a potential program has been detected (for example, turn on the power switch, then run the program again to see what

else might be wrong). A more desirable decision logic is shown in Figure 6.2

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 6.9 (troubleshootloop.cpp) incorporates a while statement so that the program’s execution continues until the problem is resolved or its resolution is beyond the capabilities of the program.

Listing 6.9: troubleshootloop.cpp

#include <iostream>

int main() {

std::cout << "Help! My computer doesn't work!\n"; char choice;

bool done = false; // Initially, we are not done

while (!done) { // Continue until we are done

std::cout << "Does the computer make any sounds "

<< "(fans, etc.) or show any lights? (y/n):" ; std::cin >> choice;

// The troubleshooting control logic

if (choice == 'n' ) { // The computer does not have power std::cout << "Is it plugged in? (y/n):"; std::cin >> choice;

if (choice == 'n') { // It is not plugged in, plug it in std::cout << "Plug it in.\n";

}

else { // It is plugged in

std::cout << "Is the switch in the \"on\" position? (y/n):"; std::cin >> choice;

if (choice == 'n') { // The switch is off, turn it on! std::cout << "Turn it on.\n";

}

else { // The switch is on

std::cout << "Does the computer have a fuse? (y/n):";

std::cin >> choice;

if (choice == 'n') { // No fuse

std::cout << "Is the outlet OK? (y/n):";

std::cin >> choice;

if (choice == 'n') { // Fix outlet

std::cout << "Check the outlet's circuit "

<< "breaker or fuse. Move to a "

<< "new outlet, if necessary.\n" ;

}

else { // Beats me!

std::cout << "Please consult a service "

<< "technician.\n" ;

done = true; // Exhausted simple fixes

}

}

else { // Check fuse

std::cout << "Check the fuse. Replace if "

<< "necessary.\n" ;

}

}

}

}

else { // The computer has power

std::cout << "Please consult a service technician.\n" ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

}

done = true; // Only troubleshoots power issues

}

The bulk of the body of the Listing 6.9 (troubleshootloop.cpp)is wrapped by a whi le statement. The Boolean variable done is often called a flag. You can think of the flag being down when the value is false and raised when it is true. In this case, when the flag is raised, it is a signal that the program should terminate.

Notice the last 11 lines of Listing |6.9| (troubleshootloop.cpp):

}

}

}

}

else { // The computer has power

std::cout << "Please consult a service technician.\n" ; done = true; // Only troubleshoots power issues

}

}

}

In the way this code is organized, the matching opening curly brace of a particular closing curly brace can be found by scanning upward in the source code until the closest opening curly brace at the same indentation level is found. Our programming logic is now getting complex enough that the proper placement of curly braces is crucial for human readers to more quickly decipher how the program should work. See Section|43] for guidelines on indentation and curly brace placement to improve code readability.

6.2 Nested Loops

Just like in i f statements, while bodies can contain arbitrary C++ statements, including other while statements. A loop can therefore be nested within another loop. To see how nested loops work, consider a program that prints out a multiplication table. Elementary school students use multiplication tables, or times tables, as they learn the products of integers up to 10 or even 12. Figure|6.3(shows a 10 x 10 multiplication table. We want our multiplication table program to be flexible and allow the user to specify the table’s size. We will begin our development work with a simple program and add features as we go. First, we will not worry about printing the table’s row and column titles, nor will we print the lines separating the titles from the contents of the table. Initially we will print only the contents of the table. We will see we need a nested loop to print the table’s contents, but that still is too much to manage in our first attempt. In our first attempt we will print the rows of the table in a very rudimentary manner. Once we are satisfied that

our simple program works we can add more features. Listing 6.10 (timestable-1 st-try.cpp) shows our first attempt at a muliplication table.

Listing 6.10: timestable-lst—try.cpp

ffinclude <iostream> int main() {

int size; // The number of rows and columns in the table std::cout << "Please enter the table size:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table captionFigure 6.3 A 10 x 10 multiplication table

X

1

2

3

4

5

6

7

8

9

10

1

1

2

3

4

5

6

7

8

9

10

2

2

4

6

8

10

12

14

16

18

20

3

3

6

9

12

15

18

21

24

27

30

4

4

8

12

16

20

24

28

32

36

40

5

5

10

15

20

25

30

35

40

45

50

6

6

12

18

24

30

36

42

48

54

60

7

7

14

21

28

35

42

49

56

63

70

8

8

16

24

32

40

48

56

64

72

80

9

9

18

27

36

45

54

63

72

81

90

10

10

20

30

40

50

60

70

80

90

100

std: : cin >> size;

// Print a size x size multiplication table int row = 1;

while (row <= size) { // Table has 10 rows.

std::cout << "Row #" << row << 1 \n' ; row++; // Next row

}

}

The output of Listing|6T0|(timestable-1 st-try.cpp) is somewhat underwhelming:

Please enter the table size: 10

Row #1

Row #2

Row #3

Row #4

Row #5

Row #6

Row #7

Row #8

Row #9

Row #10

Listing [6.10| (timestable-1 st-try.cpp) does indeed print each row in its proper place—it just does not supply the needed detail for each row. Our next step is to refine the way the program prints each row. Each row should contain size numbers. Each number within each row represents the product of the current row and current column; for example, the number in row 2, column 5 should be 2 x 5 = 10. In each row, therefore, we must vary the column number from from 1 to size. Listing 6.11 (timestable-2nd-try.cpp) contains the needed refinement.

Listing 6.11: t"imestable-2nd-try .cpp

#include <iostream> int main() {

©2018 Richard L. Halterman

Draft date: September 25, 2018

int size; // The number of rows and columns in the table std::cout << "Please enter the table size: std::cin >> size;

// Print a size x size multiplication table int row = 1;

while (row <= size) { // Table has size rows.

int column = 1; // Reset column for each row.

while (column <= size) { // Table has size columns,

int product = row*column; // Compute product std::cout << product << " "; // Display product

column++; // Next element

}

std::cout << '\n' ; // Move cursor to next row

row++; // Next row

}

}

We use a loop to print the contents of each row. The outer loop controls how many total rows the program prints, and the inner loop, executed in its entirity each time the program prints a row, prints the individual elements that make up a row.

Table captionThe result of Listing j671 l:| (timestable-2nd-try.cpp) is

Please ente

r

the

table

size: 10

1

2 3

4

5 6

7

8 9

10

2

4 6

8

10

12

14

16

18

20

3

6 9

12

15

18 21

. 24

27

30

4

8 12 16 20

24 28 32 36 40

5

10

15

20

25

30

35

40

45

50

6

12

18

24

30

36

42

48

54

60

7

14

21

28

35

42

49

56

63

70

8

16

24

32

40

48

56

64

72

80

9

18

27

36

45

54

63

72

81

90

10 20

30

40

50 60

i 70

80

90

100

The numbers within each column are not lined up nicely, but the numbers are in their correct positions relative to each other. We can use the std : : setw stream manipulator introduced in Listing 6.7 (powersof 10justified.cpp) to right justify the numbers within a four-digit area. Listing (6T2] (timestable-3rd-try.cpp) contains this alignment adjustment.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

std::cout << std::setw(4) column++;

}

std::cout << 1 \n 1 ; row++;

<< product; // Display product // Next element

// Move cursor to next row // Next row

Table captionListing |6.12|| (timestable-3rd-try.cpp) produces the table’s contents in an attractive form:

Please enter

the

table :

si ze:

10

1

2

3

4

5

6

7

8

9

10

2

4

6

8

10

12

14

16

18

20

3

6

9

12

15

18

21

24

27

30

4

8

12

16

20

24

28

32

36

40

5

10

15

20

25

30

35

40

45

50

6

12

18

24

30

36

42

48

54

60

7

14

21

28

35

42

49

56

63

70

8

16

24

32

40

48

56

64

72

80

9

18

27

36

45

54

63

72

81

90

10

20

30

40

50

60

70

80

90

100

Table captionInput values of 5:

Please i

enter

the

table size: 5

1

2

3

4

5

2

4

6

8

10

3

6

9

12

15

4

8

12

16

20

5

10

15

20

25

Table captionand 15:

Please enter

the

table :

si ze:

15

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

3

6

9

12

15

18

21

24

27

30

33

36

39

42

45

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

7

14

21

28

35

42

49

56

63

70

77

84

91

98

105

8

16

24

32

40

48

56

64

72

80

88

96

104

112

120

9

18

27

36

45

54

63

72

81

90

99

108

117

126

135

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

11

22

33

44

55

66

77

88

99

110

121

132

143

154

165

12

24

36

48

60

72

84

96

108

120

132

144

156

168

180

13

26

39

52

65

78

91

104

117

130

143

156

169

182

195

14

28

42

56

70

84

98

112

126

140

154

168

182

196

210

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

also give good results.

All that is left is to add the row and column titles and the lines that bound the edges of the table. Listing |Q3| (timestable.cpp) adds the necessary code.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table captionWhen the user supplies the value 10, Listing[6.13||(timestable.cpp) produces

Please

enter

the

table

si ze:

10

1

2

3

4

5

6

7

8

9

10

1 |

1

2

3

4

5

6

7

8

9

10

2 j

2

4

6

8

10

12

14

16

18

20

3 1

3

6

9

12

15

18

21

24

27

30

4 |

4

8

12

16

20

24

28

32

36

40

5 j

5

10

15

20

25

30

35

40

45

50

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

6

1

6

12

18

24

30

36

42

48

54

60

7

1

7

14

21

28

35

42

49

56

63

70

8

1

8

16

24

32

40

48

56

64

72

80

9

1

9

18

27

36

45

54

63

72

81

90

n

10

20

30

40

50

60

70

80

90

100

Table captionAn input of 15 yields

Please

enter

1 2

the

3

table size:

4 5 6

15

7

8

9

10

11

12

13

14

15

1

1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

2

1

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

3

1

3

6

9

12

15

18

21

24

27

30

33

36

39

42

45

4

1

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

5

1

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

6

1

6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

7

1

7

14

21

28

35

42

49

56

63

70

77

84

91

98

105

8

1

8

16

24

32

40

48

56

64

72

80

88

96

104

112

120

9

1

9

18

27

36

45

54

63

72

81

90

99

108

117

126

135

10

1

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

11

1

11

22

33

44

55

66

77

88

99

110

121

132

143

154

165

12

1

12

24

36

48

60

72

84

96

108

120

132

144

156

168

180

13

1

13

26

39

52

65

78

91

104

117

130

143

156

169

182

195

14

1

14

28

42

56

70

84

98

112

126

140

154

168

182

196

210

15

1

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

Table captionIf the user enters 7, the program prints

Please

enter

the

table

si ze:

7

1

2

3

4

5

6

7

+

—

—

—

—

—

—

1 |

1

2

3

4

5

6

7

2 |

2

4

6

8

10

12

14

3 1

3

6

9

12

15

18

21

4 |

4

8

12

16

20

24

28

5 |

5

10

15

20

25

30

35

6 j

6

12

18

24

30

36

42

7 |

7

14

21

28

35

42

49

As we can see, the table automatically adjusts to the size and spacing required by the user’s input.

This is how Listing |6.13|| (timestable.cpp) works:

• It is important to distinguish what is done only once (outside all loops) from that which is done repeatedly. The column heading across the top of the table is outside of all the loops; therefore, it is printed all at once.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• The work to print the heading for the rows is distributed throughout the execution of the outer loop. This is because the heading for a given row cannot be printed until all the results for the previous row have been printed.

• A code fragment like

if (x < 10)

std::cout << " " ; std::cout << x;

prints x in one of two ways: if x is a one-digit number, it prints a space before it; otherwise, it does not print the extra space. The net effect is to right justify one and two digit numbers within a two character space printing area. This technique allows the columns within the times table to be properly right aligned.

• In the nested loop, row is the control variable for the outer loop; column controls the inner loop.

• The inner loop executes si ze times on every single iteration of the outer loop. How many times is the statement

std::cout << product << " // Display product

executed? size x size times, one time for every product in the table.

• A newline is printed after the contents of each row is displayed; thus, all the values printed in the inner (column) loop appear on the same line.

Nested loops are used when an iterative process itself must be repeated. In our times table example, a whi le loop is used to print the contents of each row, but multiple rows must be printed. The inner loop prints the contents of each row, while the outer is responsible for printing all the rows.

Listing |6T4| (permuteabc.cpp) uses a triply-nested loop to print all the different arrangements of the letters A, B, and C. Each string printed is a permutation of ABC.

Listing6.14: permuteabc.cpp

// File permuteabc.cpp

#include <iostream> int main() {

char first = 'A 1 ; // The first letter varies from A to C

while (first <= 'C' ) { char second = 1 A' ;

while (second <= 1 C' ) { // The second varies from A to C if (second != first) { // No duplicate letters

char third = 1 A' ;

while (third <= 1 C' ) { // The third varies from A to C // Don't duplicate first or second letter

if (third != first && third != second)

std::cout << first << second << third << 1 \n' ; third++;

}

}

second++;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

first++;

}

Notice how the i f statements are used to prevent duplicate letters within a given string. The output of Listing (6Tl4] (perrnuteabc.cpp) is all six permutations of ABC:

ABC

ACB

BAC

BCA

CAB

CBA

6.3 Abnormal Loop Termination

By default, a whi le statement executes until its condition becomes false. The executing program checks this condition only at the “top” of the loop. This means that even if the Boolean expression that makes up the condition becomes false before the program completes executing all the statements within the body of the loop, all the remaining statements in the loop’s body must complete before the loop can once again check its condition. In other words, the while statement in and of itself cannot exit its loop somewhere in the middle of its body.

Ordinarily this behavior is not a problem. Usually the intention is to execute all the statements within the body as an indivisible unit. Sometimes, however, it is desirable to immediately exit the body or recheck the condition from the middle of the loop instead. C++ provides the break and conti nue statements to to give programmers more flexibility designing the control logic of loops.

6.3.1 The break statement

C++provides the break statement to implement middle-exiting control logic. The break statement causes the immediate exit from the body of the loop. Listing|6.f5j(addmiddleexit.cpp) is a variation of Listing |6~4] (addnonnegatives.cpp) that illustrates the use of break.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The condition of the whi le in Listing 6.15 (addmiddleexit.cpp) is a tautology. This means the condition is true and can never be false. When the program’s execution reaches the whi le statement it is guaranteed to enter the loop’s body and the whi le loop itself does not provide a way of escape. The i f statement in the loop’s body:

if (input < 0) // Is input negative

break; // If so, exit the loop immediately

provides the necessary exit. In this case the break statement, executed conditionally based on the value of the variable i nput, exits the loop. In Listing 6.15 (addmiddleexit.cpp) the break statement executes only when the user enters a negative number. When the program’s execution encounters the break statement, it immediately jumps out of the loop. It skips any statements following the break within the loop’s body. Since the statement

sum += input; // Accumulate user input

appears after the break, it is not possible for the program to add a negative number to the sum variable.

Some software designers believe that programmers should use the break statement sparingly because it deviates from the normal loop control logic. Ideally, every loop should have a single entry point and single exit point. While Listing 6.15 (addmiddleexit.cpp) has a single exit point (the break statement), some programmers commonly use break statements within while statements in the which the condition for the while is not a tautology. Adding a break statement to such a loop adds an extra exit point (the top of the loop where the condition is checked is one point, and the break statement is another). Using multiple break statements within a single loop is particularly dubious and you should avoid that practice.

Why have the break statement at all if its use is questionable and it is dispensable? The logic in Listing ||6.4|| (addnonnegatives.cpp) is fairly simple, so the restructuring of Listing |6.15|| (addmiddleexit.cpp) is straightforward; in general, the effort to restructure code to avoid a break statement may complicate the logic a bit and require the introduction of an additional Boolean variable. As shown in Figure |6i4( any program that uses a break statement can be rewritten so that the break statement is not used.

The no-break version introduces a Boolean variable, and the loop control logic is a little more complicated. The no-break version uses more memory (an extra variable) and more time to execute (requires an extra check in the loop condition during every iteration of the loop). This extra memory is insignificant, and except for rare, specialized applications, the extra execution time is imperceptible. In most cases, the more important issue is that the more complicated the control logic for a given section of code, the more difficult the code is to write correctly. In some situations, even though it violates the “single entry point, single exit point” principle, a simple break statement is an acceptable loop control option.

6.3.2 The goto Statement

The break statement exits the single loop in which it is located. A break statement is insufficient to jump completely out of the middle of a nested loop. The goto statement allows the program’s execution flow to jump to a specified location within the function. Listing f6.16| (exitnested.cpp) uses a goto statement to jump out from the middle of a nested loop.

Listing 6.16: exitnested. cpp

#include <iostream> int main() {

// Compute some products

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 6.4 The code on the left generically represents any loop that uses a break statement. It is possible to transform the code on the left to eliminate the break statement, as the code on the right shows.

bool looping =

while ( looping && Condition 1 ) {

Part A

if ( Condition 2 ) {

Part B

looping = false;

}

else {

Part C

int opl = 2; while (opl < 100) { int op2 = 2; while (op2 < 100) {

if (opl * op2 == 3731) goto end;

std::cout << "Product is " << (opl * op2) << 1 \n' ; op2++;

}

opl++;

end:

std::cout << "The end" << 1 \n 1 ;

When opl * op2 is 3731, program flow will jump to the specified label within the program. In this example, the label is named end, but this name is arbitrary. Like variable names, label names should be chosen to indicate their intended purpose. The label here named end comes after and outside the nested whi le loops.

A label’s name is an identifier (see Section |3.3| , and a label is distinguished by the colon that immediately follows its name. A label represents a target to which a goto can jump. A goto label must appear before a statement within a function.

With the goto statement, the whi le is superfluous; for example. Listing 6.2 (iterativecounttofive.cpp) could be rewritten without the whi le statement as shown in Listing 6.17 (gotoloop.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

Early programming languages like FORTRAN and early versions of BASIC did not have structured statements like whi le, so programmers were forced to use goto statements to write loops. The problem with using goto statements is that it is easy to develop program logic that is very difficult to understand, even for the original author of the code. See the Wikipedia article about spaghetti code (http : //en . wi ki pedi a . org/wi ki /Spaghetti _code). The structured programming revolution of the 1960s introduced constructs such as the whi le statement and resulted in the disappearance of the use of goto in most situations. All modern programming languages have a form of the whi le statement, so the goto statement in C++ is largely ignored except for the case of breaking out of a nested loop. You similarly should restrict your use of the goto statement to the abnormal exit of nested loops.

6.3.3 The continue Statement

When a program’s execution encounters a break statement inside a loop, it skips the rest of the body of the loop and exits the loop. The conti nue statement is similar to the break statement, except the conti nue statement does not necessarily exit the loop. The conti nue statement skips the rest of the body of the loop and immediately checks the loop’s condition. If the loop’s condition remains true, the loop’s execution resumes at the top of the loop. Listing 6.18 (continueexample.cpp) shows the conti nue statement in action.

©2018 Richard L. Halterman

Draft date: September 25, 2018

else

done = (input == 999); // 999 entry exits loop

}

std::cout << "sum = " << sum << '\n';

Programmers do not use the continue statement as frequently as the break statement since it is easy to transform code using continue into an equivalent form that does not. Listing 6.19 (nocontinueexample.cpp) works exactly like Listing 6.18 (continueexample.cpp), but it avoids the conti nue statement.

Figure [63] shows how we can rewrite any program that uses a conti nue statement into an equivalent form that does not use conti nue. The transformation is simpler than for break elimination (see Figure since the loop’s condition remains the same, and no additional variable is needed.

The version that uses conti nue is no more efficient than the version that uses else; in fact, the Visual C++ and GNU C++ compilers generate the same machine language code for Listingj|67l8||(continueexample.cpp) and Listing 6.19 (nocontinueexample.cpp). Also, the logic of the else version is no more complex than the continue version. Therefore, unlike the break statement above, there is no compelling reason to use the continue statement. Sometimes a programmer may add a continue statement at the last minute to an existing loop body to handle an exceptional condition (like ignoring negative numbers in the example above) that initially went unnoticed. If the body of the loop is lengthy, the programmer can add a conditional statement with a continue near the top of the loop body without touching the logic of the rest of the loop. The conti nue statement thus merely provides a convenient alternative for the programmer. The else version is preferred.

6.4 Infinite Loops

An infinite loop is a loop without an exit. Once the program flow enters an infinite loop’s body it cannot escape. Some infinite loops are by design; for example, a long-running server application, like a Web

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 6.5 The code on the left generically represents any loop that uses a continue statement. It is possible to transform the code on the left to eliminate the continue statement, as the code on the right shows.

whi le

( Condition 1 ) {

Part A

i i ( Condition 2 ) {

Part B

}

else {

Part C

}

}

server, may need to continuously check for incoming connections. This server application can perform this checking within a loop that runs indefinitely. All too often, however, beginning programmers create infinite loops by accident, and these infinite loops represent logic errors in their programs.

Intentional infinite loops should be made obvious. For example, while (true) {

/* Do something forever . . . */

}

The Boolean literal true is always true, so it is impossible for the loop’s condition to be false. The only ways to exit the loop is via a break statement, return statement (see Chapterj9]l, or an exit call (see Section [8,l| embedded somewhere within its body.

It is easy to write an intentional infinite loop. Accidental infinite loops are quite common, but can be puzzling for beginning programmers to diagnose and repair. Consider Listing |6720|| (findfactors.cpp) that attempts to print all the integers with their associated factors from 1 to 20.

Listing 6.20: findf actors. cpp

#include <iostream> int main() {

// List of the factors of the numbers up to 20

int n = 1; const int MAX = 20; while (n <= MAX) { int factor = 1;

©2018 Richard L. Halterman

Draft date: September 25, 2018

6.4. INFINITE LOOPS

146

on most

and then “freezes up” or “hangs,” ignoring any user input (except the key sequence Hiil _ systems which interrupts and terminates the running program). This type of behavior is a frequent symptom of an unintentional infinite loop. The factors of 1 display properly, as do the factors of 2. The first factor of 3 is properly displayed and then the program hangs. Since the program is short, the problem may be easy to locate. In some programs, though, the error may be challenging to find. Even in Listing |6.20| (findfactors.cpp) the debugging task is nontrivial since it involves nested loops. (Can you find and fix the

problem in Listing 6.20 (findfactors.cpp) before reading further?)

In order to avoid infinite loops, we must ensure that the loop exhibits certain properties:

• The loop’s condition must not be a tautology (a Boolean expression that can never be false). Lor example,

while (i >= 1 || i <= 10) {

/* Body omitted */

}

is an infinite loop since any value chosen for i will satisfy one or both of the two subconditions. Perhaps the programmer intended to use a && instead of | | to stay in the loop as long as i remains in the range 1... 10.

In Listing |6720| (findfactors.cpp) the outer loop condition is n <= MAX

If n is 21 and MAX is 20, then the condition is false, so this is not a tautology. Checking the inner loop condition:

factor <= n

we see that if f acto r is 3 and n is 2, then the expression is false; therefore, it also is not a tautology.

• The condition of a whi le must be true initially to gain access to its body. The code within the body must modify the state of the program in some way so as to influence the outcome of the condition that is checked at each iteration. This usually means code within the body of the loop modifies one of the variables used in the condition. Eventually the variable assumes a value that makes the condition false, and the loop terminates.

©2018 Richard L. Halterman

Draft date: September 25, 2018

In Listing ||6^20|| (findfactors.cpp) the outer loop’s condition involves the variable n and constant MAX. MAX cannot change, so to avoid an infinite loop it is essential that n be modified within the loop. Fortunately, the last statement in the body of the outer loop increments n. n is initially 1 and MAX is 20, so unless the circumstances arise to make the inner loop infinite, the outer loop should eventually terminate.

The inner loop’s condition involves the variables n and factor. No statement in the inner loop modifies n, so it is imperative that factor be modified in the loop. The good news is factor is incremented in the body of the inner loop, but the bad news is the increment operation is protected within the body of the i f statement. The inner loop contains one statement, the i f statement. That i f statement in turn has two statements in its body:

while (factor <= n)

if (n % factor == 0) {

std::cout << factor << " factor++;

}

If the condition of the i f is ever false, the state of the program will not change when the body of the inner loop is executed. This effectively creates an infinite loop. The statement that modifies factor must be moved outside of the i f statement’s body:

while (factor <= n) {

if (n % factor == 0)

std::cout << factor << " factor++;

}

Note that the curly braces are necessary for the statement incrementing factor to be part of the body of the whi le. This new version runs correctly.

Programmers can use a debugger to step through a program to see where and why an infinite loop arises. Another common technique is to put print statements in strategic places to examine the values of the variables involved in the loop’s control. The original inner loop can be so augmented:

while (factor <= n) {

std::cout << "factor = " << factor << " n = " << n << '\n' ; if (n % factor == 0) {

std::cout << factor << " factor++;

}

}

Table captionIt produces the following output:

1: factor = 1

n = 1

1

2: factor = 1

n = 2

1 factor = 2

n = 2

2

3: factor = 1

n = 3

1 factor = 2

n = 3

factor =2 n

= 3

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

The program continues to print the same line until the user interrupts its execution. The output demonstrates that once factor becomes equal to 2 and n becomes equal to 3 the program’s execution becomes trapped in the inner loop. Under these conditions:

1.2 < 3 is true, so the loop continues and

2. 3 % 2 is equal to 1, so the i f statement will not increment factor.

It is imperative that factor be incremented each time through the inner loop; therefore, the statement incrementing factor must be moved outside of the i f ’s guarded body.

6.5 Iteration Examples

We can implement some sophisticated algorithms in C++ now that we are armed with if and while statements. This section provides several examples that show off the power of conditional execution and iteration.

6.5.1 Drawing a Tree

Suppose we must write a program that draws a triangular tree, and the user provides the tree’s height. A tree that is five levels tall would look like

whereas a three-level tree would look like

If the height of the tree is fixed, we can write the program as a simple variation of Listing |2.4| (arrow.cpp) which uses only printing statements and no loops. Our program, however, must vary its height and width based on input from the user.

Listing [fT2T| (startree.cpp) provides the necessary functionality.

Listing6.21: startree.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <iostream>

int main() {

int height; // Height of tree std::cout << "Enter height of tree: std::cin >> height; // Get height from user int row = 0; // First row, from the top, to draw

while (row < height) { // Draw one row for every unit of height // Print leading spaces int count = 0;

while (count < height - row) { std::cout << " " ; count++;

}

// Print out stars, twice the current row plus one: // 1. number of stars on left side of tree

// = current row value

// 2. exactly one star in the center of tree

// 3. number of stars on right side of tree

// = current row value

count = 0;

while (count < 2* *row + 1) { std::cout << ;

count++;

}

// Move cursor down to next line std::cout << 1 \n 1 ;

// Change to the next row

}

}

row++;

Note 1

Note 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

Note 9

Note 10

Note 11

Note 12

Note 13

©2018 Richard L. Halterman

Note 14

ensures that the variable row increases by one each time through the loop; therefore, it eventually will equal height (since it initially had to be less than hei ght to enter the loop), and the loop will terminate. There is no possibility of an infinite loop here.

• The body of the outer loop consists of more than one statement; therefore, the body must be enclosed within curly braces. Whenever a group of statements is enclosed within curly braces a block is formed. Any variable declared within a block is local to that block. A variable’s scope (the section of the source code in which the variable exists and can be used) is from its point of declaration to the end of the block in which it is declared. For example, the variables height and row are declared in the block that is mai n’s body; thus, they are local to mai n. The variable count is declared within the block that is the body of the outer whi le statement; therefore, count is local to the outer whi le statement. An attempt to use count outside the body of the outer while statement would be an error.

What does it mean for a variable x to be local to a particular section of code? It means x does not exist outside its scope. There may be other variables in the program named x, but they are different variables. If it seems odd that you can have two different variables in the same program with the same name, consider the fact that there can be two people in the same room with the same name. They are different people, but they have the same name. Similarly, the meaning of a variable depends on its context, and its name is not necessarily unique.

The two inner loops play distinct roles;

• The first inner loop prints spaces. The number of spaces printed is equal to the height of the tree the first time through the outer loop and decreases each iteration. This is the correct behavior since each succeeding row moving down contains fewer leading spaces but more asterisks.

• The second inner loop prints the row of asterisks that make up the tree. The first time through the outer loop, row is zero, so no left side asterisks are printed, one central asterisk is printed (the top of the tree), and no right side asterisks are printed. Each time through the loop the number of left-hand and right-hand stars to print both increase by one and the same central asterisk is printed; therefore, the tree grows one wider on each side each line moving down. Observe how the 2*row + 1 value expresses the needed number of asterisks perfectly.

• While it seems asymmetrical, note that no third inner loop is required to print trailing spaces on the line after the asterisks are printed. The spaces would be invisible, so there is no reason to print them!

6.5.2 Printing Prime Numbers

A prime number is an integer greater than one whose only factors (also called divisors) are one and itself. For example, 29 is a prime number (only 1 and 29 divide into it with no remainder), but 28 is not (2, 4, 7, and 14 are factors of 28). Prime numbers were once merely an intellectual curiosity of mathematicians, but now they play an important role in cryptography and computer security.

The task is to write a program that displays all the prime numbers up to a value entered by the user. Listing |6(22| (printprimes.cpp) provides one solution.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Display primes up to what value? std::cin >> max_value;

int value = 2; // Smallest prime number

while (value <= max_value) {

// See if value is prime

bool is_prime = true; // Provisionally, value is prime // Try all possible factors from 2 to value - 1 int trial_factor = 2; while (trial_factor < value) {

if (value % trial_factor == 0) {

is_prime = false; // Found a factor

break; // No need to continue; it is NOT prime

}

trial_factor++;

}

if (is_prime)

std::cout << value << " "; // Display the prime number

value++; // Try the next potential prime number

}

std::cout << '\n' ; // Move cursor down to next line

Listing |6.22| (printprimes.cpp), with an input of 90, produces:

Display primes up to what value? 90

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89

The logic of Listing |6722| (printprimes.cpp) is a little more complex than that of Listing |6.21| (startree.cpp). The user provides a value for max_value. The main loop (outer whi le iterates over all the values from two to max_value:

• Two new variables, local to the body of the outer loop, are introduced: trial_factor and i s_pri me. i s_pri me is initialized to true, meaning value is assumed to be prime unless our tests prove otherwise, tri al_f actor takes on all the values from two to value - lintheinner loop:

int trial_factor = 2;

while (trial_factor < value) {

if (value % trial_factor == 0) {

is_prime = false; // Found a factor

break; // No need to continue; it is NOT prime

}

trial_factor++;

}

The expression value % trial_factor is zero when trial_factor divides into value with no remainder—exactly when tri al_f actor is a factor of value. If the executing program determines that any of the values of tri al_factor is a factor of value, then it sets i s_pri me to false and exits the loop via the break. If the loop continues to completion, the program never sets i s_pri me to false, which means it found no factors and value is indeed prime.

• The i f statement after the inner loop:

if (is_prime)

std::cout << value << " "; // Display the prime number

©2018 Richard L. Halterman

Draft date: September 25, 2018

simply checks the status of is_prime. If is_prime is true, then value must be prime, so it prints value along with an extra space for separation from output it may produce during subsequent iterations.

Some important questions we can ask include:

1. If the user enters a 2, will it be printed?

In this case max_value = value = 2, so the condition of the outer loop value <= max_value

is true, since 2 <= 2. i s_p r i me is set to true, but the condition of the inner loop trial_factor < value

is not true (2 is not less than 2). Thus, the inner loop is skipped, i s _ p r i me is not changed from true, and 2 is printed. This behavior is correct because 2 is the smallest prime number (and the only even prime).

2 . if the user enters a number less than 2, is anything printed?

The whi le condition ensures that values less than two are not considered. The body of the whi le will never be entered. Only the newline is printed, and no numbers are displayed. This behavior is correct.

3. Is the inner loop guaranteed to always terminate?

In order to enter the body of the inner loop, trial_factor must be less than value, value does not change anywhere in the loop. trial_factor is not modified anywhere in the if statement within the loop, and it is incremented within the loop immediately after the i f statement. trial_factor is, therefore, incremented during each iteration of the loop. Eventually, tri al_factor will equal value, and the loop will terminate.

4. Is the outer loop guaranteed to always terminate?

In order to enter the body of the outer loop, value must be less than or equal to max_value. max_value does not change anywhere in the loop, value is increased in the last statement within the body of the outer loop, and value is not modified anywhere else. Since the inner loop is guaranteed to terminate as shown in the previous answer, eventually value will exceed max_value and the loop will end.

We can rearrange the logic of the inner while to avoid the break statement. The current version is:

while (trial_factor < value) {

if (value % trial_factor == 0) {

is_prime = false; // Found a factor

break; // No need to continue; it is NOT prime

}

trial_factor++;

}

We can rewrite it as:

while (is_prime && trial_factor < value) { is_prime = (value % trial_factor != 0); trial_factor++; // Try next factor

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

This version without the break introduces a slightly more complicated condition for the whi le but removes the i f statement within its body, i s_p ri me is initialized to true before the loop. Each time through the loop it is reassigned, tri al_factor will become false if at any time value % trial_factor is zero. This is exactly when trial_factor is a factor of value. If is_prime becomes false, the loop cannot continue, and if is_prime never becomes false, the loop ends when trial_factor becomes equal to value. Due to operator precedence, the parentheses are not necessary. The parentheses do improve readability, since an expression including both == and ! = is awkward for humans to parse. When parentheses are placed where they are not needed, as in

x = (y + 2) ;

the compiler simply ignores them, so there is no efficiency penalty in the compiled code.

We can shorten the loop even further:

while (is_prime && trial_factor < value)

is_prime = (value 96 trial_factor++ != 0);

This version uses the post-increment operator within the test expression (see Section [4.9[ ). Recall that with the post-increment operator the value of the variable is used in the surrounding expression (if any), and then the variable is incremented. Since the whi le’s body now contains only one statement, the curly braces are not needed.

Chapter Notes

When a user runs Listing |6T2T|(startree.cpp) and enters 7, the program displays

Enter height of tree: 7

*

kkk

kkkkk

kkkkkkk

kkkkkkkkk

***********

*************

Listing 6.21 (startree.cpp) uses two sequential whi le loops both nested within a whi le loop. The outer whi le loop is responsible for drawing one row of the tree each time its body is executed:

• The program will execute the outer whi le loop’s body as long as the user enters a value greater than zero; if the user enters zero or less, the program terminates and does nothing. This is the expected behavior.

• The last statement in the body of the outer whi le:

row++;

Draft date: September 25, 2018

6.6 Exercises

1. In Listing 6.4 (addnonnegatives.cpp) could the condition of the i f statement have used > instead of >= and achieved the same results? Why?

2. In Listing 6.4 (addnonnegatives.cpp) could the condition of the whi le statement have used > instead of >= and achieved the same results? Why?

3. Use a loop to rewrite the following code fragment so that it uses just one std : :coutandone '\n'.

std:

: cout

<<

2

<<

' \n

3

std:

: cout

<<

4

<<

' \n

3

std:

: cout

<<

6

<<

' \n

3

std:

: cout

<<

8

<<

' \n

3

std:

: cout

<<

10

<<

' \n

3

std:

: cout

<<

12

<<

' \n

3

std:

: cout

<<

14

<<

' \n

3

std:

: cout

<<

16

<<

' \n

3

4. In Listing 6.4 (addnonnegatives.cpp) what would happen if the statement containing std : : ci n is moved out of the loop? Is moving the assignment out of the loop a good or bad thing to do? Why?

5. How many asterisks does the following code fragment print?

i nt a = 0; while (a < 100) {

std::cout << "*" ; a++ 5

>

std::cout << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

6 . How many asterisks does the following code fragment print?

int a = 0 ; while (a < 100 )

std::cout << "*" ; std::cout << '\n' ;

7. How many asterisks does the following code fragment print?

int a = 0 ; while (a > 100 ) {

std::cout << ;

a++ •

>

std::cout << '\n' ;

8 . How many asterisks does the following code fragment print?

int a = 0 ; while (a < 100 ) { int b = 0 ; while (b < 55) {

std::cout << "*" ; b++ 5

}

std::cout << '\n' ;

}

9. How many asterisks does the following code fragment print?

int a = 0 ; while (a < 100 ) {

if (a % 5 == 0)

std::cout << "*" ;

a++ •

>

std::cout << '\n' ;

10. How many asterisks does the following code fragment print?

int a = 0 ; while (a < 100 ) { int b = 0 ; while (b < 40) {

if ((a + b) 96 2 == 0) std::cout << ;

b++;

}

std::cout << '\n' ; a++ •

>

11. How many asterisks does the following code fragment print?

©2018 Richard L. Halterman

Draft date: September 25, 2018

int a = 0; while (a < 100 ) { int b = 0 ; while (b < 100 ) { int c = 0 ; while (c < 100 ) {

std::cout << "*" ;

C++;

}

b++;

}

3 ++ y

}

std::cout << ' \n' ;

12. What is printed by the following code fragment?

int a = 0 ; while (a < 100 )

std::cout << a++; std::cout << ' \n' ;

13. What is printed by the following code fragment?

int a = 0 ; while (a > 100 )

std::cout << a++; std::cout << '\n' ;

14. Rewrite the following code fragment using a break statement and eliminating the done variable. Your code should behave identically to this code fragment.

bool done = false; int n = 0 , m = 100 ; while (Idone && n != m) { std::cin >> n; if (n < 0 )

done = true;

std::cout << "n = " << n << '\n' ;

15. Rewrite the following code fragment so it eliminates the conti nue statement. Your new code’s logic should be simpler than the logic of this fragment.

int x = 100, y; while (x > 0) {

std::cin >> y; if (y == 25) { x--;

continue ;

}

std::cin >> x;

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "x = " << x << '\ n ' ;

}

16. Suppose you were given some code from the 1960s in a language that did not support structured statements like whi le. Your task is to modernize it and adapt it to C++. The following code fragment has been adapted to C++ already, but you must now structure it with a whi le statement to replace the gotos. Your code should be goto free and still behave identically to this code fragment.

int i = 0; top: if (i >= 10) goto end;

std::cout << i << '\n' ; i++;

goto top;

end:

17. What is printed by the following code fragment?

int a = 0; while (a < 100);

std::cout << a++; std::cout << '\n' ;

18. Write a C++ program that accepts a single integer value entered by the user. If the value entered is less than one, the program prints nothing. If the user enters a positive integer, n, the program prints an n x n box drawn with * characters. If the users enters 1, for example, the program prints

If the user enters a 2, it prints

An entry of three yields

and so forth. If the user enters 7, it prints

that is, a 7 x 7 box of * symbols.

19. Write a C++ program that allows the user to enter exactly twenty double-precision floating-point values. The program then prints the sum, average (arithmetic mean), maximum, and minimum of the values entered.

©2018 Richard L. Halterman

Draft date: September 25, 2018

20. Write a C++ program that allows the user to enter any number of nonnegative double-precision floating-point values. The user terminates the input list with any negative value. The program then prints the sum, average (arithmetic mean), maximum, and minimum of the values entered. The terminating negative value is not used in the computations. If the first number the user supplies is negative, the program simply prints the text NO NUMBERS PROVIDED.

21. Redesign Listing [6.211 (startree.cpp) so that it draws a sideways tree pointing right; for example, if the user enters 7, the program would print

22. Redesign Listing [6!2T| (startree.cpp) so that it draws a sideways tree pointing left; for example, if the user enters 7, the program would print

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 7

Other Conditional and Iterative Statements

The if /else and while statements are sufficient to implement any algorithms that involve conditional execution and looping. The break and conti nue statements are convenient but are not necessary. C++ provides some additional conditional and iterative statements that are more convenient to use in some circumstances. These additional statements include

• swi tch: an alternative to some multi-way i f/else statements

• the conditional operator: an expression that exhibits the behavior of an i f/else statement

• do/whi le: a loop that checks its condition after its body is executed

• f o r : a loop convenient for counting

These alternate constructs allow certain parts of algorithms to expressed more clearly and succinctly. This chapter explores these other forms of expressing conditional execution and iteration.

7.1 The switch Statement

The swi tch statement provides a convenient alternative for some multi-way i f/else statements like the one in Listing TT5| (restyleddigittoword.cpp). Listing |7.1| (switchdigittoword.cpp) is a new implementation of Listing 5.15 (restyleddigittoword.cpp) that uses a swi tch statement instead of a multi-way i f/else

statement.

Listing 7.1: switchd-ig-ittoword. cpp

ttinclude <iostream>

int main() { int value;

std::cout << "Please enter an integer in the range 0...5: " std::cin >> value; switch (value) { case 0:

std::cout << "zero"; break;

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

case 1:

std::cout << "one" ; break; case 2:

std::cout << "two" ; break; case 3:

std::cout << "three"; break; case 4:

std::cout << "four"; break; case 5:

std::cout << "five"; break; default :

if (value < 0)

std::cout << "Too small";

else

std::cout << "Too large"; break;

}

std::cout << '\n 1 ;

The general form of a swi tch is:

©2018 Richard L. Halterman

Draft date: September 25, 2018

( integral expression ) { case integral constant 1 :

statement sequence 1

break;

case integral constant 2 :

statement sequence 2

break;

case integral constant 3 :

statement sequence 3

break;

case integral constant n :

statement sequence n

break;

default :

default statement sequence

}

In a swi tch statement

• The reserved word swi tch identifies a swi tch statement.

• The required parenthesized expression that follows the word swi tch must evaluate to an integral value. Any integer type, characters, and Boolean expressions are acceptable. Floating point expressions and other non-integer types are forbidden.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• The body of the swi tch is enclosed by required curly braces.

• Each occurrence of the word case is followed by an integral constant and a colon (:). We call the integral constant a case label. This label can be either a literal value or a const symbolic value (see Section |3.6| . In particular, non-const variables and other expressions are expressly forbidden.

The case label defines a position within the code; it is not an executable statement. A case label represents a target to which the program’s execution flow can jump.

If the case label matches the switch’s expression, then the statements that follow that label are executed up until the break statement is encountered. The statements and break statement that follow each case label are optional. One way to execute one set of statements for more than one case label is to provide empty statements for one or more of the labels, as in:

std::cin >> key; // get key from user switch (key) { case 'p' : case 1 P' :

std::cout << "You choose \"P\"\n"; break ; case 'q ' : case 'Q' :

done = true; break ;

}

Here either an upper- or lowercase P result in the same action— You chose P is printed. If the user enters either an upper- or lowercase Q, the done Boolean variable is set to true. If the user enters neither P nor Q, none of the statements in the swi tch is executed.

The break statement is optional. When a case label is matched, the statements that follow are executed until a break statement is encountered. The control flow then transfers out of the body of the swi tch. In this way, the break within a swi tch works just like a break within a loop: the rest of the body of the statement is skipped and program execution resumes at the next statement following the body. A missing break statement, a common error, when its omission is not intentional, causes the statements of the succeeding case label to be executed. The process continues until a break is encountered or the end of the swi tch body is reached.

• The default label is matched if none of the case labels match. It serves as a catch all option like the final else in a multi-way i f /else statement. The default label is optional. If it is missing and none of the case labels match the expression, then no statement within the swi tch’s body is executed.

The swi tch statement has two restrictions that make it less general than the multi-way i f /else:

• The swi tch argument must be an integral expression.

• Case labels must be constant integral values. Integral literals and constants are acceptable. Variables or expressions are not allowed.

To illustrate these restrictions, consider the following i f /else statement that translates easily to an equivalent swi tch statement:

©2018 Richard L. Halterman

Draft date: September 25, 2018

if (x == 1) {

// Do 1 stuff here . . .

}

else if (x == 2 ) {

// Do 2 stuff here . . .

}

else if (x == 3) {

// Do 3 stuff here . . .

}

The corresponding swi tch statement is:

switch (x) { case 1:

// Do 1 stuff here . . . break ; case 2:

// Do 2 stuff here . . . break ; case 3:

// Do 3 stuff here . . . break ;

}

Now consider the following i f/else: if (x == y) {

// Do "y" stuff here . . .

}

else if (x > 2) {

// Do "> 2" stuff here . . .

}

else if (z == 3) {

// Do 3 stuff here . . .

}

This code cannot be easily translated into a swi tch statement. The variable y cannot be used as a case label. The second choice checks for an inequality instead of an exact match, so direct translation to a case label is impossible. In the last condition, a different variable is checked, z instead of x. The control flow of a switch statement is determined by a single value (for example, the value of x), but a multi-way i f/else statement is not so constrained.

Where applicable, a swi tch statement allows programmers to compactly express multi-way selection logic. Most programmers find a swi tch statement easier to read than an equivalent multi-way i f/else construct.

A positive consequence of the swi tch statement’s restrictions is that it allows the compiler to produce more efficient code for a swi tch than for an equivalent i f/else. If a choice must be made from one of several or more options, and the swi tch statement can be used, then the swi tch statement will likely be faster than the corresponding multi-way i f/else.

©2018 Richard L. Halterman

Draft date: September 25, 2018

7.2 The Conditional Operator

As purely a syntactical convenience, C++ provides an alternative to the if/else construct called the conditional operator. It has limited application but is convenient nonetheless. The following code fragment assigns one of two things to x:

• the result of y/z, if z is nonzero, or

• zero, if z is zero; we wish to avoid the run-time error of division by zero.

// Assign a value to x: if (z != 0)

x = y/z; // Division is possible

else

x = 0; // Assign a default value instead

This code has two assignment statements, but only one is executed at any given time. The conditional operator makes for a more compact statement:

// Assign a value to x: x— (z !—0) ? y/z : 0;

The general form of a conditional expression is:

) ? expression 1 : expression 2

( condition

• condition is a normal Boolean expression that might appear in an i f statement. Parentheses around the condition are not required but should be used to improve the readability.

• expression 1 is the overall value of the conditional expression if condition is true.

• expression 2 is the overall value of the conditional expression if condition is false.

The conditional operator uses two symbols (? and :) and three operands. Since it has three operands it is classified as a ternary operator (C++’s only one). The overall type of a conditional expression is the more dominant of exp\ and expi The conditional expression can be used anywhere an expression can be used. It is not a statement itself; it is used within a statement.

As another example, the absolute value of a number is defined in mathematics by the following formula:

■ | _ ( n , when n > 0 ' n ' [ — n, when n< 0

In other words, the absolute value of a positive number or zero is the same as that number; the absolute value of a negative number is the additive inverse (negative of) of that number. The following C++ expression represents the absolute value of the variable n:

©2018 Richard L. Halterman

Draft date: September 25, 2018

(n < 0) ? -n : n

Some argue that the conditional operator is cryptic, and thus its use reduces a program’s readability. To seasoned C++ programmers it is quite understandable, but it is used sparingly because of its very specibc nature.

7.3 The do/while Statement

An executing program checks the condition of a while statement (Section 6.1 before executing any of

the statements in its body; thus, we say a while loop is a top-checking loop. Sometimes this sequence of checking the condition first then executing the body is inconvenient; for example, consider Listing |7.2j (goodinputonly.cpp).

The loop in Listing 7.2 (goodinputonly.cpp) traps the user in the while until the user provides a number in the desired range. Here’s how it works:

• The condition of the whi le specifies a set that includes all values that are not in the desired range. The initialization of in_valueto—1 ensures the condition of the while will be true initially, and, thus, the program always will execute the loop’s body at least one time.

• The user does not get a chance to enter a value until program’s execution is inside the loop.

• The only way the user can escape the loop is to enter a value that violates the condition—precisely a value in the desired range.

The initialization of i n_value before the loop check is somewhat artificial. It is there only to ensure entry into the loop’s body. It seems unnatural to check for a valid value before the user gets a chance to enter it. A loop that checks its condition after its body is executed at least once would be more appropriate. The do/while statement is a bottom-checking loop that behaves exactly in this manner. Listing 7.3 (betterinputonly.cpp) uses a do/whi le statement to check for valid input.

Listing7.3: betterinputonly.cpp

ffinclude <iostream>

int main() {

int in_value;

std::cout << "Please enter an integer in the range 0-10: "

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 7.1 The flowcharts for while and do/while loops

while flowchart do/while flowchart

// Insist on values in the range 0...10 do

std::cin >> in_value; while (in_value < 0 || in_value > 10);

// in_value at this point is guaranteed to be within range std::cout << "Legal value entered was " << in_value << 1 \n' ;

Notice that there is no need to initialize i n_value since its value is not used until after it is assigned through the input stream std: :cin. Figure 7.1 compares the flowcharts of a while and do/while loop.

The do/while statement has the general form:

do

statement

whi le

( condition ) ;

• The reserved words do and whi le identify a do/whi le statement. The do and whi le keywords

©2018 Richard L. Halterman

Draft date: September 25, 2018

delimit the loop’s body, but curly braces are still required if the body consists of more than one statement.

• The condition is associated with the while at the end of the loop. The condition is a Boolean expression and must be enclosed within parentheses.

• The statement is exactly like the statement in the general form of the whi le loop (see Section 6J). It can be a compound statement enclosed within curly braces.

The body of a do/while statement, unlike the while statement, is guaranteed to execute at least once.

The do/whi le loop is a convenience to the programmer and is not an essential programming construct. It is easy to transform any code that uses a do/while statement into code that behaves identically that uses a whi le statement instead. In practice, programmers use whi le loops much more frequently than do/whi le loops because more algorithms require top-checking loops than bottom-checking loops. The do/whi le statement is included in C++ for a reason, however. Transforming an algorithm that can be expressed more naturally with a bottom-checking loop into one the uses a top-checking loop can lead to awkward code. Use do/whi le when appropriate.

7.4 The for Statement

Recall Listing |6T2| (iterativecounttofive.cpp). It simply counts from one to five. Counting is a frequent activity performed by computer programs. Certain program elements are required in order for any program to count:

• A variable must be used to keep track of the count; in Listing [672] (iterativecounttofive.cpp), count is the aptly named counter variable.

• The counter variable must be given an initial value. In the case of Listing| |6.2| (iterativecounttofive.cpp), the initial value is 1.

• The variable must be modified (usually incremented) as the program counts. The statement

count++;

increments count in Listing ]|6.2|| (iterativecounttofive.cpp).

• A way must be provided to determine if the counting has completed. In Listing j|6.2| (iterativecounttofive.cpp), the condition of the whi le statement determines if the counting is complete or must contine.

C++ provides a specialized loop that packages these four programming elements into one convenient statement. Called the for statement, its general form is

for ( initialization

condition

modification )

statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

• The reserved word for identifies a for statement.

• The loop is controlled by a special variable called the loop variable.

• The header, contained in parentheses, contains three parts, each separated by semicolons:

- Initialization. The initialization part assigns an initial value to the loop variable. The loop variable may be declared here as well; if it is declared here, then its scope is limited to the f o r statement. This means you may use that loop variable only within the loop. It also means you are free to reuse that variable’s name outside the loop to declare a different variable with the same name as the loop variable.

The initialization part is performed one time.

- Condition. The condition part is a Boolean expression, just like the condition of a while statement. The condition is checked each time before the body is executed.

- Modification. The modification part generally changes the loop variable. The change should be such that the condition will eventually become false so the loop will terminate. The modification is performed during each iteration after the body is executed.

Notice that the last part ( modification ) is not following by a semicolon; semicolons are used strictly to separate the three parts.

• The statement is like the body of any other loop. It may be a compound statement within curly braces.

Any for loop can be rewritten as a whi le loop. The general form of the for loop given above can be written equivalently as

initialization

whi le

( condition

) {

statement

}

modification

Table captionListing 7.4 (forcounttofive.cpp) uses a for statement to count to five.

Listing7.4: forcounttofive.cpp

#include <iostream>

int main() {

for (int count = 1; count <= 5; std::cout << count << '\n ' ;

}

count++)

// Display counter

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

With a whi le loop, the four counting components (variable declaration, initialization, condition, and modification can be scattered throughout the code. With a for loop, a programmer should be able to determine all the important information about the loop’s control by looking at one statement.

Recall Listing [6.13j (timestable.cpp) that prints a multiplication table on the screen. We can organize its code better by converting all the whi le statements to for statements. The result uses far less code, as shown in Listing|7.5j(bettertimestable.cpp).

A for loop is ideal for stepping through the rows and columns. The information about the control of both loops is now packaged in the respective for statements instead of being spread out in various places in ma i n. In the while version, it is easy for the programmer to forget to update one or both of the counter variables (row and/or column). The for makes it harder for the programmer to forget the loop variable update, since it is done right up front in the for statement header.

It is considered bad programming practice to do either of the following in a for statement:

• Modify the loop control variable within the body of the loop —if the loop variable is modified within the body, then the logic of the loop’s control is no longer completely isolated to the f o r statement’s header. The programmer must look elsewhere within the statement to understand completely how the loop works.

• Prematurely exit the loop with a break — this action also violates the concept of keeping all the loop control logic in one place (the for’s header).

©2018 Richard L. Halterman

Draft date: September 25, 2018

The language allows both of these practices, but experience shows that it is best to avoid them. If it seems necessary to violate this advice, consider using a different kind of loop. The whi le and do/whi le loops do not imply the same degree of control regularity expected in a for loop.

Listing 7.6 (permuteabcd.cpp) is a rewrite of Listing 6.14 (permuteabc.cpp) that replaces its while loops with for loops and adds an additional character.

Notice that since all the variable initialization and incrementing is taken care of in the for statement headers, we no longer need compound statements in the loop bodies, so the curly braces are unnecessary. Listing |T6](permuteabcd.cpp) prints all 24 permutations of ABCD:

ABCD

ABDC

ACBD

ACDB

ADBC

ADCB

BACD

BADC

BCAD

BCDA

BDAC

BDCA

CABD

CADB

CBAD

CBDA

CDAB

CDBA

DABC

DACB

DBAC

DBCA

DCAB

DCBA

Listing 7.7 (forprintprimes.cpp) is a rewrite of Listing 6.22 (printprimes.cpp) that replaces its while loops with for loops.

©2018 Richard L. Halterman

Draft date: September 25, 2018

As shown in Listing 7.7 fforprintprimes.cpp), the conditional expression in the for loop is not limited to a simple test of the loop control variable; it can be any legal Boolean expression. Programmers can use the logical and (&&), or {| |), and not (!) operators to create complex Boolean expressions, if necessary. The modification part of the for loop is not limited to simple arithmetic and can be quite elaborate. For example:

for (double d = 1000; d >= 1; std::cin >> d) {

/* Body goes here */

}

Here d is reassigned from the input stream. If necessary, multiple variables can be initialized in the initialization part:

for (int i = 0, j = 100; i < j; i+ + ) {

/* Body goes here */

}

While the for statement supports such complex headers, simpler is usually better. Ordinarily the for loop should manage just one control variable, and the initialization, condition, and modification parts should be straightforward. If a particular programming situation warrants an overly complicated f o r construction, consider using another kind of loop.

Any or all of the parts of the for statement (initialization, condition, modification, and body) may be omitted:

• Initialization. If the initialization is missing, as in

for (; i < 10; i++)

/* Body goes here */

then no initialization is performed by the for loop, and it must be done elsewhere.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• Condition. If the condition is missing, as in

for (int i = 0; ; i++)

/* Body goes here */

then the condition is true by default. A break or goto must appear in the body unless an infinite loop is intended.

• Modification. If the modification is missing, as in

for (int i = 0; i < 10; )

/* Body goes here */

then the for performs no automatic modification; the modification must be done by a statement in the body to avoid an infinite loop.

• Body. An empty body, as in

for (int i = 0; i < 10; i++) {}

or

for (int i = 0; i < 10; i++);

results in an empty loop. Some programmers use an empty loop to produce a non-portable delay in the program’s execution. A programmer may, for example, need to slow down a graphical animation. Such an attempt using an empty loop is non-portable for several reasons. If the program actually executes the loop, slower computers will delay longer than faster computers. The timing of the program’s delay will differ from one computer to another. Worse yet, some compilers may detect that such code has no functional effect and optimize away the empty loop. This means the compiler will ignore the for statement altogether.

As mentioned in Section 5.3 be careful about accidentally putting a semicolon at the end of the f o r header, as in

for

(int i = 0; i < 10; i+ + ) ;

/* Intended body goes here

*/

The semicolon terminates the for statement, and the intended body that follows is not the body, even though it may be properly indented.

One common C/C++ idiom to make an intentional infinite loop is to use a f o r statement with all control information missing:

for ( ;; )

/* Body goes here */

Omitting all the parts of the for header is a statement from the programmer that says “I know what I am doing—I really want an infinite loop here.” In reality the loop may not be infinite at all; its body could contain a break or goto statement.

While the f o r statement supports the omission of parts of its header, such constructs should be avoided. The intention of the for loop is to allow the programmer to see all the aspects of the loop’s control in one place. If some of these control responsibilities are to be handled elsewhere (not in the for’s header) then consider using another kind of loop.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Programmers usually select a simple name for the control variable of a for statement. Recall that variable names should be well chosen to reflect the meaning of their use within the program. It may come as a surprise that i is probably the most common name used for an integer control variable in a for loop. This practice has its roots in mathematics where variables such as i, j, and k are commonly used to index vectors and matrices. Such mathematical structures have programming analogs in arrays and vectors, which we explore in Chapter 11 Computer programmers make considerable use of for loops in array

and vector processing, so programmers have universally adopted this convention of short control variable names. Thus, it generally is acceptable to use simple identifiers like i as loop control variables.

C++ allows the break, conti nue, and goto statements to be used in the body of a for statement. Like with the while and do/whi le statements, break causes immediate loop termination, continue causes the condition to be immediately checked to determine if the iteration should continue, and goto jumps to a label somewhere in the function. As previously mentioned, however, f o r loop control should be restricted to its header, and the use of break, conti nue, and goto within for loops should be avoided.

Any for loop can be rewritten with a whi le loop and behave identically. For example, consider the f o r loop

for (int i = 1; i <= 10; i++) std::cout << i << '\n' ;

and next consider the while loop that behaves exactly the same way:

int i = 1; while (i <= 10) {

std::cout << i << '\n' ; i++;

}

Which is better? The for loop conveniently packages the loop control information in its header, but in the whi le loop this information is distributed throughout the small section of code. The for loop thus provides a better organization of the loop control code. Does one loop outperform the other? No, most compilers produce essentially the same code for both constructs. Thus, the for loop is preferred in this example.

7.5 Exercises

1. Consider the following code fragment, int x;

std::cin >> x; switch (x + 3) { case 5:

std::cout << x << '\n' ; break; case 10:

std::cout << x - 3 << ' \ n' ; break; case 20:

std::cout << x + 3 << '\ n' ; break;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

(a) What is printed when the user enters 2?

(b) What is printed when the user enters 5?

(c) What is printed when the user enters 7?

(d) What is printed when the user enters 17?

(e) What is printed when the user enters 20?

2. Consider the following code fragment.

char ch; std::cin >> ch; switch (ch) { case ' a' :

std::cout << break; case 'A' :

std::cout << break; case 'B 1 : case 'b' :

std::cout << case 'C' : case 'c' :

std::cout << break; default:

std::cout <<

}

"*\n" ; "**\n";

"***\n" ; "****\n" ; "*****\n" ;

(a)

(b)

(c)

(d)

(e)

(f)

(g)

What is printed when What is printed when What is printed when What is printed when What is printed when What is printed when What is printed when

the user enters a? the user enters A? the user enters bl the user enters B1 the user enters C? the user enters c? the user enters f?

3. What is printed by the following code fragment?

int x = 0; do {

std::cout << x << " " ; x++ 5

} while (x < 10); std::cout << '\n' ;

4. What is printed by the following code fragment?

©2018 Richard L. Halterman

Draft date: September 25, 2018

i nt x = 20 ; do {

std::cout << x << " " ; x++ 5

} while (x < 10 ); std::cout << '\n' ;

5. What is printed by the following code fragment?

for (int x = 0 ; x < 10 ; x++) std::cout << "*" ; std::cout << '\n' ;

6. Rewrite the following code fragment so that a swi tch is used instead of the i f/else statements.

Table captionint value; char ch;

std : :ci n >>

ch;

if (ch == '/

V)

value =

10;

else if (ch

==

' P'

')

value =

20;

else if (ch

==

'T'

')

value =

30;

else if (ch

==

'V'

')

value =

40;

else

value =

50;

Table captionstd::cout << value << '\n' ;

7. Rewrite the following code fragment so that a multi-way i f/else is used instead of the swi tch statement.

int value; char ch; std::cin >> ch; switch ( ch) { case 'A' :

value = 10; break; case 'P' :

std::cin >> value; break; case 'T' :

value = ch; break; case 'V' :

value = ch + 1000; break; default :

value = 50;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << value << '\n' ;

8. Rewrite the following code fragment so that a multi-way i f/else is used instead of the swi tch statement.

int value; char ch; std::cin >> ch; switch (ch) { case 'A' :

std::cout << ch << '\n' ; value = 10; break; case 'P' : case 'E' :

std::cin >> value; break; case 'T' :

std::cin >> ch; value = ch; case 'C' :

value = ch;

std::cout << "value=" << value << ", ch=" << ch << '\n' ; break; case 'V' :

value = ch + 1000; break;

}

std::cout << value << '\n' ;

9. Rewrite the following code fragment so a whi le loop is used instead of the for statement.

for (int i = 100; i > 0; i —) std::cout << i << '\ n ' ;

10. Rewrite the following code fragment so that it uses the conditional operator instead of an i f statement:

if (value % 2 != 0) // Is value even?

value = value + 1; // If not, make it even.

11. Rewrite the following code fragment so that it uses the conditional operator instead of an i f /else statement:

if (value % 2 == 0) // Is value even?

value = 0; // If so, make it zero.

else

value = value + 1; // Otherwise, make it even.

12. Would the following multi-way i f/else be a good candidate to rewrite as a swi tch statement? If so, rewrite the code using a swi tch; otherwise, explain why it is impractical to do so.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int x, y;

std::cin >> x >> y; if (x < 10)

y - is;

else if (x == 5) y = 5;

else if (x == y)

y = 0;

else if (y > 10) x = 10;

else

x = y;

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 8

Using Functions

Suppose you must write a C++ program that computes the square root of a number supplied by the user. Listing |8.1 |(computesquareroot.cpp) provides a simple implementation.

The program is based on a simple algorithm, Newton’s Method, that uses successive approximations to zero in on an answer that is within 0.0001 of the true answer.

One sample run is

©2018 Richard L. Halterman

Draft date: September 25, 2018

root is 1.5

root is 1.41667

root is 1.41422

Square root of 2 = 1.41422

The actual square root is approximately 1.4142135623730951 and so the result is within our accepted tolerance (0.0001). Another run is

Enter number: 100 root is 50.5 root is 26.2401 root is 15.0255 root is 10.8404 root is 10.0326 root is 10.0001 root is 10

Square root of 100 = 10

which is, of course, the exact answer.

While this code may be acceptable for many applications, better algorithms exist that work faster and produce more precise answers. Another problem with the code is this: What if you are working on a significant scientific or engineering application and must use different formulas in various parts of the source code, and each of these formulas involve square roots in some way? In mathematics, for example, you use square root to compute the distance between two geometric points (x\ ,}’i) and {x 2 ,yi) as

yj{x 2 -xi) 2 + {y 2 -yi) 2

and, using the quadratic formula, the solution to the equation ax 2 + bx + c = 0 is

—b ± \Jb 2 — 4ac 2 a

In electrical engineering and physics, the root mean square of a set of values {a\ ,a 2 -ai ..... a „} is

/ + ^2 + Q3 + • • ■ +

y n

Suppose we are writing one big program that, among many other things, needs to compute distances and solve quadratic equations. Must we copy and paste the relevant portions of the square root code in Listing 18711 (computesquareroot.cpp) to each location in our source code that requires a square root computation? Also, what if we develop another program that requires computing a root mean square? Will we need to copy the code from Listing [8TT| (computesquareroot.cpp) into every program that needs to compute square roots, or is there a better way to package the square root code and reuse it?

Code is made reusable by packaging it in functions. A function is a unit of reusable code. In Chapter[9j we will write our own reusable functions, but in this chapter we examine some of the functions available in the C++ standard library. C++ provides a collection of standard precompiled C and C++ code stored in libraries. Programmers can use parts of this library code within their own code to build sophisticated programs.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 8.1 Conceptual view of the square root function

16

4

8.1 Introduction to Using Functions

In mathematics, a function computes a result from a given value; for example, from the function definition f(x) = 2x + 3, we can compute /(5) = 13 and /(0) = 3. A function in C++ works like a mathematical function. To introduce the function concept, we will look at the standard C++ function that implements mathematical square root.

In C++, a function is a named sequence of code that performs a specific task. A program itself consists of a collection of functions. One example of a function is the mathematical square root function. Such a function, named sqrt, is available to C and C++ programs (see Section [8.2| . The square root function accepts one numeric value and produces a double value as a result; for example, the square root of 16 is 4, so when presented with 16.0, sqrt responds with 4.0. Figure |87T| visualizes the square root function.

For the programmer using the sqrt function within a program, the function is a black box; the programmer is concerned more about what the function does, not how it does it.

This sq rt function is exactly what we need for our square root program, Listing|8.1||(computesquareroot.cpp). The new version. Listing j |8T2|| (standardsquareroot.cpp), uses the library function sqrt and eliminates the complex logic of the original code.

The line

((include <cmath>

©2018 Richard L. Halterman

Draft date: September 25, 2018

directs the preprocessor to augment our source code with the declarations of a collection of mathematical functions in the cmath library. The sqrt function is among them. Table |8.l[ lists some of the other commonly used mathematical functions available in the cmath library. The compiler needs this augmented code so it can check to see if we are using the sqrt function properly.

The expression sqrt(input)

is a function invocation, also known as a. function call. A function provides a service to the code that uses it. Here, our mai n function is the caller 1 that uses the service provided by the sqrt function. We say mai n calls, or invokes, sq rt passing it the value of i nput. The expression sq rt(i nput) evaluates to the square root of the value of the variable input. Behind the scenes—inside the black box as it were— precompiled C code uses the value of the input variable to compute its square root. There is nothing special about this precompiled C code that constitutes the sq rt function; it was written by a programmer or team of programmers working for the library vendor using the same tools we have at our disposal. In In Chapter |9j we will write our own functions, but for now we will enjoy the functions that others have provided for us.

When calling a function, a pair of parentheses follow the function’s name. Information that the function requires to perform its task must appear within these parentheses. In the expression

sqrt(input)

i nput is the information the function needs to do its work. We say i nput is the argument, or parameter, passed to the function. We also can say “we are passing input to the sq rt function.”

While we might say “we are passing i nput to the sqrt function,” the program really is not giving the function access to mai n’s i nput variable. The sqrt function itself cannot change the value of mai n’s i nput variable, it simply uses the variable’s value to perform the computation.

The following simple analogy may help explain how the communication works between main and sqrt. The mai n function has work to do, but instead of doing all the work itself, it delegates some of the work (in this case the hard part) to sq rt. When mai n needs to compute the square root of i nput, it writes down the value of its i nput variable on a piece of paper and hands it to sqrt. mai n then sits idly until sqrt finishes its work. The sqrt function accepts mai n’s note and begins working on the task (computing the square root of the number on the note mai n gave it). When it is finished, sqrt does two things; sqrt hands back to main a different piece of paper with the answer, and sqrt throws away the piece of paper main originally passed to it. When main receives the note from sq rt it uses the information on the note and then discards the note. The mai n function then can continue with its other business.

The sq rt function thus has no access to mai n’s original i nput variable; it has only a copy of i nput, as if “written on a piece of paper.” (Similarly, if the sq rt function uses any variables to do its work, mai n is oblivious to them and has no way to access them.) After sqrt is finished and returns to main its computed answer, sqrt discards its copy of i nput (by analogy, the function “throws away” the paper with the copy of i nput that mai n gave it). Thus, during a function call the parameter is a temporary, transitory value used only to communicate information to the function. The parameter lives only as long as the function is executing.

Figure j[K2[ illustrates a program’s execution involving simple function calls.

Figure 8.2 shows that a program’s execution begins in its mai n function. Here mai n calls the sqrt function twice. A vertical bar represents the time that a function is active, or “alive.” A function’s variables

'The term client can be used as well, although we reserve the term client for code that interacts with objects (see Chapter 131.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 8.2 The diagram on the right visualizes the execution of the program on the left. Time flows from left to right. A rectangular bar represents the time that a function is active. A C++ program’s execution begins with its man n function. Here, man n calls the sqrt function twice. The shaded parts of mai n’s bar shows the times mai n has to wait for sqrt to complete.

int main() {

double value;

// Assign variable

value = 16;

// Compute s square root

double root = sqrt(value);

// Compute another

root = sqrt(100);

Program Execution

Table captionTime mai n

\

cn

* ^

\

100 / t 10

sqrt sqrt

exist while a function is active. Observe that the main function is active for the duration of the program’s execution. The sq rt becomes active twice, exactly the two times main calls it.

The sq rt function can be called in other ways, as Listing[873](usingsqrt.cpp) illustrates:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table caption8.1. INTRODUCTION TO USING FUNCTIONS 184

Figure 8.3 Conceptual view of the maximum function

4 —

7 - ►^^■1

—► 7

The sqrt function accepts a single numeric argument. The parameter that a caller can pass to sqrt can be a literal number, a numeric variable, an arithmetic expression, or even a function invocation that produces an acceptable numeric result.

Some C++ functions, like sq rt, compute a value and return it to the caller. The caller can use this result in various ways, as shown in Listing ||8.3| (usingsqrt.cpp). The next to the last statement passes the result of calling sq rt to sq rt, thereby computing \J \/256, which is 4.

If the caller code attempts to pass a parameter to the function that is incompatible with the type expected by the function, the compiler will issue an error.

std::cout << sqrt("16") << '\ n ' ; // Illegal, a string is not a number

The compiler is able to determine that the above statement is illegal based on the additional information the preprocessor added to the code via the

#include<cmath> directive.

Listing [83] (usingsqrt.cpp) shows that a program can call the sqrt function as many times and in as many places as needed. As noted in Figure |8.1j| to the caller of the square root function, the function is a black box; the caller is concerned strictly about what the function does, not how the function accomplishes its task.

We safely can treat all functions as black boxes. We can use the service that a function provides without being concerned about its internal details. We are guaranteed that we can influence the function’s behavior only via the parameters that we pass, and that nothing else we do can affect what the function does or how it does it. Furthermore, the function cannot affect any of our code, apart from what we do with the value it computes.

Some functions take more than one parameter; for example, the C++ max function requires two arguments in order to produce a result. The max function selects and returns the larger of the two parameters. The max function is visualized in Figure| [8T3|

The max function could be used as

std::cout << "The larger of " << 4 << " and " << 7 << " is " << max(4, 7) << '\n' ;

Notice that the parameters are contained in parentheses following the function’s name, and the parameters are separated by commas.

From the caller’s perspective a function has three important parts:

©2018 Richard L. Halterman

Draft date: September 25, 2018

• Name. Every function has a name that identifies the location of the code to be executed. Function names follow the same rules as variable names; a function name is another example of an identifier (see Section |373| .

• Parameter type(s). A caller must provide the exact number and types of parameters that a function expects. If a caller attempts to call a function with too many or too few parameters, the compiler will issue an error message and not compile the code. Similarly, if the caller passes parameters that are not compatible with the types specified for the function, the compiler will report appropriate error messages.

• Result type. A function can compute a result and return this value to the caller. The caller’s use of this result must be compatible with the function’s specified result type. The result type returned to the caller and the parameter types passed in by the caller can be completely unrelated.

These three crucial pieces of information are formally described for each function in a specification known as a function prototype. The prototype for the sq rt function is

double sqrt(double)

and the max function’s prototype can be expressed as 2 int max(int, int)

In a function prototype, the return type is listed first, followed by the function’s name, and then the parameter types appear in parentheses. Sometimes it is useful to list parameter names in the function’s prototype, as in

double sqrt(double n)

or

int max (int a, int b)

The specific parameter names are irrelevant. The names make it easier to describe what the function does; for example, sq rtcomputes the square root of n and max determines the larger of a and b.

When using a library function the programmer must include the appropriate # include directive in the source code. The file specified in an #i nclude directive contains prototypes for library functions. In order to use the sq rt function, a program must include the

#include <cmath>

preprocessor directive. For the max function, include ttinclude <algorithm>

although under Visual C++, includeing <i ostream> is sufficient.

Armed with the function prototypes, the compiler can check to see if the calling code is using the library functions correctly. An attempt to use the sq rt function as

std::cout << sqrt(4.0, 7.0) << '\n' ; // Error

Note 1

©2018 Richard L. Halterman

Note 2

will result in an error because the prototype for sq rt specifies only one numeric parameter, not two.

Some functions do not accept parameters; for example, the C++ function to generate a pseudorandom number, rand, is called with no arguments:

std::cout << rand() << '\n' ;

The rand function returns an i nt value, but the caller does not pass the function any information to do its task. The rand prototype is

int rand()

Notice the empty parentheses that indicate this function does not accept any parameters.

Unlike mathematical functions that must produce a result, C++ does not require a function to return a value to its caller. The C++ function exit expects an integer value from the caller, but it does not return a result back to the caller. A prototype for a function that returns nothing uses voi d as the return type, as in:

void exit (int);

The exi t function immediately terminates the program’s execution. The integer argument passed to exi t is returned to the operating system which can use the value to determine if the program terminated normally or due to an error. C++ programs automatically return zero when mai n finishes executing—no exi t call is necessary.

Note that since exi t does not return a value to the caller, code such as

std::cout << exit(8) << '\n' ; // Illegal!

will not compile since the expression exi t (8) evaluates to nothing, and the std : : cout stream object requires an actual value of some kind to print. A void function is useful for the side effects it produces instead a value it computes. Example side effects include printing something on the console, sending data over a network, or animating a graphical image.

8.2 Standard Math Functions

The cmath library provides much of the functionality of a scientific calculator. Table 8.1 lists only a few of the available functions.

©2018 Richard L. Halterman

Draft date: September 25, 2018

mathfuncti ons Module

double sqrt(double x)

Computes the square root of a number: sq rt (x) = y(x double exp(double x)

Computes e raised a power: exp (x) = e x double log(double x)

Computes the natural logarithm of a number: log (x) = log e x = lnx double logl0(double x)

Computes the common logarithm of a number: log (x) = log 10 x double cos(double)

Computes the cosine of a value specified in radians: cos (x) = cosx; other trigonometric functions include sine, tangent, arc cosine, arc sine, arc tangent, hyperbolic cosine, hyperbolic sine, and hyperbolic tangent double pow(double x, double y)

Raises one number to a power of another: pow (x,y) = x y double fabs(double x)

Computes the absolute value of a number: fabs (x) = \x\

Table 8.1: A few of the functions from the cmath library

The cmath library also defines a constant named HUGE_VAL. Programmers can use this constant to represent infinity or an undefined value such the slope of a vertical line or a fraction with a zero denominator. A complete list of the numeric functions available to C++ can be found at http : / /www .cplusplus. com/reference/clibrary/cmath/

Be careful to put the function’s arguments in the proper order when calling a function; for example, the call pow(10,2) computes 10 2 = 100, but the call pow(2,10) computes 2 10 = 1,024.

A C++ program that uses any of the functions from the cmath library must use the following preprocessor # include directive:

#include <cmath>

Functions in the cmath library are ideal for solving problems like the one shown in Figure 8.4 Suppose a spacecraft is at a fixed location in space relative to some planet. The spacecraft’s distance to the planet, therefore, also is fixed. A satellite is orbiting the planet in a circular orbit. We wish to compute how much farther away the satellite will be from the spacecraft when it has progressed 10 degrees along its orbital path.

We will let the origin of our coordinate system (0,0) be located at the center of the planet which corresponds also to the center of the circular orbital path. The satellite is initially at point (xi,yi) and the spacecraft is stationary at point (p Xl p y ). The spacecraft is located in the same plane as the satellite’s orbit. We need to compute the difference in the distances between the moving point (satellite) and the fixed point (spacecraft) at two different times during the satellite’s orbit.

Facts from mathematics provide solutions to the following two problems:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 8.4 Orbital distance problem. In this diagram, the satellite begins at point [x\,y\), a distance of d\ from the spacecraft. The satellite’s orbit takes it to point ( X 2 ,yi ) after an angle of 0 rotation. The distance to its new location is d 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

Note 9

Note 10

Listing [8~4] (orbitdist.cpp) uses these mathematical results to compute the difference in the distances.

©2018 Richard L. Halterman

Draft date: September 25, 2018

double y; // satellite moves const double PI = 3.14159;

// Location of fixed point is always (100, 0),

// AKA (p_x, p_y). Change these as necessary.

const double p_x = 100; const double p_y = 0;

// Radians in 10 degrees

const double radians = 10 * PI/180;

// Precompute the cosine and sine of 10 degrees const double COS10 = cos(radians); const double SIN10 = sin(radians);

// Get starting point from user

std::cout << "Enter initial satellite coordinates (x,y):"; std::cin >> x >> y;

// Compute the initial distance

double dl = sqrt((p_x - x)*(p_x - x) + (p_y - y)*(p_y - y));

// Let the satellite orbit 10 degrees

double x_old = x; // Remember x's original value

x = x*COS10 - y*SIN10; // Compute new x value

// x's value has changed, but y's calculate depends on

// x's original value, so use x_old instead of x.

y = x_old*SIN10 + y*COS10;

// Compute the new distance

double d2 = sqrt((p_x - x)*(p_x - x) + (p_y - y)*(p_y - y)); // Print the difference in the distances

std::cout << "Difference in distances: " << d2 - dl << '\n' ;

We can use the square root function to improve the efficiency of our primes program. Instead of trying all the factors of n up to n — 1, we need only try potential factors up to the square root of n. Listing [83] (moreefficientprimes.cpp) uses the sq rt function to reduce the number of factors that need be considered.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// root of value

for (int trial_factor = 2;

is_prime && trial_factor <= root; trial_factor++) is_prime = (value % trial_factor != 0); if (is_prime)

std::cout << value << " // Display the prime number

}

std::cout << '\n'; // Move cursor down to next line

}

The sq rt function comes in three forms:

double sqrt(double)

float sqrt(float)

long double sqrt(long double)

The function names are the same, but the parameter types differ. We say that the sqrt function is overloaded. (Overloaded functions are covered in more detail in Section fl0.3;[ ) When a caller invokes the sq rt function, the compiler matches the call to the closest matching prototype. If the caller passes a double parameter, the compiler generates code to call the double version. If the caller instead passes a float variable, the compiler selects the float version of sqrt. When an i nt is passed to sqrt, the compiler cannot decide which version to use, because an i nt can be converted automatically to either a float, double, or long double. The compiler thus needs some help to resolve the ambiguity, so we introduced an additional variable of type double so the compiler will use the double version of the sqrt function. Another option is to use a type cast to convert the integer value into one of the types acceptable to the sqrt function.

Chapter Notes

2 The prototype for the actual library function max uses generic types', generic types are beyond the scope of this introductory book, so the prototype provided here is strictly for illustrating a point.

Draft date: September 25, 2018

1. Problem: We must recompute the location of the moving point as it moves along the circle.

Solution: Given an initial position (x\ ,yi) of the moving point, a rotation of 0 degrees around the origin will yield a new point at (x 2 ,}’ 2 ), where

X 2 = xicos0 — yjsin0 yi = xi sin0 + yi cos0

2. Problem: The distance between the moving point and the fixed point must be recalculated as the moving point moves to a new position.

Solution: The distance d\ in Figure 8.4 between two points (p x .p y ) and (xi .y \) is given by the formula

d\ = \! (Xl - P x ) 1 2 + Ol - Py ) 2

Similarly, the distance d 2 in Figure |8~4| is

di = \J{x 2 - p x ) 2 + (y 2 - Py ) 2

8.3 Maximum and Minimum

C++ provides standard functions for determining the maximum and minimum of two numbers. Listing j|8.6| (maxmin.cpp) exercises the standard mi n and max functions.

To use the standard max and min functions in a program you must include the <algorithm> header.

©2018 Richard L. Halterman

Draft date: September 25, 2018

8.4 clock Function

The clock function from the <cti me> library requests from the operating system the amount of time an executing program has been running. The units returned by the call clock () is system dependent, but it can be converted into seconds with the constant CLOCKS_PER_SEC, also defined in the cti me library. Under Visual C++, the CLOCKS_PER_SEC constant is 1,000, which means the call clock () returns the number of milliseconds that the program has been running.

Using two calls to the clock function you can measure elapsed time. Listing 8.7 (timeit.cpp) measures how long it takes a user to enter a character from the keyboard.

The type clock_t is a type defined in the <ctime> header file. clock_t is equivalent to an unsi gned long, and you can perform arithmetic on clock_t values and variables just as if they are unsigned longs. In the expression

static_cast<double> (other - seconds)/CLOCKS_PER_SEC

the cast is required to force floating-point division; otherwise, the result is truncated to an integer value.

Listing [18.8j (measureprimespeed.cpp) measures how long it takes a program to display all the prime numbers up to half a million using the algorithm from ListingjL7]|(forprintprimes.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

trial_factor++)

is_prime = (value % trial_factor != 0); if (is_prime)

std::cout << value << " // Display the prime number

}

std::cout << '\n'; // Move cursor down to next line

end_time = clock();

// Print the elapsed time

std::cout << "Elapsed time: "

<< static_cast<double> (end_time - start_time)/CLOCKS_PER_SEC << " sec." << '\n' ;

On one system, the program took 93 seconds, on average, to print all the prime numbers up to 500,000. By comparison, the newer, more efficient version, Listing [875j (moreefficientprimes.cpp), which uses the square root optimization takes only 15 seconds to display all the primes up to 500,000. Exact times will vary depending on the speed of the computer.

As it turns out, much of the program’s execution time is taken up printing the output, not computing the prime numbers to print. We can compare the algorithms better by redirecting the program’s output to a file. If the executable program is named primes.exe, you can redirect its output at the command line by issuing the command

primes > runl.out

This creates a text file named runl .out that can be viewed with any text editor. Its contents are exactly what would have been printed to the screen if the redirection is not used.

When run using redirection, the time difference is even more dramatic: The unoptimized version generates the prime numbers up to 500,000 in 77 seconds, while the optimized square root version requires only 2 seconds to generate the same number of primes! An even faster prime generator can be found in Listing |ll,25| (fasterprimes.cpp); it uses a completely different algorithm to generate prime numbers.

You must #i nclude the <cti me> header to use the standard ti me function in a program.

8.5 Character Functions

The C library provides a number of character functions that are useful to C++ programmers. Listing pk9| (touppercase.cpp) converts lowercase letters to uppercase letters.

The first lines printed by Listing|8.9j (touppercase.cpp) are

©2018 Richard L. Halterman

Draft date: September 25, 2018

a => A b => B c => C d => D

Interestingly, the toupper function returns an i nt, not a char. At the enhanced warning level 4 for Visual C++ a cast is required to assign the result to the variable upper:

char upper = static_cast<char> (toupper(lower));

Some of the more useful character functions are described in Table l8.2[

charfuncti ons Module

i nt toupper(int ch)

Returns the uppercase version of the given character; returns the original character if no uppercase version exists (such as for punctuation or digits) int tolower(int ch)

Returns the lowercase version of the given character; returns the original character if no lowercase version exists (such as for punctuation or digits) int isupper(int ch)

Returns a nonzero value (true) if c h is an uppercase letter (’ A ’ - ’ Z ’); otherwise, it returns 0 (false) _

int islower(int ch)

Returns a nonzero value (true) if ch is an lowercase letter (’ a ’ - ’ z ’); otherwise, it returns 0 (false) _

int isalpha(int ch)

Returns a nonzero value (true) if ch is a letter from the alphabet (’ A ’ - ’ Z ’ or ’ a ’ - ’ z ’); otherwise, it returns 0 (false) int isdigit(int ch)

Returns a nonzero value (true) if ch is a digit (’ 0 ’ - ’ 9 ’); otherwise, it returns 0 (false)

Table 8.2: A few of the functions from the cctype library

Other functions exist to determine if a character is a punctuation character like a comma or semicolon (ispunct), a space, tab, or newline character (isspace).

To use the standard C character functions in your C++ program, you must include the <cctype> header

file.

8.6 Random Numbers

Some applications require behavior that appears random. Random numbers are useful particularly in games and simulations. For example, many board games use a die (one of a pair of dice) to determine how many places a player is to advance. (See Figure [83] .) A die or pair of dice are used in other games of chance. A die is a cube containing spots on each of its six faces. The number of spots range from one to six. A player rolls a die or sometimes a pair of dice, and the side(s) that face up have meaning in the game being played. The value of a face after a roll is determined at random by the complex tumbling of the die. A software adaptation of a game that involves dice would need a way to simulate the random roll of a die.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 8.5 A pair of dice

All algorithmic random number generators actually produce pseudorandom numbers, not true random numbers. A pseudorandom number generator has a particular period, based on the nature of the algorithm used. If the generator is used long enough, the pattern of numbers produced repeats itself exactly. A sequence of true random numbers would not contain such a repeating subsequence. The good news is that all practical algorithmic pseudorandom number generators have periods that are large enough for most applications.

C++ programmers can use two standard C functions for generating pseudorandom numbers: srand and rand:

void srand (unsigned) int rand()

srand establishes the first value in the sequence of pseudorandom integer values. Each call to rand returns the next value in the sequence of pseudorandom values. Listing [8,10j| (simplerandom.cpp) shows how a sequence of 100 pseudorandom numbers can be printed.

The numbers printed by the program appear to be random. The algorithm is given a seed value to begin, and a formula is used to produce the next value. The seed value determines the sequence of numbers generated; identical seed values generate identical sequences. If you run the program again, the same sequence is displayed because the same seed value, 23, is used. In order to allow each program run to display different sequences, the seed value must be different for each run. How can we establish a different seed value for each run? The best way to make up a “random” seed at run time is to use the ti me function which is found in the cti me library. The call ti me (0) returns the number of seconds since midnight January 1, 1970.

©2018 Richard L. Halterman

Draft date: September 25, 2018

This value obviously differs between program runs, so each execution will use a different seed value, and the generated pseudorandom number sequences will be different. Listing j8dT| (betterrandom.cpp) incorporates the ti me function to improve its randomness over multiple executions.

Each execution of Listing (8.11 (betterrandom.cpp) produces a different pseudorandom number sequence. The actual type of value that ti me returns is ti me_t, so the result from a call to time must be cast to unsi gned i nt before being used with srand.

Notice that the numbers returned by rand can be rather large. The pseudorandom values range from 0 to a maximum value that is implementation dependent. The maximum value for Visual C++s rand function is 32,767, which corresponds to the largest 16-bit si gned i nt value. The cstdli b header defines the constant RAND_MAX that represents the largest value in the range. The following statement

std::cout << RAND_MAX << '\n' ;

would print the value of RAND_MAX for a particular system.

Ordinarily we need values in a more limited range, like 1...100. Simple arithmetic with the modulus operator can produce the result we need. If n is any nonnegative integer and in is any positive integer, the expression

n % m

produces a value in the range 0... m — 1.

This means the statement int r = rand() % 100;

can assign only values in the range 0...99 to r. If we really want values in the range 1...100, what can we do? We simply need only add one to the result:

int r = rand() % 100 + 1;

This statement produces pseudorandom numbers in the range 1... 100.

We now have all we need to write a program that simulates the rolling of a die.

Listing J8.12l|(die.cpp) simulates rolling die.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing8.12: die.cpp

#include <iostream>

#include <cstdlib>

#include <ctime>

int main() {

// Set the random seed value

srand (static_cast<unsigned> (time(0)));

// Roll the die three times for (int i = 0; i < 3; i++) {

// Generate random number in the range 1...6 int value = randQ % 6 + 1;

Table caption// Show the die

Table captionstd::cout << " +-+ \n";

Table captionswitch (value) { case 1:

std::cout

<<

II 1

I \n"

std::cout

<<

II 1

*

I \n"

std::cout break;

<<

II 1

I \n"

case 2:

std::cout

<<

II 1

*

I \n"

std::cout

<<

II 1

I \n"

std::cout break;

<<

II 1

*

I \n"

case 3:

std::cout

<<

II 1

*

I \n"

std::cout

<<

II 1

*

I \n"

std::cout break;

<<

II 1

*

I \n"

case 4:

std::cout

<<

II 1

*

*

I \n"

std::cout

<<

II 1

I \n"

std::cout break;

<<

II 1

*

*

I \n"

case 5:

std::cout

<<

II 1

*

*

I \n"

std::cout

<<

II 1

*

I \n"

std::cout break;

<<

II 1

*

*

I \n"

case 6:

std::cout

<<

II 1

*

*

*

I \n"

std::cout

<<

II 1

I \n"

std::cout

<<

II 1

*

*

*

I \n"

break; default :

std::cout << " *** Error: illegal die value ***\n";

break;

}

std::cout << "+-+ \n";

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

Since the values are pseudorandomly generated, actual output will vary from one run to the next.

8.7 Exercises

1. Suppose you need to compute the square root of a number in a C++ program. Would it be a good idea to write the code to perform the square root calculation? Why or why not?

2. In C++ source code what is one way to help you distinguish a variable name from a function name?

3. Which one of the following values could be computed by the rand function?

4.5 34 -1 RAND_MAX + 1

4. What does clock_t represent?

5. What does CLOCKS_PER_SEC represent?

6. Ordinarily how often should a program call the srand function?

7. In Listing 8.2 (standardsquareroot.cpp), what does the mai n function do while the sqrt function is computing the square root of the argument that mai n provides?

8. Consider each of the following code fragments below that could be part of a C++ program. Each fragment contains a call to a standard C/C++ library function. Answer each question in one of the following three ways:

• If the code fragment contains a compile-time error, write the word error for the answer.

• If the code fragment contains no compile-time errors and you can determine its output at compile-time, provide the fragment’s literal output.

• If the code fragment contains no compile-time errors but you cannot determine its exact output at compile-time, provide one possible evaluation and write the word example for the answer and provide one possible literal output that the code fragment could produce.

©2018 Richard L. Halterman

Draft date: September 25, 2018

(a)

std :

: cout

<<

sqrt(4.5) << '\n

1 .

3

(b)

std :

: cout

<<

sqrt(4.5, 3

.1) << '

\n '

(c)

std :

: cout

<<

rand(4) <<

' \n ' ;

(d)

double d =

16.0;

std:

: cout

<<

sqrt(d) <<

' \n ' ;

(e)

std:

: cout

<<

srand() <<

' \n ' ;

(f>

std:

: cout

<<

rand() << '

\n ' ;

(g)

int

i = 16

;

std :

: cout

<<

sqrt(i) <<

' \n ' ;

(h)

std :

: cout

<<

srand(55) << '\n

1 .

3

(i)

std :

: cout

<<

tolower ( 'A'

) «

' \n

1 .

3

(j)

std :

: cout

<<

exp () << ' \n ' ;

(k)

std :

: cout

<<

sqrt() << '

\ n ' ;

(1)

std :

: cout

<<

toupper( 'E'

) «

' \ n

1 .

3

(m)

std :

: cout

<<

toupper( 'e'

) «

' \ n

1 .

3

(n)

std :

: cout

<<

toupper ("e"

) «

' \n

1 .

3

(o)

std :

: cout

<<

exp(4.5) <<

' \n '

3

(P)

std :

: cout

<<

toupper( 'h'

, 5)

<<

' \n

(q)

std :

: cout

<<

ispunct( '!'

) «

' \n

1 .

3

(r)

std :

: cout

<<

tolower ("F"

) «

' \n

1 .

3

(s)

char

ch =

' D

.

3

std:

: cout

<<

tolower(ch)

<< '

\n'

3

(t)

std:

: cout

<<

exp(4.5, 3)

<< '

\n'

3

(u)

std:

: cout

<<

toupper( '7'

) «

' \n

1 .

3

(v)

double a =

5

b = 3;

Table captionstd::cout << exp(a, b) << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 8.6 Right triangle

(w)

std:

:cout <<

exp(3, 5, 2)

<<

'\

(X)

std:

:cout <<

tolower(70)

<< '

\n

(y)

double a = 5

3

std:

:cout <<

exp(a, 3) <<

' \n

1 .

3

(z)

double a = 5

3

std :

:cout <<

exp(3, a) <<

' \n

1 .

3

9. From geometry: Write a computer program that given the lengths of the two sides of a right triangle adjacent to the right angle computes the length of the hypotenuse of the triangle. (See Figure 8.6 ) If you are unsure how to solve the problem mathematically, do a web search for the Pythagorean theorem.

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 9

Writing Functions

As programs become more complex, programmers must structure their programs in such a way as to effectively manage their complexity. Most humans have a difficult time keeping track of too many pieces of information at one time. It is easy to become bogged down in the details of a complex problem. The trick to managing complexity is to break down the problem into more manageable pieces. Each piece has its own details that must be addressed, but these details are hidden as much as possible within that piece. The problem is ultimately solved by putting these pieces together to form the complete solution.

So far all of our programs have been written within one function—mai n. As the number of statements within a function increases, the function can become unwieldy. The code within such a function that does all the work by itself is called monolithic code. Monolithic code that is long and complex is undesirable for several reasons:

• It is difficult to write correctly. All the details in the entire piece of code must be considered when writing any statement within that code.

• It is difficult to debug. If the sequence of code does not work correctly, it is often difficult to find the source of the error. The effects of an erroneous statement that appears earlier in the code may not become apparent until a correct statement later uses the erroneous statement’s incorrect result.

• It is difficult to extend. All the details in the entire sequence of code must be well understood before it can be modified. If the code is complex, this may be a formidable task.

Using a divide and conquer strategy, a programmer can decompose a complicated function (like mai n) into several simpler functions. The original function can then do its job by delegating the work to these other functions. In this way the original function can be thought of as a “work coordinator.”

Besides their code organization aspects, functions allow us to bundle functionality into reusable parts. In Chapter[8jwe saw how library functions can dramatically increase the capabilities of our programs. While we should capitalize on library functions as much as possible, sometimes we need a function exhibiting custom behavior that is not provided by any standard function. Fortunately we can create our own functions, and the same function may be used (called) in numerous places within a program. If the function’s purpose is general enough and we write the function properly, we may be able to reuse the function in other programs as well.

©2018 Richard L. Halterman

Draft date: September 25, 2018

9.1 Function Basics

Recall the “handwritten” square root code we saw in Listing |8.11 (computesquareroot.cpp). We know that the better option is the standard library function sqrt; however, we will illustrate custom function development by writing our own square root function based on the code in Listing |8.1| (computesquareroot.cpp). In Listing |9T|(customsquareroot.cpp) we see the definition for the square_root function.

Table captionThe mai n function in Listing 9.1 (customsquareroot.cpp) compares the behavior of our custom square_root function to the sqrt library function. Its output:

1

1

1.22474

1.22474

1.41422

1.41421

1.58116

1.58114

1.73205

1.73205

1.87083

1.87083

2

2

2.12132

2.12132

2.23607

2.23607

2.34521

2.34521

2.44949

2.44949

2.54952

2.54951

2.64577

2.64575

2.73861

2.73861

2.82843

2.82843

2.91548

2.91548

Table caption©2018 Richard L. Halterman Draft date: September 25, 2018

3 : 3

3.08221 : 3.08221 3.16228 : 3.16228

shows a few small differences in the results. Clearly we should use the standard sqrt function instead of ours.

There are two aspects to every C++ function:

• Function definition. The definition of a function specifies the function’s return type and parameter types, and it provides the code that determines the function’s behavior. In Listing |9.1| (customsquareroot.cpp) the definition of the square_root function appears above the mai n function.

• Function invocation. A programmer uses a function via a function invocation. The main function invokes both our square_root function and the sqrt function. Every function has exactly one definition but may have many invocations.

A function definition consists of four parts:

• Name —every function in C++ has a name. The name is an identifier (see Section 3.31. As with variable names, the name chosen for a function should accurately portray its intended purpose or describe its functionality.

• Type —every function has a return type. If the function returns a value to its caller, its type corresponds to the type of the value it returns. The special type voi d signifies that the function does not return a value.

• Parameters —every function must specify the types of parameters that it accepts from callers. The parameters appear in a parenthesized comma-separated list like in a function prototype (see Section [OJ). Unlike function prototypes, however, parameters usually have names associated with each type.

• Body —every function definition has a body enclosed by curly braces. The body contains the code to be executed when the function is invoked.

Figure [9.1 [ dissects a our square_root function definition.

The simplest function accepts no parameters and returns no value to the caller. Listing j9.2| (simplefunction.cpp) is a variation of Listing||4.1j|(adder.cpp) that contains such a simple function definition.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 9.1 Function definition dissection

Type of value the function computes

Name of function

Type of value the function requires the caller to provide

Body of function

ble square_root (double x) {

// How bad is the approximation?

diff = root * root - x;

} while (diff > 0.0001 || diff < -0.0001); return root;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

promptQ; // Call the function again

std::cin >> value2; sum = valuel + value2;

std::cout << valuel << " + " << value2 << " = " << sum << '\n' ;

The prompt function simply prints a message. The program runs as follows:

1. The program’s execution, like in all C++ programs, begins with the first executable statement in the function named mai n. The first line in the mai n function simply declares some variables needed for compiler housekeeping, so the next line actually begins the executable code.

2. The first executable statement prints the message of the program’s intent.

3. The next statement is a call of the prompt function. At this point the program’s execution transfers to the body of the prompt function. The code within prompt is executed until the end of its body or until a return statement is encountered. Since prompt contains no return statement, all of prompt’s body (the one print statement) will be executed.

4. When prompt is finished, control is passed back to the point in mai n immediately after the call of prompt.

5. The next action after prompt call reads the value of valuel from the keyboard.

6. A second call to prompt transfers control back to the code within the prompt function. It again prints its message.

7. When the second call to prompt is finished, control passes back to mai n at the point of the second input statement that assigns value2 from the keyboard.

8. The remaining two statements in mai n are executed, and then the program’s execution terminates.

As another simple example, consider Listing |93| (countto10.cpp).

which simply counts to ten:

1

2

3

4

5

6

7

8

9

10

©2018 Richard L. Halterman

Draft date: September 25, 2018

If counting to ten in this way is something we want to do frequently within a program, we can write a function as shown in Listing |9.4| (countto1 Ofunc.cpp) and call it as many times as necessary.

Listing 9.4: counttolOfunc. cpp

#include <iostream>

//

Count to ten and print each number on its own line

voi

d count_to

_10() {

for (int

i = 1 ; i <= 10; i + + )

}

std: :

cout << i << ' \n 1 ;

int

main() {

std :: cout

<< "Going to count

to

ten . .

count_to_

i0();

std :: cout

<< "Going to count

to

ten again. .

count_to_

i0();

}

Our prompt and counttolQ functions are a bit underwhelming. The prompt function could be eliminated, and each call to prompt could be replaced with the statement in its body. The same could be said for the counttolQ function, although it is convenient to have the simple one-line statement that hides the complexity of the loop. Using the prompt function does have one advantage, though. If prompt is removed and the two calls to p r ompt are replaced with the print statement within prompt, we have to make sure that the two messages printed are identical. If we simply call prompt, we know the two messages printed will be identical because only one possible message can be printed (the one in the body of prompt).

We can alter the behavior of a function through a mechanism called parameter passing. If a function is written to accept information from the caller, the caller must supply the information in order to use the function. The caller communicates the information via one or more parameters as required by the function. The counttolQ function does us little good if we sometimes want to count up to a different number. Listing |93| (countton.cpp) generalizes Listing [9(4] (countto1 Ofunc.cpp) to count as high as the caller needs.

When the caller, in this case mai n, issues the call count_to_n(10);

©2018 Richard L. Halterman

Draft date: September 25, 2018

the argument 10 is assigned to n before the function’s statements begin executing.

A caller must pass exactly one integer parameter (or other type that is assignment-compatible with integers) to count_to_n during a call. An attempt to do otherwise will result in a compiler error or warning:

count_to_n(); // Error, missing parameter during the call

count_to_n(3, 5); // Error, too many parameters during the call

count_to_n(3.2); // Warning, possible loss of data (double to int)

We can enhance the prompt function’s capabilities as shown in Listing ]9)6| (betterprompt.cpp)

In this version, prompt takes care of the input, so mai n does not have to use any input statements. The assignment statement within mai n:

valuel = promptQ ;

implies prompt is no longer a voi d function; it must return a value that can be assigned to the variable valuel. Furthermore, the value that prompt returns must be assignment compatible with an i nt because valuel’s declared type is i nt. A quick look at the first line of prompt’s definition confirms our assumption:

int prompt()

This indicates that prompt returns an int value.

Because prompt is declared to return an i nt value, it must contain a retu rn statement. A retu rn statement specifies the exact value to return to the caller. When a return is encountered during a function’s execution, control immediately passes back to the caller. The value of the function call is the value specified by the return statement, so the statement

valuel = promptQ ;

assigns to the variable valuel the value indicated when the retu rn statement executs.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Note that in Listing 9.6 (betterprompt.cpp), we declared a variable named result inside the prompt function. This variable is local to the function, meaning we cannot use this particular variable outside of prompt. It also means we are free to use that same name outside of the prompt function in a different context, and that use will not interfere with the result variable within prompt. We say that result is a local variable.

We can further enhance our prompt function. Currently prompt always prints the same message. Using parameters, we can customize the message that prompt prints. Listing |9.7| (evenbetterprompt.cpp) shows how parameters are used to provide a customized message within prompt.

In Listing |977j| (evenbetterprompt.cpp), the parameter influences the message that it printed. The user is now prompted to enter value #1 or value #2. The call

valuel = prompt(l);

passes the value 1 to the prompt function. Since prompt’s parameter is named n, the process works as if the assignment statement

n = i;

were executed as the first action within prompt.

In the first line of the function definition: int prompt (int n)

n is called the formal parameter. A formal parameter is used like a variable within the function’s body, but it is declared in the function’s parameter list; it is not declared in the function’s body. A formal parameter is a parameter as used in the formal definition of the function.

At the point of the function call:

valuel = prompt(l);

the parameter (or argument) passed into the function, 1, is called the actual parameter. An actual parameter is the parameter actually used during a call of the function. When a function is called, any actual parameters

©2018 Richard L. Halterman

Draft date: September 25, 2018

are assigned to their corresponding formal parameters, and the function begin executing. Another way to say it is that during a function call, the actual parameters are bound to their corresponding formal parameters.

The parameters used within a function definition are called formal parameters. Formal parameters behave as local variables within the function’s body; as such, the name of a formal parameter will not conflict with any local variable or formal parameter names from other functions. This means as a function developer you may choose a parameter name that best represents the parameter’s role in the function.

If you are writing a function, you cannot predict the caller’s actual parameters. You must be able to handle any value the caller sends. The compiler will ensure that the types of the caller’s parameters are compatible with the declared types of your formal parameters.

To remember the difference between formal and actual parameters, remember this:

• A formal parameter is a parameter declared and used in a function’s formal definition.

• An actual parameter is a parameter supplied by the caller when the caller actually uses (invokes or calls) the function.

When the call

valuel = prompt(l);

is executed in mai n, and the statement

std::cout << "Please enter integer #" << n <<

within the body of prompt is executed, n will have the value 1. Similarly, when the call value2 = prompt(2);

is executed in mai n, and the statement

std::cout << "Please enter integer #" << n << ":

within the body of prompt is executed, n will have the value 2. In the case of valuel = prompt(l);

n within prompt is bound to 1, and in the case of value2 = prompt(2);

n within prompt is bound to 2.

©2018 Richard L. Halterman

Draft date: September 25, 2018

A function’s definition requires that all formal parameters be declared in the parentheses following the function’s name. A caller does not provide actual parameter type declarations when calling the function. Given the square_root function defined in Listing |9.1| (customsquareroot.cpp), the following caller code fragment is illegal:

double number = 25.0;

// Legal, pass the variable's value to the function

std::cout << square_root(number) << '\n' ;

// Illegal, do not declare the parameter during the call

std::cout << square_root (double number) << '\n 1 ;

The function definition is responsible for declaring the types of its parameters, not the caller.

9.2 Using Functions

The general form of a function definition is

type name ( parameterlist ) { body

}

• The type of the function indicates the type of value the function returns. Often a function will perform a calculation and the result of the calculation must be communicated back to the place where the function was invoked. The special type voi d indicates that the function does not return a value.

• The name of the function is an identifier (see Section |33) . The function’s name should indicate the purpose of the function.

• The parameterlist is a comma separated list of pairs of the form

type name

where type is a C++ type and name is an identifier representing a parameter. The caller of the function communicates information into the function via parameters. The parameters specified in the parameter list of a function definition are called formal parameters. A parameter is also known as an argument. The parameter list may be empty; an empty parameter list indicates that no information may be passed into the function by the caller.

• The body is the sequence of statements, enclosed within curly braces, that define the actions that the function is to perform. The statements may include variable declarations, and any variables declared within the body are local to that function.

The body may contain only one statement, many statements, or no statements at all; regardless, the curly braces always are required.

Observe that multiple pieces of information can be passed into a function via multiple parameters, but only one piece of information can be passed out of the function via the return value. Recall the greatest

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 9.2 Cutting plywood

<— 6 —>

a

18 inches

v

Figure 9.3 Squares too small

1

43^

3

f

Table caption<-24 inches->

Table captiona

Table caption18 inches

Table captionv

common divisor (also called greatest common factor) from elementary mathematics. To determine the GCD of 24 and 18 we list all of their common factors and select the largest one:

24: 1,2, 3, 4, [6], 8, 12,24 18: 1,2, 3, [6], 9, 18

The greatest common divisor function is useful when reducing fractions

18

to lowest terms; for example, consider the fraction —. The greatest common divisor of 18 and 24 is 6, and

18 4-6 3

so we divide the numerator and the denominator of the fraction by 6: - = -. The GCD function has

24 4- 6 4

applications in other areas besides reducing fractions to lowest terms. Consider the problem of dividing a piece of plywood 24 inches long by 18 inches wide into square pieces of maximum size without wasting any material. Since the GCD(24, 18) = 6, we can cut the plywood into twelve 6 inch x 6 inch square pieces as shown in Figure |Sh2)

If we cut the plywood into squares of any other size without wasting the any of the material, the squares would have to be smaller than 6 inches x 6 inches; for example, we could make forty-eight 3 inch x 3 inch

squares as shown in pieces as shown in Figure 9.3

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 9.4 Squares too large

<—9 in.—>

a

18 inches

\|/

<-24 inches->

Table caption-8 in.

Waste

Table caption<-24 inches->

Table captiona

Table caption18 inches

v

If we cut squares larger than 6 inches x 6 inches, not all the plywood can be used to make the squares. Figure |9.4| shows how some larger squares would fare.

In addition to basic arithmetic and geometry, the GCD function plays a vital role in cryptography, enabling secure communication across an insecure network.

Listing 9.8: gcdprog.cpp

#include <iostream> int main() {

// Prompt user for input

int numl, num2;

std::cout << "Please enter two integers: std::cin >> numl >> num2;

// Determine the smaller of numl and num2

int min = (numl < num2) ? numl : num2;

// 1 is definitely a common factor to all ints int largestFactor = 1;

©2018 Richard L. Halterman

Draft date: September 25, 2018

for (int i = 2; i <= min; i++)

if (numl 96 i == 0 && num2 96 i == 0)

largestFactor = i; // Found larger factor std::cout << largestFactor << '\n ' ;

Listing 9.8 (gcdprog.cpp) implements a straight-forward but naive algorithm that seeks potential factors by considering every integer less than the smaller of the two values provided by the user. This algorithm is not very efficient, especially for larger numbers. Its logic is easy to follow, with no deep mathematical insight required. Soon we will see a better algorithm for computing GCD.

If we need to compute the GCD from several different places within our program, we should package the code in a function rather than copying it to multiple places. The following code fragment defines a C++ function that that computes the greatest common divisor of two integers. It determines the largest factor (divisor) common to its parameters:

int gcd(int numl, int num2) {

// Determine the smaller of numl and num2 int min = (numl < num2) ? numl : num2;

// 1 is definitely a common factor to all ints

int largestFactor = 1;

for (int i = 2; i <= min; i++)

if (numl 96 i = = 0 && num2 96 i == 0)

largestFactor = i; // Found larger factor return largestFactor;

}

This function is named gcd and expects two integer arguments. Its formal parameters are named numl and num2. It returns an integer result. Its body declares three local variables: mi n, largestFactor, and i (i is local to the for statement). The last line in its body is a return statement. A return statement is required for functions that return a value. Avoid function is not required to have a retu r n statement. If a void function does have a retu r n statement, it must simply consist of retu rn followed by a semicolon (in other words, it cannot return a value, like gcd’s return statement does). A voi d function that does not contain a retu r n statement simply returns at the end of its body.

Recall from Section |6.5| that local variables have meaning only within their scope. This means that when you write a function you can name a local variable without fear that its name may be used already in another part of the program. Two different functions can use local variables named x, and these are two different variables that have no influence on each other. Anything local to a function definition is hidden to all code outside that function definition.

Since a formal parameter is a local variable, you can reuse the names of formal parameters in different functions without a problem.

It may seem strange that we can use the same name in two different functions within the same program to refer to two distinct variables. The block of statements that makes up a function definition constitutes a context for local variables. A simple analogy may help. In the United States, many cities have a street named Main Street ; for example, there is a thoroughfare named Main Street in San Francisco, California. Dallas, Texas also has a street named Main Street. Each city and town provides its own context for the use of the term Main Street. A person in San Francisco asking “How do I get to Main Street?” will receive the directions to San Francisco’s Main Street, while someone in Dallas asking the same question will receive Dallas-specific instructions. In a similar manner, assigning a variable within a function block localizes its identity to that function. We can think of a program’s execution as a person traveling around the U.S. When

©2018 Richard L. Halterman

Draft date: September 25, 2018

in San Francisco, all references to Main Street mean San Francisco’s Main Street, but when the traveler arrives in Dallas, the term Main Street means Dallas’ Main Street. A program’s thread of execution cannot execute more than one statement at a time, which means the compiler can use its current context to interpret any names it encounters within a statement. Similarly, at the risk of overextending the analogy, a person cannot be physically located in more than one city at a time. Furthermore, Main Street may be a bustling, multi-lane boulevard in one large city, but a street by the same name in a remote, rural township may be a narrow dirt road! Similarly, two like-named variables may have two completely different types. A variable named x in one function may represent an integer, while a different function may use a string variable named x.

Another advantage of local variables is that they occupy space in the computer’s memory only when the function is executing. Space is allocated for local variables and parameters when the function begins executing. When the function is finished and control returns to the caller, the variables and parameters go out of scope, and the memory they held is freed up for other purposes within the running program. This process of local variable allocation and deallocation happens each time a caller invokes the function. More information about how C++ handles memory management during a program’s execution can be found in Section lll8.ll

Once we have written a complete function definition we can use the function within our program. We invoke a programmer-defined function in exactly the same way as a standard library function like sqrt (Section 8.2) or rand (Section 8.6). If the function returns a value (that is, it is not declared void), then we can use its invocation anywhere an expression of that type is allowed. The parameters used for the function call are known as actual parameters. The function gcd can be called as part of an assignment statement:

int factor = gcd(val, 24);

This call uses the variable val as its first actual parameter and the literal value 24 as its second actual parameter. Variables, expressions, and literals can be freely used as actual parameters. The function then computes and returns its result. This result is assigned to the variable factor.

How does the function call and parameter mechanism work? It’s actually quite simple. The actual parameters, in order, are assigned (bound) to each of the formal parameters in the function definition, then control is passed to the body of the function. When the function’s body is finished executing, control passes back to the point in the program where the function was called. The value returned by the function, if any, replaces the function call expression. In the statement

int factor = gcd(val, 24);

an integer value is assigned to factor. The expression on the right is a function call, so the function is invoked to determine what to assign. The value of the variable val is assigned to the formal parameter numl, and the literal value 24 is assigned to the formal parameter num2. The body of the gcd function is then executed. When the return statement in the body is encountered, program execution returns back to where the function was called. The argument of the return statement becomes the value that is assigned to factor. This process of copying actual parameters to formal parameters works exactly like during assignment. This means the compiler, where possible, automatically will widen or narrow (see Section |4.2j ) the value of an actual parameter to make it compatible with its corresponding formal parameter; for example, if val is declared to a cha r, its value would automatically be copied to a temporary location and converted to an i nt. This temporary value would then be bound to the formal parameter numl. Note that gcd could be called from many different places within the same program, and, since different parameter values could be passed at each of these different invocations, gcd could compute a different result at each invocation.

Other invocation examples include:

©2018 Richard L. Halterman

Draft date: September 25, 2018

• std::cout << gcd(36, 24);

This example simply prints the result of the invocation. The value 36 is bound to numl and 24 is bound to num2 for the purpose of the function call. The value 12 will be printed, since 12 is the greatest common divisor of 36 and 24..

• x — gcd(x — 2, 24);

The execution of this statement would evaluate x - 2 and bind its value to numl. num2 would be assigned 24. The result of the call is then assigned to x. Since the right side of the assignment statement is evaluated before being assigned to the left side, the original value of x is used when calculating x - 2, and the function return value then updates x.

• x — gcd(x — 2, gcd(10, 8)) ;

This example shows two invocations in one statement. Since the function returns an integer value its result can itself be used as an actual parameter in a function call. Passing the result of one function call as an actual parameter to another function call is called function composition.

The compiler will report an error if a function call does not agree with the function’s definition. Possible problems include:

• Number of actual parameters do not agree with the number of formal parameters. The number of parameters must agree exactly. For example, the statement

int factor = gcd(24); // Error: too few parameters

is illegal given the above definition of gcd, since only one actual parameter is provided when two are required.

• Passing an actual parameter that is not assignment compatible with the formal parameter. For

example, passing the std : : cout object when an i nt has been defined, as in

int factor = gcd(36, std::cout); // Error: second parameter is wrong type The compiler will detect that std: :coutis not a valid int and report an error.

• Using the result in a context where an expression of that type is not allowed. For example, a function that returns void cannot be used where an int is expected:

std::cout << srand(2); // Error: srand does not return anything

The compiler will disallow this code.

9.3 Pass by Value

The default parameter passing mechanism in C++ is classified as pass by value , also known as call by value. This means the value of the actual parameter is copied to the formal parameter for the purpose of executing the function’s code. Since it is working on a copy of the actual parameter, the function’s execution cannot affect the value of the actual parameter owned by the caller.

Listing |9)9| (passbyvalue.cpp) illustrates the consequences of pass by value.

©2018 Richard L. Halterman

Draft date: September 25, 2018

For additional drama we chose to name the actual parameter the same as the formal parameter. Since the actual parameter and formal parameter are declared and used in different contexts and represent completely different memory locations, their names can be the same without any problems.

Listing SL9](passbyvalue.cpp) produces

Before increment, x = 5 Beginning execution of increment, x = 5 Ending execution of increment, x = 6 After increment, x = 5

The memory for the variable x in mai n is unaffected since i ncrement works on a copy of the actual parameter.

C++ supports another way of passing parameters called pass by reference. Pass by reference is introduced in Section ri0.9l

A function communicates its return value to the caller in the same way that the caller might pass a parameter by value. In the prompt function we saw earlier:

int prompt(int n) { int result;

std::cout << "Please enter integer #" << n << std::cin >> result; return result;

}

the return statement is return result;

The variable result is local to prompt. We informally may say we are returning the result variable, but, in fact, we really are returning only the value of the result variable. The caller has no access to

©2018 Richard L. Halterman

Draft date: September 25, 2018

the local variables declared within any function it calls. In fact, the local variables for a function exist only when the function is active (that is, executing). When the function returns to its caller all of its local variables disappear from memory. During subsequent invocations, the function’s local variables reappear when the function becomes active and disappear again when it finishes.

9.4 Function Examples

This section contains a number of examples of how we can use functions to organize a program’s code.

9.4.1 Better Organized Prime Generator

Listing [9.10|| (primefunc.cpp) is a simple enhancement of Listing |8.5|(moreefficientprimes.cpp). It uses the square root optimization and adds a separate i s_pri me function.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing |9T0| (primefunc.cpp) illustrates several important points about well-organized programs:

• The complete work of the program is no longer limited to the mai n function. The effort to test for primality is delegated to a separate function, ma i n is focused on a simpler task: generating all the numbers to be considered and using another function (is_prime)todo the hard work of determining if a given number is prime, main is now simpler and more logically coherent. A function is coherent when it is focused on a single task. Coherence is a desirable property of functions. If a function becomes too complex by trying to do too many different things, it can be more difficult to write correctly and debug when problems are detected. A complex function should be decomposed into several, smaller, more coherent functions. The original function would then call these new simpler functions to accomplish its task. Here, mai n is not concerned about how to determine if a given number is prime; main simply delegates the work to i s_pri me and makes use of the i s_pri me function’s findings.

• Each function is preceded by a thorough comment that describes the nature of the function. It explains the meaning of each parameter, and it indicates what the function should return. The comment for mai n may not be as thorough as for other functions; this is because mai n usually has no parameters, and it always returns a code to the operating system upon the program’s termination.

• While the exterior comment indicates what the function is to do, comments within each function explain in more detail how the function accomplishes its task.

The call to i S_pri me returns true or false depending on the value passed to it. This means we can express a condition like

if (is_prime(value) == true) . . . more compactly as

if (is_prime(value)) . . .

because if i s_pri me (value) is true, true == true is true, and if i s_pri me (value) is false, false == true is false. The expression i s_prime (value) suffices.

Just as it is better for a loop to have exactly one entry point and exactly one exit point, preferably a function will have a single return statement. Simple functions with a small number of returns are generally tolerable, however. Consider the following version of i s_pri me:

bool is_prime(int n) {

for (int trialFactor = 2;

trialFactor <= sqrt(static_cast<double> (n)); trialFactor++)

if (n % trialFactor == 0) // Is trialFactor a factor? return false; // Yes, return right away return true; // Tried them all, must be prime

}

This version uses two return statements, but eliminates the need for a local variable (result). Because a return statement exits the function immediately, no break statement is necessary. The two return statements are close enough textually in source code that the logic is fairly transparent.

©2018 Richard L. Halterman

Draft date: September 25, 2018

9.4.2 Command Interpreter

Some functions are useful even if they accept no information from the caller and return no result. Listing |9TTTj(calculator.cpp) uses such a function.

Listing9.11: calculator.cpp

ffinclude <iostream> ffinclude <cmath>

/*

* help_screen

* Displays information about how the program works

* Accepts no parameters

* Returns nothing */

Table captionvoid help_screen() {

std:

: cout

<<

"Add: Adds two

numbers\n" ;

std:

: cout

<<

" Example:

a 2.5 8.0\n" ;

std:

: cout

<<

"Subtract: Subtracts two numbers\n";

std:

: cout

<<

" Example:

s 10.5 8.0\n" ;

std:

: cout

<<

"Print: Displays the result of the latest

std:

: cout

<<

" Example:

p\n" ;

std:

: cout

<<

"Help: Displays

this help screen\n";

std:

: cout

<<

" Example:

h\n";

std:

: cout

<<

"Quit: Exits the program\n";

std:

: cout

<<

" Example:

q\ n " ;

/*

* menu

* Display a menu

* Accepts no parameters

* Returns the character entered by the user.

*/

char menu() {

// Display a menu

std::cout << "=== A)dd S)ubtract P)rint H)elp Q)uit ===\n";

// Return the char entered by user

char ch;

std::cin >> ch;

return ch;

/*

* mai n

* Runs a command loop that allows users to

* perform simple arithmetic.

*/

int main() {

double result = 0.0, argl, arg2;

bool done = false; // Initially not done

do {

switch (menu()) {

case 'A 1 : // Addition

©2018 Richard L. Halterman

Draft date: September 25, 2018

case 1 a 1 :

std::cin >> argl >> arg2; result = argl + arg2; std::cout << result << '\n'; break;

case 'S': // Subtraction

case 's':

std::cin >> argl >> arg2; result = argl - arg2;

// Fall through, so it prints the result case 'P' : // Print result

case 1 p 1 :

std::cout << result << '\n'; break;

case 1 H 1 : // Display help screen

case 1 h 1 :

help_screen(); break;

case 'Q 1 : // Quit the program

case 1 q 1 :

done = true; break;

}

}

while (!done);

}

The help_screen function needs no information from mai n, nor does it return a result. It behaves exactly the same way each time it is called. The menu function returns the character entered by the user.

9.4.3 Restricted Input

Listing fOj fbetterinputonly.cpp) forces the user to enter a value within a specified range. We now can easily adapt that concept to a function. Listing 9.12 (betterinputfunc.cpp) uses a function named get_i nt_ range that does not return until the user supplies a proper value.

©2018 Richard L. Halterman

Draft date: September 25, 2018

first = last; last = temp;

}

// Insist on values in the range first...last std::cout << "Please enter a value in the range "

<< first << "..." << last << ";

int in_value; // User input value bool bad_entry; do {

std::cin >> in_value;

bad_entry = (in_value < first || in_value > last); if (bad_entry) {

std::cout << in_value << " is not in the range "

<< first << "..." << last << '\n'; std::cout << "Please try again: ";

}

}

while (bad_entry);

// in_value at this point is guaranteed to be within range

return in_value;

/* *

* mai n

* Tests the get_int_range function */

int main() {

std::cout << get_int_range(10, 20) << ' \n' ; std::cout << get_int_range(20, 10) << '\n' ; std::cout << get_int_range (5, 5) << '\n'; std::cout << get_int_range(-100, 100) << '\n' ;

Note 1

Note 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

©2018 Richard L. Halterman

Note 9

9.4.4 Better Die Rolling Simulator

Listing9.13: betterdie.cpp

#include <iostream>

#include <cstdlib>

#include <ctime>

/*

* i rvi ti ali ze_di e

* Initializes the randomness of the die */

void initialize_die() {

// Set the random seed value

srand (static_cast<unsi gned>(time(0)));

}

/*

*

*

*

*

*/

void

show_die(spots)

Draws a picture of a die with number of spots indicated

spots is the number of spots on the top face

std::cout <<

"+

--4

\n

II .

5

switch (spots)

{

case 1:

std::cout

<<

"1

I \n"

std::cout

<<

"1

*

I \n"

std::cout break;

<<

"1

I \n"

case 2:

std::cout

<<

"1

*

I \n"

std::cout

<<

"1

I \n"

std::cout break;

<<

"1

*

I \n"

case 3:

std::cout

<<

"1

*

I \n"

std::cout

<<

"1

*

I \n"

std::cout break;

<<

"1

*

I \n"

case 4:

std::cout

<<

"1

*

*

I \n"

std::cout

<<

"1

I \n"

std::cout break;

<<

"1

*

*

I \n"

case 5:

std::cout

<<

"1

*

*

I \n"

std::cout

<<

"1

*

I \n"

std::cout break;

<<

"1

*

*

I \n"

case 6:

std::cout

<<

"1

*

*

*

I \n"

std :: cout

<<

"1

I \n"

std : :cout

<<

"1

*

*

*

I \n"

Table caption©2018 Richard L. Halterman

Draft date: September 25, 2018

break; default :

std::cout << " *** Error: illegal die value ***\n";

break;

}

std::cout << " +-+ \n";

}

/*

* roll

* Returns a pseudorandom number in the range 1...6 */

int roll() {

return rand() % 6 + 1;

}

/*

* mai n

* Simulates the roll of a die three times */

int main() {

// Initialize the die initialize_die();

// Roll the die three times for (int i = 0; i < 3; i++) show_die(roll()) ;

In Listing 9.13 (betterdie.cpp), mai n is no longer concerned with the details of pseudorandom number generation, nor is it responsible for drawing the die. These important components of the program are now in functions, so their details can be perfected independently from mai n.

Note how the result of the call to roll is passed directly as an argument to show_di e.

9.4.5 Tree Drawing Function

©2018 Richard L. Halterman

Draft date: September 25, 2018

count++;

}

// Print out stars, twice the current row plus one: // 1. number of stars on left side of tree

// = current row value

// 2. exactly one star in the center of tree

// 3. number of stars on right side of tree

// = current row value

count = 0;

while (count < 2*row + 1) { std: :cout << ;

count++;

}

// Move cursor down to next line std::cout << '\n 1 ;

// Change to the next row

row++;

}

}

/*

* mai n

* Allows users to draw trees of various heights */

int main() {

int height; // Height of tree std::cout << "Enter height of tree: std::cin >> height; // Get height from user tree(height);

}

Observe that the name hei ght is being used as a local variable in mai n and as a formal parameter name in tree. There is no conflict here, and the two hei ghts represent two different locations in memory. Furthermore, the fact that the statement

tree(height) ;

uses mai n’s hei ght as an actual parameter and hei ght happens to be the name as the formal parameter is simply a coincidence. During the call, the value of mai n’s hei ght variable is copied into to the formal parameter in tree also named hei ght. The compiler can keep track of which hei ght is which based on where each is declared.

9.4.6 Floating-point Equality

Recall from Listing) 4T7| |(imprecise5th.cpp) that floating-point numbers are not mathematical real numbers; a floating-point number is finite, and is represented internally as a quantity with a binary mantissa and exponent. Just as 1/3 cannot be represented finitely in the decimal (base 10) number system, 1/10 cannot be represented exactly in the binary (base 2) number system with a fixed number of digits. Often, no problems arise from this imprecision, and in fact many software applications have been written using floating-point numbers that must perform precise calculations, such as directing a spacecraft to a distant planet. In such cases even small errors can result in complete failures. Floating-point numbers can and are used safely and effectively, but not without appropriate care.

©2018 Richard L. Halterman

Draft date: September 25, 2018

To build our confidence with floating-point numbers, consider Listing ||97T5']| (simplefloataddition.cpp), which increments a double-precision floating-point number by a double-precision floating-point amount and then checks it against a given value.

All seems well judging by the output of Listing[9.15| (simplefloataddition.cpp):

OK

Next, consider Listing |~9X6| (badfloatcheck.cpp) which attempts to control a loop with a double-precision floating-point number.

When compiled and executed. Listing |9.16[ (badfloatcheck.cpp) begins as expected, but it does not end as expected:

i = 0 i = 0.1 i = 0.2 i = 0.3 i = 0.4 i = 0.5 i = 0.6 i = 0.7 i = 0.8 i = 0.9 i = 1 i = 1.1 i = 1.2 i = 1.3 i = 1.4 i = 1.5 i = 1.6 i = 1.7

©2018 Richard L. Halterman

Draft date: September 25, 2018

i = 1.8 i = 1.9 i=2 i = 2.1

We expect it stop when the loop variable i equals 1, but the program continues executing until the user types Ctrl-C. We are adding 0.1, just as in Listing ||97T5| (simplefloataddition.cpp), but now there is a problem. Since 0.1 cannot be represented exactly within the constraints of the double-precision floating-point representation, the repeated addition of 0.1 leads to round off errors that accumulate over time. Whereas 0.1 + 0.9 rounded off may equal 1, 0.1 added to itself 10 times may be 1.000001 or 0.999999, neither of which is exactly 1.

Listing! |j9.16| (badfloatcheck.cpp) demonstrates that the == and ! = operators are of questionable worth when comparing floating-point values. The better approach is to check to see if two floating-point values are close enough, which means they differ by only a very small amount. When comparing two floatingpoint numbers x and v, we essentially must determine if the absolute value of their difference is small; for example, \x — y\ < 0.00001. The C abs function was introduced in Section 8.2 and we can incorporate it into an equals function, as shown in Listing|9.17|(floatequals.cpp).

The third parameter, named tolerance, specifies how close the first two parameters must be in order to be considered equal. The == operator must be used for some special floating-point values such as HUGE_VAL, so the function checks for == equality as well. Since C++ uses short-circuit evaluation for Boolean expressions involving logical OR (see Section |5i2) , if the == operator indicates equality, the more elaborate check is not performed.

You should use a function like equals when comparing two floating-point values for equality.

©2018 Richard L. Halterman

Draft date: September 25, 2018

9.4.7 Multiplication Table with Functions

When we last visited our multiplication table program in Listing |j7.5| (bettertimestable.cpp), we used nested for loops to display a user-specified size. We can decompose the code into functions as shown in Listing ^TOj(timestablefunction.cpp). Our goal is to have a collection of functions that each are very simple. We also want the program’s overall structure to be logically organized.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Print the body of the n x n multiplication table void print_contents (i nt n) {

for (int current_row = 1; current_row <= n; current_row++) print_row(current_row, n);

}

// Print a multiplication table of size n x n. void timestable(int n) {

// First, print column heading col_header(n);

// Print table contents

print_contents(n) ;

}

// Forces the user to enter an integer within a // specified range first is either a minimum or maximum // acceptable value last is the corresponding other end // of the range, either a maximum or minimum value // Returns an acceptable value from the user int get_int_range (i nt first, int last) {

// If the larger number is provided first,

// switch the parameters if (first > last) { int temp = first; first = last; last = temp;

}

// Insist on values in the range first...last std::cout << "Please enter a value in the range "

<< first << "..." << last << ";

int in_value; // User input value bool bad_entry; do {

std::cin >> in_value;

bad_entry = (in_value < first || in_value > last); if (bad_entry) {

std::cout << in_value << " is not in the range "

<< first << "..." << last << '\n' ; std::cout << "Please try again: ";

}

}

while (bad_entry) ;

// in_value at this point is guaranteed to be within range return in_value;

}

int main() {

// Get table size from user; allow values in the // range 1... 18.

int size = get_int_range(l, 18);

// Print a size x size multiplication table timestable(size);

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 9.5 A trace of the activation of the various functions in Listing 9.18 ftimestablefunction.cpp) when the user enters 3 for a 3 x 3 multiplication table. Time flows from left to right. The horizontal bars show the lifetimes of the various functions involved.

timestablefunc. cpp Function Call Sequence

^ Program Execution Timeline ^

.

1,18 3

.

a

3

get int range

timestable

3

i

3

l

col header

print contents

3

1 L

i

3

1,3

2,3

4i

3,3

i

r

y

col.

.numbers

print line

print row

print row

print row

1

2

3

row header

row header

row header

In Listing 9.18 (timestablefunction.cpp), each function plays a very specific role; for example, row_ header prints the label for a particular row and then prints the vertical bar that separates the row label from the body of the table. We reuse the get_i nt_range function from Listing 9.12 (betterinputfunc.cpp). Notice that there no longer appear to be any nested loops in the program. The nested loop is not really gone, it now is hidden by the program’s functional composition. Observe that the p r i nt_contents function contains a loop. Each time through the loop it calls pri nt_row, but pri nt_row itself contains a loop. The nested iteration, therefore, is still present.

Realistically, the functional decomposition within Listing |9.18| (timestablefunction.cpp) is extreme. The relative simplicity of the program does not not really justify eight separate functions each with such a narrow focus; however, more complex software systems are decomposed in this very manner. Not only does Listing [9T8 (timestablefunction.cpp) give us insight into how we can take a complicated problem and break it down into simpler, more manageable pieces, we can use the program to better understand how the function invocation process works. To see how, consider the situation where a user wishes to print a 3 x 3 multiplication table using Listing 9T8|(timestablefunction.cpp).

In Figure [93] an arrow pointing down corresponds to a function call. The labels on the down arrows represent parameters passed during the call. The up arrows indicate the return from a function. The label on an up arrow is the function’s return value. Functions of type void have no labels on their return arrows.

Each horizontal bar in Figure |9.5|represents the duration of the program’s execution that the function

is active. The mai n function always is the first function executed in a C++ program, and in Listing 9.18

(timestablefunction.cpp) mai n immediately calls the get_i nt_range function. During the lifetime of get_i nt_range’s execution notice that main is still active. This means any local variables it may maintain are still stored in memory and have not lost their values. This means that mai n’s value variable

©2018 Richard L. Halterman

Draft date: September 25, 2018

exists for the effective life of the program. This is not true for the variables used in get_i nt_range: temp, in_value, bad_entry, and the parameters first and last. These variables maintained by get_int_range appear automatically when get_i nt_range begins executing (the left end of its bar) and their space is released when get_i nt_range is finished (the right end of its bar; 1 During the printing of a 3 x 3 table the program calls pri nt_row three times, and for each call the function's parameters row and column and local variable col come to life and then disappear when the function returns.

Chapter Notes

Listing |9.12| (betterinputfunc.cpp) forces the user to enter a value within a specified range. This functionality could be useful in many programs.

In Listing ||9.12| (betterinputfunc.cpp)

• The high and low values are specified by parameters. This makes the function more flexible since it could be used elsewhere in the program with a completely different range specified and still work correctly.

• The function is supposed to be called with the lower number passed as the first parameter and the higher number passed as the second parameter. The function will also accept the parameters out of order and automatically swap them to work as expected; thus,

num = get_int_range(20, 50);

will work exactly like

num = get_int_range(50, 20);

• The Boolean variable bad_entry is used to avoid evaluating the Boolean expression twice (once to see if the bad entry message should be printed and again to see if the loop should continue).

Draft date: September 25, 2018

9.5 Organizing Functions

The code we have seen so far provides a function definition before its invocation. Listing pT9| (organization1 .cpp) organizes its functions this way.

When the compiler attempts to parse the following statement: std::cout << twice(5) << ' \n ’ ;

it needs to be able to determine if the expression twice (5) is valid in the given context; that is, it must determine if the expression twi ce (5) evaluates to something that can be sent to the std : : cout object using the << operator. The following points are important in the parsing process:

• The earlier definition of the twi ce function declares the identifier twi ce to the compiler. Consequently the compiler expects a caller to twi ce to pass a single argument that is compatible with the i nt type. The compiler also knows that the call to twi ce will return an integer value.

• The parentheses after the name twi ce in the statement indicate the expression is a function call.

• Within the parentheses is the integer literal 5, which clearly is compatible with the i nt type.

• The expression twi ce (5) thus evaluates to an i nt, and the << operator can send integer values to the std : : cout output stream object.

The compiler thus can verify that the code within the main function is using the twi ce function correctly.

If we instead place twi ce’s definition after the mai n function’s definition, the compiler will report an error where twi ce’s call appears within mai n. This is because the compiler parses C++ source code line by line from top to bottom within the .cpp file. When the compiler sees the identifier twice first at its

'Technically, the run-time environment does not allocate the space for a local variable until after its point of declaration. For variables declared within blocks, like temp with the i f body, the variable is discarded at the end of the block’s execution.

©2018 Richard L. Halterman

Draft date: September 25, 2018

invocation within mai n, it is an undefined symbol. The compiler needs to know a function’s return type and parameter types in order to verify that the caller is invoking the function correctly.

As it turns out, we can satisfy the compiler’s need to know about the twi ce function as used in mai n without providing its full definition. Listing |I9.20I| (organization2.cpp) provides a alternate organization of the source code in Listing |9.19|| (organization1 .cpp).

The statement int twice (int) ;

is a prototype that serves as a function declaration. It essentially is a function definition without the function’s body. A semicolon terminates the declaration, and no curly braces appear in a function declaration. We can provide a name the parameter, but that is not necessary. A function declaration provides all the information the compiler needs to determine if a caller is invoking the function correctly. The function is available to any callers that appear after the declaration within the source file.

Listing |9.21 [(organizations.cpp) provides a slight variation of Listingl9.20|[(organization2.cpp).

makes twice’s declaration local to main. This means that any code within main that appears after twi ce’s declaration can use twi ce, but code outside of main cannot (unless other functions themselves independently provide their own declaration of twi ce. Listing 9.22 (localfuncdefl .cpp) and Listing 9.23 (localfuncdef2.cpp) provide a concrete example of the difference between a local and a global declaration.

Listing 9.22: localfuncdefl. cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <iostream>

// Global declarations available to all functions that follow the declarations int two_times(int); int three_times(int);

int main() {

std::cout << two_times(5) << '\n'; std::cout << three_times(5) << '\n';

}

int three_times(int n) {

return two_times(n) + n; // 3n = 2n + n

}

int two_times(int n) { return 2 * n;

}

The declaration of two_ti mes appears above and outside of both main and three_ti mes, and so both mai n and three_ti mes may legitimately call two_ti mes.

The declaration for the two_times function given in main in Listing 9.23 (localfuncdef2.cpp) is not visible in the three_ti mes function; thus, the program will not compile.

Note that while C++ allows us to declare a function within the body of another function, it does not allow us to define a function inside the body of another function. C++ does not support nested function definitions.

Some programmers prefer to declare all their functions before their use within the program (as in Listing |9.20[ (organization2.cpp) or Listing |9.21l| (organizations.cpp)) and define the functions after their use

©2018 Richard L. Halterman

Draft date: September 25, 2018

within main. They argue that this better represents the way the compiled code executes—the ma i n method begins running first, and it calls the other functions. As we read the source code from top to bottom we see the details of the mai n function before seeing the implementation details of the functions that mai n calls.

A more frequent way to organize functions within C++ source code is to separate function declarations, function invocations, and function definitions into their own distinct files. The function declarations go into one or more .h header files, the function definitions appear in one or more .cpp files, and the calling code (including mai n) appear in a separate .cpp file. The compiler compiles all the .cpp files separately, producing multiple machine language object files (.obj files in Visual C++). The linker then combines these separate object files into a single executable file. Section|l0.6||covers this technique is detail.

9.6 Commenting Functions

It is good practice to comment a function’s definition with information that aids programmers who may need to use or extend the function. The essential information includes:

• The purpose of the function. The function’s purpose is not always evident merely from its name. This is especially true for functions that perform complex tasks. A few sentences explaining what the function does can be helpful.

• The role of each parameter. The parameter names and types are obvious from the definition, but the purpose of a parameter may not be apparent merely from its name. It is helpful indicate the purpose of each parameter, if any.

• The nature of the return value. While the function may do a number of interesting things as indicated in the function’s purpose, what exactly does it return to the caller? It is helpful to clarify exactly what value the function produces, if any.

Other information is often required in a commercial environment:

• Author of the function. Specify exactly who wrote the function. An email address can be included. If questions about the function arise, this contact information can be invaluable.

• Date that the function’s implementation was last modified. An additional comment can be added each time the function is updated. Each update should specify the exact changes that were made and the person responsible for the update.

• References. If the code was adapted from another source, list the source. The reference may consist of a Web URL.

The following fragment shows the beginning of a well-commented function definition:

/*

Table caption* distance (xl, yl, x2, y2)

Table caption* Computes the distance between two geometric points

xl

i s

the

X

coordinate

of

the

f i rst

poi nt

*

yi

i s

the

y

coordinate

of

the

f i rst

poi nt

x2

i s

the

X

coordinate

of

the

second

poi nt

y2

i s

the

y

coordinate

of

the

second

poi nt

Table caption* Returns the distance between (xl,yl) and (x2,y2)

Table caption* Author: Toe Algori (joe@eng-sys.net)

©2018 Richard L. Halterman

Draft date: September 25, 2018

* Last modified: 2010-01-06

* Adapted from a formula published at

* http://en.wikipedia.org/wiki/Distance */

double distance (double xl, double yl, double x2, double y2) {

From the information provided

• callers know what the function can do for them,

• callers know how to use the function,

• subsequent programmers can contact the original author if questions arise about its use or implementation,

• subsequent programmers can check the Wikipedia reference if questions arise about its implementation, and

• subsequent programmers can judge the quality of the algorithm based upon its source of inspiration (in this case, Wikipedia).

9.7 Custom Functions vs. Standard Functions

Armed with our knowledge of function definitions, we can rewrite Listing |8.l| (computesquareroot.cpp) so the program uses a custom square root function. Listingj [9(24j (squarerootfunction.cpp) shows one possibility.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

std: : ci n >> input;

// Report square root

std::cout << "Square root of " << input << " << square_root(input) << '\n';

II

Is Listing l9.24| (squarerootfunction.cpp) better than Listing l8.2| (standardsquareroot.cpp) which uses the standard sqrt function from the cmath library? Generally speaking, if you have the choice of using a standard library function or writing your own custom function that provides the same functionality, choose to use the standard library routine. The advantages of using the standard library routine include:

• Your effort to produce the custom code is eliminated entirely; you can devote more effort to other parts of the application’s development.

• If you write your own custom code, you must thoroughly test it to ensure its correctness; standard library code, while not immune to bugs, generally has been subjected to a complete test suite. Library code is used by many developers, and thus any lurking errors are usually exposed early; your code is exercised only by the programs you write, and errors may not become apparent immediately. If your programs are not used by a wide audience, bugs may lie dormant for a long time. Standard library routines are well known and trusted; custom code, due to its limited exposure, is suspect until it gains wider exposure and adoption.

• Standard routines are typically tuned to be very efficient; it takes a great deal of effort to make custom code efficient.

• Standard routines are well-documented; extra work is required to document custom code, and writing good documentation is hard work.

Listing f9.25| (squarerootcomparison.cpp) tests our custom square root function over a range of 1,000,000,000 floating-point values.

Listing 9.25: squarerootcompari son. cpp

#include <iostream> ttinclude <cmath>

// Consider two floating-point numbers equal when // the difference between them is very small, bool equals (double a, double b, double tolerance) { return a == b | | fabs(a - b) < tolerance;

}

double square_root (double x) {

// Compute a provisional square root double root = 1.0;

do { // Loop until the provisional root

// is close enough to the actual root root = (root + x/root) / 2.0;

}

while (!equals(root*root, x, 0.0001)); return root;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

int mainQ {

for (double d = 0.0; d < 100000.0; d += 0 . 0001 ) { if (!equals(square_root(d), sqrt(d), 0.001))

std::cout << d << Expected " << sqrt(d) << ", but computed " << square_root(d) << '\n';

}

}

Listing 9.25 (squarerootcomparison.cpp) uses our equals function from Listing 9.17 (floatequals.cpp). The third parameter specifies a tolerance; if the difference between the first two parameters is less than the specified tolerance, the first two parameters are considered equal. Our new custom square_root function uses the equals function. The main function uses the equals function as well. Observe, however, that the tolerance used within the square root computation is smaller than the tolerance main uses to check the result. The main function, therefore, uses a less strict notion of equality.

Table captionThe output of Listing|9T25|(squarerootcomparison.cpp):

0: Expected 0, but computed

0.0078125

0.0001:

Expected 0.01, but

computed 0.0116755

0.0008:

Expected 0.0282843,

but computed 0.0298389

0.0009:

Expected 0.03, but

computed 0.0313164

0.001:

Expected 0.0316228,

but computed 0.0327453

shows that our custom square root function produces results outside of mai n’s acceptable tolerance for five values. Five wrong answers out of one billion tests represents a 0.0000005% error rate. While this error rate is very small, indicates our square_root function is not perfect. One of values that causes the function to fail may be very important to a particular application, so our function is not trustworthy.

9.8 Exercises

1. Is the following a legal C++ program?

int proc(int x) { return x + 2;

}

int proc(int n) { return 2*n + 1;

}

int mainQ {

int x = proc(5);

}

2. Is the following a legal C++ program?

int proc(int x) { return x + 2;

}

int mainQ {

©2018 Richard L. Halterman

Draft date: September 25, 2018

int x = proc(5) , y = proc (4);

}

3. Is the following a legal C++ program?

#include <iostream>

void proc(int x) {

std::cout << x + 2 << '\n' ;

}

int mainQ {

int x = proc(5) ;

}

4. Is the following a legal C++ program?

#include <iostream>

void proc(int x) {

std::cout << x + 2 << '\n' ;

}

int mainQ { proc (5);

}

5. Is the following a legal C++ program?

#include <iostream>

int proc (int x, int y) { return 2*x + y*y;

}

int mainQ {

std::cout << proc(5, 4) << ' \ n' ;

}

6. Is the following a legal C++ program?

#include <iostream>

int proc (int x, int y) { return 2*x + y*y;

}

int mainQ {

std::cout << proc(5) << '\n' ;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

7. Is the following a legal C++ program?

#include <iostream>

int proc(int x) { return 2*x*x;

}

int mainQ {

std::cout << proc(5, 4) << '\n' ;

}

Table caption8. Is the following a legal C++ program?

#include

<iostream>

proc (i nt

x) {

std:

:cout << 2*

}

i nt

mai n

0 {

proc

(5);

}

9. The programmer was expecting the following program to print 200. What does it print instead? Why does it print what it does?

#include <iostream>

void proc(int x) { x = 2*x*x;

}

int mainQ {

int num = 10; proc(num);

std::cout << num << '\n' ;

}

10. Is the following program legal since the variable x is used in two different places (proc and mai n)? Why or why not?

#include <iostream>

int proc(int x) { return 2*x*x;

}

int mainQ {

int x = 10;

std::cout << proc(x) << '\n' ;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

11. Is the following program legal since the actual parameter has a different name from the formal parameter (y vs. x)? Why or why not?

#include <iostream>

int proc(int x) { return 2*x*x;

}

int main() {

int y = 10;

std::cout << proc(y) << '\n' ;

}

12. Complete the distance function started in Section 9.6 Test it with several point coordinates to convince yourself that your implementation is correct.

13. What happens if a caller passes too many parameters to a function?

14. What happens if a caller passes too few parameters to a function?

15. What are the rules for naming a function in C++?

16. Consider the following function definitions: #include <iostream>

int funl(int n) { int result = 0; while (n) {

result += n;

n—;

}

return result;

}

void fun2(int stars) {

for (int i = 0; i < stars; i++) std::cout << "*" ; std::cout << '\n' ;

}

double fun3(double x, double y) { return 2*x*x + 3*y;

}

bool fun4(char ch) {

return ch > = 'A' && ch <= 'Z' ;

}

bool fun5(int a, int b, int c) {

return (a <= b) ? (b <= c) : false;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

int fun6() {

return rand() % 2;

}

Examine each of the following print statements. If the statement is illegal, explain why it is illegal; otherwise, indicate what the statement will print.

(a)

std:

: cout

<<

funl(5) <<

' \n

1 .

3

(b)

std:

: cout

<<

funl() <<

' \n'

3

(c)

std:

: cout

<<

funl(5, 2)

<<

' \n

1 .

3

(d)

std:

: cout

<<

fun2(5) <<

' \n

1 .

3

(e)

fun2(5);

(f)

std:

: cout

<<

fun3(5, 2)

<<

' \n

1 .

3

(g)

std:

: cout

<<

fun3(5.0,

2.0)

<<

' \n' ;

(h)

std:

: cout

<<

fun3( 'A' ,

’ B ’ )

<<

' \n' ;

(i)

std:

: cout

<<

fun3(5.0)

<< '

\n'

3

(j)

std:

: cout

<<

fun3(5.0,

0.5,

l.:

2) <<

(k)

std :

: cout

<<

fun4( 'T' )

<< '

\n'

3

0)

std:

: cout

<<

fun4( 't' )

<< '

\n'

3

(m)

std :

: cout

<<

fun4(5000)

<<

' \n

1 .

3

(n)

fun4(5000) ;

(o)

std :

: cout

<<

fun5(2, 4,

6)

<<

' \n' ;

(P)

std :

: cout

<<

fun5(4, 2,

6)

<<

' \n' ;

(q)

std :

: cout

<<

fun5(2, 2,

6)

<<

' \n' ;

(r)

std :

: cout

<<

fun5(2, 6)

<<

' \ n

1 .

3

Table caption(s) if (fun5(2, 2, 6))

Table captionstd::cout << "Yes\n"; else

std::cout

<< "No\n";

(t)

std

::cout

<<

fun6() << '\n' ;

(u)

std

::cout

<<

fun6(4) << '\n' ;

(v)

std

::cout

<<

fun3(funl(3), 3)

<<

' \n' ;

(w)

std

::cout

<<

fun3(3, funl(3))

<<

' \n' ;

(X)

std

::cout

<<

funl(funl(funl(3)))

« '\n' ;

(y)

std

::cout

<<

fun6(fun6()) <<

' \n 1

3

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 10

Managing Functions and Data

This chapter covers some additional aspects of functions in C++. Recursion, a key concept in computer science is introduced.

10.1 Global Variables

All variables to this point have been local to functions or local to blocks within the bodies of conditional or iterative statements. Local variables have some very desirable properties:

• A local variable occupies memory only when the variable is in scope. When the program execution leaves the scope of a local variable, it frees up the memory for that variable. This freed up memory is then available for use by the local variables in other functions during their invocations.

• We can use the same variable name in different functions without any conflict. The compiler derives all of its information about a local variable used within a function from the declaration of that variable in that function. The compiler will not look for the declaration of a local variable in the definition of another function. Thus, there is no way a local variable in one function can interfere with a local variable declared in another function.

A local variable is transitory, so its value is lost in between function invocations. Sometimes it is desirable to have a variable that lives as long as the program is running; that is, until the main function completes. In contrast to a local variable, a global variable is declared outside of all functions and is not local to any particular function. In fact, any function that appears in the text of the source code after the point of the global variable’s declaration may legally access and/or modify that global variable.

Listing fK)T|| (globalcalculator.cpp) is a modification of Listing [970] (calculator.cpp) that uses a global variable named result that is shared by several functions in the program.

Listing 10.1: globalcalculator. cpp

ffinclude <iostream> #include <cmath>

/*

* help_screen

©2018 Richard L. Halterman

Draft date: September 25, 2018

* Displays information about how the program works

* Accepts no parameters

* Returns nothing */

Table captionvoid help_screen() {

std:

: cout

<<

"Add: Adds two

numbers\n" ;

std:

: cout

<<

" Example:

a 2.5

8.0\n" ;

std:

: cout

<<

"Subtract: Subtracts

two numbers\n";

std:

: cout

<<

" Example:

s 10.

5 8.0\n" ;

std:

: cout

<<

"Print: Displays the

result of the latest

std:

: cout

<<

" Example:

P\n" ;

std:

: cout

<<

"Help: Displays

thi s

help screen\n";

std:

: cout

<<

" Example:

h\n" ;

std:

: cout

<<

"Quit: Exits the program\n";

std:

: cout

<<

" Example:

q\ n " ;

}

/*

* menu

* Display a menu

* Accepts no parameters

* Returns the character entered by the user.

*/

char menuQ {

// Display a menu

std::cout << "=== A)dd S)ubtract P)rint H)elp Q)uit ===\n";

// Return the char entered by user

char ch;

std::cin >> ch;

return ch;

/*

* Global variables used by several functions */

double result = 0.0, argl, arg2;

/*

* get_input

* Assigns the globals argl and arg2 from user keyboard

* input */

void get_input() {

std::cin >> argl >> arg2;

}

/*

* report

* Reports the value of the global result */

void report() {

std::cout << result << ' \n';

}

/*

©2018 Richard L. Halterman

Draft date: September 25, 2018

* add

* Assigns the sum of the globals argl and arg2 to the global variable result

*/

void add() {

result = argl + argl;

}

/*

* subtract

* Assigns the difference of the globals argl and arg2

* to the global variable result */

void subtract() {

result = argl - arg2;

}

/*

*

*

*

*/

int

man n

Runs a command loop that allows users to perform simple arithmetic.

main() {

bool done = false; // Initially not done do {

switch (menu()) {

case 'A 1 : // Addition

case 'a' :

get_input(); add(); report(); break;

case 'S': // Subtraction

case 's':

get_input(); subtract(); report();

case 'P' : // Print result

case 'p' : reportQ; break;

case 'H' : // Display help screen

case 'h' :

help_screen(); break;

case 'Q' : // Quit the program

case 'q' :

done = true; break;

}

while (!done);

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 10.1 (globalcalculator.cpp) uses global variables result, argl, and arg2. These names no longer appear in the mai n function. These global variables are accessed and/or modified in four different functions: get_i nput, report, add, and subtract.

When in the course of translating the statements within a function to machine language, the compiler resolves a variable it encounters as follows:

• If the variable has a local declaration (that is, it is a local variable or parameter), the compiler will use the local variable or parameter, even if a global variable of the same name exists. Local variables, therefore, take precedence over global variables. We say the local declaration hides the global declaration in the scope of the local variable.

• If the variable has no local declaration but is declared as a global variable, the compiler will use the global variable.

• If the variable has neither a local declaration nor a global declaration, then the variable is undefined, and its use is an error.

In the situation where a local variable hides a global variable of the same name, there is a way to access both the local variable and like-named global variable within the local variable’s scope. Suppose a program has a global variable named x and a function with a local variable named x. The statement

x = 10;

within the scope of the local variable will assign the local x. The following statement will assign the global variable x in the scope of the local variable of the same name:

::x = 10;

The : : operator is called the scope resolution operator. This special syntax may be used whenever a global variable is accessed within a function, but usually it only used when necessary to access a hidden global variable.

If the value of a local variable is used by a statement before that variable has been given a value, either through initialization or assignment, the compiler will issue a warning. For example, the Visual C++ compiler will issue a warning about code in the following function:

void uninitialized() {

int x; // Declare the variable std::cout << x; // Then use it

}

The warning is

warning C4700: uninitialized local variable ’x’ used

(The only way to avoid this warning in Visual C++ is to turn off all warnings.) A local variable has an undefined value after it is declared without being initialized. Its value should not be used until it has been properly assigned. Global variables, however, do not need to be initialized before they are used. Numeric global variables are automatically assigned the value zero. This means the initialization of result in Listing 10.1 (globalcalculator.cpp) is superfluous, since result will be assigned zero automatically. Boolean global variables are automatically assigned zero as well, as zero represents false (see Section 5.1).

©2018 Richard L. Halterman

Draft date: September 25, 2018

When it is acceptable to use global variables, and when is it better to use local variables? In general, local variables are preferred to global variables for several reasons:

• When a function uses local variables exclusively and performs no other input operations (like using the std : : ci n object), its behavior is influenced only by the parameters passed to it. If a non-local variable appears, the function’s behavior is affected by every other function that can modify that non-local variable. As a simple example, consider the following trivial function that appears in a program:

int iincrement (i nt n) { return n + 1;

}

Can you predict what the following statement within that program will print? std::cout << increment(12) << '\n' ;

If your guess is 13, you are correct. The i ncrement function simply returns the result of adding one to its argument. The i ncrement function behaves the same way each time it is called with the same argument.

Next, consider the following three functions that appear in some program: int process(int n) {

return n + m; // m is a global integer variable

}

void assign_m() { m = 5;

}

void inc_m() { m++;

}

Can you predict the what the following statement within the program will print? std::cout << process(12) << '\n' ;

We cannot predict what this statement in isolation will print. The following scenarios all produce different results:

assign_m();

std::cout << process(12) << '\n ' ;

prints 17,

m = 10;

std::cout << process(12) << ' \n ' ;

prints 22,

m = 0; inc_m(); inc_m();

std::cout << process(12) << ' \n ' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

prints 14, and

assign_m(); inc_m(); inc_m();

std::cout << process(12) << ' \n ' ;

prints 19. The identical printing statements print different values depending on the cumulative effects of the program’s execution up to that point.

It may be difficult to locate an error if that function fails because it may be the fault of another function that assigned an incorrect value to the global variable. The situation may be more complicated than the simple examples above; consider:

assign_m();

/* 30 statements in between, some of which may change a, b, and m */

if (a < 2 && b <= 10) m = a + b - 100;

. /* 20 statements in between, some of which may change m */

std::cout << process(12) << ' \n ' ;

• A nontrivial program that uses non-local variables will be more difficult for a human reader to understand than one that does not. When examining the contents of a function, a non-local variable requires the reader to look elsewhere (outside the function) for its meaning:

// Linear function double f(double x) { return m*x + b;

}

What are m and b? How, where, and when are they assigned or re-assigned?

• A function that uses only local variables can be tested for correctness in isolation from other functions, since other functions do not affect the behavior of this function. This function’s behavior is only influenced only by its parameters, if it has any.

The exclusion of global variables from a function leads to functional independence. A function that depends on information outside of its scope to correctly perform its task is a dependent function. When a function operates on a global variable it depends on that global variable being in the correct state for the function to complete its task correctly. Nontrivial programs that contain many dependent functions are more difficult to debug and extend. A truly independent function that uses no global variables and uses no programmer-defined functions to help it out can be tested for correctness in isolation. Additionally, an independent function can be copied from one program, pasted into another program, and work without modification. Functional independence is a desirable quality.

Unlike global variables, global constants are generally safe to use. Code within functions that use global constants are dependent on those constants, but since constants cannot be changed, developers need not worry that other functions that have access to the global constants might disturb their values.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The use of global constants within functions has drawbacks in terms of program maintenance. As a program evolves, code is added and removed. If a global constant is removed or its meaning changes during the course of the program’s development, the change will affect any function using the global constant.

Listing 1 10.2l| (digitaltimer.cpp) uses global constants to assist the display of a digital timer.

Listing 10.2: digitalt-imer. cpp

ffinclude <iostream> ffinclude <iomanip> ffinclude <ctime>

Table caption// Some conversions from seconds

const clock_t SEC_

.PER.

_MIN =

60,

//

60

sec

= i

mi n

SEC_

.PER.

_H0UR

= 60 * SEC_PER_MIN,

//

60

mi n

= i

hr

SEC_

.PER.

_DAY =

24 * SEC_PER_HOUR;

//

24

hr

= 24

hr

/*

* print_time

* Displays the time in hr:min:sec format

* seconds is the number of seconds to display */

void print_time(clock_t seconds) { clock_t hours = 0, minutes = 0;

// Prepare to display time =============================

std::cout << '\n 1 ; std::cout << " " ;

// Compute and display hours ===========================

hours = seconds/SEC_PER_HOUR;

std::cout << std::setw(2) << std::setfi11( '0' ) << hours <<

// Remove the hours from seconds

seconds %= SEC_PER_HOUR;

// Compute and display minutes =========================

minutes = seconds/SEC_PER_MIN;

std::cout << std::setw(2) << std::setfi11 (' 0' ) << minutes <<

// Remove the minutes from seconds seconds %= SEC_PER_MIN;

// Compute and display seconds =========================

std::cout << std::setw(2) << std:: setfi 11 (' 0 ' ) << seconds << 1 \n' ;

}

int main() {

clock_t start = clock(); // Record starting time

clock_t elapsed = (clockQ - start)/CLOCKS_PER_SEC, // Elapsed time in sec.

previousElapsed = elapsed;

// Counts up to 24 hours (1 day), then stops while (elapsed < SEC_PER_DAY) {

// Update the display only every second if (elapsed - previousElapsed >= 1) {

// Remember when we last updated the display

©2018 Richard L. Halterman

Draft date: September 25, 2018

previousElapsed = elapsed; print_time(elapsed);

}

// Update elapsed time

elapsed = (clockQ - start)/CLOCKS_PER_SEC;

}

}

In Listing ||l0.2| (digitaltimer.cpp):

• The main function controls the time initialization and update and deals strictly in seconds. The logic in mai n is kept relatively simple.

• The code that extracts the hours, minutes, and seconds from a given number of seconds is isolated in pri nt_ti me. The pri nt_ti me function can now be used anytime a value in seconds needs to be expressed in the hours : minutes : seconds format.

• The second conversion constants (SEC_PER_HOUR, SEC_PER_MIN, and SEC_PER_DAY) are global constants so that both functions can access them if necessary. In this case the functions use different constants , but it makes sense to place all the conversion factors in one place.

Since the two functions divide the responsibilities in a way that each can be developed independently, the design is cleaner and the program is easier to develop and debug. The use of constants ensures that the shared values cannot be corrupted by either function.

The exclusion from a function’s definition of global variables and global constants does not guarantee that it will always produce the same results given the same parameter values; consider

int compute(int n) { int favorite;

std::cout << "Please enter your favorite number: std::cin >> favorite; return n + favorite;

}

The compute function avoid globals, yet we cannot predict the value of the expression compute (12). Recall the i ncrement function from above:

int increment (i nt n) { return n + 1;

}

Its behavior is totally predictable. Furthermore, i ncrement does not modify any global variables, meaning it cannot in any way influence the overall program’s behavior. We say that increment is a pure function. A pure function cannot perform any input or output (for example, use the std: :cout and std : : ci n objects), nor may it use global variables. While i ncrement is pure, the compute function is impure. The following function is impure also, since it performs output:

int increment_and_report (i nt n) {

std::cout << "Incrementing " << n << '\n' ; return n + 1;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

A pure function simply computes its return value and has no other observable side effects.

A function that uses only pure functions and otherwise would be considered pure is itself a pure function; for example:

int double_iincrement (i nt n) { return increment(n) + 1;

}

double_increment is a pure function since i nc remen t is pure; however, double_i nc rente nt_wi th_report

int double_increment_with_report (i nt n) { return increment_and_report(n) + 1;

}

is not a pure function since it calls i ncrement_and_report which is impure.

10.2 Static Variables

Space in the computer’s memory for local variables and function parameters is allocated at run time when the function begins executing. When the function is finished and returns, the memory used for the function’s local variables and parameters is freed up for other purposes. If a function is never called, the variable’s local variables and parameters will never occupy the computer’s memory.

Because a function’s locals are transitory, a function cannot ordinarily retain any information between calls. C++ provides a way in which a variable local to a function can be retained in between calls. Listing 10.3 (counter.cpp) shows how declaring a local variable staff c allows it to remain in the computer’s memory for the duration of the program’s execution.

Listing 10.3: counter.

cpp

#include <iostream>

#include <iomanip>

/*

*

count

*

Keeps track

of a count.

*

*/

Returns the

current count.

int

countQ {

// cnt's value

is retained between calls because it

// is declared

static

static int cnt

= 0;

}

return ++cnt;

// Increment and return current count

f nt

main() {

// Count to ten

for (int i = 0;

i < 10; i++)

std :: cout <<

count () << 1 ' ;

}

std :: cout << 1 \n 1 ;

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

In Listing ||10.3|| (counter.cpp), the count function is called 10 times. Each time it returns a tally of the number of times it has been called:

123456789 10

By contrast, if you remove the word stati c from Listing 10.3 (counter.cpp), recompile it, and rerun it, it prints:

because new memory is allocated for the cnt variable each time count is called.

The local declaration static int cnt = 0;

allocates space for cnt and assigns zero to it once—at the beginning of the program’s execution. The space set aside for cnt is not released until the program finishes executing.

Recall Listing |9?7| (evenbetterprompt.cpp) that included the following function:

int prompt (int n) { int value;

std::cout << "Please enter integer #" << n << std::cin >> value; return value;

}

The caller, mai n, used prompt function as follows: int valuel, value2, sum;

std::cout << "This program adds together two integers.\n" ; valuel = prompt(l); // Call the function

value2 = prompt(2); // Call the function again

sum = valuel + value2;

The first call to prompt prints the message

Please enter integer #1:

and awaits the user’s input. The second call prints the message

Please enter integer #2:

Another caller might use prompt within a loop like this: int sum = 0;

for (int i = 1; i < 10; i++) sum += prompt(i);

Notice that it is the caller’s responsibility to keep track of the proper number to pass to p r ompt. The caller may make a mistake and pass the wrong number or may not want to manage such details. It would be better to move the responsibility of tracking input count to prompt, static variables make that possible, as Listing |T074| (promptwithstatic.cpp)

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing |l0.4| (promptwithstatic.cpp) behaves just like Listing |9.7[ (evenbetterprompt.cpp) but in the new version main does not have to keep track of the number of user entries.

Local static variables were inherited from the C programming language, but their need has diminished with the introduction of objects in C++ (see Chapter 14). Functions with stati c variables provide a way to implement executable code with persistent state. Objects provide a more natural and more flexible way to achieve the same effect.

10.3 Overloaded Functions

In C++, a program can have multiple functions with the same name. When two or more functions within a program have the same name, the function is said to be overloaded. The functions must be different somehow, or else the compiler would not know how to associate a call with a particular function definition. The compiler identifies a function by more than its name; a function is uniquely identified by its signature. A function signature consists of the function’s name and its parameter list. In the parameter list, only the types of the formal parameters are important, not their names. If the parameter types do not match exactly, both in number and position, then the function signatures are different. Consider the following overloaded functions:

1. void f() { /* ... */ }

This version has no parameters, so its signature differs from all the others which each have at least one parameter.

2. void f(int x) { /* ... */ }

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Draft date: September 25, 2018

This version differs from Version 3, since its single parameter is an i nt, not a double.

3. void f (double x) { /* ... */ }

This version differs from Version 2, since its single parameter is a double, not an i nt.

4. void f(int x, double y) { /* ... */ }

This version differs from Version 5 because, even though Versions 4 and 5 have the same number of parameters with the same types, the order of the types is different.

5. void f (double x, int y) { /* ... */ }

See the comments for Version 4.

Overloaded functions are a convenience for programmers. If overloaded functions were not allowed (many programming languages do not support function overloading), new function names must be created for different functions that perform basically the same task but accept different parameter types. It is better for the programmer to choose the same name for the similar functions and let the compiler properly resolve the differences. Overloading becomes a more important issue for constructors, special functions called during object creation (Chapter[T4|.

10.4 Default Arguments

We can define functions that accept a varying number of parameters. Consider Listing |10.5|j (countdown.cpp) that specifies a function that counts down:

The formal parameter to the countdown function expressed as n = 10 represents a default parameter or default argument. If the caller does not supply an actual parameter, the formal parameter n is assigned 10. The following call

countdown() prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

but the invocation countdown(5)

displays

5

4

3

2

1

0

As we can see, when the caller does not supply a parameter specified by a function, and that parameter has a default value, the default value is used during the caller’s call.

We may mix non-default and default parameters in the parameter lists of a function declaration, but all default parameters within the parameter list must appear after all the non-default parameters. This means the following definitions are acceptable:

int sum_range (i nt n, int m=10Q) { // OK, default follows non-default

int sum = 0;

for (int val = n; val <= m; val++) sum += val; return val;

}

and

int sum_range (i nt n=0, int m=100) { // OK, both default

int sum = 0;

for (int val = n; val <= m; val++) sum += val; return val;

}

but the following definition is illegal, since a default parameter precedes a non-default parameter in the function’s parameter list:

int sum_range (i nt n=0, int m) { // Illegal, non-default follows default int sum = 0;

for (int val = n; val <= m; val++)

©2018 Richard L. Halterman

Draft date: September 25, 2018

sum += val; return val;

}

Default arguments allow programmers to provide a highly tunable function that offer a simpler interface for its typical uses.

Overloading (see Section 10.3| enables programmers to write different function definitions for two different functions that have the same name. Mixing overloading and default arguments can produce ambiguities that the compiler will not allow; for example, the following overloaded functions are acceptable:

void f() { /* .... */ } void f(int n) { /* .... */ }

as this overloads function f . If a caller invokes f as f () , the compiler will generate machine language code to call the first version of f . If instead we attempt to overload f as

void f() { /* .... */ } void f(int n=0) { /* .... */ }

the compiler cannot determine if the call f () means the first overloaded version or the second with the parameter defaulting to zero. Because of this ambiguity, the compiler will report an error for attempts to call function f with no arguments. The other possible combination is illegal:

void f(int m) { /* .... */ }

void f(int n=0) { /* .... */ }

because these functions have the same signature, f ( i nt) . C++ does not allow a program to contain multiple function definitions with the same signature.

10.5 Recursion

The factorial function is widely used in combinatorial analysis (counting theory in mathematics), probability theory, and statistics. The factorial of n is often expressed as n\. Factorial is defined for nonnegative integers as

n\ = n ■ (n — 1) • (n — 2) • (n — 3) • • • 2 • 1

and 0! is defined to be 1. Thus 6!=6-5-4-3-2-l = 720. Mathematicians precisely define factorial in this way:

( 1 if n = 0 n\ = <

[ n-(n — 1)! otherwise.

This definition is recursive since the ! function is being defined, but ! is also used in the definition. A C++ function can be defined recursively as well. Listingj [r(T6| j(factorialtest.cpp) includes a factorial function that exactly models the mathematical definition.

©2018 Richard L. Halterman

Draft date: September 25, 2018

* Computes n!

* Returns the factorial of n.

*/

int factorial(int n) { if (n == 0) return 1;

else

return n * factorial(n - 1);

}

int main() {

Table caption// Try out the factorial function

std:

: cout

<<

" 0!

= " <<

factorial(0) <<

1 \n 1

std:

: cout

<<

" 1!

= " <<

factorial(l) <<

1 \n'

std:

: cout

<<

" 6!

= " <<

factorial(6) <<

1 \n'

std:

: cout

<<

"10!

= " <<

factorial(10) <<

' \n

}

Observe that the factori al function in Listing 10.6 ffactorialtest.cpp) uses no loop to compute its result. The factori al function simply calls itself. The call factori al (6) is computed as follows:

factorial(6) =

factorial(5)

5 * factorial(4)

4 * factorial(3)

3 * factorial(2)

5 5 5 5 5 5 5 5 5 120

4

4

4

4

4

4

4

24

2

2

2

2

2

* factorial(l)

* 1 * factorial(Q) * 1*1

* 1

- 720

Note that the factori al function can be slightly optimized by changing the i f’s condition from (n == 0) to (n < 2). This change results in a function execution trace that eliminates two function calls at the end:

factorial(6)

6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 720

factorial(5)

5 * factorial(4)

5 * 4 * factorial(3)

5 * 4 * 3 * factorial(2) 5*4*3*2*1 5 * 4 * 3 * 2 5*4*6 5 * 24 120

Figure 10.1 shows the call sequence for factori al (6) invoked from within a mai n function. A correct simple recursive function definition is based on four key concepts:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 10.1 Traces the function activations of the recursive function factori al when called from mai n with an argument of 6. The arrows into an activation bar indicates the argument passed by the caller; the arrows out show the value passed back to the caller. The length of a bar represents the time during which that invocation of the function is active.

factori al(6) function call sequence (called from main)

Program Execution Timeline

720

factor!al

120

factorial

24

factorial

factorial

factorial

factorial

©2018 Richard L. Halterman

Draft date: September 25, 2018

1. The function must optionally call itself within its definition; this is the recursive case.

2. The function must optionally not call itself within its definition; this is the base case.

3. Some sort of conditional execution (such as an i f /else statement) selects between the recursive case and the base case based on one or more parameters passed to the function.

4. Each invocation that does not correspond to the base case must call itself with parameter(s) that move the execution closer to the base case. The function’s recursive execution must converge to the base case.

Each recursive invocation must bring the function’s execution closer to it base case. The factorial function calls itself in the else clause of the i f/else statement. Its base case is executed if the condition of the i f statement is true. Since the factorial is defined only for nonnegative integers, the initial invocation of facto ri al must be passed a value of zero or greater. A zero parameter (the base case) results in no recursive call. Any other positive parameter results in a recursive call with a parameter that is closer to zero than the one before. The nature of the recursive process progresses towards the base case, upon which the recursion terminates.

We can easily write a non-recursive factorial function, as Listing (T0.7[(nonrecursfact.cpp) shows.

Listing 10.7: nonrecursfact.cpp

ftinclude <iostream>

/*

* factorial(n)

* Computes n!

* Returns the factorial of n. */

int factorial(int n) { int product = 1; for (int i = n; i > 0; i--)

product *= i; return product;

}

int main() {

Table caption// Try out the factorial function

std:

: cout

<<

" 0!

= " <<

factorial)©) <<

' \n' ;

std:

: cout

<<

" 1!

= " <<

factorial(1) <<

' \n' ;

std:

: cout

<<

" 6!

= " <<

factorial(6) <<

' \n' ;

std:

: cout

<<

"10!

= " <<

factorial(10) <<

' \n' ;

}

Which factorial function is better, the recursive or non-recursive version? Generally, if the same basic algorithm is being used by both the recursive and non-recursive functions, then the non-recursive function will be more efficient. A function call is a relatively expensive operation compared to a variable assignment or comparison. The body of the non-recursive factorial function invokes no functions, but the recursive version calls a function—it calls itself—during all but the last recursive invocation. The iterative version of factorial is therefore more efficient than the recursive version.

Even though the iterative version of the factorial function is technically more efficient than the recursive version, on most systems you could not tell the difference. The execution time difference between the two versions is negligible. The reason is the factorial function “grows” fast, meaning it returns fairly large

©2018 Richard L. Halterman

Draft date: September 25, 2018

results for relatively small arguments. In particular, f acto ri al ( 13 ) is the largest value that fits within a 32-bit integer. Neither the iterative nor recursive version of f actorial can compute 14! using the 32-bit i nt type.

Recall the gcd functions from Section 9.2 It computed he greatest common divisor (also known as

greatest common factor) of two integer values. It works, but it is not very efficient. A better algorithm is used in Listing |10.8j (gcd.cpp). It is based on one of the oldest algorithms known, developed by the Greek mathematician Euclid around 300 B.C.

Running Listing 10.8 (gcd.cpp) you will see that the gcd and i terati ve_gcd functions compute the same results given the same arguments. Listing |10.8| (gcd.cpp) showcases the difference in performance between the two functions by computing the GCD of relatively large integers. The gcd function produces its result much faster than i terati ve_gcd. Note that this gcd function is recursive. The algorithm it

©2018 Richard L. Halterman

Draft date: September 25, 2018

uses is much different from our original iterative version. Because of the difference in the algorithms, this recursive version is actually much more efficient than our original iterative version. A recursive function, therefore, cannot be dismissed as inefficient just because it is recursive.

While Listing 10.8 (gcd.cpp) expresses the gcd functions recursively, it is not hard to rewrite it so that it still follows Euclid’s algorithm but uses a loop instead of recursion—this very task appears as an exercise at the end of the chapter. Often the concept of an algorithm solving certain kinds of problems is better understood when expressed recursively. Later, once the details of the recursive version are perfected, developers may rewrite the algorithm in an iterative fashion.

Listing |10.9| (histobar.cpp) provides another example of a recursive function. The segmentsl function uses iteration to draw segments that make up a bar that could be part of a histogram. The segments2 function does that same thing, except it uses recursion.

The outout of Listing] 10.9[(histobar.cpp) shows that the two functions produce the same results:

©2018 Richard L. Halterman

Draft date: September 25, 2018

A recursive function may call itself within its definition multiple times. Consider the following sequence of integer values:

0,1,1,2,3,5,8,13,21,34,55,89,144,...

This is beginning of the infinite Fibonacci sequence (see https://en.wi kipedia. org/wi ki/Fibonacc number). It is a sequence of integers beginning with 0 followed by 1. Subsequent elements of the sequence are the sum of their two immediately preceding elements; thus, the third number is 0+ 1 = 1, the fourth number is 1 + 1=2, the fifth number is 1+2 = 3, etc. The numbers that comprise the Fibonacci sequence are known as Fibonacci numbers. Note that 3 is a Fibonacci number but 4 is not.

The mathematical properties of Fibonacci numbers have bearing in such diverse fields as biology, economics, and art.

A common problem is computing the n lb Fibonacci number. Zero is the 0 th , 1 is the 1 st , 1 is also the 2 nd , 2 is the 3 rd , 3 is the 4 th , 5 is the 5 th , etc.

A recursive C++ function to compute the n th Fibonacci number follows easily from the definition of the Fibonacci sequence:

// Returns the nth Fibonacci number int fibonacci (i nt n) { if (n <= 0) return 0; else if (n == 1) return 1;

else

return fibonacci(n - 2) + fibonacci(n - 1);

}

Figure 10.2 illstrates the recursive computation of fibonacci (5) using this fibonacci function. Note that the call fibonacci (5) invokes the fibonacci function a total of 15 times.

While this facto rial function computes the correct result, this tendency to call itself so many times makes it impractical for larger values. Section [21,8| introduces an algorithm design technique that greatly improves the performance of this recursive function.

10.6 Making Functions Reusable

A function definition packages in one place functionality that we can exercise (call) from many different places within a program. Thus far, however, we have not seen how we can reuse easily function definitions

in other programs. For example, our is_p rime function in Listing 9.10 (primefunc.cpp) works well

within Listing 9.10 (primefunc.cpp), and we could put it to good use in other programs that need to test

primality (encryption software, for example, makes heavy use of prime numbers). We could use the copy

and-paste feature of our favorite text editor to copy the i s_p r i me function definition from Listing 9.10 (primefunc.cpp) into the new encryption program we are developing.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 10.2 The recursive computation offibonacci (5). Each rectangle represents an invocation of the fibonacci fuunction. The call at the top of the diagram represents the initial call offibonacci (5). An arrow pointing down indicates the argument being passed into an invocation offibonacci, and an arrow pointing up represents the value returned by that invocation. An invocation of fibonacci with no arrow pointing down away from the invocation represents a base case; observe that any invocation receiving a 0 or 1 is a base case. We see that the recursive process for fibonacci (5) invokes the function a total of 15 times.

fibonacci(3)

TTX\

Table captionl l

Table caption2 1

Table captionZ '/

fibonacci(l)

fibonacci(2)

fibonacci(2)

fibonacci(3)

Table caption7TVt

Table caption0 0 11

1 1 / \l \

Table caption77 r T 1 \

Table caption0 0 11

1 1 / \ \

Table caption7T\%

Table caption11 2 1

1/ \\

fibonacci(0) fibonacci(l) fibonacci(0) fibonacci(l) fibonacci(l) fibonacci(2)

TFXi

0 0 11

i U_ VA_

fibonacci(0) fibonacci(l)

©2018 Richard L. Halterman

Draft date: September 25, 2018

It is possible to reuse a function with this copy-and-paste technique only if the function definition does not use any programmer-defined global variables, programmer-defined global constants, nor other programmer-defined functions. If a function does use any of these programmer-defined external entities, we must copy and paste all of this extra code in order for the function to compile. If the names of the external variables or functions that we must copy into the new program conflict with existing names within the program, the program will not compile as is, and we must rename the offending variables or functions to resolve the conflicts. Changing code provides the opportunity to introduce bugs accidentally, so the process requires absolute care.

We can avoid the issues introduced by copying and pasting if the function we wish to reuse in other programs uses only local variables and parameters. Such a function is truly an independent function that can be reused easily in multiple programs.

The notion of copying source code from one program to another is not ideal, however. It is too easy for the copy to be incomplete or for some other error to be introduced during the copy. Furthermore, such code duplication is wasteful. If 100 programs on a particular system all need to use the i s _ p r i me function, under this scheme they must all include the is_prime code. This redundancy wastes space. Finally, in perhaps the most compelling demonstration of the weakness of this copy-and-paste approach, what if we discover a bug in the i s_pri me function that all 100 programs are built around? When we discover the error and fix it in one program, the other 99 programs still will contain the bug. Their source code must be updated, and they each then must be recompiled. The problem is even more complicated if the other 99 programs have 99 different authors. We then must contact multiple developers to tell them to fix their i s_pri me function. The situation would be similar if we updated a correct i s _ p r i me function to make it more efficient. The problem is this: all the programs using is_prime define their own is_prime function; while the function definitions are meant to be identical, there is no mechanism tying all these common definitions together. We really would like to reuse the function as is without copying it.

Fortunately, C++ provides a way to develop functions in separate files and combine the code from these independently developed functions into one program. We can compile the source files separately, and the linker can combine the compiled code into an executable. What we need is a way for the compiler to verify that the calling code in one source file is correctly invoking the function defined in another source file.

Listing 10.10 (prime. h) provides the first step in making a reusable i s_pri me function.

The simple one-line code in Listing [10.10 (prime. h) can be stored in a file called prime. h. In Visual Studio, you simply add a new item to your project specified as a header file, name it prime. h, and you are ready to type the one line of code into the newly created file. This file contains the prototype for our i s_pri me function (see our earlier discussion of function prototypes in Section ||| 871) . Caller code that intends to use our i s _ p r i me function must #i nclude this file so that compiler can check to see if the caller is using our i s_p r i me function properly. An attempt, for example, to pass two arguments to i s_pri me would result in a compiler error since the prototype specifies a single integer argument.

A second file, which could be named prime.cpp, appears in Listing jTOJTl [(prime.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

* is_prime(n)

* Determines the primality of a given value

* n an integer to test for primality

* Returns true if n is prime; otherwise, returns false */

bool is_prime(int n) {

bool result = true; // Provisionally, n is prime double r = n, root = sqrt(r);

// Try all possible factors from 2 to the square // root of n

for (int trial_factor = 2; result && trial_factor <= root; trial_factor++) result = (n % trial_factor != 0); return result;

The code in Listing 10.11 (prime.cpp) is placed in prime.cpp, a different file from prime. h. It provides an

implementation of the i s_pri me function. Notice the # include preprocessor directive in Listing 10.11

(prime.cpp) that references the file prime.h. While not required, this serves as a good check to see if the implementation code in this file is faithful to the prototype specified in prime.h. This prime.cpp file is compiled separately, and the compiler will report an error if the implementation of is_prime disagrees with the information in the header file.

Note that the file prime.cpp does not contain a mai n function; mai n will appear in another file. Also observe that we do not need to #i nclude the i ostream header, since the std : : cout and std : : ci n objects are not used anywhere in this file. The cmath header is #i ncluded since is_pri me uses the sqrt function.

The final piece of the program is the calling code. Suppose Listing 10.12 (primetester.cpp) is added to the project in a hie named primetester.cpp.

Note that the hie primetester.cpp uses a function named i s_pri me, but its dehnition is missing. The dehnition for i s_pri me is found, of course, in prime.cpp.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Visual Studio will automatically compile and link the . cpp files when it builds the project. Each . cpp is compiled independently on its own merits.

If you are using the Visual Studio Command Line tool, in order to build the program you would type

cl /EHsc /Za /W3 primetester.cpp prime.cpp

The executable file’s name is determined by the name of the first source file listed, in this case primetester.

If you are using the GCC tools instead of Visual Studio, in order to make the executable program named primetester (or primetester.exe under the Microsoft Windows version of the GCC tools), you would issue the command

g++ -o primetester -Wall -01 -std=c++ll prime.cpp primetester.cpp

The GNU C++ compiler will separately compile the two source files producing two machine language object files. The linker will then use those object files to create the executable. When the linker has created the executable, it automatically deletes the two object files.

The i s_pri me function is now more readily available to other programs. If it becomes an often used function in many programs, it can be compiled and placed into a special file called a library. In this form it need not be recompiled each time a new program is built that requires it. If our i s_pri me is placed in a dynamic library, its code can be loaded and linked at nin time and shared by many executing programs. We do not cover library creation in this text.

In Listing|877j(timeit.cpp), Listingj|8.8|(measureprimespeed.cpp), and Listing |ro.2|| (digitaltimer.cpp) we used the clock function from the <ctime> library to measure the elapsed time of sections of various executing programs. In each of these programs the programmer must be aware of the clock_t type and CL0CKS_PER_SEC constant, both defined in the <ctime> header file. Furthermore, the programmer must use the clock function properly and correctly perform some arithmetic and include a messy type cast operation. Armed with our knowledge of global variables (Section ||10.1| and separate compilation of multiple source files, we can provide a better programming interface to the lower-level timing functions provided to the C library.

Listing 10.13 (timermodule.h) specifies some convenient timing functions.

Listing 10.14 (timermodule.cpp) implements the functions declared in Listing 10.13 (timermodule.h).

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 10.14: timermodule.cpp

// File timermodule.h

// Implements the program timer module #include <ctime>

// Global variable that keeps track of the elapsed time, double elapsed;

// Global variable that counts the number of clock ticks since // the most recent start time. clock_t start_time;

// Global flag that indicates whether or not the // timer is running.

bool running;

// Reset the timer so it reads 0 seconds void reset_timer() { elapsed = 0.0;

running = false; // Ensure timer is not running

}

// Start the timer. The timer will begin measuring elapsed time. // Starting the timer if it already is running has no effect void start_timer() {

// Starting an already running timer has no effect if ([running) {

running = true; // Note that the timer is running

start_time = clockQ; // Record start time

}

}

// Stop the timer. The timer will retain the current elapsed // time, but it will not measure any time while it is stopped.

// Stopping the timer if it is not currently running has no effect, void stop_timer() {

// Stopping a non-running timer has no effect if (running) {

clock_t stop_time = clockQ; // Record stop time running = false; // Stop the clock

// Add to the elapsed time how long it has been since we last // started the timer

elapsed += static_cast<double> ((stop_time - start_time))

/ CLOCKS_PER_SEC;

}

}

// Return the cummulative running time (in seconds)

// kept by the timer since it last was reset double elapsed_time() {

if (running) { // Compute time since last reset

clock_t current_time = clockQ; // Record current time

return elapsed + static_cast<double> ((current_time - start_time))

©2018 Richard L. Halterman

Draft date: September 25, 2018

/ CL0CKS_PER_SEC;

}

else // Timer stopped; elapsed already computed in stop_timer return elapsed;

Observe that the code in Listing [10.14|| (timermodule.cpp) allows client code to stop the timer and restart it later without losing any previously accumulated time. The implementation uses three global variables— elapsed, sta rt_ti me, and runni ng —to maintain the state of the timer. One or more of these global variables is influenced by three functions— start_timer, stop_timer, reset_time. The fourth function returns the value of the elapsed variable.

Listing [TO. 15| (bettertimeit.cpp) simplifies Listing|8.7|(timeit.cpp) with our new timer module.

The code within Listing ) 10.15| (bettertimeit.cpp) is simpler and cleaner than the code in Listing |8.7| (timeit.cpp). All traces of the clock_t type and the messy arithmetic and casting are gone. The timer module provides a simple interface to callers that hides the details on how the timing actually happens.

Despite the ease of use of our timer module, it has a servere limitation. Suppose you wish to measure how long it takes for a function to execute and also, during that function’s execution, separately time a smaller section of code within that function. When the function is finished executing, you would like to know how long it took the function to do its job and how long a portion of its code took to execute. We essentially need two independent timers, but with our timer module it is not possible to conduct simultaneously more than one timing. We will see a far superior way to model a program execution timer in Section||16.2[ We will use objects to enable us to maintain as many simultaneous stopwatches as we need.

10.7 Pointers

Ordinarily we need not be concerned about where variables live in the computer’s memory during a program’s execution. The compiler generates machine code that takes care of those details for us. Some systems software like operating systems and device drivers need to access specific memory locations in order to interoperate with hardware. Systems programmers, therefore, must be able to write code that can access such lower-level detail. Developers of higher-level applications sometimes need to access the address of variables to achieve specialized effects.

Each byte in a computer’s memory is numbered with a unique address. The first address is 0, and the locations are numbered sequentially up to some maximum value allowed by the operating system and hardware. A C++ variable is stored in memory, so each variable lives at a particular address.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 10.3 Pointer declaration and assignment

int x;

X

?

x

X

4

If x is a variable of any type, the expression &x

represents the address of x. The & operator is called the address of operator. Regardless of the type of x, the expression

&x

is really just a number—the numeric address of the variable’s memory location, but except for some situations in systems programming, programmers rarely need to treat this value as a number.

While an address is really just a nonnegative integer value, C++ uses a special notation when dealing with addresses. In the following declaration

int *p;

the variable p is not an int itself; the * symbol in the declaration signifies that p is a pointer to an int. This means we can assign to p the address of an int. The following sequence of code

int

x;

x =

4;

int

*p;

P =

&x;

assigns the address of x to p. We can visualize the execution of these four statements in Figure! 10.3

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 10.4 Assignment via a pointer

X

int x; |~?

x

X

4

x

-P = 7 «*.

The * symbol used as shown above during a variable declaration indicates that the variable is a pointer. It will be used to refer to another variable or some other place in memory. In this case, the sequence of assignments allows pointer p to refer to variable x.

In order to access memory via a pointer, we use the unary * operator. When not used in the context of a declaration, the unary * operator is called the pointer dereferencing operator. Continuing the code sequence above,

int x; x = 4; int *p;

P = &x;

*P = 7;

the statement *P = 7;

copies the value 7 into the address referenced by the pointer p. Figure |10.4|| illustrates the full sequence. Notice that the assignment to *p modifies variable x’s value. The pointer p provides another way to

©2018 Richard L. Halterman

Draft date: September 25, 2018

access the memory allocated for x.

It is important to note that the statement *P = 5;

is the first assignment statement we have seen that uses more than just a single variable name on the left of the assignment operator. The statement is legal because the expression *p represents a memory location that can store a value. Here, *p stands in the place of the variable x, and we easily can assign a value to x.

The unary * operator has two distinct meanings depending on the context: 1. At the pointer’s declaration, for example, double *p;

the * indicates that p is a pointer to a d o u b 1 e ; it is not itself a d o u b 1 e . 2. After the pointer’s declaration, for example,

*p = 0.08;

the expression * p represents the contents of memory at the address assigned to p.

The * operator is the inverse of the & operator. & finds the address of a variable, and, when this address is assigned to a pointer variable like p, the * operator accesses the memory referenced by the pointer:

int v; // v is a normal integer variable

int *p = &v; // Pointer variable p points to v *p = 5; // Assigns 5 to variable v

We may declare a pointer and not assign it, as in int *p;

We say p is an uninitialized pointer , sometimes called a wild pointer. If p is a local variable, its contents are undetermined bits. Because of p’s declared type, we interpret these bits as an address, so the net effect is that the uninitialized pointer p points to a random location in the computer’s memory. An attempt to dereference p, as in

*p = 500;

is certainly asking for trouble. This statement attempts to write the value 500 at some unknown-to-theprogrammer memory location. Often the address is not part of the area of memory the operating system has set aside for the executing program, so the operating system steps in and issues a run-time error. This is the best possible result for misusing a wild pointer. It is possible, however, that the spurious address is within the executing program’s domain. In this case the value 500 may overwrite another variable or the compiled machine language instructions of the program itself! Such errors are difficult to track down because the overwritten value of the variable cannot be detected until the program attempts to use the variable. The statement that misuses the uninitialized pointer may be far away in the source code (even in a different source file) from the code that attempts to use the clobbered variable. When the program fails, the programmer naturally looks around in the code where the failure occurred—the code in the vicinity where

©2018 Richard L. Halterman

Draft date: September 25, 2018

the clobbered variable appears. Unfortunately, the misbehaving code is fine, and the error lies elsewhere. There often is no easy way to locate the true source of the error.

Suppose p is a variable that points in an i nt. The statement

*P = 5;

assigns the value 5 to the memory location to which p points. Compare this legal C++ statement to the following illegal C++statement:

p = 5; // Illegal statement as is

This second statement attempts to make p refer to the memory address 5; it does not assign the value 5 to the memory to which p refers. C++ is very strict about disallowing the mixing of pointers and non-pointers across assignment.

Systems programmers sometimes need to assign a pointer to a particular address in memory, and C++ permits the assignment with a special kind of type cast, the rfiinternref cast:

p = reinterpret_cast<int *>(5); // Legal

The familiar static_cast (see Section 4.2) will not work. Why is C++ so strict when it comes to assignments of pointers to non-pointers and vice versa? It is easy to make a mistake such as omitting the * operator when it is needed, so the special cast forces the programmer to pause and consider whether the mixed assignment truly is necessary or whether attempting to do so would be a mistake.

Modern C++ compiler supports the reserved word nullptr to represent a pointer to “nothing.” It stands for “null pointer.” The following statement

p = nullptr;

indicates that p is pointing nowhere. On most platforms, nullptr maps to address zero, which is out of bounds for any running program. Dereferencing p thus would result in a run-time error. Adept programmers can find the source of such a null pointer access problem quickly with a debugger.

C++ does not allow direct integer assignment to a pointer, as in

int *p = 5;

Here p must point to an integer; it is not an integer. If you wish to assign p to point to a particular memory address, you must use a special type cast:

int *p = reinterpret_cast<int *>(5);

C++ does allow the literal value 0 to be used in place of nullptr. The statement

p = Q;

achieves the same result as assigning nullptr to p. This is how C++ programmers assigned a pointer to point to nothing before the nullptr keyword was available. Since newer compilers support existing C++ source code, the literal zero assignment still works. You should use the nullptr keyword because it improves the source code readability. Since 0 can represent both an integer value and a pointer to any type, both of the following statements are legal if p has been declared to be a pointer to an integer:

©2018 Richard L. Halterman

Draft date: September 25, 2018

p = Q;

*p = 0;

The first statement assigns null to p, while the second statement sets the data to which p points to zero. Said another way, the first statement changes where p points; the second statement changes the memory to which p p points. Superficially, the two statements look very similar and are easy to confuse. Next, consider the statements

p = nullptr; // OK

*p = nullptr; // Error, will not compile

The second statement contains an error because it is illegal to assign the nullptr literal to anything other than a pointer type.

The nullptr reserved word is part of the C++11 standard. The name nullptr is simply an identifier (for example, a variable or function name) for older compilers. Before the nullptr constant became available the literal 0 (zero) was considered the null pointer reference. For backwards compatibility with older code, C++11 allows you to use 0 in place of nullptr, but if possible you should avoid this practice when writing new code. The nullptr literal allows the compiler to perform better type checking. To see why, suppose the programmer believes the variable p is a pointer to an integer, but p is instead a simple integer:

believes p is a

pointer to an integer

In this case the compiler is powerless to detect a problem because p is an integer, and zero is a valid integer value. If p really is an integer rather a pointer, the compiler will flag the following code:

// Programmer believes p is a pointer to an integer p = nullptr;

because the nullptr may not be assigned to a non-pointer type.

The nullptr constant and the notion of a pointer pointing nowhere becomes more useful when building dynamic data structures (see, for example, Section |18.3| .

10.8 Reference Variables

C++ supports another kind of variable that is many ways similar to a pointer. When the & symbol is used as part of the type name during a variable declaration, as in

i nt x; int& r = x;

we say r is a reference variable. This declaration creates a variable r that refers to the same memory location as the variable x. We say that r aliases x. Unlike a pointer variable, we may treat r as if it were an i nt variable—no dereferencing with * is necessary. Listing 10.16 (referencevar.cpp) demonstrates how reference variables can alias other variables.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 10.16: referencevar.cpp

#include <iostream>

int main() { int x = 5; int y = x;

Table captionint& r = x;

std:

: :cout

<<

"x = "

<<

X

<< 1

\n'

5

std:

: :cout

<<

" y - 1.

<<

y

<< 1

\n'

5

std:

: :cout

<<

II J- — II

<<

r

<< 1

\n'

5

std:

: :cout

<<

"Assign

7

to

x\n

II .

5

x =

7;

std:

: :cout

<<

"x = "

<<

X

<< 1

\n'

5

std:

: :cout

<<

"y = »

<<

y

<< 1

\n'

5

std:

: :cout

<<

II j- — II

<<

r

<< 1

\n'

5

std:

: :cout

<<

"Assign

8

to

y\n

II .

5

y =

8;

std:

: :cout

<<

"x = "

<<

X

<< 1

\n'

5

std:

: :cout

<<

"y = »

<<

y

<< 1

\n'

5

std:

: :cout

<<

II p- — II

<<

r

<< 1

\n'

5

std:

: :cout

<<

"Assign

2

to

r\n

II .

5

r =

2 ;

std:

: :cout

<<

"x = "

<<

X

<< 1

\n'

5

std:

: :cout

<<

My - It

<<

y

<< 1

\n'

?

std:

: :cout

<<

ll p- — II

<<

r

<< 1

\n'

5

}

The output

clearly demonstrates that the variables x and r represent the same quantity. Reassigning x changes r in exactly the same way, and reassigning r changes x in exactly the same way. The variable y, on the other hand, is independent from both x and r. Reassigning either x or r does not affect y, and reassigning y affects neither x nor r.

The space around the & symbol used to declare a reference variable is not significant; specifically, the statement

int& r = x;

©2018 Richard L. Halterman

Draft date: September 25, 2018

is equivalent to

int &r = x;

Reference variables are similar to pointer variables, but there are some important differences. Reference syntax is simpler than pointer syntax because it is not necessary to dereference a reference variable in order to assign the memory location to which it refers. If num is an i nt, ptr is a pointer to an i nt, and ref is a reference to an i nt, consider the following statements:

num = ref; // Assign num from ref, no need to deference

num = *ptr; // Assign num from ptr, must dereference with *

A reference variable has two big limitations over a pointer variable:

• A reference variable must be initialized with an actual variable when it is declared. A pointer variable may be declared without an initial value and assigned later. Consider the following statements:

int *p; // Legal, we will assign p later

int& r; // Illegal, we must initialize r when declaring it

Attempting to compile this code under Visual C++ prompts the compiler to issue the error error C2530: V : references must be initialized

• There is no way to bind a reference variable to a different variable during its lifetime. Consider the following code fragemnt:

int

x = 5, y

= 7:

»

int

*p = &x;

//'

Bi nds

p to

poi nt

to

X

int& r = x;

//

Bi nds

r to

X

P =

&y;

//

Reassi

gn p

to po

int

to

y

r =

y;

//

Assign

y' s

value

to

X

(via

The statement

r - y;

does not bind r to the y variable. The declaration of r binds r to the x variable for the life of r. This statement simply assigns y’s value to x via the reference r. In contrast, we may freely bind pointer variables to any variables we choose at any time.

A reference variable, therefore, in the examples provided here works like a pointer that must be bound to a variable and may not be redirected to point anywhere else. Also, unlike with pointers, it is illegal to attempt to assign nullptr to a reference variable. There are some other differences between references and pointers that we will not explore here. Reference variables provide a simpler syntax than pointer variables since we do not use the pointer dereferencing operator (*) when working with references.

There is one other major difference between pointers and references—C++ adopted pointers as is from the C programming language, but C does not provide references. C++ programmers often use library functions written in C, so it is important to not mix references with C code.

Section [10,91 reveals a ver Y important practical application of pointers and references in their role of enabling pass by reference to functions.

©2018 Richard L. Halterman

Draft date: September 25, 2018

10.9 Pass by Reference

The default technique for passing parameters to functions is pass by value (see Section |9.3| . C++ also supports pass by reference , also known as call by reference, which allows functions to alter the values of formal parameters passed by callers.

Consider Listing 10.17 (faultyswap.cpp), which uses a function that attempts to interchange the values of its two integer parameters.

Listing 10.17: faultyswap.cpp

ffinclude <iostream>

/*

* swap(a, b)

* Attempts to interchange the values of

* its parameters a and b. That it does, but

* unfortunately it only affects the local

* copies.

*/

void swap(int a, int b) { int temp = a; a = b; b = temp;

}

/*

* mai n

* Attempts to interchange the values of

* two variables using a faulty swap function. */

int main() {

int varl =

5,

var2 =

19;

std::cout

<<

"varl =

A

A

varl << ",

var2 =

" << var2 <<

' \n

swap(varl,

va

r2) ;

std::cout

<<

"varl =

A

A

varl << ",

var2 =

" << var2 <<

' \n

The output of Listing[I().17||(faultyswap.cpp) is

varl = 5, var2 = 19 varl = 5, var2 = 19

Unfortunately, the swap function simply interchanges copies of the actual parameters, not the actual parameters themselves. We really would like to write a function that interchanges the caller’s variables.

Pass by reference is necessary to achieve the desired effect. C++ can do pass by reference in two ways: pointer parameters and reference parameters.

10.9.1 Pass by Reference via Pointers

Pointers (see Section |10.7| allow us to access the memory locations of variables. We can use this capability to allow a function to modify the values of variables that are owned by its caller. Listing |10.18| (swapwithpointers.cpp) provides a correct version of our variable interchange program.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 10.18: swapvirithpo'inters.cpp

#include <iostream>

/* *

* swap(a, b)

* Interchanges the values of memory

* referenced by its parameters a and b.

* It effectively interchanges the values

* of variables in the caller's context.

*/

void swap(int *a, int *b) { int temp = *a;

*a = *b;

*b = temp;

}

/*

* mai n

* Interchanges the values of two variables

* using the swap function.

*/

int main() {

int varl = 5, var2 = 19;

std:

:cout << "varl =

" << varl << ",

var2 =

" << var2 <<

' \n 1 ;

swap

(&varl, &var2);

std:

:cout << "varl =

" << varl << ",

var2 =

" << var2 <<

' \n' ;

Note 1

Note 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

Note 9

Note 10

©2018 Richard L. Halterman

Note 11

• The swap function’s

*b = temp;

statement assigns the local temp value to mai n’s var2 variable, since swap’s b parameter points to mai n’s var2.

• Within mai n, the call

swap(&varl, &var2);

passes the addresses of its local variables to swap.

In reality, pass by reference with pointers is still using pass by value. Instead of passing copies of values, we are passing copies of addresses. In Listing! 10.18|(swapwithpointers.cpp), for example, the values of the addresses of varl and var2 are copied to the formal parameters a and b. The difference is we are not attempting to reassign a or b; we are reassigning memory to which a and b point. Whether we use the original address or a copy of the address, it is still the same address—the same numeric location in memory.

10.9.2 Pass by Reference via References

Both C and C++ support pass by reference with pointers (see Section jl0.9.1| . Since C++ programs often use C libraries, C++ programmers must be familiar with the pointer technique for pass by reference. C++, however, provides a simpler way of implementing pass by reference using reference parameters. (See Section 10.8 for an introduction to reference variables.) Listing 10.19 (swapwithreferences.cpp) uses reference

parameters in our variable interchange program.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The syntax of Listing! 10.19 (swapwithreferences.cpp) is a bit cleaner than that of Listing 10T8](swapwithpointers.cpp). In Listing |lOT9](swapwithreferences.cpp):

• The formal parameters to swap, a and b, are references to integers; this is signified by the & symbol following i nt in their declarations. Because a is a reference we use it exactly like an integer; there is no need to dereference it with the * operator to change the value of the integer it aliases. Because a is a reference, however, it is an alias to another variable or memory location elsewhere. This means if we modify a, we also modify the variable it references, in this case varl in mai n. The statement

int temp = a;

assigns to the local variable temp the value of a, but since a is another way to get to varl, this statement ultimately assigns varl’s value to temp.

• Within mai n, the call

swap(varl, var2);

does not require any special decoration. It looks like a normal pass by value function invocation. A programmer must be aware that swa p uses reference parameters and that any function that uses reference parameters can change the actual values passed to it.

Reference parameters were introduced into C++ so that some of the more advanced object-oriented features could be implemented more cleanly. Some argue that for simpler situations like the swa p function, pointer pass by reference is more desirable than reference parameter pass by reference because with pointer pass by reference, the caller is forced to pass addresses of the actual parameters that may be modified. In this way there can be no doubt that pass by reference is going on. With reference parameters, pass by value and pass by reference cannot be distinguished at the call site, since a call with reference parameters looks exactly like a pass by value invocation.

In general, pure pass by value functions are preferred to pass by reference functions. Functions using pass by reference cause side effects. This means they can change the state of the program in ways that can be determined only by looking inside of the function and seeing how it works. Functions that access global variables (see Section |l0.1| can also cause side effects. Program development is much easier when functions can be treated as black boxes that perform computations in isolation without the possibility of affecting anything outside of their local context. The result of a function’s work can be assigned to a variable thus changing the state of the program, but that change is the responsibility of the caller, not the responsibility of the function itself. With pass by value, the function’s parameters and local variables come into existence when the function executes, the parameters and local variables disappear when the function is finished, and nothing else is affected by the function’s execution.

Side-effect-free functions can be developed and tested in isolation from the rest of the program. Once programmers are satisfied with their correctness, they need not be touched again as the remainder of the system is developed. Functions with side effects, however, have dependencies to other parts of the program, and changes elsewhere in the system may require programmers to modify and re-evaluate existing functions.

Chapter Notes

The output of ListingflO. 18[(swapwithpointers.cpp) is

varl = 5, var2 = 19 varl = 19, var2 = 5

which is the result we were trying to achieve. The swap function can manipulate mai n’s variables directly since we passed it pointers to those variables.

In Listing 10.18 (swapwithpointers.cpp):

• The formal parameters to swap, a and b, are pointers to integers; they are not integers themselves. In order to access the integer to which the pointer named a refers, it must be dereferenced. That is why any use of a in swap’s body is prefixed with the pointer dereferencing operator, *. The statement

int temp = *a;

assigns to the local variable temp the value of the variable to which a points. Since mai n passes the address of varl as the first parameter in its call to swap, in this case a points to varl, so *a is effectively another way to access the memory location of varl in mai n. The function thus assigns the value of mai n’s varl variable to temp.

• In swap’s statement

*a = *b;

since *a is effectively main’s varl variable and *b is effectively main’s var2 variable, this statement assigns the value of mai n’s var2 to its varl variable.

Draft date: September 25, 2018

10.10 Higher-order Functions

The functions we have seen so far have accepted only data as parameters. Since functions can contain conditional statements and loops, they can do different things based on the data they receive. The code within each function, however, is fixed at compile time. Consider the following function:

©2018 Richard L. Halterman

Draft date: September 25, 2018

int evaluate (int x, int y) { return x + y;

}

The call

evaluate(10, 2)

evaluates to 12. Since the evaluate function returns the sum of its two parameters. The call evaluate(-4, 6) ;

returns 2. The function returns a different result this time because we passed different parameters to it. The evaluate function in a sense behaves differently depending on the arguments passed by its caller; however, it always adds its two parameters. There is no way we can call evaluate and expect it to multiply its two parameters instead. The evaluate function is hard-coded to perform addition.

What if we wanted the evaluate function to be able to perform different arithmetic operations at different times during a program’s execution? Unfortunately, evaluate as it currently is written cannot adapt to perform a different arithmetic operation. The good news is that we can rewrite evaluate so that it can flexibly adapt to a caller’s changing arithmetic needs.

C++ allows programmers to pass functions as parameters to other functions. A function even may return a function as a result. A function that accepts one or more functions as parameters or returns a function as a result is known as a higher-order function. As we will see, higher-order functions open up new programming possibilities enabling us to customize the behavior of a function by plugging into it different functions to achieve different effects.

C++ achieves higher-order functions via function pointers. During a program’s execution, the compiled machine language code for a function must reside in the computer’s memory for the program to be able to invoke the function. That means every function has a memory address just as each variable has its own specific memory address. A pointer to a function holds the starting address for the compiled code of a particular function.

Listing 10.20 (arithmeticeval.cpp) provides an example of a higher-order function in action.

Listing 10.20: aHthmet-iceval.cpp

ttinclude <iostream>

int add(int x, int y) { return x + y;

}

int multiply(int x, int y) { return x * y;

}

int evaluate(int (*f)(int, int), int x, int y) { return f (x, y);

}

int main() {

std::cout << add(2, 3) << '\n'; std::cout << multiply(2, 3) << '\n'; std::cout << evaluate(&add, 2, 3) << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << evaluate(&multiply, 2, 3) << '\n';

}

The first parameter of the evaluate function, int (*f) (i nt , i nt)

represents a function pointer. The parameter’s name is f , and f is a pointer to a function that accepts two integer parameters and returns an integer result. In Listing || 10.20|| (arithmeticeval.cpp), the first parameter a caller must pass to evaluate is the address of a function with a prototype that matches the formal parameter specified in evaluate’s definition. Both the add and multi ply functions qualify because they accept two integer parameters and return an integer result. The expression

evaluate(&add, 2, 3)

passes the address of the add function to evaluate. In the body of the evaluate function we see that evaluate invokes the function specified by its first parameter (f), passing to this function its second (x) and third (y) parameters as the two parameters that function expects. The net effect, therefore, of the call

evaluate(&add, 2, 3)

is the same as add(2, 3)

C++ has a somewhat relaxed syntax for function pointers that cannot be applied to pointers to data. When invoking evaluate in source code we may omit the ampersand in front of the function argument, as is

std::cout << evaluate(add , 2, 3) << '\n' ;

Since the compiler knows that add is a function and since parentheses do not follow the word add, the compiler deduces that this is not a call to add but rather the address of the add function.

When the name of a previously declared function appears by itself within C++ source code it represents a pointer to that function.

Function pointers are not restricted to function parameters. Given the definition of add above, the following code fragment is legal C++:

// Declare func to be a pointer to a function that accepts // two integer parameters and returns an integer result int (*func)(int, int);

// Assign add to func func = add;

// Call add through func std::cout << func(7, 2) << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

This code fragment as part of a complete C++ program would print 9.

Higher-order functions via function pointers provide a powerful tool for developing flexible programs. With functions as parameters we can dynamically customize the behavior of a function, essentially “plugging in” new functionality by passing in different functions. We will put higher-order functions to good use in Chapter|T2|

10.11 Exercises

1. Consider the following C++ code:

#include <iostream>

int suml(int n) { int s = 0; while (n > 0) { s++;

n—;

}

return s;

}

int input;

int sum2() { int s = 0; while (input > 0) { s++;

input--;

}

return s;

}

int sum3() { int s = 0;

for (int i = input; i > 0; i —) s++;

return s;

}

int main() {

// See each question below for details

}

(a) What is printed if mai n is written as follows?

int main() { input = 5;

std::cout << suml(input) << '\n' ; std::cout << sum2() << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << sum3() << '\n' ;

}

(b) What is printed if man n is written as follows?

int main() { input = 5;

std::cout << suml(input) << '\n ' ; std::cout << sum3() << '\n' ; std::cout << sum2() << '\n' ;

}

(c) What is printed if mai n is written as follows?

int main() { input = 5;

std::cout << sum2() << '\n' ; std::cout << suml(input) << '\n' ; std::cout << sum3() << '\n' ;

}

(d) Which of the functions suml, sum2, and sum3 produce a side effect? What is the side effect?

(e) Which function may not use the input variable?

(f) What is the scope of the variable input? What is its lifetime?

(g) What is the scope of the variable i ? What is its lifetime?

(h) Which of the functions suml, sum2, and sum3 manifest good functional independence? Why?

2. Consider the following C++ code:

#include <iostream>

int next_intl() {

static int cnt = 0; cnt++; return cnt;

}

int next_int2() { int cnt = 0; cnt++; return cnt;

}

int global_count = 0;

int next_int3() { global_count++; return global_count;

}

int mainQ {

for (int i = 0; i < 5; i++)

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout <<

next_intl()

<<

II II

<<

next_int2()

<<

II II

<<

next_int3()

<<

' \n' ;

(a) What does the program print?

(b) Which of the functions next_i ntl, next_i nt2, and next_i nt3 is the best function for the intended purpose? Why?

(c) What is a better name for the function named next_int2?

(d) The next_int3 function works in this context, but why is it not a good implementation of a function that always returns the next largest integer?

3. The following C++ program is split up over three source files. The first hie, counter.h, consists of

int read(); int increment(); int decrement();

The second hie, counter.cpp, contains static int count;

int read() {

return count;

}

int increment() { if (count < 5) count++;

}

int decrement() { if (count > 0) count--;

}

The third hie, main.cpp, is incomplete:

#include <iostream>

#include "counter.h"

int main() {

// Add code here

}

(a) Add statements to mai n that enable it to produce the following output:

©2018 Richard L. Halterman

Draft date: September 25, 2018

The restriction is that the only ouput statement you are allowed to use (three times) is std::cout << read() << '\n' ;

(b) Under the restriction of using the same output statement above, what code could you add to mai n so that it would produce the following output?

6

4. Consider the following C++ code: #include <iostream>

int max(int n) { return n;

}

max

(int m,

int n) {

return (m

> =

n) ? m

: n

5

max

(int m,

int n, int

r)

{

int

x = m;

if

(n > x)

x = n;

if

(r > x)

x = r;

return x;

mai

n() {

std

: :cout

<<

max(4)

<<

'\

n' ;

std

: :cout

<<

max(4,

5)

<<

' \n

1 .

5

std

: :cout

<<

max(5,

4)

<<

' \n

1 .

5

std

: :cout

<<

max(l,

2,

3)

<<

' \n' ;

std

: :cout

<<

max(2,

1,

3)

<<

' \n' ;

std

: :cout

<<

max(2,

1,

2)

<<

' \n' ;

(a) Is the program legal since there are three different functions named max?

(b) What does the program print?

5. Consider the following function:

int proc (int n) { if (n < 1)

return 1;

else

return proc(n/2) + proc(n - 1);

}

Evaluate each of the following expressions:

©2018 Richard L. Halterman

Draft date: September 25, 2018

(a) proc(0)

(b) proc(l)

(c) proc(2)

(d) proc(3)

(e) proc(5)

(f) proc(10)

(g) proc(-10)

6. Rewrite the gcd function so that it implements Euclid’s method but uses iteration instead of recursion.

Table caption7. If x is a variable, how would you determine its address in the computer’s memory?

Table caption8. What is printed by the following code fragment?

int

x = 5 .

i y

- 3,

p =

&x

*q

= &y;

std:

: cout

<<

"x =

II

<<

X

<<

it

3

y = "

<<

y

<<

' \n'

3

x =

y;

std:

: cout

<<

"x =

II

<<

X

<<

II

3

y = "

<<

y

<<

' \n'

3

x =

7;

std:

: cout

<<

"x =

II

<<

X

<<

II

5

y = "

<<

y

<<

' \n'

3

*P =

© i—1

std:

: cout

<<

"x =

II

<<

X

<<

II

3

y = "

<<

y

<<

' \n'

3

P =

q;

*P =

: 20;

std:

: cout

<<

"x =

II

<<

X

<<

II

3

y = "

<<

y

<<

' \n '

3

Table caption9. Given the declarations: int x, y, *p, *q;

indicate what each of the following code fragments will print.

(a) p = &x; x = 5;

std::cout << *p << ' \ n ' ;

(b) x = 5;

P = &x;

std::cout << *p << '\n' ;

(c) p = &x;

*P = 8;

std::cout << *p << '\n ' ;

(d) p = &x;

q = &y;

X = 100; y = 200;

*q = *p;

std::cout << x << ' ' << y << '\n' ; std::cout << *p << ' ' << *q << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

(e) p = &x;

q = &y;

x = 100; y = 200;

q = p;

std::cout << x << ' ' << y << '\n' ; std::cout << *p << ' ' << *q << '\n' ;

(f) x — 5;

y - iQ; p = q = &y;

std::cout << *p << ' ' << *q << '\n' ; *p = 100;

*q = i;

std::cout << x << ' ' << y << '\n' ;

(g) x = 5;

y = 10 ;

P = q = &x;

*p = *q = y;

std::cout << x << ' ' << y << '\n' ;

10. The following function does not behave as expected:

/*

* (Faulty function)

~k

* get_range

* Establishes a range of integers. The lower value must

* be greater than or equal to min, and the upper value

* must be less than or equal to max.

* min is the lowest acceptable lower value.

* max is the highest acceptable upper value.

* lower is assigned the lower limit of the range

* upper is assigned the upper limit of the range */

void get_range (i nt min, int max, int lower, int upper) {

std::cout << "Please enter a data range within the bounds "

<< min << "..." << max << ";

do { // Loop until acceptable values are provided std::cin >> lower >> upper; if (lower < min)

std::cout << lower << " is too low, please try again.\n" if (upper > max)

std::cout << upper << " is too high, please try again.\n

}

while (lower < min || upper > max);

(a) Modify the function so that it works using pass by reference with pointers.

©2018 Richard L. Halterman

Draft date: September 25, 2018

(b) Modify the function so that it works using pass by reference with reference parameters.

11. Classify the following functions as pure or impure, x is a global variable and LIMIT is a global constant.

(a)

int

f1 (i nt

m,

int n) {

return

2*m

i + 3*n;

}

(b)

int

f2 (i nt

n)

{

return

n

LIMIT;

}

(c)

int

f3 (i nt

n)

{

return

n

x;

}

(d) void f4(int n) {

std::cout << 2 *n << '\n' ;

}

(e) int f5(int n) {

int m;

std::cin >> m; return m * n;

}

(f) int f6(int n) {

int m = 2*n, p; p = 2*m - 5; return p - n;

}

12. Complete the following function that assigns to its mx and my reference parameters the components

of the midpoint of the points (xi,yi) and represented by the parameters xl, yl, x 2 , and y 2 .

// Computes the midpoint of the points (xl, yl) and (x2, y2).

// The point (mx, my) represents the midoint. void midpoint (double xl, double yl, double x2, double y2, double& mx, double& my) {

// Add your code . . .

}

13. Complete the following function that assigns to its i x and i y reference parameters the components of the point of intersection of two lines. The first line passes through the points (jci ,yi) and (x 2 ,yi)\ the second line passes through the points (x^ ,>’ 3 ) and (x 4 ,y 4 ). If the two lines do not intersect in a single point (that is, they are parallel to each other), the function should assign INFINITY to both ix and iy. INFINITY is a double-precision floating-point constant defined in the cmath header file. It represents a very large number that you effectively can treat as infinity.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Computes the point of intersection of two lines.

// The first line passes through the points

// (xl, yl) and (x2, y2). The second line passes through the // points (x3, y3) and (x4, y4). The function assigns // (ix, iy) as the intersection point.

// If the two lines do not intersect in a singal point, the function // computes (INFINITY, INFINITY).

void intersection (double xl, double yl, double x2, double y2, double x3, double y3, double x4, double y4, double& ix, double& iy) {

// Add your code . . .

}

14. Rewrite the recursive gcd function found in Listing 10.8 (gcd.cpp) so that it uses the same basic algorithm of Euclid but uses iteration instead of recursion.

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 11 Sequences

The variables we have used to this point can assume only one value at a time. As we have seen, we can use individual variables to create some interesting and useful programs; however, variables that can represent only one value at a time do have their limitations. Consider Listing 11.1 (averagenumbers.cpp) which averages five numbers entered by the user.

A sample run of Listing 11.1 (averagenumbers.cpp) looks like:

Please enter five numbers: 9 3.5 0.2 100 15.3 The average of 9.0, 3.5, 0.2, 100.0, 15.3 is 25.6

The program conveniently displays the values the user entered and then computes and displays their average.

Suppose the number of values to average must increase from five to 25. If we use Listing 11.1 (averagenumbers.cpp) as a guide, we must introduce twenty additional variables, and the overall length of the program will necessarily grow. Averaging 1,000 numbers using this approach is impractical.

Listing |LL2j(averagenumbers2.cpp) provides an alternative approach for averaging numbers.

©2018 Richard L. Halterman

Draft date: September 25, 2018

double sum = 0.0, num;

const int NUMBER_OF_ENTRIES = 5;

std::cout << "Please enter " << NUMBER_0F_ENTRIES << " for (int i = 0; i < NUMBER_0F_ENTRIES; i++) { std::cin >> num;

}

std

}

sum += num;

:cout << "The average of " << NUMBER_OF_ENTRIES << << sum/NUMBER_OF_ENTRIES << '\n' ;

numbers:

values is

II

Listing |jll.2|j (averagenumbers2.cpp) behaves slightly differently from Listing |ll.l[ (averagenumbers.cpp), as the following sample run using the same data shows:

Please enter 5 numbers: 9 3.5 0.2 100 15.3 The average of the 5 values is 25.6

Listing j 1 L2|(averagenumbers2.cpp) can be modified to average 25 values much more easily than Listing jlTT](averagenumbers.cpp) that must use 25 separate variables—-just change the constant NUMBER_OF_ENTRIES. In fact, the coding change to average 1,000 numbers is no more difficult. However, unlike the original average program, this new version does not display the numbers entered. This is a significant difference; it may be necessary to retain all the values entered for various reasons:

• All the values can be redisplayed after entry so the user can visually verify their correct entry.

• The programmer may want to display the values in some more persistent way; for example, the user may instead type the values in a graphical user interface component, like a visual grid (spreadsheet).

• A more sophisticated program may need to process the values in a different way; for example, we may wish to display just the values entered above a certain value (like greater than zero), but the limit is not determined until after the user finishes entering all the numbers.

In all of these situations we must retain the values of all the variables for future recall.

We need to combine the advantages of both of the above programs; specifically we want to be able to

• retain every individual value, and

• avoid defining separate variables to store all the individual values

These may seem like contradictory requirements, but C++ provides several standard data structures that simultaneously provide both of these advantages. In this chapter we will examine the common sequence types available in C++: vectors and arrays.

Vectors and arrays are sequence types because a sequence implies its elements are ordered. A nonempty sequence has the following properties:

• Every nonempty sequence has a unique first element.

• Every nonempty sequence has a unique last element.

• Every element in a nonempty sequence except for the first element has a unique predecessor element.

• Every element in a nonempty sequence except for the last element has a unique successor element.

©2018 Richard L. Halterman

Draft date: September 25, 2018

We call this a linear ordering. In a linear ordering you can begin at the first element and repeatedly visit successor elements until you reach the last element. There never is any ambiguity about which element comes next in a sequence.

The data structures we examine in this chapter, std : : vecto rs, primitive arrays, and std : : a r rays, are all sequence types.

11.1 Vectors

A vector in C++ is an object that manages a block of memory that can hold multiple values simultaneously; a vector, therefore, represents a collection of values. A vector has a name, and we may access the values it contains via their position within the block of memory managed by the vector. A vector stores a sequence of values, and the values must all be of the same type. A collection of values all of the same type is said to be homogeneous.

11.1.1 Declaring and Using Vectors

In order to use a vector object within a C++ program, you must add the preprocessor directive #include <vector>

The vector type is part of the standard (std) namespace, so its full name is std : : vector, just like the full name ofcoutis std: :cout (see Section 2.1). If you include the directive

using std::vector;

in your source file, you can use the shorter name vector within your code. We may declare a vector object that can hold integers as simply as std::vectorci nt> vec_a;

The type within the angle brackets may be any valid C++ data type. When declared this way, the vector vec_a initially is empty.

We can declare a vector with a particular initial size as follows: std::vectorci nt> vec_b(10);

Here vec_b initially holds 10 integers. All 10 elements are zero by default. Note that the vector’s size appears within parentheses following the vector’s name.

We may declare a vector object of a given size and specify the initial value of all of its elements:

std: :vector<int> vec_c(10, 8);

In this example vec_c initially holds 10 integers, all having the value 8. Note that the first number within the parentheses following the vector’s name indicates the number of elements, and the second argument specifies the initial value of all the elements.

We may declare a vector and specify each and every element separately:

std::vectorci nt> vec_d{10, 20, 30, 40, 50};

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.1 Four different vector declaration statements and conceptual illustrations of the resulting vectors

vectorci nt> vectorci nt> vectorci nt> vectorci nt>

vec_a; vec_b(10); vec_c(10, 8); vec_d{ 10, 20,

30, 40 };

vec_a

"\

V

)

vec_b

r

0

0

0

0

0

0

0

0

0

0

0

1

2

3

4

5

6

7

8

9

vec_

c

(

8

8

8

8

8

8

8

8

8

8

0

1

2

3

4

5

6

7

8

9

vec_d

f

\

10

20

30

40

V

0

1

2

3

)

Note that the elements appear within curly braces, not parentheses. The list of elements within the curly braces constitutes a vector initializer list. This kind of declaration is practical only for relatively small vectors. Figure 11.1 provides a conceptual illustration of the vectors vec_a, vec_b, vec_c, and vec_d.

Like any other variable, a vector can be local or global, and it must be declared before it is used.

The vector initializer list syntax:

std::vectorcf nt> vec_d{10, 20, 30, 40, 50};

is a C++11 language feature and, therefore, is not be supported by older C++ compilers; in particular, the C++ compilers available for Visual Studio editions prior to Visual Studio 2013 do not support this initializer list syntax.

Once we have a non-empty vector object, we can access its elements using the vector’s name, the square bracket operator, and a integer index:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.2 The numbers below the boxes represent indices, or positions, within the vector. Note that the first element in a vector is found at index 0, not 1.

vector<int> list(3); list[0] = 5; list[l] = -3; list [2] = 12;

li st

std:

:vector<

i nt> list(3);

//

list

[0]

5 ;

t

//

list

[1]

-3

5

//

list

[2]

12

5

//

std:

: cout

<<

list[l] << '

\ n ' ;

Declare list to be a vector of three ints

Make the first element 5

Make the second element -3

Make the last element 12

// Print the element at index 1

This code fragment shows how the square brackets allow us to access an individual element based on that element’s position within the vector. The number within the square brackets indicates the distance from the beginning of the vector. The expression li st [0] therefore indicates the element at the very beginning (a distance of zero from the beginning), and list[l] is the second element (a distance of one away from the beginning). After executing these assignment statements, the li st vector conceptually looks like Figure [lL2|

C++ classifies the square brackets, [], as a binary operator, since it requires two operands: a vector’s name and an index.

Vectors may hold any valid C++ data type. The following code fragment declares three vectors of differing types:

std::vector<i nt> list;

std:: vector<double> collectionf 1.0, 3.5, 0.5, 7.2 };

std:: vector<char> lettersf 'a', 'b' , 'c' };

Here li st is empty but can contain integer values, collecti on is a vector of double-precision floatingpoint numbers initially containing the values contained in the initializer list, and letters holds the lowercase versions of the first three letters of the English alphabet. Figure |ll,3|| illustrates these three vector objects.

We can observe two key points from Figures[TlTljjTT3(

• Vectors store their elements in a contiguous block of memory. This means, for example, the memory occupied by the element at index 2 follows immediately after the memory occupied by the element at index 1 and immediately before the element at index 3.

• Elements in a vector are located by a numeric index. The first element is at index zero , not one.

In an expression such as list[3]

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.3 Vectors containing different types of elements. Note that while two different vector objects may contain different types of elements, all the elements within a particular vector object must all have the same type.

vector<int> list;

vector<double> collection{ 1.0, 3.5, 0.5, vector<char> letters! 'a', 'b', 'c' };

7.2 };

list collection letters

r

1.0

3.5

0.5

7.2

0

1

2

3

2

f

'a'

'b'

'c'

\

0

i

2

2

the expression within the square brackets, in this case 3, is called an index or subscript. The subscript terminology comes from mathematicians who use subscripts to reference elements in a mathematical sequence (for example, V 2 represents the second element in the mathematical sequence V). Unlike the convention often used in mathematics, however, the first element in a vector is at position zero , not one. The expression li st [2] can be read aloud as “li st sub two.” As a consequence of a zero beginning index, if vector a holds n elements, the last element in a is a \n — 1], not a [n] .

An element of a vector accessed via its index behaves just like a variable of that type; for example, suppose we declare nums as

std:: vector<double> nums(10);

This declaration specifies a collection of 10 double-precision floating-point elements. The following code fragment shows how we can manipulate some of those elements:

// Print the fourth element

std::cout << nums[3] << '\n' ;

// The third element is the average of the first and last elements

nums[2] = (nums[0] + nums[9])/2;

// Assign elements at indices 1 and 4 from user input

std::cin >> nums[l] >> nums[4];

Note that the < < operator associated with the std : : cout output stream object is not designed to work with vector objects as a whole:

std::cout << nums << '\n' ; // <- Will not compile!

The expression within the [] operator must be compatible with an integer. Suppose a is a vector, x is a numeric variable, max is a function that returns a numeric value, and b is a vector that holds numeric values. The following examples illustrate the variety of expressions that qualify as legal vector indices:

• an numeric literal: a [34]

• an numeric variable: a [x]

©2018 Richard L. Halterman

Draft date: September 25, 2018

• an arithmetic expression: a[x + 3]

• an integer result of a function call that returns an numeric value: a[max(x, y)]

• an element of a vector that contains numeric values: a [b [3] ]

A floating-point index is permissible but discouraged. The compiler will issue a warning about using a floating-point index with good reason. A vector may have an element at index 2 or index 3, but it is not possible to have an element located between indices 2 and 3; therefore, the executing program will truncate a floating-point index to an integer in order to select the proper element within the vector.

11.1.2 Traversing a Vector

The action of moving through a vector visiting each element is known as traversal, f o r loops are ideal for vector traversals. If a is an integer vector containing 10 elements, the following loop prints each element in a:

for (int i = 0; i < 10; i++)

std::cout << a[i] << '\n' ;

The loop control variable, i , steps through each valid index of vector a. Variable i ’s value starts at 0 and ends at 9, the last valid position in vector a.

The following loop prints contents of vector a in reverse order:

for (int i = 9 ; i >= 0; i —)

std::cout << a[i] << '\n' ;

The following code produces a vector named set containing the integer sequence 0, 1, 2, 3, ... , 999:

std::vectorci nt> set(1000); for (int i =0; i < 1000; i++) set [i ] = i ;

We now have all the tools we need to build a program that flexibly averages numbers while retaining all the values entered. Listing |11.3| (vectoraverage.cpp) uses a vector and a loop to achieve the generality of Listing[TL2](averagenumbers2.cpp) with the ability to retain all input for later redisplay.

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Draft date: September 25, 2018

}

std::cout << "The average of

for (int i = 0; i < NUMBER_OF_ENTRIES - 1; i++)

std::cout << numbers[i] << ",

// No comma following last element

std::cout << numbers[NUMBER_OF_ENTRIES - 1] << " is << sum/NUMBER_OF_ENTRIES << 1 \n' ;

The output of Listing |TO|j (vectoraverage.cpp) is similar to the original Listing flLT| (averagenurnbers.cpp) program:

Please enter 5

numbers:

9 3.5 0.2 100 15.3

The average of

9.0, 3.5,

0.2, 100.0, 15.3 is 25.6

Unlike the original program, however, we now conveniently can extend this program to handle as many values as we wish. We need only change the definition of the NUMBER_OF_ENTRIES constant to allow the program to handle any number of values. This centralization of the definition of the vector’s size eliminates duplicating a hard-coded value and leads to a program that is more maintainable. Suppose every occurrence of NUMBER_OF_ENTRIES were replaced with the literal value 5. The program would work exactly the same way, but changing the size would require touching many places within the program. When duplicate information is scattered throughout a program, it is a common error to update some but not all of the information when a change is to be made. If all of the duplicate information is not updated to agree, the inconsistencies result in errors within the program. By faithfully using the NUMBER_OF_ENTRIES constant throughout the program instead of the literal numeric value, we eliminate the possibility of such inconsistency.

The first loop in Listing) TT3| (vectoraverage.cpp) collects all five input values from the user. The second loop only prints the first four because it also prints a trailing comma after each element. Since no comma should be displayed after the last element, the program prints the last element after the loop is finished.

The compiler will insist that the programmer use a numeric value for an index, but the programmer must ensure that the index used is within the bounds of the vector. Since the index may consist of an arbitrary integer expression whose value cannot be determined until run time, the compiler cannot check for out-of-bound vector accesses; for example, in the code

int x;

std: : vector'd nt> v(10); // Make a vector with 10 spaces available

std::cin >> x; // User enters x at run time

v[x] = 1; // Is this okay? What is x?

the compiler cannot predict what number the user will enter. This means that misuse of a vector index can lead to run-time errors. To illustrate the problem, consider Listing]! 1.4| (vectoroutofbounds.cpp).

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Draft date: September 25, 2018

Figure 11.4 Memory access error under Visual C++

std::cout << a[i] << " std::cout << '\n 1 ;

// Change all the 5s in vector a to 8s

for (int i = 0; i <= SIZE; i++) // Bug: <= should be <

a[i] = 8;

// Reprint the contents of the vector

std::cout << "a contains for (int i = 0; i < SIZE; i++) std::cout << a[i] << " "; std::cout << '\n 1 ;

Listing 111,4| (vectoroutofbounds.cpp) contains a logic error; the reassignment loop goes one past the end of vector a. Attempting to access elements outside the bounds of a vector produces what is known as undefined behavior. The C++ language standard uses this term to indicate a program’s behavior is not specified, and compiler writers are free to do whatever they want. Often, running programs that venture into undefined behavior will crash, but sometimes they may continue executing with no indication of a problem and appear to behave correctly most of the time. In other words, the actual program behavior is system dependent and compiler dependent. Consider code that represents undefined behavior to be a logic error, since its action is inconsistent across platforms and compilers. Simply said, the program’s behavior is unpredictable. Unpredictable behavior is incorrect behavior.

In most cases, an out-of-bounds access simply accesses memory outside the vector. If this includes memory that does not belong to the executing program, modern operating systems will terminate the program and produce an error message. Under Visual C++ when the program is built as a debug version (the default when using the IDE), the program prints the contents of the vector the first time but crashes before it can print it out a second time. Microsoft Windows then displays the dialog box shown in Figure fLL4[

The program running under Linux or macOS may simply print in the console:

Segmentation fault

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Draft date: September 25, 2018

If your program is using a vector, and it terminates with such a message, you should check its source code carefully for places where out-of-bounds vector accesses are possible.

The following code fragment shows some proper and improper vector accesses:

std::vector<i nt> numbers[0] = 5; numbers[9] = 2; numbers[-l] = 5; numbers[10] = 5; numbers[1.3] = 5;

numbers(10); // Declare the vector // Put value 5 first // Put value 2 last

// Out of bounds; first valid index is 0 // Out of bounds; last valid index is 9 // Compiler warning, 1.3 is not an int

In a vector traversal with a f o r loop such as

for (int i = 0; i < SIZE; i++) std::cout << a[i] << '\n' ;

where you know SIZE is the number of elements in the vector, it is easy to ensure that i cannot fall outside the bounds of vector a, but you should check an arbitrary index value before using it. In the following code:

int x;

std::vectorci nt> a(10); // Make a vector with 10 spaces available

std::cin >> x; // User enters x at run time

// Ensure x is within the bounds of the vector if (0 <= x && x < 10)

a[x] = 1; // This is safe now

else

std::cout << "Index provided is out of range\n";

the i f statement ensures the vector access is within the vector’s bounds.

C++11 supports a variation of the for statement that uses special syntax for objects like vectors that support traversal. Commonly known as the range-based for or “foreach” statement, this version of the f o r statement permits vector traversal without an index variable keeping track of the position. The following code fragment uses a range-based for statement to print the contents of an integer vector named vec:

for (int n : vec)

std::cout << n << ' ' ;

You can read this statement as “for each i nt n in vec, std : : cout << n << ' 1 ,” The colon (:) therefore is pronounced “in.” In the first interation of this range-based for loop the variable n represents the first element in the vector vec. In the second iteration n represents the second element. The third time through n is the third element, and so forth. The declared variable assumes the role of a different vector element during each iteration of the loop. Note that the range-based for loop requires no control variable to keep track of the current index within the vector; the loop itself takes care of that detail, freeing the programmer from that task.

The general form of this range-based f o r statement is

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for

element variable

statement

vector variable )

If the element variable within the range-based for loop is declared to be a reference, the code within the body of the loop may modify the vector’s elements. Listing [TT3j (foreachexarnple.cpp) allows a user to populate a vector with 10 numbers and then prints the vector’s contents.

to assign each element in the vector. The second range-based for statement does not need to use a reference variable because it does not change any of the contents of vector vec.

It is not always possible to use the range-based for statement when traversing vectors. The rangebased for statement iterates forward through the vector elements and cannot move backwards. Also, the range-based for statement is not convenient if you want to consider only a portion of the elements in the vector. Examples include visiting every other element in the vector or considering only the first third of the elements. In these specialized cases you can use a standard for loop with an integer control variable. Section|20.5|explores some other options for traversing vectors in creative ways.

11.1.3 Vector Methods

A vector is an object, and objects differ from the simple types like i nt, double, and bool, in a number of ways. Most objects have access to special functions called methods. C++ programmers often refer to methods as member functions. A method is a function associated with a class of objects. A method invocation involves a slightly different syntax than a function invocation; for example, if obj is an object that supports a method named f that accepts no parameters, we can invoke f on behalf of obj with the statement:

obj.f();

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Draft date: September 25, 2018

The dot operator connects an object with a method to invoke. Other than this special invocation syntax, methods work very much like the global functions introduced in Chapter[8] A method may accept parameters and may return a value.

Vectors support a number of methods, but we will focus on seven of them:

• push_back—inserts a new element onto the back of a vector

• pop_back—removes the last element from a vector

• operator [] —provides access to the value stored at a given index within the vector

• at—provides bounds-checking access to the value stored at a given position within the vector

• si ze —returns the number of values currently stored in the vector

• empty —returns true if the vector contains no elements; returns false if the vector contains one or more elements

• clear —makes the vector empty.

We have seen how to declare a vector of a particular size and use the space provided; however, we are not limited by a vector’s initial size. In order to add an element to a vector, we use the push_back method as follows:

std::vector<i nt> list; list.push_back(5); list.push_back(-3); list.push_back(12) ;

// Make an empty vector that can hold integers // Add 5 to the end of list // Add -3 to the end of the list // Add 12 to the end of list

After executing the three push_back calls above, the list vector conceptually looks just like Figure [ 11.2) The size of the vector adjusts automatically as new elements are inserted onto the back. Each push_back method call increases the number of elements in a vector by one.

The pop_back method performs the opposite action of push_back. A call to pop_back removes the last element from a vector, effectively reducing the number of elements in the vector by one. The following code fragment produces a vector named list that contains only the element 5.

std::vector<i nt> list; //

list.push_back(5); // list.push_back(-3); // list.push_back(12) ; // list.pop_back(); // list.pop_back(); //

Declare list to be a vector Add 5 to the end of list Add -3 to the end of the list Add 12 to the end of list Removes 12 from the list Removes -3 from the list

We have been using the operator[] method to access an element in the vector. The word operator is reserved in C++, and that makes this method even more interesting. The expression

vec. operator [](2)

is the long way to write vec[2]

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Draft date: September 25, 2018

Programmers use the shorter syntax exclusively, but the longer expression better illustrates the fact that the square bracket ( []) operator really is a method in the std : : vector class of objects.

As we have seen, a programmer must be vigilant to avoid using an out-of-bounds index with the operator [] method. The vector class provides an additional method, at, that provides index bounds checking. The expression vec[x] in and of itself provides no bounds checking and so may represent undefined behavior. The functionally equivalent expression vec . at (x) will check to ensure that the index x is within the bounds of the vector. If x is outside the acceptable range of indices, the method is guaranteed to produce a run-time error. Listing |l 1.61 (vectoroutofbounds2.cpp) is a variation of Listing ) 11.4| (vectoroutofbounds.cpp) that uses the at method instead of the operator [] method.

When compiled and executed Listing ) 11.6| (vectoroutofbounds2.cpp) is guaranteed to produce a run-time error. Run-time errors are bad, but undefined behavior is worse because it can manifest itself as unpredictable run-time errors and programs that behave differently across multiple platforms.

The size method returns the number of elements in a vector. The following code fragment prints the contents of vector list:

int n = list.sizeQ ; for (int i = 0; i < n; i++) std::cout << list[i] << " std::cout << '\n' ;

The exact type that the si ze method returns here is a std : : vectorci nt> : : si ze_type. This type is defined within the std : : vector<i nt> class. It is compatible with the unsigned type and may be assigned to an i nt variable as shown above. We can avoid the additional local variable n as follows:

for (unsigned i = 0; i < list.sizeQ; i++) std::cout << list[i] << " std::cout << '\n' ;

Notice that i’s declared type is unsigned, not int. This prevents a warning when comparing i to list.sizeQ. A comparison between signed and unsigned integer types potentially is dangerous, and

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Draft date: September 25, 2018

the compiler will alert us to that fact. To see why you should not take this warning lightly, consider the following code that we would expect to print nothing:

unsigned u = 0;

int i = 0;

while (i < u - 1) {

std::cout << i << '\n' ; i++;

}

but instead it prints as many unsi gned values as the system supports! This is because even though 0 is not less than — 1, —1 is a signed value, not an unsigned value. The unsigned data type cannot represent signed numbers. An attempt to compute unsi gned 0 minus 1 on a 32-bit system produces 4,294,967,295, which definitely is not less than zero. To be safe, assign the value of the si ze method to an i nt variable or use unsigned variables to control loop iterations. Better yet, use the range-based for statement whenever possible.

The empty method is a convenience method; if vec is a vector, the expression vec. empty () is equivalent to the Boolean expression vec.sizeQ ! = 0. Note that the empty method does not make the vector empty; it simply returns true if the vector is empty and false if it is not.

The clear method removes all the elements from a vector leaving it empty. Invoking clear on an initially empty vector has no effect. Immediately after clearing a vector, the vector’s size method will return zero, its empty method will return true, and a call to its operator [] method with an index of any value (including zero) will exhibit undefined behavior.

11.1.4 Vectors and Functions

A function can accept a vector as a parameter as shown in Listing! 11.7|(vectortofunc.cpp)

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Draft date: September 25, 2018

int result = 0; for (int elem : v) result += elem; return result;

}

int main() {

std::vector<i nt> list{ 2, 4, 6, 8, }; // Print the contents of the vector print(list);

// Compute and display sum std::cout << sum(list) << '\n';

// Zero out all the elements of list int n = list.sizeQ; for (int i = 0; i < n; i++) list[i] = 0;

// Reprint the contents of the vector

print(list);

// Compute and display sum std::cout << sum(list) << '\n';

}

Listing |TT77l(vectortofunc.cpp) produces

2 4 6 8 20

0 0 0 0 0

The print function’s definition: void print(std::vector'd' nt> v) {

shows that a vector formal parameter is declared just like a non-vector formal parameter. In this case, the print function uses pass by value, so during the program’s execution an invocation of pri nt will copy the data in the actual parameter (li st) to the formal parameter (v). Since a vector potentially can be quite large, it generally is inefficient to pass a vector by value as shown above. Pass by value requires a function invocation to create a new vector object for the formal parameter and copy all the elements of the actual parameter into the new vector which is local to the function. A better approach uses pass by reference, with a twist:

void print(const std::vectorci nt>& v) { for (int elem : v)

std::cout << elem << " std::cout << '\n' ;

}

The & symbol indicates that a caller invoking pri nt will pass v by reference (see Section 10.9). This copies the address of the actual parameter (owned by the caller) to the formal parameter v instead of making a copy of all the data in the caller’s vector. Passing the address is much more efficient because on most systems an address is the same size as a single i nt, whereas a vector could, for example, contain 1,000,000 i nts. With pass by value a function invocation would have to copy all those 1,000,000 integers from the caller’s actual parameter into the function’s formal parameter.

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Draft date: September 25, 2018

Section || rOT9| indicated that call-by-value parameter passing is preferred to call-by-reference parameter passing. This is because a function using pass by value cannot modify the actual variable the caller passed to it. Observe closely that our new pri nt function declares its formal parameter vtobeaconst reference. This means the function cannot modify the actual parameter passed by the caller. Passing a vector object as a constant reference allows us to achieve the efficiency of pass by reference with the safety of pass by value.

Passing by const reference is not the same as pass by value, though. The function receiving a parameter passed by value can modify the parameter and return a modified copy. A function using pass by const reference cannot modify the parameter passed to it.

Like the p r i nt function, the sum function in Listing 11.7 (vectortofunc.cpp) does not intend to modify the contents of its vector parameter. Since the sum function needs only look at the vector’s contents, its vector parameter should be declared as a const reference. In general, if a function’s purpose is to modify a vector, the reference should not be const. Listing jTL8| (makerandomvector.cpp) uses a function named make_random that fills a vector with pseudorandom integer values.

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Draft date: September 25, 2018

print(list); make_random(list, 5); std::cout << "2nd random vector: print(list); make_random(list, 10); std::cout << "3rd random vector: print(list);

The make_random function in Listing 11.8 (makerandomvector.cpp) calls the vector method clear which makes a vector empty. We call clear first because we want to ensure the vector is empty before we add more elements. The function then proceeds to add a random number of random integers to the empty vector.

A function may return a vector object. Listing |Tl.9|| (primelist.cpp) is a practical example of a function that returns a vector.

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Draft date: September 25, 2018

* pri mes(begin, end)

* Returns a vector containing the prime

* numbers in the range begin...end.

* begin is the first number in the range

* end is the last number in the range */

std::vector<i nt> primes(int begin, int end) { std::vector<i nt> result; for (int i = begin; i <= end; i++) if (is_prime(i))

result.push_back(i); return result;

int main() {

int low, high;

std::cout << "Please enter lowest and highest values in << "the range: "; std::cin >> low >> high;

std::vector<i nt> prime_list = primes(low, high); print(prime_list);

The pri mes function declares a local vector variable named result. The function examines every value in the range begi n... end, inclusive. The pri mes function uses i s_pri me as a helper function. If the i s_pri me function classifies a value as a prime, code within the pri mes function adds the value to the result vector. After pri mes has considered all the values in the provided range, result will contain all the prime numbers in that range. In the end, primes returns the vector containing all the prime numbers in the specified range.

When returning a local variable that is a built-in scalar type like int, double, char, etc., a C++ function normally makes a copy of the local variable to return to the caller. Making a copy is necessary because local variables exist only while the function in which they are declared is actively executing. When the function is finished executing and returns back its caller, the run-time environment reclaims the memory held by the function’s local variables and parameters so their space can be used by other functions.

The return value in pri mes is not a simple scalar type—it is an object that can be quite large, especially if the caller passes in a large range. Modern C++ compilers generate machine code that eliminates the need to copy the local vector result. The technique is known as return value optimization, and it comes into play when a function returns an object declared within the function. With return value optimization, the compiler “knows” that the variable will disappear and that the variable is to be returned to the caller; therefore, it generates machine language code that makes the space for the result in the caller’s memory space, not the called function. Since the caller is maintaining the space for the object, it persists after the function returns. Because of return value optimization you can return vectors by value in situations like this one without fear of a time-consuming copy operation.

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Draft date: September 25, 2018

Due to the fact that vectors may contain a large number of elements, you usually should pass vectors to functions as reference parameters rather than value parameters:

• If the function is meant to modify the contents of the vector, declare the vector as a non-const reference (that is, omit the const keyword when declaring the parameter).

• If the function is not meant to modify the contents of the vector, declare the vector as a const reference.

It generally is safe to return a vector by value from a function if that vector is declared local to the function. Modern C++ compilers generate optimized code that avoid the overhead of copying the result back to the caller.

11.1.5 Multidimensional Vectors

The vectors we have seen thus far have been one dimensional—simple sequences of values. C++ supports higher-dimensional vectors. A two-dimensional vector is best visualized as a table with rows and columns. The statement

std : : vector<std : : vector'd nt>> a(2, std : : vector'd nt> (3) ) ;

effectively declares a to be a two-dimensional (2D) vector of integers. It literally creates a vector with two elements, and each element is itself a vector containing three integers. Note that the type of a is a vector of vector of integers. A 2D vector is sometimes called a matrix. In this case, the declaration specifies that 2D vector a contains two rows and three columns. Figure [TT3| shows the logical structure of the vector created by the following sequence of code:

std::vector<std::vector'd' nt>> a(2, std::vector'd nt> (3) ) ; a[0][0] = 5;

a[0][1] = 19; a[0][2] = 3;

a[1][0] - 22; a[1][1] = -8; a[1][2] = 10;

The two-dimensional vector a is said to be a 2 x 3 vector, meaning it has two rows and three columns (as shown in Figure [TO) . Rows are arranged horizontally, and the values in columns are arranged vertically. In each of the assignment statements above, for example

a[1][0] = 22;

the first index (here 1) signifies the row and the second index (here 0) denotes the column of the element within the vector. Literally, the expression a [1] [0] means (a[l])[0]; that is, the element at index 0 of the vector at index 1 within a.

Using a syntax similar to the initialization lists of one-dimensional vectors, we can declare and initialize the 2D vector a from above as:

std::vector<std::vectorci nt>> a{{ 5, 19, 3},

{ 22 , - 8 , 10 }};

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Draft date: September 25, 2018

Figure 11.5 A 2 x 3 two-dimensional vector

a

I t.

0

1

5

19

3

22

-8

10

0 1 2

Note that each row appears within its own set of curly braces, and each row looks like ID vector initialization list.

To access an element of a 2D vector, use two subscripts:

a[r][c] = 4; // Assign element at row r, column c

std::cout << a[m][n] << '\n' ; // Display element at row m, column n

The following function prints the contents of a 2D vector of doubles:

void print(const std::vector<std:: vector<double>>& m) { for (unsigned row = 0; row < m.size(); row++) {

for (unsigned col = 0; col < m[row].size(); col++) std::cout << std::setw(5) << m[row][col]; std::cout << '\n' ;

}

}

We can use range-based for statements to simplify the code:

void print(const std::vector<std:: vector<double>>& m) {

for (const std:: vector<double>& row : m) { // For each row

for (int elem : row) // For each element in a row std::cout << std::setw(5) << elem; std::cout << '\n ' ;

}

return sum;

}

The declaration of the parameter m is somewhat complicated. We can simplify the syntax by using a C++ type alias declaration. The statement

using Matrix = std::vector<std: :vector<double>> ;

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Draft date: September 25, 2018

creates a new name Matrix for the existing type of a 2D vector containing doubles. Such type alias statements usually appear near the top of a source file and most often have global scope. It is less common to see a local type aliasing usi ng statement within a function body.

You may encounter a type aliasing statement that uses the typedef keyword as shown here:

typedef std::vector<std:: vector<double>> Matrix;

In this case this typedef directive works identically to the usi ng type alias. C++ inherits the typedef keyword from the C programming language. The C++ using type alias is newer and supports type aliasing capabilities beyond those provided by the more primitive typedef. For this reason, you should prefer the usi ng type aliasing to typedef when writing pure C++ code.

Given the usi ng statement defining the new type name Matri x, we may express the parameter for the pri nt function more simply:

void print(const Matrix& m) {

for (const std:: vector<double>& row : m) { // For each row

for (int elem : row) // For each element in a row std::cout << std::setw(5) << elem; std::cout << '\n' ;

}

return sum;

}

We can take advantage of the type inference capability of C++11 to simplify the print function even further (see Section [3.10j ):

void print(const Matrix& m) {

for (auto row : m) { // For each row

for (int elem : row) // For each element in a row std::cout << std::setw(5) << elem; std::cout << '\n' ;

}

return sum;

}

Here we replaced the explicit type const std : : vector <double>& with the word auto. The compiler is able to infer the type of the variable row from the context: m is a Mat r i x (that is, a std: :vector<std: :vector<double>>), so row must be an element of the 2D vector (which itself is a ID vector).

Listing 11.10 (twodimvector.cpp) experiments with 2D vectors and takes advantage of the usi ng type alias statement to simplify the code.

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Draft date: September 25, 2018

using Matrix = std::vector<std::vector <double>> ;

// Allow the user to enter the elements of a matrix

void populate_matrix(Matrix& m) {

std::cout << "Enter the " << m.size() << " rows of the matrix. \n"; for (unsigned row = 0; row < m.size(); row++) {

std::cout << "Row #" << row << " (enter " << m[row].size()

<< " values):" ; for (double& elem : m[row]) std::cin >> elem;

}

}

void print_matrix (const Matrix m) { for (auto row : m) {

for (double elem : row)

std::cout << std::setw(5) << elem; std::cout << '\n' ;

}

}

int main() {

int rows, columns;

std::cout << "How many rows? ";

std::cin >> rows;

std::cout << "How many columns? "; std::cin >> columns;

// Declare the 2D vector

Matrix mat(rows, std:: vector<double> (columns));

// Populate the vector populate_matrix(mat);

// Print the vector print_matrix(mat);

}

An expression that uses just one index with a 2D vector represents a single row within the 2D vector. This row is itself a ID vector. Thus, if a is a 2D vector and i is an integer, then the expression

a [i ]

is a ID vector representing row i.

We can build vectors with dimensions higher than two. Each “slice” of a 3D vector is simply a 2D vector, a 4D vector is a vector of 3D vectors, etc. For example, the statement

matrix[x][y] [z] [t] = 1.0034;

assigns 1.0034 to an element in a 4D vector of doubles. In practice, vectors with more than two dimensions are rare, but advanced scientific and engineering applications sometimes require higher-dimensional vectors.

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Draft date: September 25, 2018

11.2 Arrays

C++ is an object-oriented programming language, and a vector is an example of a software object. C++ began as an extension of the C programming language, but C does not directly support object-oriented programming. Consequently, C does not have vectors available to represent sequence types. The C language uses a more primitive construct called an array. True to its C roots, C++ supports arrays as well as vectors. Some C++ libraries use arrays in instead of vectors. In addition, C++ programs can use any of the large number of C libraries that have been built up over the past 40+ years, and many of these libraries process arrays. While a more modern construct like std : : vector may be better suited for may of the roles an array has played in the past, it nonetheless is important for C++ programmers to be familiar with arrays.

An array is a variable that refers to a block of memory that, like a vector, can hold multiple values simultaneously. An array has a name, and the values it contains are accessed via their position within the block of memory designated for the array. Also like a vector, the elements within an array must all be of the same type. Arrays may be local or global variables. Arrays are built into the core language of both C and C++. This means you do not need to add any # include directives to use an array within a program.

11.2.1 Static Arrays

Arrays come in two varieties, static and dynamic. A programmer must supply the size of a static array when declaring it; for example, the following statement:

// list is an array of 25 integers

int list[25];

declares li st to be an array of 25 integers. The value within the square brackets specifies the number of elements in the array, and the size is fixed for the life of the array. The value within the square brackets must be a constant value determined at compile time. It can be a literal value or a symbolic constant, but it cannot be a variable. This is in contrast to vector declarations in which the initial vector size may be specified by a variable with a value determined at run time:

int x;

std::cin >> x; // Get x's value from the user at run time

int list_l[x]; // Illegal for a static array

std::vectorci nt> list_2(x); // OK for a vector

It is possible to declare an array and initialize it with a sequence of elements, with a syntax similar to that of vectors:

double collection^ = { 1.0, 3.5, 0.5, 7.2 };

The compiler can count the elements in the initializer list, so you need not supply a number within the square brackets. If you provide a number within the square brackets, it should be at least as large as the number of elements in the initialization list. The equals symbol is required for array initialization. You optionally can use the equals symbol as shown here when initializing vectors, but it is not required for vectors.

If the declaration omits an initializer list, as in: int arr[100];

the initial values of the elements of the array depend on the context of the declaration:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.6 A simple array with three elements

int list[3] ; list[0] = 5; list[l] = -3; list[2] = 12;

5 -3 12

0 1 2

• An executing program does not initialize the contents of a local arrays.

• The run-time environment initializes the values of global numeric arrays to all zeros.

As with vectors, once we declare an array, we can access its elements using the square bracket operator:

int list[3];

//

Declare

list[0] = 5 ;

//

Make

the

list[l] = -3 ;

//

Make

the

list[2] = 12 ;

//

Make

the

i nts

This code fragment shows that the square brackets used after the point of declaration allow us to access an individual element based on that element’s position within the block of memory assigned to the array. This syntax is identical to that used with vector objects. As with vectors, the very first element in an array appears at index 0.

After executing these assignment statements, the list array conceptually looks like Figure

11.6

©2018 Richard L. Halterman

Draft date: September 25, 2018

The array square brackets operator has two distinct meanings depending on the context:

1. At the array’s declaration, for example, double nums[10];

the number within the square brackets specifies the number of elements that the array can hold. The compiler uses this number along with the type of the array to determine how much memory to allocate for the array.

2. After the array’s declaration, for example,

nums[3] = 10.45;

the number within the square brackets represents an index locating a specific element within the memory allocated to the array.

Unlike with vectors, the compiler will insist that the programmer use an integral value for an index; for example, the following statement:

numbers[1.3] = 5;

is illegal if numbers is an array. Identically to vectors, the programmer must ensure that the array index is within the bounds of the array. Accessing an element via an index outside the bounds of an array results in undefined behavior.

We can pass an array to a function, as shown in Listing 11.11 farraytofunc.cpp), the array-based version

of Listing ||11.7||(vectortofunc.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

int result = 0; for (int i = 0; i < n; i++) result += a [i]; return result;

}

int main() {

int list[] = { 2, 4, 6, 8 };

// Print the contents of the array print(list, 4);

// Compute and display sum std::cout << sum(list, 4) << '\n';

// Zero out all the elements of list for (int i =0; i <4; i++) list[i] = 0;

// Reprint the contents of the array print(list, 4);

// Compute and display sum std::cout << sum(list, 4) << '\n';

}

As shown in the pri nt function’s definition: void print(int a[], int n)

empty square brackets follow the name of an array formal parameter. The programmer can supply a number within the square brackets, but the compiler will ignore it. When calling a function that accepts an array parameter, as in

print(list, 4);

the programmer must pass the array’s size along with the array name. This is because an array simply references a block of memory and has has no notion of its size.

An undecorated array name by itself in C++ source code behaves like a constant pointer to the beginning element of the array. Consequently, when an array is passed as an actual parameter during a function call, as in Listing |lTTri|| (arraytofunc.cpp):

print(list, 4) ;

the function is passed the address of the array—the array’s address is bound to the formal parameter. So, while the function cannot affect the address of the array itself, the function has total access to the array’s

contents. In Listing 11.12 (cleararray.cpp), the function clear modifies the contents of any array sent to it, making all the elements zero.

Listing 11.12: cleararray.cpp

#include <iostream>

/*

*

*

*

*

*/

void print(int a[]

print(a, n)

Prints the contents of an int array a is the array to print n is the size of the array

int n) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table caption11.2. ARRAYS

Table caption315

for (int i

= 0; i

< n; i++)

std::cout <<

a[i] << "

std::cout <

< 1 \n 1

5

}

/*

*

clear(a, n)

*

Makes all the

elements of array a zero

*

a is the

array

to zero out

*

n is the

size

of the array

*/

voi c

clear(int

a [] , i

nt n) {

for (int i

= 0; i

< n; i++)

a [i] =

0;

}

int

main() {

int list[]

= { 2,

4, 6, 8 };

// Print the contents of the array

print(list,

4);

// Zero out

the a

rray

clear(list,

4);

// Reprint

the contents of the array

print(list,

4);

}

The output of Listing 11.12 (cleararray.cpp) is

2 4

0 0

6 8

0 0

_i

The clear function actually modifies the contents of main’s list array. The function works on the array’s actual elements, not copies of its elements.

Arrays, therefore, by default are passed by reference with respect to the elements they contain. By default, an array’s contents are open to corruption by errant functions. In order to protect an array so that a function may read its contents but not modify its contents, the parameter must be declared const, as in

int sum(const int a[], int n)

In Listing 11.11 (arraytofunc.cpp) there is no reason why the pri nt and sum functions should be able to to modify the contents of their array parameters, so the const specifier should be added to their definitions.

As a general rule, all functions that accept array parameters should declare the array contents as const unless they need to modify the elements of the array.

©2018 Richard L. Halterman

Draft date: September 25, 2018

As a general rule, all functions that accept array parameters should declare the array contents as const unless they need to modify the elements of the array. For example, use

int sum(const int a[], int n) rather than

int sum(int a[], int n)

if the sum function must be able to examine the contents of the array but is not intended to modify its contents.

C++ does not directly support empty arrays. A physical array must contain at least one element. Sometimes it is appropriate to consider an array that is conceptually empty; for example, what if we wish to pass an “empty” array to the sum function? We can pass 0 as the second parameter since an empty array contains no elements, but what should we pass as the first parameter? Any array will do, but there is no need create an real array when none truly is needed. Instead, we may use nullptr:

quanitity = sum(nullptr, 0);

If you scrutinize the body of the sum function, you will see that this call will assign to quanti ty the correct answer, namely zero.

11.2.2 Pointers and Arrays

An array name used in C++ source code references a location in memory, the address of the first element (element at index 0) in the array. In this way an array name is similar to a constant pointer (see Section |10,7| for more information about C++ pointers). Because of this, we can treat in some ways an array identifier like a pointer. Similarly, we can direct a pointer to point to an array, and then treat the pointer itself as if it were an array.

The statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

p = &a[0] ;

sets p to point to the first element of array a. A shorter way to accomplish the same thing is P = a;

since a is itself a reference to the array’s location in memory. This assignment statement clearly demonstrates the association between array variables and pointer variables. Note that the opposite assignment (a = p) is impossible, because array a declared as above may not appear by itself on the left side of the assignment operator.

Pointer variables can participate in addition and subtraction expressions. The statement p + +;

changes the address stored in p so subsequently the pointer will point to the next integer position in memory. If p is assigned to array a, incrementing p redirects it to point to a’s next element. 1 In Figure 11.7 pointer p is assigned to array a and then incremented to refer to various elements within a.

The expression p[0]

is another way to write *P

so the array indexing operator ([]) can be used with pointers. The expression P [5]

represents the element at index 5 within the array pointed to by p.

Listing 11.14 (pointerprint2.cpp) uses pointers in a different way to traverse an array.

1 Each byte in memory has a unique numeric address. Since most C++ types require more than one byte of storage, incrementing a pointer by 1 does not simply add 1 to the address it holds. The amount added depends on the type of the pointer; for example, on systems using 32-bit (4 byte) integers, adding 1 to an integer pointer variable increments its address by 4, not 1. The compiler knows the type of the pointer variable because programmers must declare all variables. The compiler, therefore, can automatically adjust the arithmetic to work properly. If a pointer points to memory within an array and is of the same type as the array, incrementing the pointer correctly repositions the pointer to point to the next element in the array.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.7 Incrementing a pointer to an array

-int a [] = { 2, 4, 6, 8 }, *p

a

p = a;

a

a

a

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

std::cout << '\n 1 ;

In Listing p~1.14|| (pointerprint2.cpp), the code

cursor = begin; while (cursor != end) {

std::cout << ^cursor << ' ' ; // Print the element

cursor++; // Increment cursor so it points to the next element

}

can be expressed more succinctly as a for loop:

for (cursor = begin; cursor != end; cursor++)

std::cout << ^cursor << ' ' ; // Print the element

If pointer p points to an array, the element at index i can be accessed as either p[i]or*(p + i). The expression * ( p + i ) dereferences the address that is i positions away from the address referenced by p.

Sometimes pointer notation is used to represent an array parameter to a function. The array print function that begins

void print(const int a[], int n)

could instead be written void print(const int *a, int n)

where a is a pointer to an array. The compiler treats the two forms identically in the machine language it produces.

Listing 11.15 (recursivearrayprint.cpp) uses two array printing functions, iterati ve_print and recu rsi ve_pri nt. Both use the pointer notation when declaring their array parameters.

Listing 11.15: recursivearrayprint.cpp

#include <iostream>

/*

* iterative_print(a,n)

* Prints the contents of array a

* a is the array to print; a is not modified

* n is number of elements in a

*/

void iterative_print(const int *a, int n) { for (int i = 0; i < n; i++) std::cout << a[i] << 1

}

/*

* recursive_print(a,n)

* Prints the contents of array a

* a is the array to print; a is not modified

* n is number of elements in a

©2018 Richard L. Halterman

Draft date: September 25, 2018

*/

void recursive_print(const int *a, int n) { if (n > 0) {

std::cout << *a << ' // Print the first element of the array

recursive_print(a + 1, n - 1); // Print rest of the array

}

}

int main() {

int list[] = { 23, -3, 4, 215, 0, -3, 2, 23, 100, 88, -10 }; iterative_print(list, 11); recursive_print(list, 11);

}

The function iterative_print uses a loop, while recursive_print uses recursion instead. Inside the recursive_print function, the expression a + 1 points to the second element in array a. a + 1 essentially represents the rest of the array—everything except for the first element. The statement

recursive_print(a + 1, n - 1) ;

calls the function recursively, passing the remainder of the array (a + 1) with a length that is one less fn - 1) than before. The recursion terminates when the array’s length is zero.

Instead of passing a pointer to an array and the array’s size, we can pass two pointers. The first pointer points to the beginning of the array and another pointer points just past the end of the array. The following pri nt function illustrates:

void print(int *begin, int *end) {

for (int *elem = begin; elem != end; elem++) std::cout << *elem ;

std::cout << '\n' ;

}

Notice that this code does not appear to be using arrays at all! This code takes advantage of pointer arithmetic to move the elem pointer from the first element to each successive element in the array. Since the memory devoted to an array is a continuous, contiguous block of memory addresses, pointer arithmetic

simply redirects a pointer from one element in an array to another element in that array. Listing 11.16 (pointerarithmetic.cpp) provides some more examples of pointer arithmetic in action.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.8 Pointer arithmetic. Incrementing pointer p moves it to the next element in the array.

int arr[] = {10, 20, 30, 40, 50}; int *p = arr;

p

<

>

arr

10

20

30

40

50

0

1

2

3

4

P

\

arr

10

20

30

40

50

0

1

2

3

4

std:

: cout

<<

p[0]

c

V

V

//

Prints

40,

does

not

change

P

std:

: cout

<<

p[l]

« '\n ' ;

//

Prints

50,

does

not

change

P

p—;

//

Moves

p back one

■ pla

ce

std:

: cout

<<

*p <<

' \ n ' ;

//

Prints

30,

does

not

change

P

Figure|11 ^[illustrates how Listing)! 1.16 (pointerarithmetic.cpp) works.

Listing p~l.16K pointerarithmetic.cpp) also shows how we can use the square bracket array access operator with a pointer. The expression p [/] refers to the element in memory i positions from the location pointed to by p.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Going back to the print function that uses pointers:

void print(int *begin, int *end) {

for (int *elem = begin; elem != end; elem++) std::cout << *elem << ' ' ; std::cout << '\n' ;

}

the pointer elem first points to the same element to which begi n points (that is, the first element in the array), and within the loop it moves to the next element repeatedly until it passes the last element. A caller could invoke the function as

int list[25]; // Allocate a static array

for (int i = 0; i < 25; i++)

list[i] = rand() % 1000; // Fill with pseudorandom values

print(list, list + 25); // Print the elements of list

The advantage of the begin/end pointer approach is that it allows a programmer to pass a slice of the array to the function; for example, if we wish to print the elements of the array from index 3 to index 7, we would call the function as

print(list + 3, list +8); // Print elements at indices 3, 4, 5, 6, 7

11.2.3 Dynamic Arrays

Programmers need not worry about managing the memory used by static arrays. The compiler and run-time environment automatically ensure the array has enough space to hold all of its elements. The space held by local arrays is freed up automatically when the local array goes out of the scope of its declaration. Global arrays live for the lifetime of the executing program. Memory management for static arrays, therefore, works just like scalar variables.

Static arrays have a significant limitation: The size of a static array is determined at compile time. The programmer may change the size of the array in the source code and recompile the program, but once the program is compiled into an executable program any static array’s size is fixed. For many applications the circumstances of the executing program must determine the size of an array. Static arrays lack such flexibility.

One approach to implement a flexibly-sized array defines the array to hold as many items as it conceivably will ever need. Listingjl 1.17 (largearrayaverage.cpp) uses this approach.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std: : cin >> size;

}

if

}

(size > 0) { // Nothing to do with no entries

std::cout << "Please enter " << size << " numbers: // Allow the user to enter in the values, for (int i = 0; i < size; i++) { std::cin >> numbers[i]; sum += numbers[i];

}

std::cout << "The average of "; for (int i = 0; i < size - 1; i++)

std::cout << numbers[i] << ", ";

//No comma following last element std::cout << numbers[size - 1] << " is "

<< sum/size << '\n 1 ;

II .

Listing |l 1.17| (largearrayaverage.cpp) creates an array that can hold one million entries. The variable si ze keeps track of the actual size needed by the user. While the array’s maximum size is one million, the part of the array actually used during a given execution may be much smaller.

Notice that the array numbers is a global variable and is not local to mai n. This is because most systems limit the amount of storage available to local variables within functions. Local variables reside in an area of memory known as the stack. Local variables exist in memory only when the function that uses them is invoked; therefore, the stack grows and shrinks as functions execute and return. Global variables, on the other hand, exist in the computer’s memory for the life of the program’s execution. Global variables are stored in what is known as static memory. There is a limit to the amount of static memory available for global variables (the amount of memory in RAM or virtual memory on disk, if nothing else), but the global limit usually is much higher then the local limit. One million double-precision floating-point numbers consumes 8,000,000 bytes (8 megabytes) in Visual C++ and on many other systems. The default stack size for local variables under Visual C++ is only one megabyte, although the stack size can be increased by adjusting the compiler and linker build options.

While the approach taken in Listing 11.17 (largearrayaverage.cpp) works, it wastes memory resources. In modern computing, a user may have multiple programs open at the same time. If each program is tying up the maximum amount of memory it may ever need, there may not be enough real memory (RAM) to go around, and the computer will be forced to use more virtual memory (shuttling portions of the running program’s memory to and from the disk drive). Virtual memory access greatly degrades the speed of a program, and so the user’s experience suffers. It is important that each program uses its resources wisely. Statically allocating the largest array that might ever be needed is not a good approach.

Fortunately, there is a way for a programmer to create an array of the exact size needed, even if that size is not known until run time. Listingjll.l81(flexiblearrayaverage.cpp) shows how.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Please enter number of values to process: std::cin >> size;

if (size > 0) { // Nothing to do with no entries

std::cout << "Please enter " << size << " numbers:

// Allocate the exact size needed

numbers = new double [size]; // Dynamically allocated array

// Allow the user to enter in the values, for (int i = 0; i < size; i++) { std::cin >> numbers[i]; sum += numbers[i];

}

std::cout << "The average of "; for (int i =0; i < size - 1; i++)

std::cout << numbers[i] << ", ";

//No comma following last element std::cout << numbers[size - 1] << " is "

<< sum/size << '\n 1 ;

delete [] numbers; // Free up the space held by numbers

}

}

Notice that numbers is not declared to be an array; it is a pointer: double *numbers; // Note: numbers is a pointer, not an array

This statement makes space for a single pointer, merely four bytes on a 32-bit system or eight bytes on a 64-bit system. The expression

new double[size]

allocates at run time a block of memory for an array that can hold exactly si ze double-precision floatingpoint elements. The value of this expression is the starting address of the newly allocated memory block.

The statement

numbers = new double [size]; // Dynamically allocated array

therefore assigns to numbers the address of the allocated memory. A dynamic array is simply a pointer

(see Section [10.7f that points to a dynamically allocated block of memory. As Listing jl 1.18| (flexiblearrayaverage.cpp)

shows, the value within the square brackets in a dynamic array allocation may be a variable determined at

run time. Figure ||TTT9|| compares the conceptual differences among of static and and dynamic arrays and

vectors.

While we access a dynamic array via a pointer, a static array array behaves like a constant pointer; that is, a pointer that we cannot reassign to point elsewhere.

The reserved word new allocates memory for the array’s elements, new technically is classified as an operator. The area of memory used for dynamic allocation via new is different from both the area used for local variables (the stack) and global variables (static memory). Dynamic memory comes from the heap.

Section ! 18.1 [ provides more details about the memory available to an executing C++ program, but here it is sufficient to note that the heap has a capacity much larger than the stack.

The variable numbers is local to mai n, so it lives on the stack. It is a pointer, so it stores a memory address. The new expression returns an address to memory in the heap. So, even though the numbers

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.9 Comparing static arrays, dynamic arrays, and vectors

Int list_l[5];

int *list_2 = new int[5];

vector<int> list_3(5);

list 1

?

?

?

?

?

0 1

list_2

2

3

4

H—►

0

0

0

0

0

0

1

2

3

4

list 3

\

0

0

0

0

0

V

0

1

2

3

4

)

©2018 Richard L. Halterman

Draft date: September 25, 2018

variable itself is stored on the stack, the memory it references is located in the heap. We do not need to worry about our array being too big to be local to mai n, since its contents do not consume stack space.

An executing program automatically allocates on the stack the local variables of a function when a caller invokes the function. The executing program also automatically deallocates local variables when the function returns. The programmer does not need to explicitly manage local variables. Dynamically allocated memory, however, requires more attention on the part of the programmer. The statement

delete [] numbers; // Free up the space held by numbers

uses the delete operator to free up the memory held by the numbers array. The programmer is responsible for deallocating memory that was allocated with new. Every use of the new operator should have a corresponding use of delete somewhere later in the program’s execution. Notice that the square brackets ([]) are empty. The run-time environment keeps track of the amount of memory to free up.

You should develop the habit of ensuring that every use of the new operator has an associated call of delete. If the delete statement is omitted from Listing 11.18 (flexiblearrayaverage.cpp), the program in this case likely will behave no differently since most operating systems reclaim all the dynamic memory a program holds when the program finishes executing. Serious problems arise in longer running programs that must allocate and deallocate dynamic memory over time. Programs that run for extended periods of time, like web servers and operating system kernels, can crash due to failures to properly deallocate memory. The condition is known as a memory leak —the program overtime allocates more and more memory via new but never releases the memory back with delete. Eventually the program uses up all of the available heap space and crashes.

11.2.4 Copying an Array

It is important to remember that within C++ source code a static array variable behaves similarly to a constant pointer. At first it may seem plausible to make a copy of an array as follows:

int a[10] , for (int i a [i ] b = a;

b[10] ;

= 0; i < 10; i++)

i;

// Declare two arrays // Populate one of them // a is filled with increasing values // Make a copy of array a?

Since b behaves like a constant pointer, we cannot reassign it; that is, the name b cannot appear on the left side of the assignment operator all by itself. Wherever b points, it must continue to point there during its lifetime. The code above will not compile.

Perhaps the solution is to use a dynamic array (see Section 11.2.3| for information about dynamic arrays). If b is not const, can we copy the array through simple assignment? The following code is legal:

int a[10], *b; for (int i = 0;

a[i] = i ; b = a;

//

i < 10; i++) //

//

//

Declare two arrays, one dynamic Populate one of them a is filled with increasing values Make a copy of array a?

but b is not a copy of a. b aliases a, so changing the contents of a will also change the contents of b identically, since b refers to the exact memory to which a refers. Figure 11.10 illustrates the aliasing.

This illustrates another key difference between vectors and arrays: It is not possible to assign one array variable to another through a simple assignment statement that copies all the elements from one array into another. If the arrays are static arrays, the simple assignment is illegal. If the arrays are dynamic arrays, the

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.10 Faulty array copy

int a[] = { 2, 4, 6, 8 }, *b;

assignment simply makes the two pointers point to the same block of memory, which is not the same effect as vector assignment.

The following code shows the proper way to make a copy of array a:

int a[10], *b; // Declare two arrays, one dynamic

for (int i = 0; i < 10; i++) // Populate one of them

a[i] = i; // a is filled with increasing values

// Really make a copy of array a b = new int[10]; // Allocate b

for (int i = 0; i < 10; i++)

b[i] = a[i];

Separate space for the dynamic array must be allocated, and then each element from the original array must be copied into the new array. Figure [TT7111| shows how this process works.

It is important to note that since the code above allocates b dynamically with new, code elsewhere within the program should eventually use delete to free up b’s space when it is no longer used. Failure to properly deallocate b constitutes a memory leak.

Consider the following scenario:

int *a = new int [10],

*b = new int [10];

// Do somethings with arrays a and b, and then b = a;

Here dynamic array b already was in use before the assignment. Not only does this simple assignment create an alias, but it also creates a memory leak. If the reassigned array originally was pointing to a block of memory allocated on its behalf, and no other pointers reference that block of memory, that block is unreachable by the executing program.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.11 Correct array copy

int a[] = { 2, 4, 6, 8 }, *b; a

2 4 6 8

>> Declare

o 1

-> ?

b = new int[4]; a

0 1

Allocate >■ space for copy

0 12 3

for ( int i = 0; i < 4; i++ ) b[i] = a [i];

y Copy the f elements

o 1

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 11.18) (flexiblearrayaverage.cpp) requires the user to enter up front the number of values to average. This is inconvenient, and people are notoriously poor counters. One solution is to allocate a minimal size array, and then resize it as necessary when it fills up. Listing 1 1.19[ (resizearray.cpp) uses this approach.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Notice that the programmer of Listing )! 1.19| (resizearray.cpp) is expending a lot of effort to implement the functionality provided by std : : vector. Unlike vectors, an array has a fixed size. It is impossible to change the size of a static array (short of editing the source code and recompiling). In order to change at run time the size of a dynamic array, you must

1. allocate a different block of memory of the desired size,

2. copy all of the existing elements into the new memory,

3. use delete to deallocate the previous memory block to avoid a memory leak, and

4. reassign the original dynamic array pointer to point to new memory block.

Listing 11.19 (resizearray.cpp) contains the code to perform this array resizing. A vector object manages a dynamic array, and its push_back method takes care these details for us.

11.2.5 Multidimensional Arrays

Just as C++ supports higher-dimensional vectors, it also supports multidimensional arrays. The following statement:

int a[2] [3] ;

declares a to be a two-dimensional (2D) array of integers. In this case, the declaration specifies that array a contains two rows and three columns. Figure |l 1.12) shows the logical structure of the array created by the following sequence of code:

int a[2] [3]; // a is a 2D array

a[0][0] = 5;

a[0] [1] = 19;

a[0][2] = 3;

a[1][0] = 22; a[1][1] = -8; a [1] [2] = 10;

The two-dimensional array a is said to be a 2 x 3 array, meaning it has two rows and three columns (as shown in Figure |T1.12j ). Rows are arranged horizontally, and the values in columns are arranged vertically. In each of the assignment statements above, for example

a[1][0] = 22;

the first index (here 1) signifies the row and the second index (here 0) denotes the column of the element within the array.

Using a syntax similar to 2D vectors, we could have declared and created the 2D array above as:

int a [2][3] = { { 5, 19, 3 },

{ 22 , - 8 , 10 } };

You may omit the first index, as shown here:

int a[][3] = { { 5, 19, 3 },

{ 22 , - 8 , 10 } };

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.12 A 2 x 3 two-dimensional array

0 1

0 1 2

a

5

19

3

22

-8

10

For 2D arrays initialized in this manner the first subscript is optional, but the second subscript (that is, the size of each column) is required.

To access an element of a 2D array, use two subscripts:

a[r][c] = 4; // Assign element at row r, column c

std::cout << a[m][n] << '\n' ; // Display element at row m, column n

The following function prints the contents of a ROWS x COLUMNS 2D array of doubles, where both ROWS and COLUMNS are constants:

void print(const double m[ROWS][COLUMNS]) { for (int row = 0; row < ROWS; row++) {

for (int col = 0; col < COLUMNS; col++)

std::cout << std::setw(5) << m[row][col]; std::cout << '\n' ;

}

}

We can omit the ROW size in the parameter declaration, but second set of square brackets must constant a constant integral expression. The declaration of the parameter m is quite complicated, and, as we did for 2D vectors, we can simplify the syntax by using a C++ type aliasing statement, statement

using Matrix = double [ROWS][COLUMNS] ; defines a new type named Matrix.

Given the type alias using statement defining the new type name Mat r i x, we can express the parameter for the pri nt function more simply:

void print(const Matrix m) {

for (int row = 0; row < ROWS; row++) {

for (int col = 0; col < COLUMNS; col++)

std::cout << std::setw(5) << m[row][col]; std::cout << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

}

Listing 11.20 (twodimarray.cpp) experiments with 2D arrays and takes advantage of the type alias statement to simplify the code.

An expression that uses just one index with a 2D array represents a single row within the 2D array. This row is itself a ID array. Thus, if a is a 2D array and i is an integer, then the expression

a [i ]

is a ID array representing row i.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.13 Physical layout of a C string

•H’

'o’

V

'd'

y

'\0'

0 1 2 3 4 5 6

As with vectors, C++ allows arrays with dimensions higher than two. Each “slice” of a 3D array is simply a 2D array, a 4D array is an array of 3D arrays, etc. For example, the statement

matrix[x][y][z][t] = 1.0034;

assigns 1.0034 to an element in a 4D array of doubles. In practice, arrays with more than two dimensions are rare, but advanced scientific and engineering applications sometimes require higher-dimensional arrays.

11.2.6 C Strings

A string is a sequence of characters. C and C++ implement strings as arrays of char. The C++ language additionally supports string objects (see Section 13.11. In the C language, the only option is a char array. We use the term C string to refer to an array of characters as used in the C language. In this section, any mention of the term string refers to a C string.

A string is an array of characters. A string literal is a sequence of characters enclosed within quotation marks, as in

std::cout << "Howdy!\n" ;

All proper C strings are null terminated. This means the last character in the array is ASCII zero, which C++ represents by the character literal ' \0 ' . Figure 11.13 shows the physical layout of the string "Howdy ! " in memory.

Since strings are actually arrays, care must be taken when using string variables:

• Enough space must be reserved for number of characters in the string, including the null terminating character.

• The array of characters must be properly null terminated.

The following code fragment is safe and acceptable:

char *word = "Howdy!"; std::cout << word << '\n' ;

The variable word is declared to be a pointer to a character, and it is initialized to point to a string literal.

The following code fragment is less safe:

char word[256]; std::cin >> word;

©2018 Richard L. Halterman

Draft date: September 25, 2018

The string word can hold 255 viable characters plus the null terminator. If the user types in relatively short words (length less than 255 characters), there is no problem. If at any time the user types in more characters than will fit in the word array, the executing program will have a problem. The problem is known as a buffer overrun. In the best case, buffer overruns lead to buggy programs. In the worst case, clever users can exploit buffer overruns to compromise software systems. Buffer overruns are always logic errors and you should take great care to avoid them.

The following code provides a safe way to get user input:

char word[10]; fgets(word, 10, stdin); std::cout << word << ' \n ' ;

The f gets function is a standard C function. The second parameter specifies the maximum length of the string, including the terminating null character, that will be placed in the string word. The last argument, stdi n is a C construct related to the C++ object std : : ci n. In order to use f gets within a program you must include the <cstdio> header.

The following code begs for disaster:

char *word;

std::cin >> word;

In this case word points to a random location in memory (it is uninitialized), and the code allocates no buffer to receive the input characters from std : : ci n. The program’s behavior executing this code is undefined, but it likely will lead to the program crashing. Insidiously, depending on how the operating system manages memory, the program may run fine much of the time and crash only rarely. Regardless, the program contains a serious bug.

When passing an array to a function a caller must provide the size of the array so that the function may process the array properly. Since C strings are null terminated, such size information is not necessary. The find_cha r function in Listing 11.21 (findchar.cpp) determines if a particular character is present in a string.

Listing 11.21: findchar.cpp

ffinclude <iostream>

bool find_char (const char *s, char ch) {

while (*s != '\0' ) { // Scan until we see the null character

if (*s == ch)

return true; // Found the matching character s++; // Advance to the next position within the string

}

return false; // Not found

int main() {

const char *phrase = "this is a phrase";

// Try all the characters a through z for (char ch = 'a'; ch <= 'z' ; ch++) {

std::cout << 1 \ 11 << ch << 1 \ 1 ' << " is "; if (!find_char(phrase, ch)) std::cout << "NOT " ;

std::cout << "in " << '\' << phrase << '\" 1 << '\n';

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

The output o

a 1

is

in "

this is a

phrase"

b'

is

NOT

in "this

is a phrase"

c 1

is

NOT

in "this

is a phrase"

d'

is

NOT

in "this

is a phrase"

e 1

is

in "

this is a

phrase"

f 1

is

NOT

in "this

is a phrase"

g'

is

NOT

in "this

is a phrase"

h'

is

in "

this is a

phrase"

i 1

is

in "

this is a

phrase"

j'

is

NOT

in "this

is a phrase"

k'

is

NOT

in "this

is a phrase"

1'

is

NOT

in "this

is a phrase"

m 1

is

NOT

in "this

is a phrase"

n 1

is

NOT

in "this

is a phrase"

o 1

is

NOT

in "this

is a phrase"

P'

is

in "

this is a

phrase"

q'

is

NOT

in "this

is a phrase"

r 1

is

in "

this is a

phrase"

s'

is

in "

this is a

phrase"

t'

is

in "

this is a

phrase"

u'

is

NOT

in "this

is a phrase"

v'

is

NOT

in "this

is a phrase"

w 1

is

NOT

in "this

is a phrase"

x'

is

NOT

in "this

is a phrase"

y'

is

NOT

in "this

is a phrase"

z'

is

NOT

in "this

is a phrase"

The find_char function in Listing 11.21 (findchar.cpp) uses pointer notation to traverse the string. It does not need to know in advance the number of characters in the string because it starts at the beginning and keeps scanning each character in turn until it finds the character it is looking for or encounters the null terminating character.

Recall from Section 5.1 that for Boolean conditions C++ treats a zero value as false and any non-zero value as true. Because of such a loose interpretation of Boolean expressions, we can write the find_char function from Listing1 11.21|(findchar.cpp) more compactly as the following:

char find_char (const cha

// Scan until we see // we seek

while (*s != '\0' && s++; // Advance

return *s; // Null

r *s, char ch) {

the null character or the character *s != ch)

to the next position within the string character = false, any other is true

}

The only way out of the loop is to scan the null terminating character or the character sought. Here, if the loop encounters the null terminating character, it exits and returns that null character. The null character is simply ASCII zero—Boolean false. If the loop locates the sought character, it exits and returns that character which will not be ASCII zero. Any character except the null character has an ASCII value greater than zero; therefore, the calling code interprets the returned character as Boolean true.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Most routines that process strings depend on the strings to be null terminated in order to work properly.

Some standard C string functions include

• i nt strlen (const char *s) returns the number of characters in string s, not including the null terminator.

• char *strcpy(char *s, const char *t) copies the contents of string t into string s up to and including the null terminator; s must point to a buffer large enough to hold all the characters of C string t.

• char *strncpy (char *s, const char *t, unsigned n) works like strcpy but copies a maximum of n characters; s must point to a buffer that can hold at least n characters.

• i nt strcmp(const char *s, const char *t) compares two strings for lexicographic (dictionary) ordering. The function returns an integer less than zero if s appears lexicographically before t. The function returns an integer greater than zero if s appears lexicographically after t. The function returns zero if the two strings are identical.

The following code fragment

std:

: cout

<<

strcmp(

"ABC",

"XYZ")

<<

' \n' ;

std:

: cout

<<

strcmp(

"XYZ" ,

"ABC")

<<

' \n' ;

std:

prints

: cout

<<

strcmp(

"ABC",

"ABC")

<<

' \n ' ;

• int strncmp (const char *s, const char *t, int n ) compares the first n characters of two strings for lexicographic (dictionary) ordering. The function returns an integer less than zero if the first n characters of s appear lexicographically before the first n characters of t; that is, s would appear before t is a dictionary. The function returns an integer greater than zero if the first n characters of s appear lexicographically after the first n characters of t. The function returns zero if the first n characters of the two strings are identical.

You should be familiar with C strings because C++ code can use C libraries, and C libraries often use C strings. Since C strings tend to be problematic, however, in most cases you should use the newer stri ng objects (see Sectionfl3.l) whenever possible.

11.2.7 Command-line Arguments

Some programs executed from the command line accept additional arguments. For example, in a Microsoft Windows command prompt the command

copy count.cpp count2.cpp

makes a copy of a file. The macOS and Linux equivalent would be

cp count.cpp count2.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

These filenames are called command-line arguments. They are provided in addition to the program’s name. Command-line arguments allow the user to customize in some way the behavior of the program when launching it. In the example above, the user specifies which file to copy and the name of its copy. C++ programs that process command-line arguments do so via an array.

Listing 11.22 (cmdlineargs.cpp) is a program meant to be executed from the command line with extra arguments. It simply reports the extra information the user supplied.

The following shows one run of Listing |Tl722| (cmdlineargs.cpp):

C:\Code>cmdlineargs -h 45 extra [cmdlineargs]

[-h]

[45]

[extra]

The program did not print the first line shown in this program run. The command shell printed C:\Code> awaiting the user’s command, and the user typed the remainder of the first line. In response, the program printed the remaining four lines. The parameter argc contains the number (count) of arguments on the command line typed by the user. The declaration cha r *a rgv [] indicates a rgv is an array of C strings. Notice that a rgv [0] is simply the name of the file containing the program. argv[l] is the string "-h", argv[2] is the string "45", and a rgv [3] is the string "extra".

In Listing 11,23 (sqrtcmdline.cpp), the user supplies a range of integers on the command line. The program then prints all the integers in that range along with their square roots.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Feature

Vectors

Arrays

First element at index 0

Yes

Yes

Keeps track of its own size

Yes

No

Capacity expands automatically as needed

Yes

No

May be empty

Yes

No

Table captionTable 11.1: Vectors compared to arrays

Since the command-line arguments are strings, not integers. Listing |Tl. 23| (sqrtcmdline.cpp) must convert the string parameters into their integer equivalents. The following shows some sample runs of Listing ]! L23 (sqrtcmdline.cpp):

C:\Code>sqrtcmdline Supply range of values

C:\Code>sqrtcmdline 2 Supply range of values

C:\Code>sqrtcmdline 2 10

2 1.41421

3 1.73205

4 2

5 2.23607

6 2.44949

7 2.64575

8 2.82843

9 3

10 3.16228

11.3 Vectors vs. Arrays

It is important to note is that arrays are not objects and, therefore, have no associated methods. The square bracket notation when used with arrays does not represent a special operator method. The square bracket array access notation is part of the core C++ language inherited from C. The creators of the C++ vector library designed vectors to behave as much as possible like primitive C arrays. Arrays have been part of the C language since its beginning, but vectors (added by C++) have adopted the syntactical features of arrays. Both arrays and vectors use square brackets for element access, and both locate their first element at index zero. Both provide access to a block of memory that can hold multiple elements. A vector object adds some additional capabilities and conveniences that make vectors the better choice for C++ developers. Table 111.1 1| summarizes many of the differences between vectors and arrays.

Vectors have a close association with arrays—a vector object is a thin wrapper around a dynamic array. A vector object simply manages several pointers that point to its dynamic array. Figure 11.14 provides a more accurate picture of the vector-array relationship.

The figure shows that a vector essentially maintains three pointers:

• The pointer labeled _begi n points to the beginning of the block of memory allocated for the array that the vector manages. This corresponds to the location of the first element in the array.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 11.14 A vector and its associated array.

vector<int> list;

li st

• The pointer labeled _end points to the position in the array just past the last viable element in the vector.

• The _capaci ty pointer points to the memory location just past the block of memory allocated for the array.

The _capacity pointer is present because the array managed by a vector often will have more space allocated than the vector currently needs. An algorithm determines the amount of extra space needed to balance the demands of storage economy and fast push_back calls. When an executing program attempts to push_back an element onto a vector that has not reached its capacity, the operation is very fast; however, an attempt to push_backan element onto a vector that is at its capacity forces the run-time memory manager to do the following:

• allocate a large enough space elsewhere in memory to store the contents of the larger array, plus some extra room for future expansion,

• copy all the elements from the original array to the newly allocated array,

• add the new element onto the end of the newly allocated array,

• delete the memory held by the original array, and

• redirect the three pointers in the vector object to point to the appropriate places in the newly allocated array.

Resizing and copying the array is a relatively time-consuming process, especially as the size of the vector grows. The vector’s capacity is tuned so that the average time to perform push_backis fast without the need to consume too much extra memory.

A vector adds value to a raw array by providing convenient methods for adding elements and resizing the array it manages. A vector keeps track of its own size. Arrays provide none of the convenient methods that vectors do. The overhead that a vector imposes over a raw dynamic array is negligible. You should prefer vectors over arrays when writing C++ code.

©2018 Richard L. Halterman

Draft date: September 25, 2018

What if you are using vectors, but you need to use a C library that accepts only arrays? Fortunately it is easy to “unwrap” the array that the vector manages. If vec is a vector, the expression &vec [0] is the address of the first element within the vector. Given a function such as

void print(int a[], int n) {

for (int i = 0; i < n; i++) std::cout << a[i] << ' ' ; std::cout << '\n' ;

}

that expects an array and its size, you can invoke it with your vec vector object as print(&vec[0], vec.sizeQ);

Note that the first parameter is the starting address of the wrapped array, and the second parameter is the number of elements. Suppose instead you have a function that uses a pointer range, as in the following example:

void print(int *begin, int *end) {

for (int *elem = begin; elem != end; elem++) std::cout << *elem << ' ' ; std::cout << '\n' ;

}

Here begi n points to the beginning of an array, and end points to one position past the end of the array. You can invoke this function with your vec vector object as

print(&vec[0] , &vec[0] + vec.sizeQ);

Note that the first parameter is the starting address of the wrapped array, and the second parameter uses pointer arithmetic to compute the memory address just past the end of the wrapped array.

Since the C++11 standard, the std: :vector class has a method named data that returns a pointer to the first element of the array the vector manages. We can rewrite the above statement as

print(vec.data() , vec.dataQ + vec.sizeQ); or better yet as

auto p = vec.dataQ ; print(p, p + vec.sizeQ);

which avoids calling the data method twice.

As these examples show, you may use vector objects instead of arrays without any danger of not being able to use libraries that deal only with arrays.

If you happen to be using an array and need to use a function that expects a vector instead, it is easy to make a vector out of an existing array. If a r r is a raw integer array containing n elements, the statement

std::vectorci nt> vec(arr, arr + n) ;

creates a new vector object vec with elements that are identical to a r r . One disadvantage of this technique is that it copies all the elements in arr to a new dynamic array managed by the vector. This is because a vector object demands full control over the array it manages. A vector automatically frees up the memory of its array when it goes out of scope. Forcing a vector to manage a preexisting array could lead to problems in two ways:

©2018 Richard L. Halterman

Draft date: September 25, 2018

• The code that created the array could later delete the contents of the array out from under the vector. Any attempted use of the vector after that point would be a problem.

• When the vector goes out of scope it automatically deallocates the array it manages. The code that originally created the array could afterward attempt to access the deallocated array with similar predictably disastrous results.

For these reasons the developers of the standard library designed the std : : vector class to be in full control of its managed array. We thus cannot create a vector object from array created elsewhere without making a copy of the array.

We will see in Chapter jjT9] that it is relatively easy to write a function in a generic way so that it can accept and process either a vector or an array with equal efficiency.

Vectors are convenient data structures for working with dynamically-allocated arrays. C++ provides an object-oriented type equivalent to static C arrays. The std: : array is the preferred way to represent statically-allocated arrays in C++.

In order to use the std : : a r ray class you must use the following preprocessor directive: ttinclude <array>

Instead of declaring a static array as int arr[100];

you can write

std::array<i nt , 100> arr;

The first expression in the angle brackets specifies the type of elements held by the array, and the second expression specifies the array’s statically-allocated size. The compiler must be able to compute the size; this means the size must be an integral literal or defined integral constant. Like a static C array, this size cannot be specified at run time. Also unlike std : : vectors, the size of a std : :array object remains fixed for the duration of the program’s execution. Like a std: : vector, however, a std: :array object keeps track of its own size and supports reassignment. Listing [ 11.24[ (stdarray.cpp) shows that we can determine the number of elements in a std : : a r ray object via its size method, just as we would with a std: :vector object.

Listing |TL24| (stdarray.cpp) prints

10

Because of the limitations of std : : a r rays compared to std : : vectors, the std : : ar ray class does not see as much use in C++ programs compared to the std : : vector class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Programmers must manage primitive arrays and associated pointers very carefully because array and pointer misuse is a common source of difficult to find and repair bugs within programs. Vectors effectively take care of much of the memory management problems that plague raw arrays. Additionally, vectors provide functionality and convenience that arrays cannot. As we have seen, it is easy to adapt a vector to a context that requires an array.

11.4 Prime Generation with a Vector

Listing [l 1,25| (fasterprimes.cpp) uses an algorithm developed by the Greek mathematician Eratosthenes who lived from 274 B.C. to 195 B.C. The principle behind the algorithm is simple: Make a list of all the integers two and larger. Two is a prime number, but any multiple of two cannot be a prime number (since a multiple of two has two as a factor). Go through the rest of the list and mark out all multiples of two (4, 6, 8, ...). Move to the next number in the list (in this case, three). If it is not marked out, it must be prime, so go through the rest of the list and mark out all multiples of that number (6, 9, 12, ...). Continue this process until you have listed all the primes you want.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

}

std::cout << // Print the std::cout << << <<

'\n' ; // Move cursor down to next line

elapsed time "Elapsed time: "

static_cast<double> (clock() - start_time)/CLOCKS_PER_SEC " seconds\n";

©2018 Richard L. Halterman

Draft date: September 25, 2018

for (int trial_factor = 2;

is_prime && trial_factor <= root; trial_factor++) is_prime = (value % trial_factor != 0); if (is_prime)

count++; // Count the prime number

}

// Print the elapsed time

std::cout << "Count = " << count << " std::cout << "Elapsed time: "

<< static_cast<double> (clock() - start_time)/CLOCKS_PER_SEC << " seconds\n";

void count_primes3() { int count = 0;

clock_t start_time = clock(); // Record start time

// First prime number is 2; 0 and 1 are not prime

nonprimes[0] = nonprimes[l] = true;

// Start at the first prime number, 2. for (int i = 2; i < MAX; i++) {

// See if i is prime if (! nonpri mes [i ]) {

count++; // It's prime, so count it // It is prime, so eliminate all of its // multiples that cannot be prime for (int j = 2*i; j < MAX; j += i) nonprimes[j] = true;

}

}

// Print the elapsed time

std::cout << "Count = " << count << " ";

std::cout << "Elapsed time: "

<< static_cast<double> (clock() - start_time)/CLOCKS_PER_SEC << " seconds\n";

int main() {

count_primesl(); count_primes2(); count_primes3();

Recall Listing pL8| (measureprimespeed.cpp), which also prints all the prime numbers up to 500,000. Using redirection (see Section [8T4| , Listing |8.8| (measureprimespeed.cpp) takes 77 seconds. In comparison, Listing fll ,25| (fasterprimes.cpp) takes about one second to perform the same task on the system. This is comparable to the square root version. Listing |83](rnoreefficientprirnes.cpp), which takes two seconds to run. If the goal is to print the prime numbers up to 1,000,000, the original version averages 271 seconds, or about four and one-half minutes. The square root version averages 4.5 seconds. The new, vector-based version averages 2 seconds. For 5,000,000 values the unoptimized original version takes a little over an hour and 33 minutes, the square root version takes a respectable 39 seconds, but vector version averages only 9 seconds to run.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Both the vector and array types represent linear sequences of elements. Vectors and arrays are convenient for storing collections of data, but they have some limitations. In Section [2TTj we will consider another kind of aggregate data structure called an associative container. Associative containers permit element access via a key rather than an index. Unlike an index, a key is not restricted to an integer expression. Associative containers are a better choice for some kinds of problems.

11.5 Exercises

1. Can you declare a vector to hold a mixture of i nts and doubles?

2. What happens if you attempt to access an element of a vector using a negative index?

3. Given the declaration

std::vector<i nt> list(100);

(a) What expression represents the very first element of li st?

(b) What expression represents the very last element of li st?

(c) Write the code fragment that prints out the contents of li st.

(d) Is the expression list[3.0] legal or illegal?

4. Given the declarations

std::vector<i nt> list{2, 3, 1, 14, 4}; i nt x = 2;

evaluate each of the following expressions:

(a)

li

st

[1]

(b)

li

st

[X]

(c)

li

st

.size()

(d)

li

st

.empty()

(e)

li

st

• at(3)

(f)

li

st

[x] + 1

(g)

li

st

[x + 1]

(h)

li

st

[list[x]]

(i)

li

st

[list.sizeQ - 1]

5. Is the following code fragment legal or illegal?

std:: vector<int> listl(5), list2{ 3, 3, 3, 3, 3 }; listl = list2;

6. Provide a single declaration statement that declares an integer vector named li st that contains the values 45, —3, 16 and 8?

7. Does a vector keep track of the number of elements it contains?

8. Does an array keep track of the number of elements it contains?

©2018 Richard L. Halterman

Draft date: September 25, 2018

9. Does the std : : a r ray class have more in common with a static array or a dynamic array?

10. Complete the following function that adds up all the positive values in an integer vector. For example, if vector vec contains the elements 3, -3, 5, 2, —1, and 2, the call sum_posi ti ve (vec) would evaluate to 12, since 3 + 5 + 2 + 2= 12. The function returns zero if the vector is empty. The function does not affect the contents of the vector.

int sum_positive (const std::vectorci nt>& v) {

// Add your code...

}

11. Complete the following function that counts the even numbers in an integer vector. For example, if vector vec contains the elements 3, 5, 4, —1, and 0, the call count_evens (vec) would evaluate to 2, since the vector contains two even numbers: 4 and 0. The function returns zero if the vector is empty. The function does not affect the contents of the vector.

int count_evens (const std::vectorci nt>& v) {

// Add your code...

}

12. Complete the following function that counts the even numbers in a 2D vector of integers.

int count_evens (const std::vector<std::vectorci nt>>& v) {

// Add your code...

}

13. Complete the following function that compares two integer vectors to see if they contain exactly the same elements in exactly the same positions. The function returns true if the vectors are equal; otherwise, it returns false. For example, if vector vecl contains the elements 3, 5, 2, —1, and 2, and vector vec2 contains the elements 3, 5, 2, —1, and 2, the call equals (vecl, vec2) would evaluate to true. If instead vector vec2 contains the elements 3, 2, 5, —1, and 2, the call equals (vecl, vec2) would evaluate to false (the second and third elements are not in the same positions). Two vectors of unequal sizes cannot be equal. The function does not affect the contents of the vectors.

bool equals(const std::vectorci nt>& vl, const std::vectorci nt>& v2) {

// Add your code...

}

14. Complete the following function that determines if all the elements in one vector also appear in another. The function returns true if all the elements in the second vector also appear in the first; otherwise, it returns false. For example, if vector vecl contains the elements 3, 5, 2, —1, 7, and 2, and vector vec2 contains the elements 5, 7, and 2, the call contai ns (vecl, vec2) would evaluate to true. If instead vector vec2 contains the elements 3, 8, —1, and 2, the call contai ns (vecl, vec2) would evaluate to false (8 does not appear in the first vector). Also If vector vec2 contains the elements 5, 7, 2, and 5, the call contai ns (vecl, vec2) would evaluate to false (5 appears twice in vec2 but only once in vecl, so vecl does not contain all the elements that appear in vec2). The function does not affect the contents of the vectors.

bool contains (const std::vectorci nt>& vl,

const std::vectorci nt>& v2) {

// Add your code...

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

15. Suppose your task is to implement the function with the prototype

void proc (std : : vector'd' nt> v) ;

When you implement the body of proc, how can you determine the size of vector v?

16. Consider the declaration

std::vector<std::vector <int>> collection(100, std::vector <int> (200))

(a) What does the expression collecti on [15] [29] represent?

(b) How many elements does collecti on hold?

(c) Write the C++ code that prints all the elements in collecti on. All the elements in the same row should appear on the same line, and but each successive row should appear on its own line.

(d) What does the expression collecti on [15] represent?

17. Consider the declaration

std::vector<std::vector<std::vector<std::vectorci nt>>>> mesh(100, std::vectorci nt> (200, std: :vector<int> (100,

std::vector <int> (50))));

How many elements does mesh hold?

18. How is a C++ array different from a vector?

19. What advantages does a C++ vector provide over an array?

20. Provide the statement(s) that declare and create a static array named a that can hold 20 integers.

21. Provide the statement(s) that declare and ceate a dynamic array named a that can hold 20 integers.

22. What extra attention does a programmer need to give to a static array when its use within a program is finished?

23. What extra attention does a programmer need to give to a dynamic array when its use within a program is finished?

24. What extra attention does a programmer need to give to a vector array when its use within a program is finished?

25. Consider the following function that processes the elements of an array using a range:

bool proc(const int *begin, const int *end) {

// Details omitted . . .

}

and an array and vector declared as shown here:

int a[10] ;

std::vectorci nt> v;

(a) Provide the statement that correctly calls proc with array a.

(b) Provide the statement that correctly calls proc with vector v.

©2018 Richard L. Halterman

Draft date: September 25, 2018

26. Can you declare an array to hold a mixture of i nts and doubles?

27. What happens if you attempt to access an element of an array using a negative index?

28. Given the declaration

int list[100];

(a) What expression represents the very first element of li st?

(b) What expression represents the very last element of li st?

(c) Write the code fragment that prints out the contents of li st.

(d) Is the expression list[3.0] legal or illegal?

29. Is the following code fragment legal or illegal?

int listl[5], list2[5] = { 3, 3, 3, 3, 3 }; listl = list2;

30. Provide a single declaration statement that declares an integer array named li st that contains the values 45, —3, 16 and 8?

31. Does an array keep track of the number of elements it contains?

32. Complete the following function that adds up all the positive values in an array of integers. For example, if array ar r contains the elements 3, -3, 5, 2, — 1, and 2, the call sum_positive(arr) would evaluate to 12, since 3+5 + 2 + 2= 12. The function returns zero if the array is empty (that is, n < 1).

// Array a with length n

int sum_positive (const int *a, int n) {

// Add your code...

}

33. Complete the following function that sums the even numbers in an array of integers. For example, if array arr contains the elements 3, 5, 2, —1, and 2, the call sum_evens (arr) would evaluate to 4, since 2 + 2 = 4. The function returns zero if the array is empty (that is, n < 1). The function does not affect the contents of the array.

// Array a with length n

int sum_evens (const int *a, int n) {

// Add your code...

}

34. Suppose your task is to implement the function with the prototype

void proc (i nt a []);

When you implement the body of proc, how can you determine the size of array a?

35. Consider the declaration

int collection[100][200];

What does the expression collecti on [15] [29] represent?

©2018 Richard L. Halterman

Draft date: September 25, 2018

36. Consider the declaration

int collection[100][200];

How many elements does collection hold?

37. Consider the declaration

int collection[100][200];

Write the C++ code that prints all the elements in collecti on. All the elements in the same row should appear on the same line, and but each successive row should appear on its own line.

38. Consider the declaration

int collection[100][200];

What does the expression collecti on [15] represent?

39. Consider the declaration

int mesh[100][200][100] [50] ;

How many elements does mesh hold?

40. Rewrite the following expressions using pointer notation instead of array notation.

(a) a [4]

(b) a [1]

(c) a [0]

41. Rewrite the following expressions using array notation instead of pointer notation.

(a) *(a + 3)

(b) *a

(c) * (a + 0)

42. Rewrite the following code fragment using array notation instead of pointer notation:

void display(i nt *a, int n) { while (n) {

std::cout << *a << " " ; a++ •

n—;

}

std::cout << '\n' ;

}

43. Rewrite the following code fragment using pointer notation instead of array notation:

int sum (int *a, int n) { int s = 0;

for (int i = 0; i < n; i++) s += a [ i] ; return s;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

44. Consider the following declaration:

char *word = "abcde";

Evaluate each of the following expressions. If an expression indicates undefined behavior, write UB.

(a) word [1]

(b) *word

(c) word [5]

45. Suppose your task is to implement the function with the prototype

void proc(char *s) ;

where s is a C string. When you implement the body of p r oc, how can you determine the length of string s?

46. Given the following declarations which appear in a function body:

double nums[100], *grid = new double[100];

(a) Where will the elements of the nums array live—static memory, the stack, or the heap?

(b) Where will the elements of the grid array live—static memory, the stack, or the heap?

47. What operator should eventually be used when the new operator is used to allocate memory? What is the consequence of its omission?

48. List some common errors programmers make when dealing with dynamic memory.

49. Complete the following function that counts the number of negative values in a 10 x 10 integer 2D array.

int count_negatives (i nt a[lO][10]) {

// Add your code...

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 12

Sorting and Searching

Chapters |TT] introduced the fundamentals of making and using vectors. In this chapter we explore some common algorithms for ordering elements within a vector and for locating elements by their value rather than by their index.

12.1 Sorting

We will use the generic term sequence to refer to either a vector or an array. Sorting—arranging the elements within a sequence into a particular order—is a common activity. For example, a sequence of integers may be arranged in ascending order (that is, from smallest to largest). A sequence of words (strings) may be arranged in lexicographical (commonly called alphabetic) order. Many sorting algorithms exist, and some perform much better than others. We will consider one sorting algorithm that is relatively easy to implement.

The selection sort algorithm is relatively easy to implement, and it performs acceptably for smaller sequences. If A is a sequence, and i and j represent indices within the sequence, selection sort works as follows:

1. Set 1 = 0.

2. Examine all the elements A[j], where j > i. If any of these elements is less than A[i], then exchange A[i] with the smallest of these elements. (This ensures that all elements after position i are greater than or equal to A[i].)

3. If i is less than the length of A, increase i by 1 and goto Step 2.

If the condition in Step 3 is not met, the algorithm terminates with a sorted sequence. The command to “goto Step 2” in Step 3 represents a loop. We can begin to translate the above description into C++ as follows:

// n is A's length

for (int i = 0; i < n - 1; i++) {

// Examine all the elements // A[ j ], where j > i .

// If any of these A[j] is less than A[i] ,

©2018 Richard L. Halterman

Draft date: September 25, 2018

// then exchange A[i] with the smallest of these elements.

}

The directive at Step 2 beginning with “Examine all the elements A[y], where j > i” also requires a loop. We continue refining our implementation with:

// n is A's length

for (int i = 0; i < n - 1; i++) {

for (int j = i + 1; j < n; j++) {

// Examine all the elements // A[j], where j > i.

}

// If any A[j] is less than A[i],

// then exchange A[i] with the smallest of these elements.

In order to determine if any of the elements is less than A [ i ], we introduce a new variable named small. The purpose of small is to keep track of the position of the smallest element found so far. We will set small equal to i initially because we wish to locate any element less than the element found at position i.

// n is A's length

for (int i = 0; i < n - 1; i++) {

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less than A[i] int small = i;

for (int j = i + 1; j < n; j++) {

"if (A[j] < A[small])

small = j; // Found a smaller element, update small

}

// If small changed, we found an element smaller than A[i] if (small != i)

// exchange A[small] and A[i ]

}

Listing 12.1 (sortintegers.cpp) provides the complete C++ implementation of the selecti on_sort function within a program that tests it out.

Listing 12.1: sortintegers.cpp

#include <iostream> #include <vector>

/*

*

*

*

*

*

*/

void swap(int& a, int& b) { int temp = a; a = b; b = temp;

swap(a, b)

Interchanges the values of memory referenced by its parameters a and b. It effectively interchanges the values of variables in the caller's context.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

* selection_sort

* Arranges the elements of vector a into ascending order.

* a is a vector that contains integers.

*/

void selection_sort(std:: vector<int>& a) { int n = a.size();

for (int i = 0; i < n - 1; i++) {

// Note: i,small, and j represent positions within a // a[i], a[small], and a[j] represents the elements at // those positions.

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less // than a[i] int small = i ;

// See if a smaller value can be found later in the vector for (int j = i + 1; j < n; j++)

"if (a [ j ] < a[small])

small = j; // Found a smaller value // Swap a[i] and a[small], if a smaller value was found if (i != small)

swap(a[i], a[small]);

}

}

/*

* print

* Prints the contents of a vector of integers.

* a is the vector to print.

* a is not modified.

*/

void print(const std::vector <i nt>& a) { int n = a.size(); std::cout << '{' ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a [ i]; // Print the rest

}

std::cout << '}' ;

int main() {

std::vector<int> list{23, -3, 4, 215, 0, -3, 2, 23, 100, 88, -10};

std::cout << "Before: ";

print(list);

std::cout << 1 \n 1 ;

selection_sort(list);

std::cout << "After: ";

print(list);

std::cout << 1 \n 1 ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 12.1 (sortintegers.cpp) uses a fancier print routine, separating the vector’s elements with commas. The program’s output is

Before: {23,-3,4,215,0,-3,2,23,100,88,-10} After: {-10,-3,-3,0,2,4,23,23,88,100,215}

We really do not need to write our own function to interchange the values of two integers as shown in Listing 12.1 (sortintegers.cpp). The C++ standard library includes std : : swap that works just like the swap function in Listing [T2J~j| (sortintegers.cpp); therefore, if you remove our custom swap definition in Listing 12.1 (sortintegers.cpp) and replace the call to swap with a call to std : : swap, the program will work just as well.

12.2 Flexible Sorting

What if we want to change the behavior of the sorting function in Listing [12.11 (sortintegers.cpp) so that it arranges the elements in descending order instead of ascending order? It is actually an easy modification; simply change the line

"if (a [ j ] < a[small])

to be

"if (a [ j ] > a[small])

Suppose we want to change the sort so that it sorts the elements in ascending order except that all the even numbers in the vector appear before all the odd numbers? This would take a little more effort, but it still is possible to do.

The next question is more intriguing: How can we rewrite the selecti on_sort function so that, by passing an additional parameter, it can sort the vector in any way we want?

We can make our sort function more flexible by making it higher-order function (see Section [10.10 1 that accepts an ordering function as a parameter. Listing |||12T2| (flexibleintsort.cpp) arranges the elements in a vector two different ways using the same selecti on_sort function.

Listing 12.2: flexible! ntsort.cpp

#include <iostream>

#include <vector>

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

bool less_than (i nt a, int b) { return a < b;

}

/*

* greater_than(a, b)

©2018 Richard L. Halterman

Draft date: September 25, 2018

* Returns true if a > b; otherwise, returns

* false.

*/

bool greater_than (i nt a, int b) { return a > b;

}

/*

* selection_sort(a, compare)

* Arranges the elements of a in an order determined

* by the compare function.

* a is a vector of integers.

* compare is a function that compares the ordering of

* two integers.

*/

void selection_sort(std:: vector<int>& a, bool (*compare) (int, int)) { int n = a . size ();

for (int i = 0; i < n - 1; i++){

// Note: i,small, and j represent positions within a // a[i], a[small], and a[j] represents the elements at // those positions.

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less // than a[i] int small = i ;

// See if a smaller value can be found later in the vector for (int j = i + 1; j < n; j++) if (compare(a[j] , a[small]))

small = j; // Found a smaller value // Swap a[i] and a[small], if a smaller value was found if (i != small)

std::swap(a[i], a[small]); // Uses std::swap

}

}

/*

* print

* Prints the contents of an integer vector

* a is the vector to print.

* a is not modified.

*/

void print(const std::vector <i nt>& a) { int n = a . size(); std::cout << ' { ' ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << 1 , 1 << a[i]; // Print the rest

}

std::cout << 1 } ' ;

int main() {

std::vector<i nt> list{ 23, -3, 4, 215, 0, -3, 2, 23, 100,

88 , -10 };

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Original:

print(list);

std::cout << 1 \n 1 ;

selection_sort(list, less_than);

std::cout << "Ascending:

print(list) ;

std::cout << 1 \n 1 ;

selection_sort(list, greater_than); std::cout << "Descending: print(list) ; std::cout << 1 \n ' ;

Listing[l2l2|(flexibleintsort.cpp) takes advantage of the standard swap function (see Section [HTTp.

The output of Listing[T2i2|(flexibleintsort.cpp) is

Original: {23,-3,4,215,0,-3,2,23,100,88,-10} Ascending: {-10,-3,-3,0,2,4,23,23,88,100,215} Descending: {215,100,88,23,23,4,2,0,-3,-3,-10}

The comparison function passed to the sort routine customizes the sort’s behavior. The basic structure of the sorting algorithm does not change, but its notion of ordering is adjustable. If the second parameter to selecti on_sort is less_than, the sort routine arranges the elements into ascending order. If the caller passes greater_than instead, selecti on_sort rearranges vector’s elements into descending order. More creative orderings are possible with more elaborate comparison functions.

Selection sort is a relatively efficient simple sort, but more advanced sorts are, on average, much faster than selection sort, especially for large data sets. One such general purpose sort is Quicksort , devised by C. A. R. Hoare in 1962. Quicksort is the fastest known general purpose sort. Since sorting is a common data processing activity, the standard C library provides a function More information about Quicksort and qsort is available at Quicksort

named qsort that implements Quicksort, http://en.wikipedia.org/wiki/

12.3 Search

Searching a vector for a particular element is a common activity. We will consider the two most common search strategies: linear search and binary search.

12.3.1 Linear Search

Listing 12.3 (linearsearch.cpp) uses a function named locate that returns the position of the first occurrence of a given element in a vector of integers; if the element is not present, the function returns —1.

©2018 Richard L. Halterman

Draft date: September 25, 2018

* locate(a, seek)

* Returns the index of element

* Returns -1 if seek is not an

* a is the vector to search.

* seek is the element to find.

*/

int locate(const std::vector <i nt>& a, int seek) { int n = a . size (); for (int i = 0; i < n; i++) if (a[i] == seek)

return i; // Return position immediately return -1; // Element not found

}

seek in vector a. element of a.

/*

* format(i)

* Prints integer i right justified in a 4-space

* field. Prints "****" if i > 9,999.

*/

void format(int i) { if (i > 9999)

std::cout << "****" << '\n' ; // Too big!

else

std::cout << std::setw(4) << i;

/*

* print(v)

* Prints the contents of an int vector.

* v is the vector to print.

*/

void print(const std::vector <i nt>& v) { for (int i : v) format(i);

}

/*

* display(a, value)

* Draws an ASCII art arrow showing where

* the given value is within the vector.

* a is the vector.

* value is the element to locate.

*/

void display (const std:: vector<int>& a, int value) { int position = locate(a, value); if (position >= 0) {

print(a); // Print contents of the vector

std::cout << '\n 1 ;

position = 4*position + 7; // Compute spacing for arrow

std::cout << std::setw(position);

std::cout << " A " << '\n' ;

std::cout << std::setw(position);

std::cout << " | " << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << std::setw(position); std::cout << " +— " << value << '\n';

}

else {

std::cout << value << " not in print(a);

std::cout << '\n 1 ;

}

std::cout << "======" << '\n';

int main() {

std::vector<i nt> list{ 100, 44, 2, 80, 5, 13, 11, 2, 110 };

display(list, 13);

display(list, 2);

display(list, 7) ;

display(list, 100);

display(list, 110);

The output of Listing 12.3 (linearsearch.cpp) is

100 44

2 80

5

13 11 2 110

A

1

+ -- 13

100 44

2 80

A

5

13 11 2 110

1

+ -- 2

7 not in

100 44

2

80 5 13 11 2 110

100 44

2 80

5

13 11 2 110

A

1

+-- 100

100 44

2 80

5

13 11 2 110

A

1

+-- 110

The key function in Listing 12.3 (linearsearch.cpp) is locate; all the other functions simply lead to a more interesting display of locate’s results. If locate finds a match, it immediately returns the position of the matching element; otherwise, if locate considers all the elements of the vector and finds no match, it returns — 1. — 1 is a good indication of failure, since — 1 is not a valid index in a C++ vector.

The other functions are

• format prints an integer right justified within a four-space field. Extra spaces pad the beginning of the number if necessary.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 12.1 Linear search. The grayed out elements are not considered during the search process.

int list[] = { 100, 44, int x = locate(list, 9,

2, 80, 5, 13, 11, 2, 110 }; 13);

li st

13?

1

■ 1.'

■1.'

* '

r*—

o

o <

44

2

80

5

13

11

2

110

5

• pri nt prints out the elements in any vector using the format function to properly format the values. This alignment simplifies the di splay function.

• display uses locate, pri nt, and setw to provide a graphical display of the operation of the locate function.

The kind of search performed by locate is known as linear search, since the process takes a straight line path from the beginning to the end of the vector, and it considers each element in order. Figure [12,1 1| illustrates linear search.

12.3.2 Binary Search

Linear search is acceptable for relatively small vectors, but the process of examining each element in a large vector is time consuming. An alternative to linear search is binary search. In order to perform binary search a vector’s elements must be in sorted order. Binary search exploits this sorted structure of the vector using a clever but simple strategy that quickly zeros in on the element to find:

1. If the vector is empty, return — 1.

2. Check the element in the middle of the vector. If the element is what you are seeking, return its position. If the middle element is larger than the element you are seeking, perform a binary search on the first half of the vector. If the middle element is smaller than the element you are seeking, perform a binary search on the second half of the vector.

This approach is analogous to looking for a telephone number in the phone book in this manner:

1. Open the book at its center. If the name of the person is on one of the two visible pages, look at the phone number.

2. If not, and the person’s last name is alphabetically less the names on the visible pages, apply the search to the left half of the open book; otherwise, apply the search to the right half of the open book.

3. Discontinue the search with failure if the person’s name should be on one of the two visible pages but is not present.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing j!2]4| (binarysearch.cpp) contains a C++ function that implements the binary search algorithm.

©2018 Richard L. Halterman

Draft date: September 25, 2018

/* *

* display(a, value)

* Draws an ASCII art arrow showing where

* the given value is within the vector.

* a is the vector.

* value is the element to locate.

*/

void display (const std:: vector<int>& a, int value) { int position = binary_search(a, value); if (position >= 0) {

print(a); // Print contents of the vector

std::cout << '\n 1 ;

position = 4*position + 7; // Compute spacing for arrow

std::cout << std::setw(position) ; std::cout << " A " << '\n'; std::cout << std::setw(position) ;

std::cout <<

<<

1 \n 1

std::cout << std::setw(position);

std::cout <<

+— " << value << '\n'

}

else {

std::cout << value << " not in print(a);

std::cout << 1 \n 1 ;

}

std::cout << "======" << '\n';

int main() {

// Check binary search on even- and odd-length vectors and //an empty vector

std::vector<i nt> even_list{ 1, 2, 3, 4, 5, 6, 7, 8 }, odd_list{ 1, 2, 3, 4, 5, 6, 7, 8, 9 }, empty_list;

for (int i = -1; i <= 10; i++) display(even_list, i); for (int i = -1; i <= 10; i++) display(odd_list, i); for (int i = -1; i <= 10; i++) display(empty_list, i);

Note 1

Note 2

Note 3

Note 4

Note 5

©2018 Richard L. Halterman

Note 6

Figure 12.2 Binary search. The grayed out elements are not considered during the search.

std::vectorcint> list = { 10, 14,

34, 45,

int x = binary_search(list, 33);

20, 28, 29, 33, 48 };

li st

33?--.

A /

— F

\ ^

',1

[To 14 20 28

29

33

34

45

48

o 1

Table caption7

5

• The variable mid represents the midpoint value between first and last, and it is computed in the statement

mid = first + (last - first + l)/2;

This arithmetic may look a bit complex. The more straightforward way to compute the average of two values would be

mid = (first + last)/2; // Alternate calculation

The problem with this method of computing the midpoint is it fails to produce the correct results more times than the version found in Listing j|12.4|| (binarysearch.cpp). The problem arises if the vector is large, and first and last both have relatively large values. The expression first + last can overflow the range of integers producing a meaningless result. The subsequent division by two is too late to help. The result of the expression first + last would overflow the range of integers more often than the expression first + (last - first + 1) /2 because (last - first + l)/2 would be a much smaller value to add to fi r st. If you are thinking “I would never have thought of that problem,” don’t worry too much. A large number of competent, professional software engineers have fallen prey to this oversight (see http : //googleresearch. blogspot. com/2006/ 06/extra-extra-read-all-about-i t-nearly. html).

The calculation of mid ensures that first < mid < last.

• If mi d is the location of the sought element (checked in the first i f statement), the loop terminates, and returns the correct position.

• The second i f statement ensures that either last decreases or first increases each time through the loop. Thus, if the loop does not terminate for other reasons, eventually first will be larger than last, and the loop will terminate. If the loop terminates for this reason, the function returns —1. This is the correct behavior.

• The second i f statement excludes the irrelevant elements from further search. The number of elements remaining to consider is effectively cut in half.

Figure |l2.2| illustrates how binary search works.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The implementation of the binary search algorithm is more complicated than the simpler linear search algorithm. Ordinarily simpler is better, but for algorithms that process data structures that potentially hold large amounts of data, more complex algorithms employing clever tricks that exploit the structure of the data (as binary search does) often dramatically outperform simpler, easier-to-code algorithms.

For a fair comparison of linear vs. binary search, suppose we want to locate an element in a sorted vector. That the vector is ordered is essential for binary search, but it can be helpful for linear search as well. The revised linear search algorithm is

// This version requires vector a to be sorted in

// ascending order.

int linear_search (const std::vector<i nt>& a, int seek) { int n = a.size () ;

for (int i =0; i < n && a[i] <= seek; i++) if (a[i] == seek)

return i; // Return position immediately return -1; // Element not found

}

Notice that, as in the original version of linear search, the loop will terminate when all the elements have been examined, but it also will terminate early when it encounters an element larger than the sought element. Since the vector is sorted, there is no need to continue the search once you have begun seeing elements larger than your sought value; seek cannot appear after a larger element in a sorted vector.

Suppose a vector to search contains n elements. In the worst case—looking for an element larger than any currently in the vector — the loop in linear search takes n iterations. In the best case—looking for an element smaller than any currently in the vector—the function immediately returns without considering any other elements. The number of loop iterations thus ranges from 1 to n, and so on average linear search requires ^ comparisons before the loop finishes and the function returns.

Now consider binary search of a vector that contains n elements. After each comparison the size of the vector left to consider is one-half the original size. If the sought item is not found on the first probe, the number of remaining elements to search is |. After the next time through the loop, the number of elements left to consider is one-half of j, or After the third iteration, search space in the vector drops to one-half of which is This process of cutting the search space in half continues each time through the loop until the process locates the sought element or runs out of elements to consider. The problem of determining how many times a set of things can be divided in half until only one element remains can be solved with a base-2 logarithm. For binary search, the worst case scenario of not finding the sought element requires the loop to make log 2 u iterations.

How does this analysis help us determine which search is better? The quality of an algorithm is judged by two key characteristics:

• How much time (processor cycles) does it take to run?

• How much space (memory) does it take to run?

In our situation, both search algorithms process the sequence with only a few extra local variables, so for large sequences they both require essentially the same space. The big difference here is speed. Binary search performs more elaborate computations each time through the loop, and each operation takes time, so perhaps binary search is slower. Linear search is simpler (fewer operations through the loop), but perhaps its loop executes many more times than the loop in binary search, so overall it is slower.

We can deduce the faster algorithm in two ways: empirically and analytically. An empirical test is an experiment; we carefully implement both algorithms and then measure their execution times. The analyt

©2018 Richard L. Halterman

Draft date: September 25, 2018

ical approach analyzes the source code to determine how many operations the computer’s processor must perform to run the program on a problem of a particular size.

Listing jT23| (searchcompare.cpp) measures the running times of the two kinds of searches to compare the two algorithms empirically.

Listing 12.5: searchcompare.cpp

ffinclude <iostream> ffinclude <iomanip> ffinclude <vector>

#include <ctime>

/*

* binary_search(a, seek)

* Returns the index of element seek in vector a;

* returns -1 if seek is not an element of a

* a is the vector to search; a's contents must be

* sorted in ascending order.

* seek is the element to find.

*/

int binary_search(const std:: vector<int>& a, int seek) { int n = a.size();

int first = 0, // Initially the first element in vector

last = n - 1, // Initially the last element in vector

mid; // The middle of the vector

while (first <= last) {

mid = first + (last - first + l)/2; if (a[mid] == seek)

return mid; // Found it

else if (a[mid] > seek)

last = mid - 1; // continue with 1st half

else // a[mid] < seek

first = mid + 1; // continue with 2nd half

}

return -1; // Not there

/*

* linear_search(a, seek)

* Returns the index of element seek in vector a.

* Returns -1 if seek is not an element of a.

* a is the vector to search.

* seek is the element to find.

* This version requires vector a to be sorted in

* ascending order.

*/

int linear_search(const std:: vector<int>& a, int seek) { int n = a.size();

for (int i = 0; i < n && a[i] <= seek; i++) if (a[i] == seek)

return i; // Return position immediately return -1; // Element not found

©2018 Richard L. Halterman

Draft date: September 25, 2018

/*

* Tests the execution speed of a given search function on a

* vector.

* search - the search function to test

* v - the vector to search

* trials - the number of trial runs to average

* Returns the elapsed time in seconds

* The C++ chrono library defines the types

* system_clock::time_point and microseconds.

*/

double time_execution (int (*search) (const std:: vector<int>&, int),

std::vector <i nt>& v, int trials) {

int n = v.size();

// Average the time over a specified number of trials double elapsed = 0.0;

for (int iters = 0; iters < trials; iters++ ) {

clock_t start_time = clockQ; // Start the timer for (int i = 0; i < n; i++) // Search for all elements

search(v, i);

clock_t end_time = clockQ; // Stop the timer

elapsed += static_cast<double> (end_time - start_time)/CLOCKS_PER_SEC;

Chapter Notes

In the bi nary_search function:

• The initializations of first and last:

int first =0, // Initially the first position

last = a.size() - 1, // Initially the last position

ensure that first is less than or equal to last for a nonempty vector. If the vector is empty, first is zero, and last is equal to n — 1 which equals —1. So in the case of an empty vector bi na ry_sea rch will skip the loop body and immediately return —1. This is correct behavior because an empty vector cannot possibly contain any item we seek.

Draft date: September 25, 2018

}

return elapsed/trials; // Mean elapsed time per run

}

int mainQ {

std : : cout << "-\n" ;

std::cout << " Vector Linear Binary\n";

std::cout << " Size Search Search\n";

std : : cout << "-\n" ;

// Test the sorts on vectors with 1,000 elements up to // 10,000 elements.

for (int size = 0; size <= 50000; size += 5000) {

std::vector<i nt> list(size); // Make a vector of the appropiate size

// Ensure the elements are ordered low to high for (int i = 0; i < size; i++) list[i] = i;

std::cout << std::setw(7) << size;

// Search for all the elements in list using linear search // Compute running time averaged over five runs

std::cout << std::fixed << std::setprecisi on(3) << std::setw(12) << time_execution(linear_search, list, 5)

<< " sec";

// Search for all the elements in list binary search // Compute running time averaged over 25 runs

std::cout << std::fixed << std::setprecisi on(3) << std::setw(12) << time_execution(binary_search, list, 25)

<< " sec\n";

}

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing |T23| (searchcompare.cpp) applies linear search and binary search to vectors of various sizes and displays the results. The vector sizes range from 0 to 50,000. The program uses the function ti me_executi on to compute the average running times of linear search and binary search. The main function directs which search ti me_executi on should perform by passing as the first parameter a pointer to the appropriate function. The second parameter to ti me_executi on specifies the number of runs the function should use to compute the average. Notice that in this program we average linear search over five runs and execute binary search over 25 runs. We subject the binary search function to more runs since it executes so quickly, and five runs is not an adequate sample size to evaluate its performance, especially for smaller vectors where the binary search’s execution time is close to the resolution of the timer. Besides, since binary search does execute so quickly, we easily can afford to let ti me_executi on run more tests and compute a more accurate average.

In Listing 12.5 (searchcompare.cpp) we use stream manipulators std : : fixed and std : : setpreci si on to dress up the output. The std : : fixed manipulator adjusts std : : cout to use a fixed number of decimal places, and the std : : setpreci si on manipulator specifies the number of digits to display after the decimal point. The two manipulators in tandem allow us to align the columns of numbers by their decimal points.

A sample run of Listing! 12. 5||(searchcompare.cpp) displays

Vector

Li near

Binary

Si ze

Search

Search

0

0.000

sec

0.000

sec

5000

0.112

sec

0.001

sec

10000

0.444

sec

0.002

sec

15000

1.003

sec

0.003

sec

20000

2.172

sec

0.007

sec

25000

3.444

sec

0.005

sec

30000

5.254

sec

0.006

sec

35000

7.216

sec

0.008

sec

40000

9.701

sec

0.009

sec

45000

11.709

sec

0.018

sec

50000

12.287

sec

0.012

sec

With a vector of size 50,000 linear search takes on average about 12 seconds on one system, while binary search requires a small fraction of a one second. The times for binary search are so small that the progression of times wanders a bit from perfectly ascending order. This is because the operating system is performing other tasks while our program is running. It gives each active program its own slice of processor time to run. The operating system can interrupt executing programs to give other tasks time to run. For most programs this processor time sharing is imperceptible, but it can make a significant difference in shortrunning programs. We can see in the results that the operating system must have attending to some other matters during the binary search of vectors of size 20,000 and 45,000, as these times are slightly higher than we would expect from the pattern of values. Ideally we would perform the tests multiple times and average the results to get a more accurate picture.

If we increase the vector’s size to 500,000, linear search runs in 830 seconds (13 minutes, 50 seconds), while binary search still takes less than one second! Empirically, binary search performs dramatically better than linear search.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Action

Operations

Operation Cost

Iterations

Cost

n = a.size()

=,a.size

2

1

2

i = 0

=

1

1

1

i < size && a[i] <= seek

<=,&&,[],<=

4

n/2

2 n

a[i ] == seek

[],==

2

n/2

n

return i or return -1

return

1

1

1

Table captionTotal Cost 3 n + 4

Table captionTable 12.1: Analysis of Linear Search

One might wonder why a binary search on vector with 45,000 items is slightly slower than one on a vector containing 50,000 elements. This particular execution was performed on a computer running Microsoft Windows. Microsoft Windows’ timer resolution via the clock function is milliseconds, so the values for binary search are near that timer’s resolution. Windows is a multitasking operating system, meaning it manages a number of tasks (programs) simultaneously. The measurements above were performed on a “lightly loaded system,” which means during the program’s execution the user was not downloading files, browsing the web, or doing anything else in particular. Windows, as all modern multitasking OSs, runs a lot of services (other programs) in the background that steal processor time slices. It continually checks for network connections, tracks the users mouse movement, etc. The binary search algorithm’s speed coupled with a multitasking OS with millisecond timer resolution can lead to such minor timing anomalies.

In addition to using the empirical approach, we can judge which algorithm is better by analyzing the source code for each function. Each arithmetic operation, assignment, logical comparison, and vector access requires time to execute. We will assume each of these activities requires one unit of processor “time.” This assumption is not strictly true, but it will give acceptable results for relative comparisons. Since we will follow the same rules when analyzing both search algorithms, the relative results for comparison purposes will be fairly accurate.

We first consider linear search:

int li near_search (const std : : vector'd' nt>& a, int seek) { int n = a.size () ;

for (int i = 0; i < n && a[i] <= seek; i++) if (a[i] == seek)

return i; // Return position immediately return -1; // Element not found

}

We determined that, on average, the loop makes § iterations for a vector of length n. The initialization of i happens only one time during each call to linear_search. All other activity involved with the loop except the return statements happens | times. The function returns either i or —1, and only one return is executed during each call. Table |12.1| shows the breakdown for linear search.

The running time of the li nea r_sea rch function thus can be expressed as a simple linear function: L(n) = 3n + 4.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Action

Operations

Operation Cost

Iterations

Cost

n = a.size()

= , a . size

2

1

2

first = 0

=

1

1

1

last = n - 1

“ y ~

2

1

2

first <= last

< =

1

log 2 «

l°g 2 n

mid = first + (last - first + l)/2

5

log 2 n

5 log 2 «

v[mid] == seek

[],==

2

log 2 n

2log 2 n

v[mid] > seek

□ ,>

2

log 2 «

21og 2 n

last = mid - lor first = mid + 1

= >±

2

log 2 «

21og 2 n

return mid or return -1

return

1

1

1

Total Cost

121og 2 n + 6

Table captionTable 12.2: Analysis of Binary Search

Next, we consider binary search:

int binary_search (const std::vectorci nt>& a, int seek) { int n = a.size(), // Number of elements

// Initially the first element in vector // Initially the last element in vector // The middle of the vector

1 ,

first + 1)/2;

first = 0, last = n mi d;

while (first <= last) { mid = first + (last if (a[mid] == seek)

return mid; // Found it

else if (a[mid] > seek)

last = mid - 1; // continue with 1st half

else // a[mid] < seek

first = mid + 1; // continue with 2nd half

}

return -1; // Not there

We determined that in the worst case the loop in bi na ry_sea rch iterates log 2 n times if the vector contains n elements. The two initializations before the loop are performed once per call. Most of the actions within the loop occur log 2 n times, except that only one return statement can be executed per call, and in the i f/else statement only one path can be chosen per loop iteration. Table 12.2 shows the complete analysis of binary search.

We will call our binary search function B(n). Figure 12.3 shows the plot of the two functions L(n) = 3n +4 and B(n) = 121og 2 n +6.

For n < 17, the linear function 3n + 4 is less than the binary function 12 log 0 n + 6. This means that linear search should perform better than binary search for vector sizes less than 17. This is because the code for linear search is less complicated, and it can complete its work on smaller vectors before the binary search finishes its more sophisticated computations. At n = 17, however, the two algorithms should perform about the same because

L(17) =3(17) +4 = 51 +4 = 55 « 55.05 =49.05+6= 12(4.09) +6= 121og 2 17 + 6 = 5(17)

Figure [12.31 shows that for all n > 17 binary search outperforms linear search, and the performance gap increases rapidly as n grows. This wide performance discrepancy agrees with our empirical observations

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 12.3 A graph of the functions derived from analyzing the linear and binary search routines

0 10 20 30 40 50 60 70 80 90

List Size

we obtained from Listing fT23| (searchcompare.cpp). Unfortunately we cannot empirically compare the running times of the two searches for vectors small enough to demonstrate that linear search is faster for very small vectors. As the output of Listing 12.5 (searchcompare.cpp) shows, both searches complete their work in time less than the resolution of our timer for vectors with 1,000 elements. Both empirically and analytically, we see that binary search is fast even for very large vectors, while linear search is impractical for large vectors.

12.4 Vector Permutations

Sometimes it is useful to consider all the possible arrangements of the elements within a vector. A sorting algorithm, for example, must work correctly on any initial arrangement of elements in a vector. To test a sort function, a programmer could check to see if it produces the correct result for all arrangements of a relatively small vector. A rearrangement of a collection of ordered items is called a permutation. Listing [!2i6|(vectorpermutations.cpp) prints all the permutations of the contents of a given vector.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

std::cout << "}" ;

/*

* Prints all the permutations of vector a in the

* index range begin...end, inclusive. The function's

* behavior is undefined if begin or end

* represents an index outside of the bounds of vector a.

*/

void permute(std:: vector<int>& a, int begin, int end) { if (begin == end) { print(a);

std::cout << '\n' ;

}

else {

for (int i = begin; i <= end; i++) {

// Interchange the element at the first position // with the element at position i std::swap(a[begin], a [i]);

// Recursively permute the rest of the vector

permute(a, begin + 1, end);

// Interchange the current element at the first position // with the current element at position i std::swap(a[begin], a [i]);

}

}

/*

* Tests the permutation functions */

int main() {

// Get number of values from the user

std::cout << "Please enter number of values to permute: "

int number;

std::cin >> number;

// Create the vector to hold all the values

std::vector<i nt> list(number);

// Initialize the vector for (int i = 0; i < number; i++) li st [i ] = i ;

// Print original list print(list);

std:: cout << "\n- \n";

// Print all the permutations of list permute(list, 0, number - 1); std:: cout << "\n- \n";

// Print list after all the manipulations pri nt (li st);

A sample run of Listing) 12.6||(vectorpermutations.cpp) when the user enters 4 prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

Please enter number of values to permute: 4 {0,1,2,3}

{0,1,2,3} { 0 , 1 , 3 , 2 } {0,2,1,3} {0,2,3,1} {0,3,2,1} {0,3,1,2} { 1 , 0 , 2 , 3 } {1,0,3,2} {1,2,0,3} {1,2,3,0} {1,3,2,0} {1,3,0,2} {2,1,0,3} {2,1,3,0} {2,0,1,3} {2,0,3,1} {2,3,0,1} {2,3,1,0} {3,1,2,0} {3,1,0,2} {3,2,1,0} {3,2,0,1} {3,0,2,1} {3,0,1,2}

{0,1,2,3}

The permute function in Listing jTZ6j (vectorpermutations.cpp) is a recursive function, as it calls itself inside of its definition. We have seen how recursion can be an alternative to iteration; however, the permute function here uses both iteration and recursion together to generate all the arrangements of a vector. At first glance, the combination of these two algorithm design techniques as used here may be difficult to follow, but we actually can understand the process better if we ignore some of the details of the code.

First, notice that in the recursive call the argument begi n is one larger, and end remains the same. This means as the recursion progresses the ending index never changes, and the beginning index keeps increasing until it reaches the ending index. The recursion terminates when begin becomes equal to end.

In its simplest form the function looks like this:

void permute(int *a, int begin, int end) { if (begin == end)

// Print the whole vector

else

// Do the interesting part of the algorithm

}

Let us zoom in on the interesting part of the algorithm (less the comments): for (int i = begin; i <= end; i++) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

swap(a[begin], a[i]); permute(a, begin + 1, end); swap(a[begin], a [i]);

}

If the mixture of iteration and recursion is confusing, eliminate iteration!

If a loop iterates a fixed number of times, you may replace the loop with the statements in its body duplicated that number times; for example, we can rewrite the code

for (int i = 0; i < 5; i++) std::cout << i << '\n' ;

as

std::cout << 0 << ' \n ' ;

std::cout << 1 << '\n ' ;

std::cout << 2 << ' \n ' ;

std::cout << 3 << '\n ' ;

std::cout << 4 << ' \n ' ;

Notice that the loop is gone. This process of transforming a loop into the series of statements that the loop would perform is known as loop unrolling. Compilers sometimes unroll loops to make the code’s execution faster. After unrolling the loop the loop control variable (in this case i) is gone, so there is no need to initialize it (done once) and, more importantly, no need to check its value and update it during each iteration of the loop.

Our purpose for unrolling the loop in pe r f o rm is not to optimize it. Instead we are trying to understand better how the algorithm works. In order to unroll perform’s loop, we will consider the case for vectors containing exactly three elements. In this case the for in the perform function would be hardcoded as

for (int i = 0; i <= 2; i++) { swap(a[begin], a [i]); permute(a, begin + 1, end); swap(a[begin], a [i]);

}

and we can transform this code into

swap(a[begin], a[0]); permute(a, begin + 1, end); swap(a[begin], a[0]);

swap(a[begin] , a[l]); permute(a, begin + 1, end); swap(a[begin], a[l]);

swap(a[begin] , a [2]); permute(a, begin + 1, end); swap(a[begin] , a [2]);

Once the loop is gone, we see we have simply a series of recursive calls of permute sandwiched by calls to swap. The first call to swap interchanges an element in the vector with the first element. The second call to swap reverses the effects of the first swap. This series of swap-permute-swap operations allows

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 12.4 A tree mapping out the recursive process of the permute function operating on the vector {}•

i =0

rA i -> O

{ 0 , 1 , 2 }

’Sis. L)

{0,2,1}i£?{0,2,1}

i =2

00 1 =i o 1=1 () ^{ 1 , 0 , 2 }-^ { 1 , 0 , 2 }

{0,1,2} ^ {1,0,2}

n

^{ 1 , 2 , 0 }-^ { 1 , 2 , 0 }

i =2

i =2

1 =| O

( 2,1,OS||T{2,1,0}

{2,1,0}^ Q

SS {2,0,1'}^ {2,0,1}

JL

i =2

JL

J

Initial call to permute Recursive call Base case

begin =0 begin =1 begin =2

end = 2 end = 2 end = 2

each element in the vector to have its turn being the first element in the permuted vector. The permute recursive call generates all the permutations of the rest of the list. Figure || 12.4| traces the recursive process of generating all the permutations of the vector {0,1,2}.

The leftmost third of Figure [12.4 shows the original contents of the vector and the initial call of permute. The three branches represent the three iterations of the for loop: i varying from begin (0) to end (2). The vectors indicate the state of the vector after the first swap but before the recursive call to permute.

The middle third of Figure 12.4| shows the state of the vector during the first recursive call to permute. The two branches represent the two iterations of the for loop: i varying from begi n f 1) to end (2). The vectors indicate the state of the vector after the first swap but before the next recursive call to permute. At this level of recursion the element at index zero is fixed, and the remainder of the processing during this chain of recursion is restricted to indices greater than zero.

The rightmost third of Figure |12.4| shows the state of the vector during the second recursive call to permute. At this level of recursion the elements at indices zero and one are fixed, and the remainder of the processing during this chain of recursion is restricted to indices greater than one. This leaves the

©2018 Richard L. Halterman

Draft date: September 25, 2018

element at index two, but this represents the base case of the recursion because begi n (2) equals end (2). The function makes no more recursive calls to itself. The function merely prints the current contents of the vector.

The arrows in Figure; 12.4| represent a call to, or a return from, permute. They illustrate the recursive call chain. The arrows pointing left to right represent a call, and the arrows pointing from right to left represent a return from the function. The numbers associated with arrow indicate the order in which the calls and returns occur during the execution of permute.

The second column from the left shows the original contents of the vector after the first swa p call but before the first recursive call to permute. The swapped elements appear in red. The third column shows the contents of the vector at the second level of recursion. In the third column the elements at index zero are fixed, as this recursion level is using begi n with a value of one instead of zero. The for loop within this recursive call swaps the elements highlighted in red. The rightmost column is the point where begi n equals end, and so the permute function does not call itself effectively terminating the recursion.

While Listing ||T2T6| (vectorpermutations.cpp) is a good exercise in vector manipulation and recursion, the C++ standard library provides a function named next_permutati on that rearranges the elements of a vector. Listing 12.7 (stlpermutations.cpp) uses next_permutati on within a loop to print all the permutations of the vector’s elements.

©2018 Richard L. Halterman

Draft date: September 25, 2018

12.5 Randomly Permuting a Vector

Section 112.4| showed how we can generate all the permutations of a vector in an orderly fashion. More often, however, we need to produce one of those permutations chosen at random. For example, we may need to randomly rearrange the contents of an ordered vector so that we can test a sort function to see if it will produce the original ordered sequence. We could generate all the permutations, put each one in a vector of vectors, and select a permutation at random from that vector of vectors. This approach is very inefficient, especially as the length of the vector to permute grows larger. Fortunately, we can randomly permute the contents of a vector easily and quickly. Listing |T2T8( (randompermute.cpp) contains a function named permute that randomly permutes the elements of an vector.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Select a pseudorandom location from the current // location to the end of the collection std::swap(a[i], a[random(i, n)]);

} }

// Tests the permute function that randomly permutes the // contents of a vector int main() {

// Initialize random generator seed srand (static_cast<i nt>(time(0)));

// Make the vector {1,2,3,4,5,6,7,8}

std::vector<i nt> vec { 1, 2, 3, 4, 5, 6, 7, 8 };

// Print vector before

print(vec) ;

std::cout << '\n 1 ;

permute(vec);

// Print vector after

print(vec);

std::cout << '\n 1 ;

}

One run of Listing 12.8|(randompermute.cpp) produces

12345678

27164835

Notice that the permute function in Listing |T£8~| (randompermute.cpp) uses a simple un-nested loop and no recursion. The permute function varies the i index variable from 0 to the index of the next to last element in the vector. Within the loop, the function obtains via rand (see Section 8.6) a pseudorandom index greater than or equal to i. It then exchanges the elements at position i and the random position. At this point all the elements at index i and smaller are fixed and will not change as the function’s execution continues. The loop then increments index i, and the process continues until all the i values have been considered.

To be correct, our permute function must be able to generate any valid permutation of the vector. It is important that our permute function is able to produce all possible permutations with equal probability; said another way, we do not want our permute function to generate some permutations more often than others. The permute function in Listing fl2TS| (randompermute.cpp) is fine, but consider a slight variation of the algorithm:

// Randomly permute a vector?

void faulty_permute(std::vectorci nt>& a) { int n = a.size() for (int i = 0; i < n; i++) {

// Select a pseudorandom position somewhere in the vector swap(a[i], a[random(0, n)]);

} }

©2018 Richard L. Halterman

Draft date: September 25, 2018

Do you see the difference between f aulty_permute and permute? The faulty_permute function chooses the random index from all valid vector indices, whereas permute restricts the random index to valid indices greater than or equal to i . This means that faulty_permute can exchange any element within vector a with the element at position i during any loop iteration. While this approach superficially may appear to be just as good as permute, it in fact produces an uneven distribution of permutations. Listing 12.9 (comparepermutations.cpp) exercises each permutation function 1,000,000 times on the vector {1, 2 , 3} and tallies each permutation. There are exactly six possible permutations of this threeelement vector.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::swap(a[i] , a[random(i, n)]);

} }

/* Randomly permute a vector? */

void faulty_permute(std:: vector<int>& a) { int n = a.size(); for (int i = 0; i < n; i++) {

// Select a pseudorandom position somewhere in the collection std::swap(a[i], a[random(0, n)]);

} }

/*

int

Classify a vector as one of the six permutations */ classify (const std:: vector<int>& a) { switch (100*a[0] + 10*a[l] + a[2]) { case 123: return 0;

1 ;

case 132: case 213: case 231: case 312: case 321:

}

return -1;

return return 2; return 3; return 4; return 5;

Table caption/* Report the accumulated statistics */ void report(const std::vector<int>& a) {

std :

: cout

<<

"1,2,3:

II

<<

a [0]

<<

' \n

5

std:

: cout

<<

"1,3,2:

II

<<

a [1]

<<

' \n

5

std:

: cout

<<

"2,1,3:

II

<<

a [ 2 ]

<<

' \n

5

std:

: cout

<<

"2,3,1:

II

<<

a [3]

<<

' \n

5

std :

: cout

<<

"3,1,2:

II

<<

a [4]

<<

' \n

5

std :

: cout

<<

"3,2,1:

II

<<

a [5]

<<

' \n

?

}

/*

* Fill the given vector with zeros.

* a is the vector, and n is its length. */

void clear(std:: vector<int>& a) { int n = a.size(); for (int i = 0; i < n; i++) a [i ] = 0;

}

int main() {

// Initialize random generator seed srand (static_cast<i nt>(time(0)));

// permutation_tally vector keeps track of each permutation pattern // permutation_tally[0] counts {1,2,3}

// permutation_tally[1] counts {1,3,2}

// permutation_tally[2] counts {2,1,3}

// permutation_tally[3] counts {2,3,1}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// permutation_tally[4] counts {3,1,2}

// permutation_tally[5] counts {3,2,1}

std::vector<i nt> permutation_tally { 0, 0, 0, 0, 0, 0 };

// original always holds the vector {1,2,3} const std::vector<i nt> original { 1, 2, 3 };

// working holds a copy of original that gets permuted and tallied std::vector<i nt> working;

// Run each permutation one million times const int RUNS = 1000000;

std::cout << "- Random permute #1 - \n";

clear(permutation_tally);

for (int i = 0; i < RUNS; i++) { // Run 1,000,000 times // Make a copy of the original vector working = original;

// Permute the vector with the first algorithm permute(working);

// Count this permutation

permutation_tally[classify(working)]++;

}

report(permutation_tally); // Report results

std::cout << "- Random permute #2 - \n";

clear(permutation_tally) ;

for (int i = 0; i < RUNS; i++) { // Run 1,000,000 times // Make a copy of the original vector working = original;

// Permute the vector with the second algorithm

faulty_permute(working);

// Count this permutation

permutation_tally[classify(working)]++;

}

report(permutation_tally); // Report results

In Listing f!2,9| (comparepermutations.cpp)’s output, permute #1 corresponds to our original permute function, and permute #2 is the faulty_permute function. The output of Listing 12.9 (comparepermutations.cpp) reveals that the faulty permutation function favors some permutations over others:

- Random permute

#1

1,2,3:

166608

1,3,2:

166820

2,1,3:

166350

2,3,1:

166702

3,1,2:

166489

3,2,1:

167031

- Random permute

#2

1,2,3:

148317

1,3,2:

184756

2,1,3:

185246

2,3,1:

185225

3,1,2:

148476

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

Figure 12.5 A tree mapping out the ways in which f aulty_permute can transform the vector 1, 2, 3 at each iteration of its f o r loop

of 12? of o 7 o o 7 cj 7 sIPq

3,2,1: 147980

In one million runs, the permute function provides an even distribution of the six possible permutations of {1, 2, 3}. The fa ulty_ permute function generates the permutations {1, 3, 2}, {2, 1, 3}, and { 2, 3 , 1} more often than the permutations {1, 2, 3},{3, 1, 2}, and { 3, 2 , 1}.

To see why faulty_permute misbehaves, we need to examine all the permutations it can produce during one call. Figure 12.5 shows a hierarchical structure that maps out how faulty_permute transforms the contents of its vector parameter each time through the for loop.

The top of the tree shows the original vector, {1, 2, 3}. The second row shows the three possible resulting configurations after the first iteration of the for loop. The leftmost 3-tuple represents the element at index zero swapped with the element at index zero (effectively no change). The second 3-tuple on the second row represents the interchange of the elements at index 0 and index 1. The third 3-tuple on the second row results from the interchange of the elements at positions 0 and 2. The underlined elements represent the elements most recently swapped. If only one item in the 3-tuple is underlined, the function merely swapped the item with itself. The bottom row of 3-tuples contains all the possible outcomes of the faulty_permute function given the vector {1, 2, 3}.

As Figure 12.5 shows, the vector {1, 3, 2}, {2, 1, 3}, and {2, 3, 1} each appear five times in the last row, while {1, 2, 3}, {3, 1, 2}, and {3, 2, 1} each appear only four times. There

4

are a total of 27 possible outcomes, so some permutations appear — = 14.815% of the time, while the

others appear — = 18.519% of the time. Notice that these percentages agree with our experimental results from Listing |l2i9|(comparepermutations.cpp).

Compare Figure (12.5 to Figure p~2T6| The second row of the tree for permute is identical to the second row of the tree for faulty_permute, but the third row is different. The second time through its loop the permute function does not attempt to exchange the element at index zero with any other elements. We see that none of the first elements in the 3-tuples in row three are underlined. The third row contains exactly one instance of each of the possible permutations of {1, 2 , 3}. This means that the correct permute function is not biased towards any of the individual permutations, and so the function can

1

generate all the permutations with equal probability. The permute function has a - = 16.667% probability

6 __

of generating a particular permutation; this number agrees with our the experimental results of Listing 12.9 (comparepermutations.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 12.6 A tree mapping out the ways in which permute can transform the vector 1, 2, 3 at each iteration of its for loop

123

12.6 Exercises

1. Complete the following function that reorders the contents of a vector so they are reversed from their original order. For example, a vector containing the elements 2, 6, 2, 5, 0, 1, 2, 3 would be transformed into 3, 2, 1, 0, 5, 2, 6, 2. Note that your function must physically rearrange the elements within the vector, not just print the elements in reverse order.

void reverse(std::vectorci nt>& v) {

// Add your code...

}

2. Complete the following function that reorders the contents of a vector so that all the even numbers appear before any odd number. The even values are sorted in ascending order with respect to themselves, and the odd numbers that follow are also sorted in ascending order with respect to themselves. For example, a vector containing the elements 2, 1, 10, 4, 3, 6, 7, 9, 8, 5 would be transformed into 2, 4, 6, 8, 10, 1, 3, 5, 7, 9 Note that your function must physically rearrange the elements within the vector, not just print the elements in reverse order.

void special_sort(std::vectorci nt>& v) {

// Add your code...

}

3. Complete the following function that shifts all the elements of a vector backward one place. The last element that gets shifted off the back end of the vector is copied into the first (0th) position. For example, if a vector containing the elements 2, 1, 10, 4, 3, 6, 7, 9, 8, 5 is passed to the function, it would be transformed into 5, 2, 1, 10, 4, 3, 6, 7, 9, 8 Note that your function must physically rearrange the elements within the vector, not just print the elements in the shifted order.

void rotate(std::vectorci nt>& v) {

// Add your code...

}

4. Complete the following function that determines if the number of even and odd values in a vector is the same. The function would return true if the vector contains 5, 1, 0, 2 (two evens and two odds), but it would return false for the vector containing 5, 1, 0, 2, 11 (too many odds). The function should

©2018 Richard L. Halterman

Draft date: September 25, 2018

return true if the vector is empty, since an empty vector contains the same number of evens and odds (0). The function does not affect the contents of the vector.

bool balanced (const std::vector<i nt>& v) {

// Add your code...

}

5. Complete the following function that returns true if vector a contains duplicate elements; it returns false if all the elements in a are unique. For example, the vector 2, 3, 2, 1, 9 contains duplicates (2 appears more than once), but the vector 2, 1,0, 3, 8, 4 does not (none of the elements appear more than once).

An empty vector has no duplicates.

The function does not affect the contents of the vector.

bool has_duplicates (const std::vectorci nt>& v) {

// Add your code...

}

6. Can binary search be used on an unsorted vector? Why or why not?

7. Can linear search be used on an unsorted vector? Why or why not?

8. Complete the following function i s_ascendi ng that returns true if the elements in a vector of integers appear in ascending order (more precisely, non-descending order, if the vector contains duplicates). For example, the following statement

std::cout << is_ascending({3, 6, 2, 1, 7}) << '\ n ' ; would print false, but the statement

std::cout << is_ascending({3, 6, 7, 12, 27}) << ' \ n ' ;

would print true. The nonexistent elements in an empty vector are considered to be in ascending order because they cannot be out of order.

bool is_ascending(std::vector<i nt>& v) {

// Add your code...

}

9. Consider a sort function that uses the i s_ascendi ng function from the previous problem. It uses a loop to test the permutations of a vector of integers. When it finds a permutation that contains all of the vector’s elements in ascending order it exits the loop. Do you think this would be a good sorting algorithm? Why or why not?

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 13

Standard C++ Classes

In the hardware arena, a desktop computer is built by assembling

• a motherboard (a circuit board containing sockets for a processor and assorted supporting cards),

• a processor,

• memory,

• a video card,

• an input/output card (USB ports, parallel port, and mouse port),

• a disk controller,

• a disk drive,

• a case,

• a keyboard,

• a mouse, and

• a monitor.

(Some of these components like the I/O, disk controller, and video may be integrated with the motherboard.)

The video card is itself a sophisticated piece of hardware containing a video processor chip, memory, and other electronic components. A technician does not need to assemble the card; the card is used as is off the shelf. The video card provides a substantial amount of functionality in a standard package. One video card can be replaced with another card from a different vendor or with another card with different capabilities. The overall computer will work with either card (subject to availability of drivers for the operating system) because standard interfaces allow the components to work together.

Software development today is increasingly component based. Software components are used like hardware components. A software system can be built largely by assembling pre-existing software building blocks. C++ supports various kinds of software building blocks. The simplest of these is the function that we investigated in Chapter [8] and Chapter [9] A more powerful technique uses built-in and user designed software objects.

©2018 Richard L. Halterman

Draft date: September 25, 2018

C++ is object-oriented. It was not the first OO programming language, but it was the first OO language that gained widespread use in a variety of application areas. An OO programming language allows the programmer to define, create, and manipulate objects. Variables representing objects can have considerable functionality compared to the primitive numeric variables like i nts and doubles. Like a normal variable, every C++ object has a type. We say an object is an instance of a particular class , and class means the same thing as type. An object’s type is its class. We have been using the std : : cout and std : : ci n objects for some time, std : : cout is an instance of the std : : ostream class—which is to say std : : cout is of type std : : ostream. std : : ci n is an instance of the std : : i stream class.

Code that uses an object is a client of that object; for example, the following code fragment std::cout << "Hello\n";

uses the std : : cout object and, therefore, is a client of std : : cout. Many of the functions we have seen so far have been clients of the std : : cout and/or std : : ci n objects. Objects provide services to their clients.

13.1 String Objects

A string is a sequence of characters, most often used to represent words and names. The C++ standard library provides the class stri ng which specifies string objects. In order to use string objects, you must provide the preprocessor directive

ttinclude <string>

The stri ng class is part of the standard namespace, which means its full type name is std : : stri ng. If you use the

using namespace std; or

using std::string;

statements in your code, you can use the abbreviated name stri ng.

You declare a stri ng object like any other variable: string name;

You may assign a literal character sequence to a st ri ng object via the familiar string quotation syntax:

string name = "joe"; std::cout << name << '\n' ; name = "jane"; std::cout << name << '\n' ;

You may assign one stri ng object to another using the simple assignment operator:

string namel = "joe", name2; name2 = namel;

std::cout << namel << " " << name2 << ' \n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

In this case, the assignment statement copies the characters making up namel into name2. After the assignment both namel and name2 have their own copies of the characters that make up the string; they do not share their contents. After the assignment, changing one string will not affect the other string. Code within the string class defines how the assignment operator should work in the context of string objects.

Like the vector class (Section 11.1.3), the string class provides a number of methods. Some stri ng methods include:

• operator [] —provides access to the value stored at a given index within the string

• operator^— assigns one string to another

• operator+=— appends a string or single character to the end of a stri ng object

• at—provides bounds-checking access to the character stored at a given index

• length—returns the number of characters that make up the string

• si ze—returns the number of characters that make up the string (same as length)

• find—locates the index of a substring within a stri ng object

• substr—returns a new stri ng object made of a substring of an existing stri ng object

• empty—returns true if the string contains no characters; returns false if the string contains one or more characters

• clea r—removes all the characters from a string

The following code fragment string word = "computer";

std::cout << "\"" << word << "\" contains " << word.length() << " letters." << '\n' ;

prints

"computer" contains 8 letters.

The expression: word.length()

invokes the length method on behalf of the word object. The stri ng class provides a method named si ze that behaves exactly like the length method.

The stri ng class defines a method named operator[] that allows a programmer to access a character within a stri ng, as in

std::cout << "The letter at index 3 is " << word. operator [](3) << '\n' ;

Here the operator[] method uses the same syntax as the length method, but the operator[] method expects a single integer parameter. The above code fragment is better written as

std::cout << "The letter at index 3 is " << word[3] << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

The expression word. operator [](3)

is equivalent to the expression word[3]

We see that operator[] works exactly like its namesake in the std: :vector class Section 11.1.3

The following code fragment exercises some of the methods available to string objects:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 13.1 Extracting the new string "od-by" from the string "Good-bye"

string word = "Good-bye"; string other = word.substr(2, word

■G'

'o'

'o'

'

'y'

'e'

0

1

3

4

5

6

7

other

r

'o'

' - '

'y'

\

0

1

2

3

4

y

5);

if (first == "XYZ")

std::cout << "equal\n";

else

std::cout << "not equal\n";

The statement word = "good";

is equivalent to

word. operator^ ("good") ;

Here we see the explicit use of the dot (.) operator to invoke the method. Similarly, word += "-bye";

is the syntactally sweetened way to write word. operator+= ( "-bye" );

The + operator performs string concatenation, making a new string by appending one string to the back of another.

With the substr method we can extract a new string from another, as shown in Figure 13.1

In addition to string methods, the standard stri ng library provides a number of global functions that process strings. These functions use operator syntax and allow us to compare strings via <, ==, >=, etc. A more complete list of string methods and functions can be found at http://www.cplusplus. com/reference/string/

©2018 Richard L. Halterman

Draft date: September 25, 2018

13.2 Input/Output Streams

We have used i ostream objects from the very beginning, std : : cout is the output stream object that prints to the screen, std : : ci n is the input stream object that receives values from the keyboard. The precise type of std : : cout is std : : ostream, and std : : ci n’s type is std : : i stream.

Like other objects, std : : cout and std : : ci n have methods. The << and >> operators actually are the methods operator<< and operator>>. (The operators << and >> normally are used on integers to perform left and right bitwise shift operations; see Section [47TD| for more information.) The following code fragment

std::cin >> x; std::cout << x;

can be written in the explicit method call form as:

cin. operator>> (x) ; cout. operator<< (x);

The first statement calls the operator>> method on behalf of the std : : ci n object passing in variable x by reference. The second statement calls the operator<< method on behalf of the std : : cout object passing the value of variable x. A statement such as

std::cout << x << '\n' ;

is a more pleasant way of expressing

cout. operator <<(x). operator <<(' \n' );

Reading the statement left to right, the expression cout. operator<< (x) prints x’s value on the screen and returns the std : : cout object itself. The return value (simply std : : cout) then is used to invoke the operator<< method again with ' \n ' as its argument.

A statement such as

std::cin >> x >> y;

can be written

cin. operator>> (x). operator>> (y);

As is the case of opera tor << with std : : cout, reading left to right, the expression cin.operator>>(x) calls the operator>> method passing variable x by reference. It reads a value from the keyboard and assigns it to x. The method call returns std : : ci n itself, and the return value is used immediately to invoke operator>> passing variable y by reference.

You probably have noticed that it is easy to cause a program to fail by providing input that the program was not expecting. For example, compile and run Listing jl3)2|(naiveinput.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Please enter an integer: std::cin >> x;

std::cout << "You entered " << x << '\n';

Listing |T372|| (naiveinput.cpp) works fine as long as the user enters an integer value. What if the user enters the word “five,” which arguably is an integer? The program produces incorrect results. We can use some additional methods available to the std : : ci n object to build a more robust program. Listing 13.3 (betterintinput.cpp) detects illegal input and continues to receive input until the user provides an acceptable value.

We learned in Section ;6.1 that the expression std::cin >> x

has a Boolean value that we may use within a conditional or iterative statement. If the user enters a value with a type compatible with the declared type of the variable, the expression evaluates to true; otherwise, it is interpreted as false. The negation

!(std::cin >> x)

is true if the input is bad, so the only way to execute the body of the loop is provide illegal input. As long as the user provides bad input, the program’s execution stays inside the loop.

While determining whether of not a user’s entry is correct seems sufficient for the programmer to make corrective measures, it is not. Two additional steps are necessary:

• The bad input characters the user provided cause the std : : ci n object to enter an error state. The input stream object remains in an error state until the programmer manually resets it. The call

cin.clear();

resets the stream object so it can process more input.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• Whatever characters the user typed in that cannot be assigned to the given variable remain in the keyboard input buffer. Clearing the stream object does not remove the leftover keystrokes. Asking the user to retry without clearing the bad characters entered from before results in the same problem— the stream object re-enters the error state and the bad characters remain in the keyboard buffer. The solution is to flush from the keyboard buffer all of the characters that the user entered since the last valid data entry. The statement

cin.ignore(numeric_limits<streamsize>::max(), '\n' ) ;

removes from the buffer all the characters, up to and including the newline character ( ' \ n ' ). The function call

numeric_limits<streamsize>::max()

returns the maximum number of characters that the buffer can hold, so the ignore method reads and discards characters until it reads the newline character ( ' \ n ' ) or reaches the end of the buffer, whichever comes first.

Once the stream object has been reset from its error state and the keyboard buffer is empty, user input can proceed as usual.

The ostream and i stream classes have a number of other methods, but we will not consider them here.

i stream objects use whitespace (spaces and tabs) as delimiters when they get input from the user. This means you cannot use the operator>> to assign a complete line of text from the keyboard if that line contains embedded spaces. Listing [T3.4| (faultyreadline.cpp) illustrates.

A sample run of Listing||T3.4||(faultyreadline.cpp) reveals:

Please enter a line of text: Mary had a little lamb. You entered: "Mary"

As you can see. Listing 13.4 (faultyreadline.cpp) does not assign the complete line of text to the sting variable li ne. The text is truncated at the first space in the input.

To read in a complete line of text from the keyboard, including any embedded spaces that may be present, use the global getli ne function. As Listing 13.5 (readline.cpp) shows, the getli ne function accepts an i stream object and a stri ng object to assign.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int main() {

std::string line;

std::cout << "Please enter a line of text: getline(std::cin, line);

std::cout << "You entered: \"" << line << << '\n' ;

A sample run of Listing! 13.5||(readline.cpp) produces:

Please enter a line of text: Mary has a little lamb. You entered: "Mary has a little lamb."

13.3 File Streams

Many applications allow users to create and manipulate data. Truly useful applications allow users to store their data to files; for example, word processors can save and load documents.

Vectors would be more useful it they were persistent. Data is persistent when it exists between program executions. During one execution of a particular program the user may create and populate a vector. The user then saves the contents of the vector to disk and quits the program. Later, the user can run the program again and reload the vector from the disk and resume work.

C++ fst ream objects allow programmers to build persistence into their applications. Listing 13.6

(numberlist.cpp) is a simple example of a program that allows the user to save the contents of a vector to a text file and load a vector from a text file.

©2018 Richard L. Halterman

Draft date: September 25, 2018

* save_vector(filename, v)

* Writes the contents of vector v.

* filename is name of text file created. Any file

* by that name is overwritten.

* v is a vector holding integers, v is unchanged by the

* function.

*/

void save_vector (const std::string& filename, const std:: vector<int>& vec) { // Open a text file for writing std::ofstream out(filename);

if (out.goodQ) { // Make sure the file was opened properly

int n = vec.size(); for (int i =0; i <n; i++)

out << vec[i] << " // Space delimited

out << 1 \n' ;

}

else

std::cout << "Unable to save the file\n";

/*

* load_vector(filename, v)

* Reads the contents of vector v from text file

* filename, v's contents are replaced by the file's

* contents. If the file cannot be found, the vector v

* is empty.

* v is a vector holding integers.

*/

void load_vector (const std::string& filename, std:: vector<int>& vec) { // Open a text file for reading std::ifstream in(filename);

if (in.good()) { // Make sure the file was opened properly

vec.clearQ; // Start with empty vector int value;

while (in >> value) // Read until end of file vec.push_back(value);

}

else

std::cout << "Unable to load in the file\n";

int main() {

std::vector<i nt> list; bool done = false; char command; while (Idone) {

std::cout << "I)nsert <item> P)rint "

<< "S)ave <filename> L)oad <filename> " << "E)rase Q)uit: "; std::cin >> command; int value;

std::string filename; switch (command) { case 1 1 1 : case 1 i 1 :

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cin >> value; list.push_back(value); break; case 1 P 1 : case 1 p 1 :

print_vector(list); break; case 'S': case 's':

std::cin >> filename; save_vector(filename, list); break; case 1 L 1 : case 1 1 1 :

std::cin >> filename; load_vector(filename, list); break; case 1 E 1 : case 1 e 1 :

list.clearQ ; break; case 1 Q 1 : case 1 q 1 :

done = true; break;

}

}

}

Listing |13,6j| (numberlist.cpp) is command driven with a menu, and when the user types S datal .text the program saves the current contents of the vector to a file named datal .text. The user can erase the contents of the vector:

I)nsert <item> P)rint S)ave <filename> L)oad <filename> E)rase Q)uit: E

and then restore the contents with a load command:

I)nsert <item> P)rint S)ave <filename> L)oad <filename> E)rase Q)uit: L datal.text

The user also may quit the program, and later re-run the program and load in the previously saved list of numbers. The user can save different number lists to different files using different file names.

Notice that in the save_vector and load_vector functions we pass the std : : stri ng parameter as a const reference. We do this for the same reason we do so for std: :vector objects (see Section [11,1.4[ )—this technique avoids making a copy of the string to pass the functions. These functions can “see” the caller’s actual string via the reference, rather than working with a copy of the string object. The const specifier prevents the functions from modifying the string passed. It takes time to copy a string (especially a long string), and the copy would occupy extra memory. In this case the copy really is not necessary, so passing by const reference is the ideal approach.

An std : : of stream object writes data to files. The statement std::ofstream out(filename);

©2018 Richard L. Halterman

Draft date: September 25, 2018

associates the object named out with the text file named filename. This opens the file as the point of declaration. We also can declare a file output stream object separately from opening it as

std::ofstream out; out.open(filename);

The save_vector function in Listing 13.6 (numberlist.cpp) passes a std : : stri ng object to open the file, but file names can be string literals (quoted strings) as well. Consider the following code fragment:

std::ofstream fout("myfile.dat") ;

int x = 10;

if (fout.good()) // Make sure the file was opened properly fout << "x = " << x << '\n' ;

else

std::cout << "Unable to write to the file \"myfile.dat\"\n";

After opening the file, programmers should verify that the method correctly opened the file by calling the file stream object’s good method. An output file stream may fail for various reasons, including the disk being full or insufficient permissions to create a file in a given folder.

Once we have its associated file open, we can use a std : : ofstream object like the std : : cout output stream object, except the data is recorded in a text file instead of being printed on the screen. Just like with std : : cout, you can use the << operator and send a std : : ofstream object stream manipulators like std : : setw. The std : : cout object and objects of class std : : ofstream are in the same family of classes and related through a concept known as inheritance. We consider inheritance in more detail in ChapterjTTj For our purposes at this point, this relationship means anything we can do with the std : : cout object we can do a std : ofstream object. The difference, of course, is the effects appear in the console window for std : : cout and are written in a text file given a std: :ofstream object.

After the executing program has written all the data to the file and the std: :ofstream object goes out of scope, the file object automatically will close the file ensuring that all data the program writes to the file is saved completely on disk. The std: : ofstream class provides also a close method that allows programmers to manually close the file. This sometimes is useful when using the same file object to recreate the same file, as in Listing fl3.7|| (endltest.cpp).

In Listing 13.6 (numberlist.cpp), a std : : i fstream object reads data from files. The statement std::ifstream in(filename);

associates the object named in with the text file named filename. This opens the file as the point of declaration. We also can declare a file output stream object separately from opening it as

std::ifstream in; in.open(filename);

As with std : : ofstream objects, filename is a string file name identifying the file to read.

After opening the file the program should call good to ensure the file was successfully opened. An input stream object often fails to open properly because the file does not exist; perhaps the file name is misspelled, or the path to the file is incorrect. An input stream can also fail because of insufficient permissions or because of bad sectors on the disk.

Once it opens its associated file, an input file stream object behaves like the std : : ci n object, except its data comes from a text file instead the keyboard. This means the familiar >> operator and getli ne function are completely compatible with std: : i fstr earn objects. The std: : ci n object and std : :ifstream

©2018 Richard L. Halterman

Draft date: September 25, 2018

objects are related through inheritance simmilar to the way the std : : cout object and std: :ofstream objects are related.

As with an output stream object, a std : : i fstream object automatically will close its associated file when it goes out of scope.

Input and output streams use a technique known as buffering. Buffering relies on two facts:

• It is faster to write data to memory than to disk.

• It is faster to write one block of n bytes to disk in a single operation than it is to write n bytes of data one byte at a time using n operations.

A buffer is a special place in memory that holds data to be written to disk. A program can write to the buffer much faster than directly to the disk. When the buffer is full, the program (via the operating system) can write the complete contents of the buffer to the disk.

To understand the concept of buffering, consider the task of building a wall with bricks. Estimates indicate that the wall will require about 1,350 bricks. Once we are ready to start building the wall we can drive to the building supply store and purchase a brick. We then can drive to the job site and place the brick in its appropriate position using mortar as required. Now we are ready to place the next brick, so we must drive back to the store to get the next brick. We then drive back to the job site and set the brick. We repeat this process about 1,350 times.

If this seems very inefficient, it is. It would be better to put as many bricks as possible into the vehicle on the first trip, and then make subsequent trips to the store for more loads of bricks as needed until the wall is complete.

In this analogy, the transport vehicle is the buffer. The output stream object uses a special place in memory called a buffer. Like the vehicle used to transport our bricks, the memory buffer has a fixed capacity. A program can write to the buffer much more quickly than directly to the disk. The << operator writes the individual values to save to the buffer, and when the buffer is full, the output stream sends all the data in the buffer out to the disk with one request to the operating system. As with the bricks, this is more efficient than sending just one character at a time to the display. This buffering process can speed up significantly the input and output operations of programs.

After the std : : of stream object writes all its data to its buffer and its lifetime is over, it flushes the remaining data from the buffer to disk, even if the buffer is not full. The buffer is a fixed size, so the last part of the data likely will not completely fill the buffer. This is analogous to the last load of bricks needed for our wall that may not make up a full load. We still need to get those remaining bricks to our almost complete wall even though the vehicle is not fully loaded.

In some situations it is necessary to ensure the buffer is flushed before it is full and before closing the file completely. With any output stream object writing text we can use the std: : endl stream object to flush the buffer without closing the file. We mentioned std: : endl briefly in Section 3.1 We can use std : : endl interchangeably with ' \ n ' to represent newlines for console printing. Because of the performance advantage buffering provides to file input and output, the choice of std: :endl and ' \ n ' can make a big difference for file processing. Listing ||13.7|| (endltest.cpp) compares the performance of std : : endl and ' \ n ' in various situations.

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <vector>

#include <cstdlib>

// Make a convenient alias for the long type name using Sequence = std::vector <int> ;

Sequence make_random_sequence (int size, int max) {

Sequence result(size); for (int i = 0; i < size; i++) result[i] = randQ % max; return result;

}

void print_with_endl(const Sequence& vs, std::ostream& out) { for (auto elem : vs)

out << elem << std::endl;

}

void print_with_n(const Sequence^ vs, std::ostream& out) { for (auto elem : vs)

out << elem << 1 \n 1 ;

}

int main() {

// Sequence up to 100,000 elements, with each element < 100. auto seq = make_random_sequence(100000, 100);

// Time writing the elements to the console with std::endl newlines clock_t start_time = clock(); print_with_endl(seq, std::cout); unsigned elapsedl = clockQ - start_time;

// Time writing the elements to the console with '\n' newlines

start_time = clockQ ;

print_with_n(seq, std::cout);

unsigned elapsed2 = clockQ - start_time;

// Time writing the elements to a text file with std::endl newlines

std::ofstream fout ("temp.out" ); start_time = clockQ; print_with_endl(seq, fout); fout.close();

unsigned elapsed3 = clockQ - start_time;

// Reopen the file for writing

fout.open( "temp.out" );

// Time writing the elements to a text file with 1 \n' newlines start_time = clockQ; print_with_n(seq, fout); fout.close() ;

unsigned elapsed4 = clockQ - start_time;

std::cout << "With std::endl (console): " << elapsedl << ' \n'; std::cout << "With 1 \\n' (console): " << elapsed2 << ' \n';

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "With std::endl (file): " << elapsed3 << ' \n';

std::cout << "With '\\n' (file): " << elapsed4 << ' \n';

Listing 1 13.7| |(endltest.cpp) writes a vector containing 100,000 integers to the console and a text file. Each number appears on its own line. Since std : : endl flushes the stream object’s buffer in addition to printing a ' \ n ' , we would expect it to reduce the program’s performance since it would minimize the benefit of buffering in this case. Multiple runs of Listing 13.7 (endltest.cpp) on one system revealed that using ' \ n ' to terminate lines generally was only slightly faster than std : : endl (but not always) when writing to the console window. The ' \ n ' terminator was consistently about three times faster than std : : endl when writing to a text file.

Listing 13.7 (endltest.cpp) also exploits the special relationship between std : cout and any std : : of stream object. The pri nt_wi th_endl and pri nt_wi th_n functions both accept a std : : ostream object as their second parameter. Note that the caller, mai n, passes both the std : : cout object and the fout object to these printing functions at various times, and the compiler does not complain. We defer an explanation of how this works until Chapter [TT]

13.4 Complex Numbers

C++ supports mathematical complex numbers via the std : : complex class. Recall from mathematics that a complex number has a real component and an imaginary component. Often written as a + bi, a is the real part, an ordinary real number, and bi is the imaginary part where b is a real number and r = — 1.

The std : : complex class in C++ is a template class like vector. In the angle brackets you specify the precision of the complex number’s components:

std:: complex<float> fc;

std:: complex<double> dc;

std:: complex<long double> Idc;

Here, the real component and imaginary coefficient of fc are single-precision floating-point values, dc and Idc have the indicated precisions. Listing 13.8 (complex.cpp) is a small example that computes the product of complex conjugates (which should be real numbers).

Listing 13.8: complex.cpp

// File complex.cpp

#include <iostream>

#include <complex>

int main() {

// cl = 2 + 3i, c2 = 2 - 3i; cl and c2 are complex conjugates

std:: complex<double> cl(2.0, 3.0), c2(2.0, -3.0);

// Compute product "by hand"

double reall = cl.realQ, imagl = cl.imag(), real2 = c2.real() , imag2 = c2.imag() ;

std::cout << cl << " * " << c2 << " = "

<< reall*real2 + imagl*real2 + reall*imag2 - imagl*imag2

©2018 Richard L. Halterman

Draft date: September 25, 2018

« ' \n' ;

// Use complex arithmetic

std::cout << cl << " * " << c2 << " = " << cl*c2 << '\n';

Listing [LL8] (complex.cpp) prints

Observe that the program displays the complex number 2 — 3 i as the ordered pair (2,-3). The first element of the pair is the real part, and the second element is the imaginary coefficient. If the imaginary part is zero, the number is a real number (or, in this case, a double).

Imaginary numbers have scientific and engineering applications that exceed the scope of this book, so this concludes our brief into C++’s complex class. If you need to solve problems that involve complex numbers, more information can be found at http : / /www. c plus plus .com/reference/std/ complex/

13.5 Better Pseudorandom Number Generation

Listing |T2i9| (comparepermutations.cpp) showed that we must use care when randomly permuting the contents of a vector. A naive approach can introduce accidental bias into the result. It turns out that our simple technique for generating pseudorandom numbers using rand and modulus has some issues itself.

Suppose we wish to generate pseudorandom numbers in the range 0.. .9,999. This range spans 10,000 numbers. Under Visual C++ RAND_MAX is 32,767, which is large enough to handle a maximum value of 9,999. The expression rand() % 10000 will evaluate to number in our desired range. A good pseudorandom number generator should be just as likely to produce one number as another. In a program that generates one billion pseudorandom values in the range 0.. .9,999, we would expect any given number 1 , 000 , 000,000

to appear approximately- ^ - = 100,000 times. The actual value for a given number will vary

slightly from one run to the next, but the average over one billion runs should be very close to 100,000.

Listing 13.9 (badrand.cpp) evaluates the quality of the rand with modulus technique by generating one billion pseudorandom numbers within a loop. It counts the number of times the pseudorandom number generator produces 5 and also it counts the number of times 9,995 appears. Note that 5 is near the beginning of the range 0.. .9,999, and 9,995 is near the end of that range. To verify the consistency of its results, it repeats this test 10 times. The program reports the results of each individual trial, and in the end it computes the average of the 10 trials.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Verify the largest number that rand can produce std::cout << "RAND_MAX = " << RAND_MAX << '\n' ;

// Total counts over all the runs.

// Make these double-precision floating-point numbers

// so the average computation at the end will use floating-point

// arithmetic.

double total5 = 0.0, total9995 = 0.0;

// Accumulate the results of 10 trials, with each trial // generating 1,000,000,000 pseudorandom numbers

const int NUMBER_OF_TRIALS = 10;

for (int trial = 1; trial <= NUMBER_OF_TRIALS; trial++) {

// Initialize counts for this run of a billion trials int count5 = 0, count9995 = 0;

// Generate one billion pseudorandom numbers in the range // 0...9,999 and count the number of times 5 and 9,995 appear for (int i = 0; i < 1000000000; i++) {

// Generate a pseudorandom number in the range 0...9,999 int r = randQ 96 10000; if (r == 5)

count5++; // Number 5 generated, so count it

else if (r == 9995)

count9995++; // Number 9,995 generated, so count it

}

// Display the number of times the program generated 5 and 9,995

std::cout << "Trial #" << std::setw(2) << trial << " 5: " << count5

<< " 9995: " << count9995 << '\n';

total5 += count5; // Accumulate the counts to

total9995 += count9995; // average them at the end

}

std : : cout << "-\n" ;

std::cout << "Averages for " << NUMBER_OF_TRIALS << " trials: 5: "

<< total5 / NUMBER_OF_TRIALS << " 9995: "

<< total9995 / NUMBER_OF_TRIALS << '\n';

The output of Listing 13.9 (badrand.cpp) shows that our pseudorandom number generator favors 5 over 9,995:

Table captionRAND_MAX = 32767

Trial

#

1

5:

122295

9995:

91255

Trial

#

2

5:

121789

9995:

91862

Trial

#

3

5:

122440

9995:

91228

T ri al

#

4

5:

121602

9995:

91877

Tri al

#

5

5:

122599

9995:

91378

Tri al

#

6

5:

121599

9995:

91830

Trial

#

7

5:

122366

9995:

91598

Trial

#

8

5:

121839

9995:

91387

Trial

#

9

5:

122295

9995:

91608

Tri al

#10

5:

121898

9995:

91519

Table captionAverages for 10 trials: 5: 122072 9995: 91554.2

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 13.2 If shown in full, the table would contain 10,000 rows and 32,768 individual numbers. The values in each row are equivalent modulus 10,000. All the columns except the rightmost column contain 10,000 entries.

Elements in each row are equivalent modulus 10,000

0 10,000 20,000

1 10,001 20,001

2,768 rows ■<

10,000 rows -<

7,232 rows ^

2.766

2.767

2.768

9.997

9.998

9.999

12.766

12.767

12.768

19.997

19.998

19.999

22.766

22.767

22.768

29.997

29.998

29.999

30,000 ^ 30,001

; 2 10,002 20,002 30,002 ;

3 10,003 20,003 30,003^

Four ways to obtain y any value in the range 0... 2,767

32.766

32.767 J

>

Only three ways to obtain any value in the range 2,768 ... 9,999

The first line verifies that the largest pseudorandom number that Visual C++ can produce through rand is 32,767. The next 10 lines that the program show the result of each trial, monitoring the activity of the one billion number generations. Since we are dealing with pseudorandom numbers, the results for each trial will not be exactly the same, but over one billion runs each they should be close. Note how consistent the results are among the runs.

While we expected both 5 and 9,995 to appear about the same number of times—each approximately 100,000 times—in fact the number 5 appeared consistently more that 100,000 times, averaging 122,072 times. The number 9,995 appeared consistently less than 100,000 times, averaging 91,554.2. Note that 122,072

^ ^ = 1.33; this means the value 5 appeared 1.33 times more often than 9,995. Looking at it another

4

way, 1.33 ~ —, so for every four times the program produced a 5 it produced 9,995 only three times. As we soon will see, this ratio of 4:3 is not accidental.

Figure 13.2 shows why the expression rand () % 10000 does not produce an even distribution.

Figure 13.2 shows an abbreviated list of all the numbers the rand function can produce before applying the modulus operation. If you add the missing rows that the ellipses represent, the table would contain 10,000 rows. All of the four values in each row are equivalent modulus 10,000; thus, for example.

2 = 10,002 = 20,002 = 30,002

©2018 Richard L. Halterman

Draft date: September 25, 2018

and

1,045 = 11,045 = 21,045 = 31,045

Since the rand function cannot produce any values in the range 32,678... 39,999, the rightmost column is not complete. Because the leftmost three columns are complete, the modulus operator can produce values in the range 0.. .2,767 four different ways; for example, the following code fragment

std::cout << 5 % 10000 <<''<< 10005 & 10000 << ' '

<< 20005 % 10000 <<''<< 30005 % 10000 << '\n' ;

prints

5 5 5 5

The rand function cannot return a value greater than 32,767; specifically, in our program above, rand cannot produce 39,995. Listing 13.9 (badrand.cpp), therefore, using rand and modulus we can produce 9,995 in only three different ways: 9,995, 19,995, and 29,995. Based on our analysis, Listing [LL9| (badrand.cpp) can generate the number 5 four different ways and 9,995 three different ways. This 4:3 ratio agrees with our empirical observations of the behavior of Listing |l3. 9|| (badrand.cpp). The consequences of this bias means that values in the relatively small range 0.. .2,767 will appear disproportionately more frequently than numbers in the larger range 2,768.. .9,999. Such bias definitely is undesirable in a pseudorandom number generator.

We must use more sophisticated means to produce better pseudorandom numbers. Fortunately C++11 provides several standard classes that provide high-quality pseudorandom generators worthy of advanced scientific and mathematical applications.

The rand function itself has another weakness that makes it undesirable for serious scientific, engineering, and mathematical applications, rand uses a linear congruential generator algorithm (see http : // en.wikipedia.org/wiki/Linear_congruential_generator). rand has a relatively small period. This means that the pattern of the sequence of numbers it generates will repeat itself exactly if you call rand enough times. For Visual C++, rand’s period is 2,147,483,648. Listing 13.10 (randperiod.cpp) verifies the period of rand.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 13.10 (randperiod.cpp) uses the C++standard long long int integer data type because it needs to count above the limit of the i nt type, 2,147,483,647. The short name for long long i nt is just long long. Visual C++ uses four bytes to store both i nt and long types, so their range of values are identical. Under Visual C++, the type long long occupies eight bytes which allows the long long data type to span the range —9,223,372,036,854,775,808 .. .9,223,372,036,854,775,807. To represent a literal long long within C++ source code, we append the LL suffix, as in 12LL. The expression 12 represents the ~i nt (4-byte version) of 12, but 12LL represents the long long (8-byte version) of 12.

Table captionListing 13.10|| (randperiod.cpp) prints the first 10 pseudorandom numbers it generates, then it prints numbers 2,147,483,645 through 2,147,483,658. Finally the program prints its 4,294,96,729th through 4,294,967,309th pseudorandom numbers. Listing[T37l~0| (randperiod.cpp) displays

1

175

2

400

3

17869

4

30056

5

16083

6

12879

7

8016

8

7644

9

15809

10

1769

2147483645

25484

2147483646

21305

2147483647

6359

2147483648

0

2147483649

175

2147483650

400

2147483651

17869

2147483652

30056

2147483653

16083

2147483654

12879

2147483655

8016

2147483656

7644

2147483657

15809

2147483658

1769

4294967293

25484

4294967294

21305

4294967295

6359

4294967296

0

4294967297

175

4294967298

400

4294967299

17869

4294967300

30056

4294967301

16083

4294967302

12879

4294967303

8016

4294967304

7644

4294967305

15809

4294967306

1769

4294967307

32409

4294967308

29950

4294967309

13471

Table captionNotice that after 2,147,483,648 iterations the program begins to print the same numbers in the same sequen

©2018 Richard L. Halterman

Draft date: September 25, 2018

tial order as it began. 2,147,483,648 iterations later (after 4,294,967,296 total iterations) the sequence once again repeats. A careful observer could detect this repetition and thus after some time be able to predict the next pseudorandom value that the program would produce. A predictable pseudorandom number generator is not a good random number generator. Such a generator used in a game of chance would render the game perfectly predictable by clever (and patient!) players. A better pseudorandom number generator would have a much longer period.

The Mersenne twister (see http://en.wi kipedia.org/wiki /Mersenne_twi ster) is a widelyused, high-quality pseudorandom number generator. It has a very long period, 2 ly y:,/ — 1, which is approximately 4.3154 x lO 6001 . If an implementation of the Mersenne twister could generate 1,000,000,000 (one billion) pseudorandom numbers every second, a program that generated such pseudorandom numbers exclusively and did nothing else would need to run about 1.36 84 x 10 5,985 years before it began to repeat itself. It is safe to assume that an observer will not be able to wait around long enough to be able to witness a repeated pattern in the sequence.

The standard C++ library contains the mtl9937 class from which programmers can instantiate objects used to generate pseudorandom numbers using the Mersenne twister algorithm. Generating the pseudorandom numbers is one thing, but ensuring that the numbers fall uniformly distributed within a specified range of values is another concern. Fortunately, the standard C++ library provides a multitude of classes that allow us to shape the production of an mtl9937 object into a mathematically sound distribution.

Our better pseudorandom generator consists of three pieces:

• an object that produces a random seed value,

• a pseudorandom number generator object that we construct with the random seed object, and

• a distribution object that uses the pseudorandom number generator object to produce a sequence of pseudorandom numbers that are uniformly distributed.

The C++ classes for these objects are

• The seed object is an instance of the random_devi ce class.

• The pseudorandom number generator object is an instance of the mtl9937 class.

• The distribution object is an instance of the uni form_i nt_di stri buti on class.

We use the random_device object in place of srand. The mtl9937 object performs the role of the rand function, albeit with much better characteristics. The uni form_i nt_di stri buti on object constrains the pseudorandom values to a particular range, replacing the simple but problematic modulus operator. Listing 13.11 (highqualityrandom.cpp) upgrades Listing j|13.9|| (badrand.cpp) with improved random number generation is based on these classes.

Listing 13.11: highqual-ityrandom.cpp

#include <iostream>

#include <iomanip>

#include <random>

int main() {

std::random_device rdev; // Used to establish a seed value // Create a Mersenne Twister random number generator with a seed // value derived from rd std::mtl9937 mt(rdevQ);

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Create a uniform distribution object. Given a random // number generator, dist will produce a value in the range // 0...9999.

std::uniform_int_distributi on<i nt> dist(0, 9999);

// Total counts over all the runs.

// Make these double-precision floating-point numbers

// so the average computation at the end will use floating-point

// arithmetic.

double total5 = 0.0, total9995 = 0.0;

// Accumulate the results of 10 trials, with each trial // generating 1,000,000,000 pseudorandom numbers

const int NUMBER_OF_TRIALS = 10;

for (int trial = 1; trial <= NUMBER_OF_TRIALS; trial++) {

// Initialize counts for this run of a billion trials int count5 = 0, count9995 = 0;

// Generate one billion pseudorandom numbers in the range // 0...9,999 and count the number of times 5 and 9,995 appear for (int i = 0; i < 1000000000; i++) {

// Generate a pseudorandom number in the range 0...9,999 int r = dist(mt); if (r == 5)

count5++; // Number 5 generated, so count it

else if (r == 9995)

count9995++; // Number 9,995 generated, so count it

}

// Display the number of times the program generated 5 and 9,995

std::cout << "Trial #" << std::setw(2) << trial << " 5: " << std::setw(6) << count5

<< " 9995: " << std::setw(6) << count9995 << '\n';

total5 += count5; // Accumulate the counts to

total9995 += count9995; // average them at the end

}

std::cout << "-" << ' \n ' ;

std::cout << "Averages for " << NUMBER_OF_TRIALS << " trials: 5: " << std::setw(6) << total5 / NUMBER_OF_TRIALS << " 9995: " << std::setw(6) << total9995 / NUMBER_OF_TRIALS << '\n' ;

One run

of!

Li

sting

13.11 (highqi

jalityrar

idom.cpp) reports

Trial

#

1

5:

99786

9995

100031

Trial

#

2

5:

99813

9995

99721

Trial

#

3

5:

99595

9995

100144

Trial

#

4

5:

100318

9995

100243

T ri al

#

5

5:

99570

9995

100169

Trial

#

6

5:

99860

9995

99724

Trial

#

7

5:

99821

9995

100263

Trial

#

8

5:

99851

9995

99887

Trial

#

9

5:

100083

9995

100204

Tri al

#10

5:

100202

9995

99943

Averages

for

10 trials:

5: 99889.9 9995: 100033

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

During this particular program run we see that in 1,000,000,000 attempts the program generates the value 5 on average 99,889.9 times and generates 9,995 on average 100,033 times. Both of these counts approximately equal the expected 100,000 target. Examining the 10 trials individually, we see that neither the count for 5 nor the count for 9,995 is predisposed to be greater than or less than the other. In some trials the program generates 5 slightly less than 100,000 times, and in others it appears slightly greater than 100,000 times. The same is true for 9,995. These multiple trials show that in over 1,000,000,000 iterations the program consistently generates 5 approximately 100,000 times and 9,995 approximately 100,000 times. Listing || 13. ll|j (highqualityrandom.cpp) shows us that the pseudorandom numbers generated by the Mersenne Twister object in conjunction with the distribution object are much better uniformly distributed than those produced by rand with the modulus operation.

Notice in Listing 13.11|(highqualityrandom.cpp) how the three objects work together:

• The uniform_int_distribution object produces a pseudorandom number from the mtl9937 generator object. The mt 19937 object generates a pseudorandom number, and the uni f orm_i nt_di stri buti on object constrains this pseudorandom number to the desired range.

• Programmers create an mtl9937 object with a random_devi ce object. The random_devi ce object provides the seed value, potentially from a hardware source, to the mtl9937 generator object. We also can pass a fixed integer value to mtl9937’s constructor if we want the generator to produce a perfectly reproducible sequence of values; for example, the following code fragment

mtl9937 gen(20); // Use fixed seed instead of random_device

uniform_int_distribution<i nt> dist(0, 9999);

std:

: cout

<<

dist(gen)

<<

' \n' ;

std:

: cout

<<

dist(gen)

<<

' \n' ;

std:

: cout

<<

dist(gen)

<<

' \n' ;

always prints

7542

6067

6876

The use of random_devi ce, mtl9937, and uni form_i nt_di stri buti on is a little more complicated than using srand and rand with the modulus operator, but the extra effort is worth it for many applications. This object-oriented approach is more modular because it allows us to substitute an object of a different pseudorandom number generator class in place of mtl9937 if we so choose. We also may swap out the normal distribution for a different distribution. Those familiar with probability theory may be familiar with a variety of different probability distributions, such as Bernoulli, Poisson, binomial, chi-squared, etc. The C++ standard library contains distribution classes that model all of these probability distributions and many more. Programmers can mix and match generator objects and distribution objects as needed to achieve specialized effects. While this flexibility is very useful and has its place, the

random_device, mtl9937, and uniform_int_distribution classes as used in Listing 13.11 (highqualityrandom.cpp) suffice for most applications needing to simulate random processes.

13.6 Exercises

1. Suppose s is a std : : stri ng object.

(a) What expression represents the number of characters that make up s?

©2018 Richard L. Halterman

Draft date: September 25, 2018

(b) What expression represents the first character in s?

(c) What statement would insert the character ' x ' onto the front of S?

(d) What statement would append the character ' x ' onto the back of s?

2. Compared to C strings (see Section 11.2.6), what advantages does the C++std : : stri ng type offer to programmers?

3. A palindrome is a string of text that reads the same forwards and backwards. Examples include:

• “TENET”

• “STEP ON NO PETS”

• “RATS LIVE ON NO EVIL STAR”

All these strings are examples of strict palindromes where spacing and punctuation must reverse exactly. Complete the following function that determines if a given string is a strict palindrome. It should return true if the string is a strict palindrome and false otherwise.

The empty string reads the same forward and backward, so it is a palindrome. Your function should ignore capitalization (that is, the string “Tenet” is regarded as a palindrome).

bool palindrome (const string& s) {

// Your code goes here . . .

}

4. What is the class of the std : : cout object?

5. What is the class of the std : : ci n object?

6. Suppose the user types in a line of text and presses the enter key. For example, the user might type the following:

The sky is blue

What C++ statement could you use to assign to a std : : stri ng variable named msg the complete line of text, including spaces?

7. Consider the following C++ program:

#include <iostream>

#include <fstream> ttinclude <string>

int mainQ {

std::string w;

std::ifstream x ("results" );

while (x >> w)

std::cout << '[' << w << "]\n";

}

(a) Explain what the program accomplishes.

(b) What does the variable x represent?

(c) As it currently is written, what does the program expect that may not be true?

(d) What would cause the program to print nothing?

(e) How can you improve the program so that it always provides feedback to the user, even it the expectation in part #7cj?

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 14 Custom Objects

In earlier times programmers wrote software in the machine language of the computer system because compilers had yet to be invented. The introduction of variables in association with higher-level programming languages marked a great step forward in the late 1950s. No longer did programmers need to be concerned with the lower-level details of the processor and absolute memory addresses. Named variables and functions allow programmers to abstract away such machine-level details and concentrate on concepts such as integers and characters that transcend computer electronics. Objects provide a level of abstraction above that of simple variables. Objects allow programmers to go beyond simple values—developers can focus on more complex things like geometric shapes, bank accounts, and aircraft wings. Programming objects that represent these real-world things can possess capabilities that go far beyond the simple variables we have studied to this point.

A C++ object typically consists of a collection of data and code. By bundling data and code together, objects store information and provide services to other parts of the software system. An object forms a computational unit that makes up part of the overall computer application. A programming object can model a real-world object more naturally than can a collection of simple variables since it can encapsulate considerable complexity. Objects make it easier for developers to build complex software systems.

C++ is classified as an object-oriented language. Most modem programming languages have some degree of object orientation. This chapter shows how programmers can define, create, and use custom objects.

14.1 Object Basics

Consider the task of dealing with geometric points. Mathematicians represent a single point as an ordered pair of real numbers, usually expressed as (x.y). In C++, the double type serves to approximate a subset of the mathematical real numbers. We can model a point with coordinates within the range of double-precision floating-point numbers with two double variables. We may consider a point as one thing conceptually, but we here we would be using two variables. As a consequence, a function that computes the distance between two points requires four parameters— x\, y\, X 2 , and yj —rather than two points— (x\.y i) and (* 2 , 12 )- Ideally, we should be able to use one variable to represent a point.

One approach to represent a point could use a two-element vector, for example:

std:: vector<double> pt { 3.2, 0.0 };

©2018 Richard L. Halterman

Draft date: September 25, 2018

This approach has several problems:

• We must use numeric indices instead of names to distinguish between the two components of a point object. We may agree that pt[0] means the x coordinate of point pt and pt[l] means the y coordinate of point pt, but the compiler is powerless to detect the error if a programmer uses an expression like pt [19] or pt [-3] .

• We cannot restrict the vector’s size to two. A programmer may accidentally push extra items onto the back of a vector meant to represent a point object. The compiler could not defend against a program treating an empty vector as a point object.

• We cannot use a vector to represent objects in general. Consider a bank account object. A bank account object could include, among many other diverse things, an account number (an integer), a customer name (a string), and an interest rate (a double-precision floating-point number). A vector implementation of such an object is impossible because the elements in a vector must all be of the same type.

In addition to storing data, we want our objects to be active agents that can do computational tasks. We need to be able associate code with a class of objects. We need a fundamentally different programming construct to represent objects.

Before examining how C++ specifically handles objects, we first will explore what capabilities are desirable. Consider an automobile. An automobile user—the driver—uses the car for transportation. The user’s interface to the car is fairly simple, considering an automobile’s overall complexity. A driver provides input to the car via its steering wheel, accelerator and brake pedals, turn signal control, shift lever, etc. The automobile produces output to the driver with its speedometer, tachometer, various instrument lights and gauges, etc. These standardized driver-automobile interfaces enable an experienced driver to drive any modern car without the need for any special training for a particular make or model.

The typical driver can use a car very effectively without understanding the details of how it works. To drive from point A to point B a driver does not need to know the number of cylinders in the engine, the engine’s horsepower, or whether the vehicle is front-wheel drive or rear-wheel drive. A driver may look under the hood at the engine, but the driver cannot confirm any details about what is inside the engine itself without considerable effort or expense. Many details are of interest only to auto enthusiasts or mechanics. There may be only a select few automotive engineers capable of understanding and appreciating other more esoteric details about the vehicle’s design and implementation.

In some ways programming objects as used in object-oriented programming languages are analogous to automobile components. An object may possess considerable capability, but a programmer using the object needs to know only what the object can do without needing to know how it works. An object provides an interface to any client code that wishes to use that object. A typical object selectively exposes some parts of itself to clients and keeps other parts hidden from clients. The object’s designer, on the other hand, must know the complete details of the object’s implementation and must be an expert on both the what the object does and how it works.

Programmers define the structure of a new type of object using one of two keywords: struct or class. The two constructs are very similar. We will use the class construct in this chapter, and we will consider structs in Section |15.9l

A class serves as a pattern or template from which an executing program may produce objects. In this chapter we will concentrate on four things facilitating object-oriented programming with C++ classes:

1. specifying the data that constitute an object’s state.

©2018 Richard L. Halterman

Draft date: September 25, 2018

2. defining the code to be executed on an object’s behalf that provides services to clients that use the object,

3. defining code that automatically initializes a newly-created object ensuring that it begins its life in a well-defined state, and

4. specifying which parts of objects are visible to clients and which parts are hidden from clients.

A class is a programmer-defined type. An object is an instance of a class. The terms object and instance may be used interchangeably.

14.2 Instance Variables

The simplest kind of object stores only data. We can define a mathematical point type as follows:

class Point { public :

double x; double y;

};

Notice the semicolon that follows the close curly brace of the class definition. This semicolon is required, but it is easy to forget. By convention class names begin with a capital letter, but class names are just identifiers like variable names and function names. Here, our class name is Poi nt. The body of the class appears within the curly braces.

The elements declared within a class are known as members of the class. The Poi nt class specifies two double-precision floating-point data components named x and y. These components are known as instance variables. The C++ community often refers to these as member data or data members. Other names for instance variables include fields and attributes. The declarations for x and y appear within the class body after the publi c label. We say that x and y are public members of the Poi nt class; this means client code using a Poi nt object has full access to the object’s x and y fields. Any client may examine and modify the x and y components of a Poi nt object.

Once this Poi nt class definition is available, a client can create and use Poi nt objects as shown in Listing [T4~T| (mathpoints.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 14.1 Two Point objects with their individual data fields

P tl

X

y

v_ W

8.5

0.0

Pt2

r~

X

y

I_ f

-4.0

2.5

ptl.x = 8.5; // Use the dot notation to get to a part of the object ptl.y = 0.0; pt2.x = -4; pt2.y = 2.5;

// Print them

std::cout << "ptl =

(" << ptl.x << "

II

5

<<

ptl.y

<<

")\n";

std::cout << "pt2 =

(" << pt2.x << "

II

5

<<

pt2.y

<<

")\n";

// Reassign one point from the other

ptl = pt2;

std::cout << "ptl = (" << ptl.x << "

II

5

<<

ptl.y

<<

")\n";

std::cout << "pt2 =

(" << pt2.x << "

II

5

<<

pt2.y

<<

")\n";

// Are ptl and pt2

aliases? Change

ptl

's

x coordinate and

ptl.x = 0;

std::cout << "ptl =

(" << ptl.x << "

II

5

<<

ptl.y

<<

")\n";

// Note that pt2 is std::cout << "pt2 =

unchanged

(" << pt2.x << "

II

5

<<

pt2.y

<<

")\n";

Table captionListing jl4Tj(mathpoints.cpp) prints

ptl =

(8.

5,0)

pt2 =

(-4

,2.5)

ptl =

(-4

,2.5)

pt2 =

(-4

,2.5)

ptl =

(0,

2.5)

pt2 =

(-4

,2.5)

It is important to note that Poi nt is not an object. It represents a class of objects. It is a type. The variables ptl and pt2 are the objects, or instances, of the class Poi nt. Each of the objects ptl and pt2 has its own copies of fields named x and y. Figure|fl4.l|provides a conceptual view of point objects ptl and pt2.

Double-precision floating-point numbers on most systems require eight bytes of memory. Since each Point object stores two doubles, a Poi nt object uses at least 16 bytes of memory. In practice, an object may be slightly bigger than the sum its individual components because most computer architectures restrict

©2018 Richard L. Halterman

Draft date: September 25, 2018

how data can be arranged in memory. This means some objects include a few extra bytes for “padding.” We can use the si zeof operator to determine the exact number of bytes an object occupies. Under Visual C++, the expression si zeof ptl evaluates to 16.

A client may use the dot (.) operator with an object to access one of the object’s members. The expression ptl. x represents the x coordinate of object ptl. The dot operator is a binary operator; its left operand is an expression representing a class instance (object), and its right operand is the name of a member of the class.

The assignment statement in Listing [l4.1| (mathpoints.cpp) ptl = pt2;

and the statements that follow demonstrate that we may assign one object to another directly without the need to copy each individual member of the object. The above assignment statement accomplishes the following:

ptl.x = pt2.x; // No need to assignment this way;

ptl.y = pt2.y; // direct object assignment does this

As another example, suppose we wish to implement a simple bank account object. We determine that the necessary information for each account consists of a name, ID number, and a balance (amount of money in the account). We can define our bank account class as

class Account { public :

std::string name; // The name of the account's owner int id; // The account number

double balance; // The current balance

};

The name, i d, and balance fields constitute the Account class, and the fields represent three different types.

We can define a vector that holds instances of our Account class as easily as std::vector<Account> accounts(5000);

Here the accounts variable represents a sequence of 5,000 bank account objects.

Listing j42](bankaccount.cpp) is a simple program that uses Account objects.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Allows the user to enter via the keyboard information // about an account and adds that account to the database, void add_account(std::vector<Account>& accts) { std::string name; int number; double amount;

std::cout << "Enter name, account number, and account balance: std::cin >> name >> number >> amount;

Account acct; acct.name = name; acct.id = number; acct.balance = amount; accts.push_back(acct);

}

// Print all the accounts in the database

void print_accounts (const std::vector<Account>& accts) { int n = accts.sizeQ ; for (int i = 0; i < n; i++)

std::cout << accts[i].name << << accts[i].id

<< << accts[i].balance << '\n' ;

}

void swap(Account& erl, Account& er2) { Account temp = erl; erl = er2; er2 = temp;

}

bool less_than_by_name (const Account& el, const Account& e2) { return el.name < e2.name;

}

bool less_than_by_id(const Account& el, const Account& e2) { return el.id < e2.id;

}

bool less_than_by_balance(const Account& el, const Account& e2) { return el.balance < e2.balance;

}

// Sorts a bank account database into ascending order

// The comp parameter determines the ordering

void sort(std::vector<Account>& db,

bool (*comp) (const Account&, const Account&)) { int size = db.sizeQ; for (int i = 0; i < size - 1; i++) { int smallest = i;

for (int j = i + 1; j < size; j++) if (comp(db[j], db[smallest])) smallest = j; if (smallest != i)

©2018 Richard L. Halterman

Draft date: September 25, 2018

swap(db[i], db[smallest]);

}

}

// Allows a user interact with a bank account database, int main() {

// The simple database of bank accounts

std::vector<Account> customers;

// User command

char cmd;

// Are we done yet?

bool done = false;

do {

std::cout << "[A]dd [N]ame [I]D [BJalance [Q]uit==> " std::cin >> cmd; switch (cmd) { case 1 A 1 : case 'a ' :

// Add an account add_account(customers); break ; case 'P' : case 1 p 1 :

// Print customer database

print_accounts(customers); break ; case 1 N 1 : case 1 n 1 :

// Sort database by name

sort(customers, less_than_by_name); print_accounts(customers); break; case 1 1' : case ' i ' :

// Sort database by ID (account number)

sort(customers, less_than_by_id); print_accounts(customers); break ; case 1 B 1 : case 1 b 1 :

// Sort database by account balance

sort(customers, less_than_by_balance); print_accounts(customers); break; case 1 Q 1 : case 1 q 1 :

done = true; break;

}

}

while (!done);

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

Listing ||14.2|| (bankaccount.cpp) stores bank account objects in a vector (see Section 11.1). Also, a bank account object contains a std : : stri ng object as a field. This shows that objects can contain other objects and implies that our objects can have arbitrarily complex structures.

A sample run of Listing ;14.2[ (bankaccount.cpp) prints

[A]dd [Njame [I]D [Bjalance [Q]uit==> a

Enter name, account number, and account balance: Sheri 34 100.34 [A]dd [Njame [I]D [Bjalance [Q]uit==> a

Enter name, account number, and account balance: Mary 10 1323.00 [Ajdd [Njame [I]D [Bjalance [Q]uit==> a

Enter name, account number, and account balance: Larry 88 55.05 [Ajdd [Njame [I]D [Bjalance [Q]uit==> a

Enter name, account number, and account balance: Terry 33 423.50 [Ajdd [Njame [I]D [Bjalance [Q]uit==> a

Enter name, account number, and account balance: Gary 11 7.27

[Ajdd [Njame [I]D [Bjalance [Q]uit==> n

Gary,11,7.27

Larry,88,55.05

Mary,10,1323

Sheri,34,100.34

Terry,33,423.5

[Ajdd [Njame [I]D [Bjalance [Q]uit==> i

Mary,10,1323

Gary,11,7.27

Terry,33,423.5

Sheri,34,100.34

Larry,88,55.05

[Ajdd [Njame [I]D [Bjalance [Q]uit==> b

Gary,11,7.27

Larry,88,55.05

Sheri,34,100.34

Terry,33,423.5

Mary,10,1323

[Ajdd [Njame [I]D [Bjalance [Q]uit==> q

The program allows users to sort the bank account database in several different ways using different comparison functions. Notice that the less_than_by_name and similar comparison functions use const reference parameters for efficiency (see Section i I 1.1.4:).

Observe that the add_account function has a local variable named name. All Account objects have a field named name. The add_account function uses the name identifier in both ways without a problem. The compiler can distinguish between the two uses of the identifier because one is qualified with an object variable before the dot (.) operator and the other is not; that is, acct. name refers to the data member name in the acct object, while the variable name by itself is the local variable. Despite their similar names, the data to which acct. name and name refer live in two completely different memory locations.

©2018 Richard L. Halterman

Draft date: September 25, 2018

14.3 Member Functions

The classes we have developed so far. Pen nt and Account, have been passive entities that have no builtin functionality. In addition to defining the structure of the data for its objects, a class can define functions that operate on behalf of its objects.

Recall the bank account class, Account, from Section fT4L2[

class Account { public :

// String representing the name of the account's owner string name;

// The account number int id;

// The current account balance double balance;

};

Suppose this design is given to programmer Sam who must write a wi thd raw function. Sam is a careful programmer, so his wi thd raw function checks for overdrafts:

/ '*******************************************************

* withdraw(acct, amt)

* Deducts amount amt from Account acct, if possible.

* Returns true if successful; otherwise, it returns false.

* A call can fail if the withdraw would

* cause the balance to fall below zero

*

* acct: a bank account object

* amt: funds to withdraw

~k

* Author: Sam Coder

* Date: April 17, 2018

*******************************************************[

bool withdraw(Account& acct, double amt) {

bool result = false; // Unsuccessful by default if (acct.balance - amt >= 0) { acct.balance -= amt; result = true; // Success

}

return result;

}

The following code fragment shows the expected code a client might write when withdrawing funds from the bank:

// Good client code //

// A simple database of bank customers

std::vector<Account> accountDB;

// Populate the database via some function

©2018 Richard L. Halterman

Draft date: September 25, 2018

accountDB = initialize_db();

// Get transaction information

int number; double debit;

std::cout << "Please enter account number and amount to withdraw:"; std::cin >> number >> debit;

// Locate account index

int n = accountDB.size(), i = 0; while (i < n) {

if (accountDB[i].id == number) break; // Found the account

i++;

}

// Perform the transaction, if possible if (i < n) {

if (withdraw(accountDB[i], debit))

std::cout << "Withdrawal successful\n" ;

else

std::cout << "Cannot perform the withdraw\n";

}

else

std::cout << "Account does not exist\n";

Unfortunately, nothing prevents a client from being sloppy:

// Bad client code

//

// A simple database of bank customers

std::vector<Account> accountDB;

// Populate the database via some function

accountDB = initialize_db() ;

// Get transaction information

int number; double debit;

std::cout << "Please enter account number and amount to withdraw:"; std::cin >> number >> debit;

// Locate account index

int n = accountDB.size(), i = 0; while (i < n) {

if (accountDB[i].id == number) break; // Found the account

i++;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Perform the transaction if (i < n)

accountDB[i] -= debit; // What if debit is too big?

else

std::cout << "Account does not exist\n";

Nothing in an Account object itself can prevent an overdraft or otherwise prevent clients from improperly manipulating the balance of an account object.

We need to be able to protect the internal details of our bank account objects and yet permit clients to interact with them in a well-defined, controlled manner.

Consider a non-programming example. If 1 deposit $1,000.00 dollars into a bank, the bank then has custody of my money. It is still my money, so I theoretically can reclaim it at any time. The bank stores money in its safe, and my money is in the safe as well. Suppose I wish to withdraw $100 dollars from my account. Since I have $1,000 total in my account, the transaction should be no problem. What is wrong with the following scenario:

1. Enter the bank.

2. Walk past the teller into a back room that provides access to the safe.

3. The door to the safe is open, so enter the safe and remove $100 from a stack of $20 bills.

4. Exit the safe and inform a teller that you got $100 out of your account.

5. Leave the bank.

This is not the process a normal bank uses to handle withdrawals. In a perfect world where everyone is honest and makes no mistakes, all is well. In reality, many customers might be dishonest and intentionally take more money than they report. Even though I faithfully counted out my funds, perhaps some of the bills were stuck to each other and I made an honest mistake by picking up six $20 bills instead of five. If I place the bills in my wallet with other money already there, I may never detect the error. Clearly a bank needs a more controlled procedure for handling customer withdrawals.

When working with programming objects, in many situations it is better to restrict client access to the internals of an object. Client code should not be able to change directly bank account objects for various reasons, including:

• A withdrawal should not exceed the account balance.

• Federal laws dictate that deposits above a certain amount should be reported to certain government agencies, so a bank would not want customers to be able to add funds to an account in a way to circumvent this process.

• An account number should never change for a given account for the life of that account.

How do we protect the internal details of our bank account objects and yet permit clients to interact with them in a well-defined, controlled manner? The trick is to hide completely from clients the object’s fields and provide special functions called member functions or methods that have access to the hidden fields. These methods provide the only means available to clients of changing the object’s internal state.

In the following revised Account class:

©2018 Richard L. Halterman

Draft date: September 25, 2018

class Account {

// String representing the name of the account's owner string name;

// The account number int id;

// The current account balance double balance; public :

// Methods will be added here . . .

};

all the fields no longer reside in the public section of the class definition. This makes the following client code impossible:

Account acct;

// Set the account's balance

acct. balance = 100; // Illegal, compiler reports an error

// Withdraw some funds

acct. balance -= 20; // Illegal, compiler reports an error

The balance field is in the private area of the class.

You may use the literal pri vate label, as in

class Account { private :

// String representing the name of the account's owner string name;

// The account number int id;

// The current account balance double balance; public :

// Methods will be added here . . .

};

Because any parts of a class not explicitly labeled are implicitly private, the private label is not necessary if you place all the private members in the first unlabeled section of the class. Said another way, all members of a class are automatically private unless otherwise labeled. Some programmers like to put the public members before the private members within a class definition, as in

class Account { public :

// Methods will be added here . . . private :

// String representing the name of the account's owner string name;

// The account number int id;

// The current account balance double balance;

};

©2018 Richard L. Halterman

Draft date: September 25, 2018

In this case the pri vate label is necessary.

In order to enforce the spirit of the wi thd raw function, we will make it a method, and add a deposi t method to put funds into an account. Listing [14T3| | (newaccount.cpp) enhances the Account class with methods.

In this new definition of Account, the members named deposit and withdraw are not fields; they are method definitions. A method definition looks like a function definition, but it appears within a class definition. Because of this, a method is also known as a member function.

A client accesses a method with the dot (.) operator:

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Withdraw money from the Account object named acct acct.withdraw(100.00);

The withdraw method definition uses three variables: amt, result, and balance. The variables amt and result are local to withdraw—amt is the method’s parameter, and result is declared within the body of wi thd raw. Where is balance declared? It is the field declared in the private section of the class. The wi thd raw method affects the balance field of the object upon which it is called:

// Affects the balance field of acctl object acctl.withdraw(100.00);

// Affects the balance field of acctl object acct2.withdraw(25.00);

When you see a variable used within the code of a method definition, it can be one of several kinds of variables. The compiler establishes the exact nature of the variable in the following order:

1. Method parameter—If the variable is declared in the method’s parameter list, it is a parameter to the method. As in the case of free functions, a method parameter is a variable local to that method.

2. Local variable—If the variable is declared in the body of the method, the variable is local to the method. Do anything you please with the local variable, and it will not affect any variables outside of that function.

3. Instance variable—If the variable is not a parameter to the method, is not declared within the method body, but is declared as an instance variable within the class, it is an instance variable of the object the client used to invoke the method.

4. Global variable—If the variable is not a parameter to the method, is not declared within the method body, and is not declared as an instance variable within the class, it must be a global variable. If no such global variable exists, the variable is undeclared, and the compiler will report the error.

It is important to note that the compiler checks in this order. That means it is legal to give a parameter to a method or a local variable the same name as an instance variable within the class. In this case the method’s code cannot access the instance variable or global variable by using its simple name. We say the local variables hide the instance or global variables from view. Section [753]shows how we can gain access to these hidden variables.

Methods may be overloaded just like global functions (see Section |10.3| . This means multiple methods in the same class may have the same names, but their signatures must be different. Recall that a function’s signature consists of its name and parameter types; a method’s signature too consists of its name and parameter types.

We saw in Section 14.2 that each object provides storage space for its own data fields. An object does not require any space for its methods. This means the only things about an individual object that an executing program must maintain are the object’s fields. While the exact organization of memory varies among operating systems, all the data processed by a program appears in one of three sections: stack, heap, or static memory. As with simple data types like i nts, the fields of an object declared local to a function or method reside in the segment of memory known as the stack. Also like simple data types, the fields of an object allocated with the new operator appear on the heap. The fields in global and stati c local objects reside in the static section of the executing program’s memory.

Consider the following simple class:

class Counter {

©2018 Richard L. Halterman

Draft date: September 25, 2018

int count; public :

// Allow clients to reset the counter to zero void clear() { count = 0;

}

// Allow clients to increment the counter void inc() { count++;

}

// Return a copy of the counter's current value int get() {

return count;

}

};

For this code we see that each Counter object will store a single integer value (its count field). Under Visual C++ sizeof Counter is the same as sizeof int — that is, four. A local Counter object consumes four bytes of stack space, a global Counter object uses four bytes of static memory, and a dynamically-allocated Counter object uses four bytes of heap space.

In addition to static, stack, and heap memory used for data, executing programs reserve a section of memory known as the code segment which stores the machine language for all the program’s functions and methods. The compiler translates methods into machine language as it does regular functions. Internally, the method i nc in the Counter class is identified by a longer name. Counter : : i nc. Although Counter : : i nc is a method, in the compiled code it works exactly like a normal function unrelated to any class. In the client code

Counter Ctrl, ctr2; // Declare a couple of Counter objects Ctrl .clear(); // Reset the counters to zero

ctr2.clear();

ctrl.incQ; // Increment the first counter

the statement ctrl.clear();

sets the private count field of Ctrl to zero, while the statement ctr2.clear();

sets ctr2’s count field to zero. Since all Counter objects share the same reset method, how does each call to Counter : : clear reset the field of the proper Counter object? The trick is this: While it appears that the reset method of the Counter class accepts no parameters, it actually receives a secret parameter that corresponds to the address of the object on left side of the dot. The C++ source code statement

Ctrl .clear(); // Actual C++ code

internally is treated like

Counter::clear(&ctrl); // <— Not real C++ code! Do not write this!

©2018 Richard L. Halterman

Draft date: September 25, 2018

in the compiled code. The code within the method can influence the field of the correct object via the pointer it receives from the caller. The clear method contains the single statement

count = 0;

Since the count variable is not declared locally within the clea r method and it is not a global variable, it must be the field named count of the object pointed to by the secret parameter passed to clear. This means the call

Ctrl .clear(); // Actual C++ code

thus modifies the count instance variable of the Ctrl counter object.

Section jj53jshows how programmers can access this secret pointer passed to methods.

14.4 Constructors

One crucial piece still is missing. How can we make sure the fields of an object have reasonable initial values before a client begins using the object? A class may define a constructor that ensures an object will begin in a well-defined sate. A constructor definition looks similar to a method definition. The code within a constructor executes on behalf of an object when a client creates the object. For some classes, the client can provide information for the constructor to use when initializing the object. As with functions and methods, class constructors may be overloaded. Listing )14.4j(bankaccountmethods.cpp) exercises an enhanced Account class that offers deposi t and wi thd raw methods, as well as a constructor.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Deducts amount amt from the account's balance,

// if possible.

// Returns true if successful; otherwise, it returns false. // A call can fail if the withdraw would // cause the balance to fall below zero bool withdraw(double amt) {

bool result = false; // Unsuccessful by default if (balance - amt >= 0) { balance -= amt; result = true; // Success

}

return result;

}

};

// Displays information about the void displayQ {

std::cout << "Name: " << name << ", Balance: " <<

}

account object

<< ", ID: " << id balance << '\n' ;

int main() {

Account acctl( "doe" , 2312, 1000.00);

Account acct2("Moe", 2313, 500.29); acctl.displayO ; acct2.display();

std::cout << "-" << '\n';

acctl.withdraw(800.00); acct2.deposit(22.00); acctl.displayO ; acct2.displayO ;

}

Table captionListing|jl4.4|(bankaccountmethods.cpp) produces

Name:

Doe,

ID:

2312,

Balance:

1000

Name:

Moe,

ID:

2313,

Balance:

500.29

Name:

Doe,

ID:

2312,

Balance:

200

Name:

Moe,

ID:

2313,

Balance:

522.29

The following characteristics differentiate a constructor definition from a regular method definition:

• A constructor has the same name as the class.

• A constructor has no return type, not even void.

The constructor in Listing[ T4.4] (bankaccountmethods.cpp) initializes all the fields with values supplied by the client. The comma-separated list between the colon and the curly brace that begins the body of the constructor is called the constructor initialization list. An initialization list contains the name of each field with its initial value in parentheses. All of the fields that make up an object must be initialized before the body of the constructor executes. In this case the code within the constructor adjusts the balance to zero and issues a warning if a client attempts to create an account with an initial negative balance. The constructor

©2018 Richard L. Halterman

Draft date: September 25, 2018

thus ensures an account object’s balance can never begin with a negative value. The wi thdraw method ensures that, once created, an Account object’s balance will never be negative. Notice that the client provides the required constructor parameters at the point of the object’s declaration:

// Client creating two Account objects

Account acctl ("Joe" , 2312, 1000.00);

Account acct2("Moe", 2313, 500.29);

Since the Account class contains a constructor definition which requires arguments, it now is impossible for a client to declare an Account object like

Account acct3; // Illegal, must supply arguments for constructor

With constructors, unlike with normal methods, we can use curly braces in place of parentheses, as in

// Client creating two Account objects

Account acctl{"Joe", 2312, 1000.00};

Account acct2{"Moe", 2313, 500.29};

If acct is a Account object defined as in Listing ) 14.4| (bankaccountmethods.cpp), the following code is illegal:

acct.balance -= 100; // Illegal, balance is private

Clients do not have direct access to the balance field since it is private. Clients instead should use the appropriate method call to adjust the balance of an Account object:

Account acct("Joe", 1033, 50.00); // New bank account object acct.deposit(1000.00); // Add some funds

acct.withdraw(2000.00); // Method should disallow this operation

The details of depositing and withdrawing funds are the responsibility of the object itself, not the client code. The attempt to withdraw the $2,000 dollars above would not change the account’s balance, and the client can check the return value of wi thd raw to provide appropriate feedback to the user about the error. The program then could take steps to correct the situation.

A constructor that specifies no parameters is called a default constructor. If the programmer does not specify any constructor for a class, the compiler will provide a default constructor that does nothing. If the programmer defines any constructor for a class, the compiler will not generate a default constructor. See Section|T5.2|for the consequences of this constructor policy.

If you do not define a constructor for your class, the compiler automatically will create one for you—a default constructor that accepts no parameters. The compiler-generated constructor does not do anything to affect the state of newly created instances.

If you define any constructor for your class, the compiler will not provide a default constructor.

©2018 Richard L. Halterman

Draft date: September 25, 2018

14.5 Defining a New Numeric Type

C++’s class feature allows us to define our own complete types. We will define a new numeric type that models mathematical rational numbers. In mathematics, a rational number is defined as the ratio of two integers, where the second integer must be nonzero. Commonly called a fraction, a rational number’s two integer components are called numerator and denominator. Rational numbers possess certain properties; for example, two fractions can have different numerators and denominators but still be considered equal (j = |). Listing 14.5 (simplerational.cpp) shows how we can define and use rational numbers.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Allows a client to see the denominator's value, int get_denominator() { return denominator;

}

};

// Returns the product of two rational numbers

SimpleRational multiply(SimpleRational fl, SimpleRational f2) { return {f1.get_numerator() * f2.get_numerator(),

fl.get_denominator() * f2.get_denominator()};

}

void print_fraction(SimpleRational f) {

std::cout << f.get_numerator() << "/" << f.get_denominator();

}

int main() {

SimpleRational fract(l, 2); // The fraction 1/2

std::cout << "The fraction is

print_fraction(fract);

std::cout << '\n 1 ;

fract.set_numerator(19);

fract.set_denominator(4);

std::cout << "The fraction now is

print_fraction(fract);

std::cout << '\n 1 ;

// Alternate syntax uses {} with constructor instead of ()

SimpleRational fractlfl, 2}, fract2{2, 3};

auto prod = multi ply(fracti, fract2);

std::cout << "The product of

print_fraction(fracti);

std::cout << " and " ;

print_fraction(fract2);

std::cout << " is " ;

print_fraction(prod);

std::cout << '\n 1 ;

}

Listing 114.5|| (simplerational.cpp) prints the following:

The fraction is 1/2

The fraction now is 19/4

The product of 1/2 and 2/3 is 2/6

The SimpleRational class defines a new numeric type that C++ does not natively provide—the rational number type. (It is named SimpleRational because it is our first cut at a rational number class; a better version is to come in Listing 16.1 (rational.cpp).) This Si mpleRati onal class defines two overloaded constructors. One constructor accepts the numerator and denominator values from the client. The other constructor allows a client to declare a Si mpleRati onal object as

SimpleRational frac;

without supplying the initial numerator and denominator values. This default constructor assigns y to the object. Both constructors ensure that a Si mpleRati onal object’s denominator will not be zero.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The function multiply:

SimpleRational multi ply(SimpleRational fl, SimpleRational return {f1.get_numerator() * f2.get_numerator(),

f1.get_denominator() * f2.get_denominator()};

}

f 2)

{

accepts two Si mpleRati onal objects as arguments and returns a Si mpleRati onal result. It is a free function, not a method (or member function) of the Si mpleRati onal class. The function’s return statement requires special attention. Because of the function’s declaration the compiler knows the function returns a Si mpleRati onal object. The expression within curly braces after the retu rn keyword:

{f1.get_numerator() * f2.get_numerator () , fl.get_denominator() * f2.get_denominator()}

is exactly the expression we can pass to the compiler to create a Si mpleRati onal object. The retu r n statement therefore creates a fraction object with a numerator that is the product of the numerators of the objects supplied by the caller. Similarly, the denominator of the returned object is the product of the denominators of the function’s parameters.

We can use this curly brace initialization syntax when passing parameters to functions; for example, we can simplify the following statements:

SimpleRational fract{2, 3};

print_fraction(fract);

into a single statement: print_fraction({2, 3});

The compiler knows that print_fraction accepts a single SimpleRational object as a parameter. The compiler generates code that uses the caller’s curly brace initialization list to create a Si mpleRati onal object to pass to the function.

Our new numeric type certainly leaves a lot to be desired. We cannot display one of our rational number objects with std : : cout very conveniently. We cannot use the standard arithmetic operators like + or *, and we cannot compare two rational numbers using == or <. In Section )16.1 | we address these shortcomings.

14.6 Encapsulation

When developing complex systems, allowing indiscriminate access to an object’s internals can be disastrous. It is all too easy for a careless, confused, or inept programmer to change an object’s state in such a way as to corrupt the behavior of the entire system. A malicious programmer may intentionally tweak one or more objects to sabotage the system. In either case, if the software system controls a medical device or military missile system, the results can be deadly.

C++ provides several ways to protect the internals of an object from the outside world, but the simplest strategy is the one we have been using: We can qualify fields and methods, genetically referred to as class members, as either publi c or pri vate.

The compiler enforces the inaccessibility of private members. In Listing [14.5|| (simplerational.cpp), for example, client code cannot directly modify the denomi nator instance variable of a Si mpleRati onal object making it zero. A client may influence the values of numerator and denomi nator only via methods provided by the class designer.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Accessibility rules, also called visibility rules or permissions, determine what parts of a class and/or object are accessible to the outside world. C++ provides a great deal of flexibility in assigning access permissions, but some general principles exist that, if followed, foster programs that are easier to build and extend.

• In general, fields should be p r i vate. Clients should not be able to arbitrarily change the state of an object. Allowing such might allow client code to put an object into an undefined state (for example, changing the denominator of a fraction to zero). An object’s state should only change as a result of calling the object’s methods.

The built-in primitive types like i nt and double offer no protection from client access. One exception to the private fields rule applies to simple objects that programmers naturally would treat as primitive types. Recall the geometric Poi nt class found in Listing 14.1 (mathpoints.cpp). The x and y fields of a point object safely may assume any legitimate floating-point value, and it may be reasonable in some applications for clients to treat a Poi nt object as a primitive type. In this case it is appropriate to make the x and y fields public.

• Methods that provide a service to client code should be part of the publi c section of the class. The author of the class must ensure that the public methods cannot place the object into an illegal state. For example, consider the following method:

void set_denominator(i nt d) { denominator = d;

}

If this method were part of the Si mpleRati onal class, it would permit client code to sabotage a valid fraction with a simple statement:

tract.set_denominator(0);

• Methods that assist the service methods but that are not meant to be used by the outside world should be in the pri vate section of the class. This allows a publi c method to be decomposed into simpler, perhaps more coherent activities without the threat of client code accessing these more primitive methods. These private methods are sometimes called helper methods or auxiliary methods.

Why would a programmer intentionally choose to limit access to parts of an object? Restricting access obviously limits the client’s control over the objects it creates. While this may appear to be a disadvantage at first glance, this access restriction actually provides a number of advantages:

• Flexibility in implementation. A class conceptually consists of two parts:

- The class interface—the visible part. Clients see and can use the public parts of an object. The public methods and public variables of a class constitute the interface of the class. A class’s interface specifies what it does.

- The class implementation—the hidden part. Clients cannot see any private methods or private variables. Since this private information is invisible to clients, class developers are free to do whatever they want with the private parts of the class. A class’s implementation specifies how it accomplishes what it needs to do.

We would like our objects to be black boxes: clients shouldn’t need to know how the objects work but merely rely on what objects can do.

©2018 Richard L. Halterman

Draft date: September 25, 2018

A good rale of thumb in class design is this: make data private, and make methods that provide a service to clients public.

Many real-world objects follow this design philosophy. Consider a digital wristwatch. Its display gives its user the current time and date. It can produce different output in different modes; for examples, elapsed time in stopwatch mode or wake up time in alarm mode. It presents to its user only a few buttons for changing modes, starting and stopping stopwatches, and setting the time. How it does what is does is irrelevant to most users; most users are concerned with what it does. Its user risks great peril by opening the watch and looking at its intricate internal details. The user is meant to interact with the watch only through its interface—the display and buttons.

Similarly, an automobile presents an accelerator pedal to its user. The user knows that pushing the pedal makes the car go faster. That the pedal is connected to the fuel injection system (and possibly other systems, like cruise control) through a cable, wire, or other type of linkage is of concern only to the automotive designer or mechanic. Most drivers prefer to be oblivious to the under-the-hood details.

Changing the interface of a class can disturb client code that already has been written to use objects of that class. For example, what if the maintainers of the Si mpleRati onal class decide that S i mp 1 e Ra t i o n a 1 objects should be immutable; that is, after a client creates a S i mp le Ra t i o n a 1 object the client cannot adjust the numerator or denomi nator values. The set_numerator and set_denomi nator, therefore, would have to disappear. Unfortunately, both of these methods are public and thus part of Si mpleRati onal's interface to client. Existing client code may be using these methods, and removing them, making them private, altering the types of their parameters or any other changes to the interface would render existing client code incompatible. Client code that has been written to use set_numerator according to its original interface no longer will be correct. We say the change in Si mpleRati onal’s interface breaks the client code.

Class authors have no flexibility to alter the interface of a class once the class has been released for clients to use; any changes risk breaking existing client code. On the other hand, altering the private information in a class will not break existing client code that uses that class, since private class information is invisible to clients. When the private parts of a class change, clients need only recompile their code; client programmers do not need to modify their source code. A class, therefore, becomes less resilient to change as more of its components become exposed to clients. To make classes as flexible as possible, which means maximizing the ability to make improvements to the class in the future, hide as much information as possible from clients.

• Reducing programming errors. Client code cannot misuse the parts of a class that are private since the client cannot see the private parts of a class. Properly restricting client access can make it impossible for client code to put an object into an ill-defined state. In fact, if a client can coax an object into an illegal state via the class interface, then the design and/or implementation of the class is faulty. As an example, if a client can somehow make a Si mpleRati onal object’s denominator zero, then one of the methods or a constructor must contain a logic error. Clients should never be able to place an object into an illegal state.

• Hiding complexity. Objects can provide a great deal of functionality. Even though a class may provide a fairly simple interface to clients, the services it provides may require a significant amount of complex code to accomplish their tasks. One of the challenges of software development is dealing with the often overwhelming complexity of the task.

©2018 Richard L. Halterman

Draft date: September 25, 2018

It is difficult, if not impossible, for one programmer to be able to comprehend at one time all the details of a large software system. Classes with well-designed interfaces and hidden implementations provide a means to reduce this complexity. Since private components of a class are hidden, their details cannot contribute to the complexity the client programmer must manage. The client programmer needs not be concerned with exactly how an object works, but the details that make the object work are present nonetheless. The trick is exposing details only when necessary:

- Class designer. The class designer must be concerned with the hidden implementation details of the class. Since objects of the class may be used in many different contexts, the class designer usually does not have to worry about the context in which the class will be used. From the perspective of the class designer, the complexity of the client code that may use the class is therefore eliminated.

- Applications developer using a class. The developer of the client code must be concerned with the details of the application code being developed. The application code will use objects. The hidden details of the class these objects represent are of no concern to the client developers. From the perspective of the client code designer, therefore, the complexity of the code that makes the objects work is eliminated.

This concept of information hiding is called encapsulation. Details are exposed to particular parties only when appropriate. In sum, the proper use of encapsulation results in

• software that is more flexible and resilient to change,

• software that is more robust and reliable, and

• a software development process that programmers can more easily comprehend and manage.

Finally, the C++ encapsulation model has its limits. It is not possible to protect an object from code within itself. Any method within a class has full access to any member defined within that class. If you believe that parts of a class should be protected from some of its methods, you should split up the class into multiple classes with suitable restrictions among the resulting component classes.

14.7 Exercises

1. Given the definition of the Si mpleRati onal number class in Listing 14.5 (simplerational.cpp), complete the function named add:

SimpleRational add(SimpleRational rl, SimpleRational r2) {

// Details go here

}

that returns the rational number representing the sum of its two parameters. Recall that adding fractions is more involved than multiplying them; you must find a common denominator, adjust the fractions so they both have the same denominator, and then add just the numerators.

2. Given the definition of the geometric Poi nt class in Listing 15.6 (point.cpp), complete the function named distance:

double distance(Point rl, Point r2) {

// Details go here

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

that returns the distance between the two points passed as parameters.

3. What is the purpose of a class constructor?

4. May a class constructor be overloaded?

5. Given the definition of the Si mpleRati onal number class in Section 14.3, complete the following method named reduce:

class SimpleRational {

// Other details omitted here ...

// Returns an object of the same value reduced // to lowest terms SimpleRational reduce() {

// Details go here

}

};

that returns the rational number that represents the object reduced to lowest terms; for example, the fraction 10/20 would be reduced to 1/2.

6. Given the definition of the Si mpleRati onal number class in Section 14.3, complete the following free function named reduce:

// Returns a fraction to lowest terms

SimpleRational reduce(SimpleRational f) {

// Details go here

}

that returns the rational number that represents the object reduced to lowest terms; for example, the fraction 10/20 would be reduced to 1/2.

7. Given the definition of the geometric Poi nt class in Section 14.2 add a method named distance:

class Point {

// Other details omitted

// Returns the distance from this point to the

// parameter p

double distance(Point p) {

// Details go here

}

that returns the distance between the point on whose behalf the method is called and the parameter p.

8. Consider the following C++ code: #include <iostream>

class IntPoint { public :

i nt x; int y;

©2018 Richard L. Halterman

Draft date: September 25, 2018

IntPoint(i nt x, int y): x(x), y(y) {}

};

class Rectangle {

IntPoint corner; // Location of the rectangle's lower-left corner int width; // The rectangle's width

int height; // The rectangle's width

public :

Rectangle(IntPoint pt, int w, int h):

corner((pt.x < -100) ? -100 : (pt.x > 100 ? 100 : pt.x), (pt.y < -100) ? -100 : (pt.y > 100 ? 100 : pt.y)), width((w < 0) ? 0 : w), height((h < 0) ? 0 : h) {}

int peri meter () {

return 2*width + 2*height;

}

int area() {

return width * height;

}

int get_width() { return width;

}

int get_height() { return height;

}

// Returns true if rectangle r overlaps this

// rectangle object.

bool intersect(Rectangle r) {

// Details omitted

}

// Returns the length of a diagonal rounded to the nearest

// integer.

int diagonalQ {

// Details omitted

}

// Returns the geometric center of the rectangle with // the (x,y) coordinates rounded to the nearest integer. IntPoint centerQ {

// Details omitted

}

bool is_inside(IntPoint pt) {

// Details omitted

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

};

int main() {

Rectangle recti(IntPoint(2, 3), 5, 7), rect2(IntPoint(2, 3), 1, 3), rect3(IntPoint(2, 3), 15, 3), rect4(IntPoint(2, 3), 5, 3);

std

:cout

<<

recti.get_width() <<

' \n' ;

std

:cout

<<

recti.get_height() <<

' \n'

5

std

:cout

<<

rect2.get_width() <<

' \n' ;

std

:cout

<<

rect2.get_height() <<

' \n'

5

std

:cout

<<

rect3.get_width() <<

' \n' ;

std

:cout

<<

rect3.get_height() <<

' \n'

5

std

:cout

<<

rect4.get_width() <<

' \n' ;

std

:cout

<<

rect4.get_height() <<

' \n'

5

std

:cout

<<

recti.get_perimeter()

<< '

\ n ' ;

std

:cout

<<

recti.get_area() << '

\ n ' ;

std

:cout

<<

rect2.get_perimeter()

<< '

\ n ' ;

std

:cout

<<

rect2.get_area() << '

\ n ' ;

std

:cout

<<

rect3.get_perimeter()

<< '

\ n ' ;

std

:cout

<<

rect3.get_area() << '

\n' ;

std

:cout

<<

rect4.get_perimeter()

<< '

\ n ' ;

std

:cout

<<

rect4.get_area() << '

\n' ;

(a) What does the program print?

(b) With regard to a Rectangle object’s lower-left corner, what are the minimum and maximum values allowed for the x coordinate? What are the minimum and maximum values allowed for the y coordinate?

(c) What is a Rectangle object’s minimum and maximum width?

(d) What is a Rectangle object’s minimum and maximum height?

(e) What happens when a client attempts to create a Rectangle object with parameters that are outside the acceptable ranges?

(f) Implement the diagonal method.

(g) Implement the center method.

(h) Implement the intersect method.

(i) Implement the i s_i nsi de method.

(j) Complete the following function named corner:

IntPoint corner(Rectangle r) {

// Details go here

};

that returns the lower-left corner of the Rectangle object r passed to it. You may not modify the Rectangle class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

9. Develop a Circle class that, like the Rectangle class above, provides methods to compute perimeter and area. The Rectangle instance variables are not appropriate for circles; specifically, circles do have corners, and there is no need to specify a width and height. A center point and a radius more naturally describe a circle. Build your Circle class appropriately.

10. Given the Rectangle and Ci rcle classes from questions above, write an encloses function:

// Returns true if rectangle rect is large enough to

// completely enclose circle circ

bool encloses(Rectangle rect, Circle circ) {

// Details omitted

}

so that it returns true if circle ci re’s dimensions would allow it to fit completely within rectangle rect. Ifcircis too big, the function returns false. The positions of rect and ci rc do not influence the result.

11. Consider the following C++ code:

class Widget { int value; public :

Widget();

Widget (i nt v); int get(); void bump();

};

Widget::Widget() { value = 40;

}

Widget::Widget (i nt v) { if (v >= 40) value = v;

else

value = 0;

}

int Widget::get() const { return value;

}

void Widget::bump() { if (value < 50) value++;

}

int main() {

Widget wl, w2(5); std::cout << wl.getQ << ' \ n ' ; std::cout << w2.get() << ' \n ' ; wl.bumpO; w2.bump();

©2018 Richard L. Halterman

Draft date: September 25, 2018

std:

:cout <<

wl,

■ get

0 «

' \n'

1 .

3

std:

:cout <<

w2,

■ get

0 «

' \n'

1 .

3

for

(int i =

0;

i <

20; i

++)

{

Table captionwl.bump(); w2.bump();

}

std::cout << wl.getQ << ' \ n ' ; std::cout << w2.get() << '\n' ;

(a) What does the program print?

(b) If wi d is a Wi dget object, what is the minimum value the expression wi d . get () can return?

(c) If wi d is a Wi dget object, what is the maximum value the expression wi d . get () can return?

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 15

Fine Tuning Objects

In Chapter [l4]we introduced the basics of object-oriented programming: private data, public methods, and automatic initialization. In this chapter examine some details that enable C++ programmers to fine tune class design.

15.1 Passing Object Parameters

Recall the pri nt_f racti on function from Listing 14.5 (simplerational.cpp):

void print_fraction(SimpleRational f) {

std::cout << f.get_numerator() << "/" << f.get_denominator();

}

Observe that the function accepts its parameter f using the call by value protocol. This means that during the execution of the following client code:

SimpleRational my_rational{3, 4}; print_fraction(my_rational);

the program makes a new Si mpleRati onal object (the formal parameter f in pri nt_f racti on’s definition) and copies the member data from the actual parameter my_rati onal into f. At this point the program has two copies of the fraction 3/4; the client has a 3/4 rational object in its variable my_ rati onal, and the executing pri nt_functi on has a 3/4 rational object in its formal parameter f. When the print_fraction function finishes executing, the formal parameter f goes out of scope and its memory is freed. The function returns back to the caller, leaving the caller’s 3/4 rational object as the sole remaining one.

Even though Si mpleRati onal objects are relatively small (four bytes under Visual C++), this process of creating a new object serving as the formal parameter, copying the contents from the actual parameter into the formal parameter, and finally cleaning up the formal parameter is all unnecessary work on the part of the executing program.

We noted in Section 11.1.4 that declaring std : : vector objects as const reference parameters to functions provides the efficiency of pass by reference with the safety of pass by value:

• Efficiency of pass by reference: The function has access to the caller’s object via its location in

©2018 Richard L. Halterman

Draft date: September 25, 2018

memory. Pass by reference sends a single memory address to the function. There is no need to copy the object’s data into the function.

• Safety of pass by value: The function cannot modify the caller’s actual parameter since the formal parameter is declared const.

We revisited this concept of pass by const reference for std : : stri ng objects in Section 13.3

It turns out that it is a good idea to prefer passing objects by const reference instead of pass by value. This means the following function should replace the original pri nt_f racti on function:

void print_fraction (const SimpleRational& f) {

std::cout << f.get_numerator() << "/" << f.get_denominator();

}

Rewriting multi ply also is in order. The following provides the new implementation:

// Returns the product of two rational numbers

SimpleRational multi ply (const SimpleRational& fl,

const SimpleRational& f2) { return {f1.get_numerator() * f2.get_numerator(),

fl.get_denominator() * f2.get_denominator()};

}

In this new version of multi ply the const reference parameters avoid the construction, member data copying, and memory clean up of two Si mpleRati onal objects for each call to multi ply.

If passing object types by const reference for object types is the better approach why does C++ not do this automatically for us? C++ defaults to pass by value as the default. This guarantees safety for all types at the expense of reduced efficiency for some types.

When is pass by value warranted for object types? A caller may make an object and then pass a copy of the object to a function that would modify that object and return the modified version back to the caller. The caller then could have both the original object plus the modified object returned by the function. Doing this via passing by const reference is possible, but requires a little more code. The following sample code illustrates:

SimpleRational zerol(const SimpleRational& f) {

SimpleRational resultff}; // Make a copy of parameter f result.set_numerator(0); return result;

}

SimpleRational zero2(SimpleRational f) {

// Just use f; it is a copy of the caller's actual parameter f.set_numerator(0); return f;

}

Here ze rol must explicitly copy its formal parameter to a new local variable it eventually will return. The zero2 function does not need to copy its formal parameter; its formal parameter already is a copy of the caller’s actual parameter.

A caller could use the zerol and zero2 functions as shown here:

©2018 Richard L. Halterman

Draft date: September 25, 2018

SimpleRational one_third{l, 3}; auto other = zerol(one_third) ;

// Caller owns two objects: one_third (1/3) and other (0/3).

15.2 Pointers to Objects and Object Arrays

Given the Poi nt class from Section 14.2 the statement Point pt;

declares the variable pt to be a Poi nt object. As with primitive data, we can declare pointers to objects:

Point pt;

Point *p_pt;

Here, p_pt is a pointer to a Poi nt object. Before we use the pointer we must initialize it to point to a valid object. We can assign the pointer to refer to an existing object, as in

p_pt = &pt;

or use the new operator to dynamically allocate an object from the heap: p_pt = new Point;

If the class has a constructor that accepts parameters, we need to provide the appropriate arguments when using new. Recall the Account class from Section |l4.4| . Given the declarations

Account acct("Joe", 3143, 90.00);

Account *acct_ptr;

before we use acct_ptr it must point to a valid object. As in the Poi nt class example, we can assign the pointer to refer to an existing object, as in

acct_ptr = &acct;

or use the new operator to dynamically allocate an object from the heap: acct_ptr = new Account ("Moe" , 400, 1300.00);

Note that we include the arguments expected by the Account class constructor. This statement allocates memory for one Account object and executes the constructor’s code to initialize the newly created object. Figure [15.1 [ illustrates a pointer to an account object.

As with any dynamically allocated entity, a programmer must be careful to use the delete operator to deallocate any objects created via new.

The dot operator syntax to access a field of a object through a pointer is a bit awkward:

Point *p = new Point;

(*p).x = 253.7;

(*P)-y = -00.5;

The parentheses are required since the dot (.) has higher precedence than the pointer dereferencing operator (*). Without the parentheses, the statement would be evaluated as if the parentheses were placed as shown here

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Figure 15.1 A pointer to an Account object

*(p.x) = 253.7; // Error

The variable p is not a Poi nt object, but a pointer to a Poi nt object, so it must be dereferenced with the * operator before applying the . operator. C++ provides a simpler syntax to access fields of an object through a pointer. The pointer operator eliminates the need for the parentheses:

Point *p = new Point; p->x = 253.7; p->y = -00.5;

The pair of symbols -> constitute one operator (no space in between is allowed), and the operator is meant to look like an arrow pointing right. There is no associated left pointing arrow in C++.

You can use the -> operator to access the methods of an object referenced by a pointer:

Account *acct_ptr = new Account("3oe" , 400, 1300.00); if (acct_ptr->withdraw(10.00))

std::cout << "Withdrawal successful\n" ;

else

std::cout << "*** Insufficient funds ***\n";

An executing program will not automatically deallocate the memory allocated via new; It is the programmer’s responsibility to manually deallocate the memory when the object is no longer needed. The delete operator with no [] decoration frees up a single dynamically allocated object:

// acct_ptr points to an Account object previously allocated // via new delete acct_ptr;

The following function has a logic error because it fails to free up memory allocated with new: void faulty_func() {

Account *acct_ptr = new Account ("Joe" , 400, 1300.00); if (acct_ptr->withdraw(10.00))

std::cout << "Withdrawal successful\n" ;

else

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Draft date: September 25, 2018

std::cout << "*** Insufficient funds ***\n"; acct_ptr->display();

}

Here, acct_pt r is a local variable, so it occupies space on the stack. It represents a simple address, essentially a number. The space for the acct_ptr variable is automatically deallocated when faulty_func completes. The problem is acct_ptr points to memory that was allocated with new, and this memory is not freed up within the function. The pointer acct_ptr is the only way to get to that memory, so when the function is finished, that memory is lost for the life of the program. The condition is known as a memory leak. If the program runs to completion quickly, the leak may go undetected. In a longer running program such as a web server, memory leaks can cause the program to crash after a period of time. The problem arises when code that leaks memory is executed repeatedly and eventually all of available memory becomes used up.

The corrected function would be written void corrected_func() {

Account *acct_ptr = new Account ("Joe" , 400, 1300.00); if (acct_ptr->withdraw(10.00))

std::cout << "Withdrawal successful\n" ;

else

std::cout << "*** Insufficient funds ***\n"; acct_ptr->display(); delete acct_ptr;

}

If we step back and take an honest look at this cor rected_func function, we will see that there really is no reason for using pointers and dynamic memory at all. This cor rected_func offers no advantage over the following function:

void even_better_func() {

Account acct("Joe", 400, 1300.00); if (acct.withdraw(10.00))

std::cout << "Withdrawal successful\n" ;

else

std::cout << "*** Insufficient funds ***\n"; acct.displayO ;

}

So why consider pointers to objects at all? Programmers commonly use pointers to objects to build elaborate linked data structures. Section 118.3I describes one such data structure.

C++ supports vectors and arrays of objects, but they present special challenges. First, consider a simple situation. The Poi nt class defines no constructor, so the following code is valid:

std::vector<Point> pts(100); // Okay

The compiler happily generates code that at run time will allocate enough space for 100 Poi nt objects. No special initializations are needed since Point has no constructor. What if a class defines a constructor that accepts arguments and does not supply also a constructor that requires no arguments? Consider the Account class. The following statement is illegal:

std::vector<Account> accts(100); // Illegal, the Account class has

// no default constructor

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When creating the space for the accts elements, C++ expects a default constructor to properly initialize all of the vector’s elements. The only constructor in the Account class requires arguments, and so the compiler refuses to accept the declaration of accts. The compiler has no means by which it can produce the code needed to initialize the vector’s elements before the programmer begins using the vector.

One solution uses a vector of pointers, as in

std::vector<Account *> accts(100); // A vector of account pointers

Note that this does not create any Account objects. The programmer subsequently must iterate through the vector and use new to create individually each account element. An example of this would be

std::vector<Account *> accts(100); // A vector of account pointers

for (int i = 0; i < 100; i++) {

// Get information from the user std::cin >> name >> id >> amount;

// Create the new account object accts[i] = new Account(name, id, amount);

}

In this case, when the program no longer needs the accts vector, it must execute code like

for (int i = 0; i < 100; i++) { delete accts[i];

to reclaim the dynamic memory held by each of the Account objects.

An alternative approach that avoids pointers uses the vector push_back method to add objects one at a time, as shown here:

std::vector<Account> accts; // Vector initially empty for (int i = 0; i < 100; i++) { std::string name; int id;

double amount;

// Get information from the user std::cin >> name >> id >> amount;

// Create the new account object accts.push_back({name, id, amount});

}

In this case there is no need to use delete later.

Recall (see |10.7| that in C++ there is one literal value to which a pointer of any type may be assigned— nullptr:

Account *p_rec = nullptr; // p_rec is null

A pointer with the value nullptr is interpreted to mean a pointer that is pointing to nothing. An attempt to delete a null pointer is legal and does nothing.

15.3 The thi s Pointer

Recall our Counter class from Section|ll4.3| reproduced here:

class Counter { int count; public :

// Allow clients to reset the counter to zero void clear() { count = 0;

}

// Allow clients to increment the counter void inc() { count++;

}

// Return a copy of the counter's current value int get() {

return count;

}

};

In Section 14.3 we saw that an expression such as Ctrl, clear () passes the address of ctr 1 as a secret parameter during the call to the clear method. This is how the method determines which count held to reset— Ctrl.clear () resets Ctrl’s count held, and ctr2.clear() would reset ctr2’s count held.

Within a method dehnition a programmer may access this secret parameter via the reserved word this. Within a method body the this expression represents a pointer to the object upon which the method was called. We can rewrite the Counter class to make the thi s pointer explicit, as shown here:

// Uses this directly

class Counter { int count; public :

// Allow clients to reset the counter to zero void clear() {

this->count = 0;

}

// Allow clients to increment the counter void inc() {

thi s->count++;

}

// Return a copy of the counter's current value int get() {

return this->count;

}

};

Within a method of the Counter class, thi s->count is an alternate way of writing just count. Some programmers always use the this pointer as shown here to better communicate to human readers that the count variable has to be a held, and it cannot be a local or global variable.

The this pointer is handy when a method parameter has the same name as a field:

class Point { double x; double y; public :

void set_x(double x) {

// Assign the parameter's value to the field this->x = x;

}

// Other details omitted . . .

};

In the set_x method the parameter x has the same name as field x. This is legal in C++; a method parameter or local variable of a method may have the same name as a field within that class. The problem is that the local variable or parameter hides the access to the field. Any unqualified use of the name x refers to the parameter x, not the field x. One solution would be to name the parameter something else: perhaps _x or x_param. A strong argument can be made, though, that x is the best name for the field, and x is also the best name for the parameter to the set_x method. To get access to the field in this case, use the thi s pointer. Since thi s is a reserved word, the expression thi s->x cannot be mistaken for anything other than the x field of the object upon which the method was invoked.

Another use of the this pointer involves passing the current object off to another function or method. Suppose a global function named log exists that accepts a Counter object as shown here:

void log(Counter c) {

// Details omitted . . .

}

If within the clear method we wish to call the log function passing it the object on whose behalf the clea r method was executing, we could write

class Counter {

// . . .

public:

void clear() { count = 0;

// Pass this object off to the log function log(*this) ;

}

// • • •

We pass the expression *thi s as the actual parameter to log because the log function expects an object, not a pointer to an object. Remember the syntax of pointers: If thi s is a pointer, *thi s is the object to which this points.

Since thi s serves as an implicit parameter passed to methods, it is illegal to use the this expression outside of the body of a method.

©2018 Richard L. Halterman

Draft date: September 25, 2018

15.4 const Methods

Given the Si mpleRational class in Listing 14.5 (simplerational.cpp), the following code produces a compiler error:

const SimpleRational fract(l, 2); // Constant fraction 1/2

fract.set_numerator(2); // Error, cannot change a constant

This behavior is desirable, since the set_numerator method can change the state of aSi mpleRati onal object, and our tract object is supposed to be constant. Unfortunately, this correct behavior is accidental. The compiler does not analyze our methods to determine exactly what they do. Consider the following code that also will not compile:

const SimpleRational fract(l, 2); // Constant fraction 1/2

std::cout << fract.get_numerator(); // Error!

Since the get_numerator method does not modify a Si mpleRati onal object, we would expect that invoking it on a constant object should be acceptable, but the compiler rejects it. Again, the compiler cannot understand what get_numerator is supposed to do; specifically, it is not designed to be able to determine that a method will not change the state of an object. The programmer must supply some additional information to help the compiler.

If a method is not supposed to change the state of an object, that method should be declared const. In the Si mpleRati onal class, the methods get_numerator and get_denomi nator simply return, respectively, copies of the fraction’s numerator and denominator. Neither method is intended to modify any instance variables. If we look at the code for those methods, we see that indeed neither method changes anything about a Si mpleRati onal object. What if the programmer made a mistake—perhaps a spurious copy and paste error—and the statement

numerator = 0;

made its way into the get_numerator method? Unfortunately, the way things stand now, the compiler cannot detect this error, and get_numerator will contain a serious logic error.

We can remove the possibility of such an error by declaring get_numerator (and get_denomi nator) const:

class SimpleRational { public :

/* ... stuff omitted ... */ int get_numerator() const { return numerator;

}

int get_denominator() const { return denominator;

}

/* ... other stuff omitted ... */

The const keyword goes after the closing parenthesis of the parameter list and before the opening curly brace of the method’s body. If we accidentally attempt to reassign an instance variable in a const method, the compiler will report an error.

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Declaring a method const is not merely a good defensive programming strategy used by a class developer. Methods declared to be const can be called with const objects, while it is illegal to invoke a non-const method with a const object. With the new const version of Si mpleRati onal's get_numerator method, the following code

const Rational fract(l, 2); // Constant fraction 1/2

fract.set_numerator(2); // Error, cannot change a constant

is still illegal, since Rati onal: : set_numerator is not const, but

const Rational fract(l, 2); // Constant fraction 1/2

std::cout << fract.get_numerator(); // Okay with const get_numerator

now is legal.

You should declare const any method that has no need to change any field within the object. Similarly, do not declare const any method that is supposed to change a field in an object. A const method can be used with both const and non-const objects, but a non-const method cannot be used with const objects. For maximum flexibility, always declare a method to be const unless doing so would prevent the method from doing what it is supposed to do.

You can invoke a const method from both const and non-const objects, but you cannot invoke a non-const method from a const object. For maximum flexibility, always declare a method to be const unless doing so would prevent the method from doing what it is supposed to do.

15.5 Separating Method Declarations and Definitions

It is common in larger C++ projects to separate a method implementation from its declaration. A simple example illustrates how to do this; consider the class MyClass:

class MyClass { public :

void my_method() const {

std::cout << "Executing \"my_method\"\n" ;

}

};

This version of MyClass uses what is known as an inline method definition ; that is, the method my_method is defined completely with a body in the same place as it is declared. Compare the inline version to the following equivalent representation split across two files: myclass.h and myclass.cpp. The code in myclass.h is shown in Listing[l5.1|(myclass.h).

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No body for my_method appears in the declaration of the class MyClass in myclass.h; instead, the method implementation appears elsewhere, in myclass.cpp. Listing |l5j2| (myclass.cpp).

Without the prefix MyClass : : the definition of my_method in myclass.cpp simply would be global function definition like all the ones we have seen since Chapter j9j The class name and scope resolution operator (: :) binds the definition of the method to the class to which is belongs.

We would ffinclude the .h header file in all source files that need to use MyClass objects; the myclass.cpp file is compiled separately and linked into the rest of the project’s .cpp files.

Listing jl5.3jj (pointinline.h) shows a point class written inline.

Listing |l 15.4|(pointsplit.h) and Listing |ll5.5| (pointsplit.cpp) show how we can separate the method declarations from their implementations.

Listing 15.5: poi ntsplit.cpp

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Table caption15.5. SEPARATING METHOD DECLARATIONS AND DEFINITIONS

Table caption448

// Point constructor

Point::Point (double x, double y): x(x)

y(y) {}

// Get the x value

double Point::get_x() const { return x;

}

// Get the y value

double Point::get_y() const { return y;

}

// Set the x value

void Point::set_x (double x) { this->x = x;

}

// Set the y value

void Point::set_y (double v) { this->y = y;

}

The class name prefix such as Poi nt : : is necessary not only so the compiler can distinguish a method definition such as get_x from a global function definition, but also to distinguish the method from a method with the same name and parameter types that might appear in a different class. A method signature for a method is just like a global function signature, except a method signature includes the class name as well. Each of the following represent distinct signatures:

• get_x () is the signature for a global function named get_x that accepts no parameters.

• Poi nt: : get_x () is the signature for a method of the Poi nt class named get_x () that accepts no parameters.

• Li near Equation: :get_x() is the signature for a method of the Li near Equation class named get_x () that accepts no parameters.

Recall from Section 10.3 that the return type is not part of a function’s signature, methods.

The same is true for

Many C++ programmers avoid the inline style of class declarations and use the separate class declaration and method definition files for several reasons:

• If the class is meant to be used in multiple programs, the compiler must recompile the methods each time the header file is #included by some C++ source file. When the method declarations and definitions are separate, the compiler can compile the code for the definitions once, and the linker can combine this compiled code with the client code that uses it.

• Client programmers can look at the contents of header files. If method definitions are Mined, client programmers can see exactly how the methods work. This can be a disadvantage; for example, a client programmer may make assumptions about how fast a method takes to execute or the particular order in which a method processes data in a vector. These assumptions can influence how the client code calls the method. If the class maintainer changes the implementation of the method, the client

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programmer’s previous assumptions may be invalid. A certain ordering of the data that before the change resulted in faster processing may now be slower. An improvement in a graphics processing algorithm may cause an animation to run too quickly when the method is rewritten. For the class designer’s maximum flexibility, client programmers should not be able to see the details of a method’s implementation because then they cannot form such assumptions.

Client programmers need to know what the method does, not how it accomplishes it.

To enforce this hidden method implementation:

1. Separate the method declarations from their definitions. Put the class declaration in the header file and the method definitions in a . cpp file.

2. Compile the .cpp file into an object file.

3. Provide the client the . h file and the compiled object file but not the source file containing the method definitions.

4. The client code can now be compiled by including the . h file and linked with the object file, but the client programmer has no access to the source code of the method definitions.

• Some programmers find the inline style difficult since it provides too much detail. It complicates determining what objects of the class are supposed to do because the how is sprinkled throughout the class declaration.

Despite the disadvantages mentioned above, inline methods are sometimes appropriate. For simple classes defined in the same file that uses them, the inline style is handy, as Listing[T5.6|(point.cpp) shows.

Here the Poi nt class is very simple, and the constructor and method implementations are obvious. The inline structure makes more sense in this situation.

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Listing |T577] (trafficlight.h) contains the interface for a class used to create objects that simulate stopcaution-go traffic signals.

Si gnalColo r is an enumerated type that clients may use. (Section 3.9 introduced enumerated types.) By using an enumerated type, we restrict a traffic light object’s color to the three specified by Si gnalColo r.

The traffic signal implementation code in Listing 15.8 (trafficlight.cpp) defines the Trafficlight methods.

Listing 15.8: trafficlight.cpp

#include "trafficlight.h"

// Ensures a traffic light object is in the state of // red, green, or yellow. A rogue value makes the // traffic light red

Trafficlight::Trafficlight(SignalColor initial_color) { switch (initial_color) { case SignalColor::Red: case SignalColor::Green: case SignalColor::Yellow: color = initial_color; break; default :

color = SignalColor::Red; // Red by default, just in case

}

}

// Ensures the traffic light's signal sequence

void Trafficlight::change() {

// Red --> green, green —> yellow, yellow --> red

if (color == SignalColor::Red) color = SignalColor::Green; else if (color == SignalColor::Green) color = SignalColor::Yellow; else if (color == SignalColor::Yellow) color = SignalColor::Red;

}

// Returns the light's current color so a client can // act accordingly

SignalColor Trafficlight::get_color() const {

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return color;

}

The code within Listing 15.8 (trafficlight.cpp) must #i nclude the trafficlight.h header so the compiler is exposed to the Trafficlight class declaration; otherwise, when compiling trafficlight.cpp the compiler would not know if the method implementations faithfully agreed with declarations. If the method definition of TrafficLi ght: : change in trafficlight.cpp specified parameters but its declaration within trafficlight.h did not, that would be a problem. Furthermore, without including trafficlight.h, the type SignalColor would be an undefined type within trafficlight.cpp.

Notice that outside the class declaration in Listing T5T7] (trafficlight.h) we must prefix the method names with TrafficLi ght : :. Without this prefix the compiler would treat the identifiers as globals. It would interpret them as free functions, not methods. Si gnalColor is declared outside of the TrafficLi ght class, so it does not need the TrafficLight: : prefix. SignalColor is a global type available to any code that #i ncludes trafficlight.h.

Listing 15.9 (trafficmain.cpp) shows how a client could use the Trafficli ght class.

Listing [T3I9| (trafficmain.cpp) first prints

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The program’s execution continues in this manner within its infinite loop until the user presses

Observe that the color variable within the Trafficli ght class is private. That means that once the client creates a traffic light object the only way a client can influence the value of color is via the change method. This makes it impossible for a client to force a traffic light object to cycle incorrectly; for example, a client cannot make a traffic light change directly from yellow to green (it would have to pass through red on the way from yellow to green).

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Draft date: September 25, 2018

15.6 Preventing Multiple Inclusion

C++ follows the one definition rule , or ODR, which means a variable, function, class, instance variable, or method may not have more than one definition in the same context. The code within the following function definition violates the one definition mle:

int sum_and_display (const std::vector<i nt>& list) { int s = 0, size = list.sizeQ;

// Add up the values in the list int i = 0; while (i < size) { s += list[i]; i + +;

}

// Print the contents of the list

int i = 0; // Illegal, variable i already defined above

while (i < size) {

std::cout << std::setw(5) << list[i] << '\n' ; i + +;

}

std : :cout << "-\n" ;

std::cout << std::setw(5) << s << '\n' ;

}

The line

int s = 0, size = list.sizeQ;

is not a problem even though the identifier size appears twice. The first appearance denotes the local variable named si ze, and the second use is a call to the si ze method of the std : : vector class. This statement defines (declares) only the variable size; the size method already has been defined in the std : : vector class (and the compiler processed its definition from the <vector> header file).

The variable i has two distinct definitions in the same context, so its redeclaration right before the display code is an error.

Like a variable, a class may have only one definition. When we build general purpose classes meant to be used widely in our programs we must take care that we do not violate the one definition mle. In fact, we can violate the one definition rule accidentally even if we define a class only once!

To see how we can accidentally violate the one definition rule, consider the following simple example. Suppose we have a simple counter class declared in count.h:

class Counter { int count; public :

// Allow clients to reset the counter to zero void clear();

// Allow clients to increment the counter void inc();

// Return a copy of the counter's current value

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int get() const;

};

with its implementation in count.cpp:

// Allow clients to reset the counter to zero

void Counter::clear() { count = 0;

}

// Allow clients to increment the counter

void Counter::inc() { count++;

}

// Return a copy of the counter's current value int Counter::get() const { return count;

}

Next, consider the following two header files defining objects that themselves use Counter objects, widget.h:

// File widget.h

#include "count.h"

class Widget {

Counter meter; public:

// Other stuff omitted

};

and gadget.h:

// File gadget.h

#include "count.h"

class Gadget {

Counter ticker; public :

// Other stuff omitted

};

The preprocessor directive #include "count.h"

is required in the file widget, h, because the compiler must be acquainted with the type Counter to properly handle the instance variable meter. Similarly, the count.h header must be included in gadget.h in order for the compiler to accept Gadget’s declaration of its ti cker field.

Client code that wishes to use Wi dget objects must use the appropriate #i nclude statement:

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#include "widget.h"

int main() {

Widget myWidget;

// Use the myWidget object

}

Similarly, client code that uses Gadget objects must include at the top of its file: ttinclude "gadget.h"

int main() {

Gadget myGadget;

// Use the myGadget object

}

Both of these client programs will build without any problems. Sometimes, however, a program may need to use both Wi dget objects and Gadget objects. Since the widget.h header file does not know anything about the Gadget class and the gadget.h header file has no information about Wi dgets, we must include both header files in code that uses both classes. The appropriate include directives would be

#include "widget.h" ttinclude "gadget.h"

int main() {

Widget myWidget;

Gadget myGadget;

// Use the myWidget and myGadget objects

}

Including one of the header files without the other is insufficient since the compiler must be able to check if the client is using both types correctly. This client code, however, will not compile. In this case the problem is with count.h. Including both widget.h and gadget.h includes the definition of the Counter class twice, so the compiler sees two definitions of Counter. Even though the two definitions are identical, this violates the one definition rule and so results in a compiler error.

The issue here is known as multiple inclusion, and it can arise when header files #i nclude other header files. Multiple inclusion is a problem, but it often is necessary because the programmer may have a legitimate need for both types of objects within the same program. Fortunately, the solution is simple. The standard way to prevent multiple inclusion is to wrap a class definition as follows:

ttifndef COUNT_H_

#define COUNT_H_

class Counter { int count; public :

// Allow clients to reset the counter to zero void clear();

// Allow clients to increment the counter void inc () ;

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// Return a copy of the counter's current value int get() const;

#endif

Do not use semicolons at the end of the lines beginning with #i fndef, ttdefine, and #endi f because these are preprocessor directives, not C++ statements. The word following the #i fndef and #define preprocessor directives can be any valid identifier, but best practice produces a unique word tied to the name of the header file in which it appears. The convention is to use all capital letters and underscores as shown above (an identifier cannot contain a dot). Putting an underscore after the header file name further makes it less likely that name will be used elsewhere within the program. If the header file is named myheader.h, the preprocessor wrapper would be

#ifndef MYHEADER_H_ ttdefine MYHEADER_H_

/* Declare your classes here */

#endif

Like a C++ program, the preprocessor can maintain a collection of variables. These preprocessor-defined variables can influence the compilation process. Preprocessor-defined variables are merely an artifact of compilation and are unavailable to an executing C++ program. The preprocessor directive #i fndef evaluates to true if the preprocessor has not seen the definition of a given preprocessor variable; #i fndef returns false if it has seen the definition of the preprocessor variable. The #define directive defines a preprocessor variable. The net effect of the #i fndef/#define/#endf f directives is that the preprocessor will not include the header file more than once when it is processing a C++ source file. This means the compiler will see the class definition exactly once, thus satisfying the one definition rule.

The #i f ndef...#define...#endi f preprocessor directives should be used to wrap the class declaration in the header file and do not appear in the . cpp file containing the method definitions. Since you cannot always predict how widespread the use of a class will become, it is good practice to use this preprocessor trick for all general purpose classes you create. By doing so you will avoid the problem of multiple inclusion.

15.7 Overloaded Operators

We can overload many of the C++ operators to work with programmer-defined types. Table 15.1 shows some operators that have been defined to work with several of the standard object classes.

We can define how specific operators work for the types we devise. We may express operators for classes either global functions or member functions.

15.7.1 Operator Functions

Consider a simple mathematical point class:

class Point { public :

©2018 Richard L. Halterman

Draft date: September 25, 2018

operator<< std: :ostream Right-hand operand is sent to the stream specified

by the left-hand operand

operator>> std: :istream Right-hand operand is extracted from the stream

specified by the left-hand operand

operator[] std::vector Right-hand operand (the integer within the square

brackets) is used to locate an element within the lefthand operand (a vector)

operator== std : : stri ng Right-hand operand (a stri ng) is compared with

the left-hand operator (also a st ri ng) to determine if they contain exactly the same characters in exactly the same order

std::cout << x; std::cin >> x; x = v[2];

Chapter

Chaptei

Section

:r 4

if (word == "Please") proceedQ; Chapter

TJ

Table 15.1: Some Overloaded Operators for Objects

double x; double y;

Suppose we wish to define the operation of addition on points as follows:

(xi, yi) + (x' 2 , yi) = (xi+yi, X 2 +yi)

Thus, the x coordinate of the sum of two points is the sum of the x coordinates, and the y coordinate is the sum of the y coordinates.

We can overload the addition operator to work on Poi nt objects with the following global function:

Point operator+(const Point& pi, const Point& p2) {

Point result; result.x = pl.x + p2.x; result.y = pl.y + p2.y; return result;

}

With a slightly more sophisticated Poi nt definition: class Point {

double x; // Fields are now private double y; public :

// Add a constructor

Point(double x, double y);

// Add some methods to access the private data members double get_x() const; double get_y() const;

with the expected constructor and method implementations:

// Initialize fields

Point::Point (double x, double y): x(x), y(y) {}

double Point::get_x() const {

return x; // Return a copy of the x member

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

double Point::get_y() const {

return y; // Return a copy of the y member

}

we can write the operator function in one line:

Point operator+(const Point& pi, const Point& p2) {

return {pl.get_x() + p2.get_x(), pl.get_y() + p2.get_y()};

}

It often is convenient to overload the output stream << operator for custom classes. The std : : cout object (and, therefore, the std: :ostream class) has overloaded methods named operator<< that allow us to print the primitive types like integers and floating-point numbers. If we create a new type, such as Poi nt or Rati onal, the std : : ostream class has no operator<<method built in to handle objects of our new type. In order to use std : : cout’s << operator with programmer-defined objects we must define a global operator function of the form:

std::ostream& operator<< (std::ostream& os, const X& x)

where X represents a programmer-defined type. Notice that the function returns type std : : ostream&. This is because the first parameter is also an std : : ost ream&, and the function returns the same object that was passed into it. If x is a programmer-defined type, the expression

operator<< (std::cout, x)

thus evaluates to a reference to std : : cout. This process of returning the object that was passed allows us to chain together the < < operator, as in

std::cout << x << y << '\n' ;

This is the beautified syntax for

operator<<(operator<<(operator<< (std::cout, x), y), ' \n ' ) ;

If you examine this expression carefully, you will see that the first argument to all the calls ofoperator<< is simply std : : cout.

For our enhanced Poi nt class, operator<< could look like:

std::ostream& operator<< (std::ostream& os, const Point& pt) { os << '(' << pt.get_x() << << pt.get_y() <<

return os;

}

The function simply returns the same std: :ostream object reference that was passed into it via the first parameter.

Given the above definitions of operator+ and operator<<, clients can write code such as

Point my_point(l, 2), your_point(0.45, 0); std::cout << "Point 1: " << my_point << '\n' ; std::cout << "Point 2: " << my_point << '\n' ; std::cout << my_point << " + " << your_point

<< " = " << my_point + your_point << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

which displays

Point 1: (1.0, 2.0)

Point 2: (0.45, 0.0)

(1.0, 2.0) + (0.45, 0.0) = (1.45, 2.0)

When class developers provide such an operator<< function, clients can print out objects just as easily as printing the basic data types.

The << operator is not overloaded for the std : : vector class, but we now easily can do it ourselves as needed. For a vector of integers, the following function

ostream& operator<< (ostream& os, const std::vector<i nt>& vec) { os << ' { ' ; int n = vec.size(); if (n != 0) {

os << vec[Q]

for (int i = 1; i < n; i++) os << ',' << vec[i];

}

os << '}' ; return os;

}

provides the necessary functionality. Given this operator<< function, clients can display vectors as they would a built in type:

std:: vector<int> list(10, 5); std::cout << list << '\n' ;

This code fragment prints

{SjSjSjSjSjSjSjSjSjS}

15.7.2 Operator Methods

A class may define operator methods. A method for a unary operator accepts no parameters, and a method for a binary operator accepts only one parameter. The “missing” parameter is the object upon which the operator is applied; that is, the this pointer. To see how operator methods work, consider an enhanced rational class:

class EnhancedRational { int numerator; int denominator; public :

/* Other details omitted */

// Unary plus returns the double-precision floating-point // equivalent of the rational number, double operator+() const {

return static_cast<double> (numerator)/denominator;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Binary plus returns the rational number that results // from adding another rational number (the parameter) to // this object.

Rational operator+(const Rational& other) const { int den = denominator * other.denominator, num = numerator * other.denominator

+ other.numerator * denominator; return {num, den};

}

The following code fragment shows how clients can use these operator methods:

Rational fractl(l, 2), fract2(l, 3), fract3; double value = +fractl; // Assigns 0.5 fract3 = fractl + fract2; // fract3 is 5/6

The statement

fract3 = fractl + fract2;

is syntactic sugar for the equivalent statement fract3 = fractl. operator+ (fract2) ;

Here we see how the righthand operand of the plus operator, f ract2, becomes the single parameter to the binary operator+ method of EnhancedRati onal.

The statement

double value = +fractl;

is the syntactically sugared version of double value = fractl. operator+ ();

While programmers may change the meaning of many C++ operators in the context of objects, the precedence and associativity of all C++ operators are fixed. In the Rational class, for example, it is impossible to enable the binary + operator to have a higher precedence than the binary * in the context of Rati onal objects or any other classes of objects.

15.8 stati c Members

Variables declared in a class declaration are known as instance variables because each instance (object) of that class maintains its own copy of the variables. This means, for example, that changing the numerator of one Rational object will not affect the numerator of any other Rational object.

Sometimes it is convenient to have variables or constants that all objects of a class share. Global variables and constants certainly will work, but globals are not tied to any particular class. C++ uses the stati c keyword within a class to specify that all objects of that class share a field; for example.

©2018 Richard L. Halterman

Draft date: September 25, 2018

class Widget { int value;

static int quantity;

};

Each individual Wi dget object has its own value variable, but only one quanti ty variable exists and is shared by all Wi dget objects.

One unusual thing about static fields is that must be defined outside of the class declaration. For the Wi dget class above, we must supply the statement

int Widget::quantity;

somewhere in the source code outside of the class declaration.

Consider a widget factory in which each widget object must have a unique serial number. Serial numbers are sequential, and a new widget object’s serial number is one larger than the widget produced immediately before. Important for warranty claims, a client should not be able to alter a serial number of a widget object. The Widget class in Listing 15.10 (serialnumber.cpp) shows how to use a static variable to manage serial numbers for widget objects.

Listing 15.10: serialnumber.cpp

#include <iostream> class Widget {

// All Widget objects share serial_number_source static int serial_number_source;

// Each Widget object is supposed to have its own // unique serial_number int serial_number; public :

// A Widget object's serial number is initialized from // the shared serial_number_source variable which is // incremented each time a Widget object is created WidgetQ: serial_number(serial_number_source++) {}

// Client's can look at the serial number but not touch int get_serial_number() const { return serial_number;

}

};

// Initialize the initial serial number; the first // Widget made will have serial number 1 int Widget::serial_number_source = 1;

// Make some widgets and check their serial numbers int main() {

Table captionWidget wl, w2, w3, w4;

std:

: cout

<<

"wl

serial

number = " <<

wl.get_serial_number()

<<

' \n

std:

: cout

<<

"w2

serial

number = " <<

w2.get_serial_number()

<<

' \n

std:

: cout

<<

"w3

serial

number = " <<

w3.get_serial_number()

<<

' \n

std:

: cout

<<

"w4

serial

number = " <<

w4.get_serial_number()

<<

' \n

}

The output of Listing 15.10 (serialnumber.cpp) is

©2018 Richard L. Halterman

Draft date: September 25, 2018

wl serial number = 1 w2 serial number = 2 w3 serial number = 3 w4 serial number = 4

Each Wi dget object has its own seri al_number variable, but all Wi dget objects have access to the shared seri al_number_source variable. The executing program initializes seri al_number_sou rce one time at the beginning of the program’s execution before it calls the main function. This means seri al_number_sou rce is properly initialized to 1 before the program creates any Wi dget objects. Each time the client creates a new Widget object, the constructor assigns the individual object’s serial number from the stati c variable. The constructor also increments seri al_number_sou rce’s value, so the next object created will have a serial number one higher than the previous Wi dget.

C++ programmers often use class static fields to provide public constants available to clients. Consider Listing |15.111 (trafficsignal.h) that models a simple traffic light a little differently from Listing |15.7| (trafficlight.h). It uses symbolic integer constants instead of enumeration types.

The state of a traffic light object—which of its lamps is illuminated—is determined by an integer value: 0 represents red , 1 stands for green , and 2 means yellow. It is much more convenient for clients to use the symbolic constants RED, GREEN, and YELLOW than to try to remember which integer values stand for which colors. These constants are publi c, so clients can freely access them, but, since they are constants, clients cannot alter their values. An additional benefit to being const is this: You may initialize a stati c const field within the class body itself. You do not need to re-define a stati c const field outside the class body as you do for a non-const stati c field.

Listing 15.12 (trafficsignal.cpp) provides the implementation of the methods of T rafficSi gnal class.

Listing 15.12: trafficsignal.cpp

ffinclude "trafficsignal.h"

// Ensures a traffic light object is in the state of // red, green, or yellow. A rogue integer value makes the // traffic light red

©2018 Richard L. Halterman

Draft date: September 25, 2018

TrafficSignal::TrafficSignal (i nt initial_color) { switch (initial_color) { case RED: case GREEN: case YELLOW:

color = initial_color; break; default :

color = RED; // Red by default

}

}

// Ensures the traffic light's signal sequence void TrafficSignal::change() {

// Red --> green, green —> yellow, yellow --> red color = (color + 1) % 3;

}

// Returns the light's current color so a client can // act accordingly

int TrafficSignal::get_color() const { return color;

}

Within the methods of the TrafficSi gnal class we can use the simple names RED, GREEN, and YELLOW.

Code outside of the TrafficSi gnal class can access the color constants because they are public but must use the fully-qualified names TrafficSi gnal: : RED, TrafficSi gnal: : GREEN, and TrafficSi gnal: :YELLOW.

A client can create a traffic light object as

TrafficSignal light(TrafficSignal::YELLOW);

Since the client code is outside the TrafficSi gnal class it must must use the full TrafficSi gnal: : YELLOW name. This statement makes an initially yellow traffic light. Since the RED, GREEN, and YELLOW public fields are constants, clients cannot modify them to subvert the behavior of a traffic light object.

It may not be obvious, but the color constants in the T rafficSi gnal class must be declared stati c.

To see why, consider a minor change to TrafficSi gnal in the class we will call TrafficSi gnalAlt:

class TrafficSignalAlt {

int color; // The light's current color: RED, GREEN, or YELLOW public :

// Constant instance fields available to clients const int RED; // Note: NOT static

const int GREEN; const int YELLOW;

TrafficSignalAlt (i nt initial_color);

void change();

int get_color() const;

};

The TrafficSi gnalAlt class is identical to TrafficSi gnal, except that the color constants are constant instance fields instead of constant class (stati c) fields. Observe that just like the T rafficSi gnal

©2018 Richard L. Halterman

Draft date: September 25, 2018

class, the TrafficSignalAlt class constructor accepts no arguments, and piler will not automatically provide a as

has no default constructor. Recall from Section 14.4 that a default that if a programmer provides any constructor for a class, the corndefault constructor. This means the client cannot write code such

Traff'icSignal light;

or

TrafficSignalAlt light2;

During the object’s creation the client must provide an integer argument representing a traffic light color. If RED, GREEN, and YELLOW are constant instance variables (that is, constant non-stati c fields), every TrafficSi gnalAlt object has its own copy of the fields, and the RED, GREEN, and YELLOW fields cannot exist outside of any traffic light object. This leads to a chicken-and-egg problem—how can we create the first TrafficSi gnalAlt object using the symbolic constants RED, GREEN, or YELLOW? These constants do not exist unless we have a traffic light object, yet we need a traffic light object to have any of these constants!

An executing program initializes stati c class fields before it invokes the mai n function. This means any data pertaining to a class that must exist before any object of that class is created must be declared stati c. A stati c class variable exists outside of any instance of its class.

C++ allows methods to be declared stati c. A stati c method executes on behalf of the class, not an instance of the class. This means that a stati c method may not access any instance variables (that is non-stati c fields) of the class, nor may they call other non-stati c methods. Since a stati c method executes on behalf of the class, it has no access to the fields of any particular instance of that class. That explains the restriction against static methods accessing non-static data members. Since a nonstati c method may access instance variables of an object upon which it is called, a stati c method may not call a non-stati c method and thus indirectly have access to instance variables. The restriction goes only one way—any class method, stati c or non-stati c, may access a stati c data member or call astatic method.

Looking at it from a different perspective, all non-stati c methods have the thi s implicit parameter (Section 15.3). No stati c method has the thi s parameter. This means it is a compile-time error to use thi s within a stati c method.

15.9 Classes vs. structs

All members of a C++ class are pri vate by default. The class

class Point { public:

double x; double y;

};

must use the public label so clients can access a Poi nt object’s fields. The struct keyword is exactly like the class keyword, except that the default access to members is public:

struct Point {

double x; // These fields now are public double y;

©2018 Richard L. Halterman

Draft date: September 25, 2018

};

The C language supports the struct feature, but not the class keyword. C structs do not support methods and constructors. In C++ (unlike in C), a struct can contain methods and constructors. By default, members in st ructs are public, but you can apply the p ri vate and publi c labels as in a class to fine tune client access.

Despite their similarities, C++ programmers favor classes over structs for programmer-defined types with methods. The struct construct is useful for declaring simple composite data types that are meant to be treated like primitive types. Consider the i nt type, for example. We can manipulate directly integers, and integers do not have methods or any hidden parts. Likewise, a geometric point object consists of two coordinates that can assume any valid floating-point values. It makes sense to allow client code to manipulate directly the coordinates, rather than forcing clients to use methods like set_x and set_y. On the other hand, it is unwise to allow clients to modify directly the denominator of a Rati onal object, since a fraction with a zero denominator is undefined.

In C++, by default everything in an object defined by a struct is accessible to clients that use that object. In contrast, clients have no default access to the internals of an object that is an instance of a class. The default member access for struct instances is public, and the default member access for class instances is private.

The struct feature is, in some sense, redundant. It is a carryover from the C programming language. By retaining the struct keyword, however, C++ programs can use C libraries that use C structs. Any C++ program that expects to utilize a C library using a struct must restrict its struct definitions to the limited form supported by C. Such struct definitions may not contain non-publi c members, methods, constructors, etc.

15.10 Friends

The private members of a class by default are inaccessible to code outside of that class. Ordinarily only methods within the class itself have permission to see and modify the private instance variables and invoke the private methods within that class. This access protection allows programmers to modify the implementation of the hidden internals of a class without affecting existing client code that uses the class.

For some class designs this all-or-nothing access dictated by the public and pri vate labels within a class or struct is too limiting. At times it can be advantageous to design a class that grants special access to some precisely specified functions or classes of objects outside of the class.

As an example, consider a variation of the Si mpleRati onal class from Listing 14.5 (simplerational.cpp). Our new class, named OpaqueRati onal is shown here:

// Models a mathematical rational number

class OpaqueRational { int numerator; int denominator;

public :

// Initializes the components of an OpaqueRational object

OpaqueRational (i nt n, int d): numerator(n), denominator(d) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

if (d == 0) {

// Display error message

std::cout << "Zero denominator error\n";

exit(l); // Exit the program

}

}

// The default constructor makes a zero rational number

// 0/1

OpaqueRational(): OpaqueRational(0, 1) {}

Note that clients can make an OpaqueRati onal object, but after its creation clients can neither see nor change the internals of the object. Gone are the set_numerator, set_denomi nator, get_numerator, and get_denomi nator methods of the Si mpleRati onal class.

We would like to able to print an OpaqueRati onal object as easily as the following:

OpaqueRational frac{l, 2}; // Make the fraction 1/2

std::cout << frac << '\n' ;

We would like the std : : cout statement to print the text

1/2

This would require an operator<< function overloaded to accept a OpaqueRati onal object, and this operator<< function would need to be able to access the private instance variables of the OpaqueRational object.

A class can grant access to an outside function or another class via the f ri end reserved word. In Listing 15.13 (printonlyrational.cpp) we specify a f ri end function that allows clients to display in humanreadable form an opaque rational number object via operator<< with an output stream object.

Listing 15.13: printonlyrational.cpp

#include <iostream>

#include <cstdlib>

// Models a mathematical rational number

class PrintOnlyRational { int numerator; int denominator; public :

// Initializes the components of an PrintOnlyRational object PrintOnlyRational(int n, int d): numerator(n), denominator(d) { if (d == 0) {

// Display error message

std::cout << "Zero denominator error\n";

exit(l); // Exit the program

}

}

// The default constructor makes a zero rational number // 0/1

PrintOnlyRational(): PrintOnlyRational(0, 1) {}

©2018 Richard L. Halterman

Draft date: September 25, 2018

};

// This operator can access the internal details of an // object of this class.

friend std::ostream& operator<< (std::ostream& os,

const PrintOnlyRational& f);

std::ostream& operator<< (std::ostream& os, const PrintOnlyRational& f) { os << f.numerator << '/' << f.denominator; return os;

}

int main() {

PrintOnlyRational fract{l, 2}; std::cout << "The fraction is " PrintOnlyRational fract2{2, 3}; std::cout << "The fraction is "

}

// The fraction 1/2 << fract << 1 \n 1 ;

// The fraction 2/3 << fract2 << '\n ' ;

Listing 15.13 (printonlyrational.cpp) prints the following:

The fraction is 1/2 The fraction is 2/3

Observe that the operator<< function is not a member function of the Pri ntOnlyRational class. Ordinarily operator<< would be unable to access the numerator and denominator fields of a Pri ntOnlyRational object. We can see, however, that the compiler allows theoperator<< function to access the private instance variables of its f parameter.

We chose in Listing 15.13 (printonlyrational.cpp) to implement the operator<< function outside of the Pri ntOnlyRati onal class; however, we just as well could have implemented it inline within the body of the class, as shown here:

class PrintOnlyRational {

// Other details about the private members of the class omitted here public :

// Other details about the public members of the class omitted here . friend std::ostream& operator<< (std::ostream& os,

const PrintOnlyRational& f) {

os << f.numerator << '/' << f.denominator; return os;

}

};

Implementing operator<< inline in this way makes it look very much like an inline method implementation, but it is not a member function. The reserved word f ri end at the front indicates to the compiler that is it indeed a free function; C++ does not allow member functions to be declared as friends.

Listing ^5.14||(friendclass.cpp) provides an example of a friend class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

class Widget { int data; public :

Widget(int d): data(d) {} friend class Gadget;

};

class Gadget { int value; public :

// A Gadget objects copies the private data from a Widget object Gadget(const Widget& w): value(w.data) {} int get() const { return value;

}

bool compare (const Widget& w) const { return value == w.data;

}

};

int main() {

Widget wid{45};

Gadget gad{wid};

std::cout << gad.getQ << '\n';

if (gad.compare(wid))

std::cout << "They are the same" << '\n' ;

}

In Listing 15.14 (friendclass.cpp) the Gadget constructor accesses the private data element of a Wi dget object to initialize a Gadget object. The Gadget: : compare method accesses the data of a Wi dget parameter passed to it. Neither of these accesses would be possible if the Wi dget class did not declare Gadget to be a friend. Note that while a Gadget object may freely access the private members of any Wi dget object, no Wi dget object has special access to any Gadget object. Friendship is not automatically symmetric; that is, the f ri end declaration is one directional. For the relationship to be mutual, the programmer would have to declare the Wi dget class to be a friend within the Gadget class; then objects of both classes could freely access the internal details of each other.

Note that a class grants friendship unilaterally to an outside class or function; there is no way for an outside class or function to become a friend of a class that has not specified it as a f ri end. This gives the class designer full control over the code that accesses the private members of the class.

Suppose A, B, and C are classes. Further suppose that class B is a friend of class A and that class C is a friend of class B. The friendship is not transitive; this means that C being a friend of B and B being a friend of A does not automatically make C a friend of A. C++ is very strict about the friendship relationship. The designer of class A would need to declare C as an additional friend of A. A class may have as many friend functions and classes as needed.

Good object-oriented design avoids friends as much as possible. Ideally, if class A grants friendship to class B, the design of classes A and B should be under the control of the same developers. Otherwise, friendship weakens encapsulation (see Section|jl4.6|. If class A grants friendship to class B and class B is not under the control of the developer of class A, one or more of the methods in class B could manipulate the internals of an object of type A and potentially place it in an ill-defined state.

Some would argue that the Listing 1 15.13| (printonlyrational.cpp) example could be better written as

©2018 Richard L. Halterman

Draft date: September 25, 2018

shown in Listing 15.15 (readonlyrational.cpp).

The get_numerator and get_denomi nator methods eliminate the need for a friend function. Note that a Readonly Rati onal object is subtly different from an Pri ntOnlyRati onal object. Clients can see the numerator and denominator fields of a ReadOnlyRational object as desired, but Pri ntOnlyRati onal objects are “print only;” clients readily can print an Pri ntOnlyRati onal object but cannot easily discern the individual numerator and denomi nator values.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Both the Pri ntOnlyRati onal and Readonly Rati onal classes represent read-only fraction objects—once a client creates one these objects the client cannot change its value. In truth, the Readonly Rati onal class is more versatile, as programmers could incorporate ReadOnlyRati onal objects into an application that displays its output via a graphical interface. Pri ntOnlyRati onal objects limit their access to output streams. The Pri ntOnlyRati onal class may better serve applications that need such limited access.

15.11 Exercises

1. Suppose Widget is a class of objects, and function proc accepts a single Widget object as a parameter. Without knowing anything about class Widget, which of the following definitions of function proc is considered better, and why?

Option #1:

void proc(Widget obj) { /* Details omitted ...*/}

Option #2:

void proc(const Widget& obj) { /* Details omitted ...*/}

2. Suppose you have the following definition for class Assembly:

class Assembly { public:

int value;

};

and the variable ptr_a declared and initialized as so:

Assembly *ptr_a = new Assembly;

(a) What statement using the dot operator (.) could you use to assign 5 to the value field of the object to which ptr_a points?

(b) What statement using the arrow operator (->) could you use to assign 5 to the value field of the object to which ptr_a points?

3. Suppose you have the following definition for class Gadget:

class Gadget { int value; public :

Gadget(int v): value(v) {} int get() const { return value;

}

};

Consider the following code fragment:

Gadget x(5); int y = x.get();

©2018 Richard L. Halterman

Draft date: September 25, 2018

(a) What value does the second statement assign to y?

(b) Rewrite Gadget: : get so it explicitly uses the thi s pointer.

(c) During the execution of Gadget: : get on the second line, what is the value of the method’s this pointer?

(d) What can a client do to alter the value field of a Gadget object after the object’s creation?

4. What are the consequences of declaring a method to be const?

5. Why are const methods necessary in C++?

6. Given the following Counter class declaration:

class Counter { int value; public :

CounterQ: value(Q) {} void incrementQ { value++;

}

int get() const { return value;

}

};

and Counter objects declared as shown here:

Counter cl; const Counter c2;

determine if each of the following statements is legal.

(a) cl.increment(); c2.increment();

(b) int x = cl.get(); int y = c2.get();

(3) Given the following Counter class declaration:

class Counter { int value; public :

CounterQ: value(0) {} void incrementQ { value++;

}

int get() {

return value;

}

};

©2018 Richard L. Halterman

Draft date: September 25, 2018

and Counter objects declared as shown here:

Counter cl; const Counter c2;

determine if each of the following statements is legal.

(a) cl. i ncrementQ ; c2.increment();

(b) int x = cl.get(); int y = c2.get();

(&) Consider the following class declaration:

class Counter { int value; public :

CounterQ: value(0) {} void incrementQ { value++;

}

int decrementQ { value--;

}

int get() const { return value;

}

(a) Show how you would properly separate the code of the Counter class into two source files: its declaration in a counter.h file and its method implementations in a counter.cpp file.

(b) Would client code ordinarily #include both the counter.h and counter.cpp files in its source code?

(c) How can you protect your counter.h file to prevent clients from accidentally #i nclude-ing the contents of the header file more than once?

(d) What advantages does separating the class declaration and method implementations provide?

9. What are the consequences of declaring a method to be stati c?

10. Consider the following class declaration:

class ValType { public :

int valuel; static int value2;

(a) If a client creates 100 ValType objects, how many valuel fields will exist in memory?

©2018 Richard L. Halterman

Draft date: September 25, 2018

(b) If a client creates 100 ValType objects, how many value2 fields will exist in memory?

11. How is a C++ struct similar to a class?

12. How does a C++ struct differ from a class?

13. Given the following custom type declarations:

class X {

int valuel; public :

static int value2; int value3;

X(): valuel(5) {} void f() {

valuel = 0;

}

static void g() { value2 = 0;

}

};

int X::value2 = 3;

struct Y {

int quantityl;

Y(): quantityl(5) {} void f() {

quantityl = 0;

}

private :

int quantity2;

};

and the following variable declarations:

X x_obj;

Y y_obj;

determine if each of the following statements is legal.

(a)

x_

_obj.valuel = 0;

(b)

x_

_obj.value2 = 0;

(c)

x_

_obj.value3 = 0;

(d)

X:

::valuel = 0;

(e)

X:

::value2 = 0;

(f)

X:

::value3 = 0;

(g)

y.

_obj.quantityl =

(h)

y.

_obj.quantity2 =

0)

Y:

::quantityl = 0;

(j)

Y:

::quantity2 = 0;

Table caption©2018 Richard L. Halterman

Draft date: September 25, 2018

(k) x_obj .f ();

(l) x_obj - g ();

(m) X::f() ;

(n) X: :g();

14. What privileges does function f have with respect to the class that declares f to be its f ri end?

15. Consider the following class declaration:

class ValType { int value; public :

ValTypeQ: value(0) {} void set(int vl) { value = vl;

}

void show() const {

std::cout << value << '\n' ;

}

friend int f (const ValType& x);

};

and determine the legality of each of the following function definitions:

(a) int f (const ValType& x) {

return 2 * x.value;

}

(b) int g(const ValType& x) {

return 2 * x.value;

}

(c) int f (const ValType& x) {

x.showQ ; return 0;

}

(d) int g(const ValType& x) {

x.showQ ; return 0;

}

(e) int f(const ValType& x, int n) { return n * x.value;

}

16. What are the risks associated with using the f ri end construct?

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 16

Building some Useful Classes

This chapter uses the concepts from the past few chapters to build some complete, practical classes.

16.1 A Better Rational Number Class

Listing 16.1 (rational.cpp) enhances the Si mpleRati onal class (Listing 14.5 (simplerational.cpp)) providing a more complete type.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Default fraction is 0/1

Rationale): numerator(0), denominator(l) {}

int get_numerator() const { return numerator;

}

int get_denominator() const { return denominator;

}

Rational reduceQ const {

// Find the factor that numerator and denominator have in common... int factor = ged(numerator, denominator);

// ...then divide it out in the new fraction

//return Rational(numerator/factor, denominator/factor);

return {numerator/factor, denominator/factor};

}

// Equal fractions have identical numerators and denominators bool operator== (const Rational& fract) const {

// First, find the reduced form of this fraction and the parameter... Rational fl = reduceQ,

f2 = fract.reduce();

// ...then see if their components match.

return (fl.numerator == f2.numerator)

&& (fl.denominator == f2.denominator);

}

// Unequal fractions are not equal bool operator != (const Rational& other) { return !(*this == other);

}

// Compute the sum of fract and the current rational number Rational operator+ (const Rational& fract) const {

// Find common denominator

int commonDenominator = lcm(denominator, fract.denominator);

// Add the adjusted numerators

int newNumerator = numerator * commonDenominator/denominator

+ fract.numerator * commonDenominator/fract.denominator; return {newNumerator, commonDenominator};

}

};

// Compute the product of fract and the current rational number Rational operator*(const Rational& fract) const { return Rational(numerator * fract.numerator,

denominator * fract.denominator).reduce();

}

// Allow a Rational object to be displayed in a nice // human-readable form.

std::ostream& operator<< (std::ostream& os, const Rational& r) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

os << r.get_numerator()

<<

H i ii

<<

r.get_denominator();

}

return os;

int

mainQ {

Rational fl(l, 2),

f2(l,

3)

5

std::cout << f1 <<

II _|_ II

<<

f 2

<<

" = " <<

(fl +

f 2) <<

' \n

std::cout << f1 <<

II * II

<<

f 2

<<

" = " <<

(fl *

f 2) <<

' \n

}

Listing 11671 [ (rational, cpp) produces

1/2 + 1/3 = 5/6 1/2 * 1/3 = 1/6

This rational number type has some notable features:

• Constructors. The overloaded constructors permit convenient initialization and make it impossible to create an undefined fraction.

Private static methods. Rational provides two private static methods: gcd and 1cm. The algorithm for the recursive gcd (greatest common divisor) method was introduced in Section 10.5 The 1cm (least common multiple) method is derived from the mathematical relationship:

gcd (m,n) x lcm (m,n) = m x n

These two methods are declared pri vate because they are not meant to be used directly by client code. Greatest common divisor and least common multiple are concepts from number theory of which Rational clients have no direct need. Client code expects functionality typical of rational numbers, such as addition and reduction; these two private methods are used by other, public, methods that provide functionality more closely related to rational numbers. These two private methods are stati c methods because they do not use instance variables. An object is not required to compute the greatest common divisor of two integers. It is legal for gcd and 1cm to be instance methods, but instance methods should be used only where necessary, since they have the power to alter the state of an object. Faulty coding that accidentally modifies an instance variable can be difficult to track down. If a class method is used, however, the compiler can spot any attempt to access an instance variable immediately.

• Public instance methods. None of the instance methods (operator==, reduce, operator+, and ope rato r *) modify the state of the object upon which they are invoked. Thus, the Rational class still produces immutable objects. The methods operator+, operator*, and reduce use the private helper methods to accomplish their respective tasks.

• Global « operator. operator<<isa global function that allows aRational object to be sent to the std : : cout object to be displayed as conveniently as a built-in type.

16.2 Stopwatch

The linear search vs. binary search comparison program (Listing) 12.5[(searchcompare.cpp)) accessed the system clock in order to time the execution of a section of code. The program used the clock function from the standard C library and an additional variable to compute the elapsed time. The following skeleton code fragment:

©2018 Richard L. Halterman

Draft date: September 25, 2018

clock_t seconds = clockQ; // Record starting time

/*

• Do something here that you wish to time

*/

clock_t other = clockQ; // Record ending time

std::cout << static_cast<double> (other - seconds)/CLOCKS_PER_SEC << " seconds\n";

certainly works and can be adapted to any program, but it has several drawbacks:

• A programmer must take care to implement the timing code correctly for each section of code to be timed. This process is error prone:

- clock_t is a specialized type that is used infrequently. It is not obvious from its name that clock_t is equivalent to an unsigned integer, so a programmer may need to consult a library reference to ensure its proper use.

- The programmer must specify the correct arithmetic:

(other - seconds)/CLOCKS_PER_SEC

- The type cast to double of the time difference is necessary but easily forgotten or applied incorrectly. If a programmer incorrectly applies parentheses as so

static_cast<double> ((other - seconds)/CLOCKS_PER_SEC)

the result will lose precision. Worse yet, the following parenthetical grouping

static_cast<double> (other) - seconds/CLOCKS_PER_SEC

will result in an incorrect value, since division has precedence over subtraction.

• The timing code is supplemental to the actual code that is being profiled, but it may not be immediately obvious by looking at the complete code which statements are part of the timing code and which statements are part of the code to be timed.

Section [l0.6j offered a solution to the above shortcomings of using the raw types, constants, and functions available from the C time library. Listing ] 10. 14| (timermodule.cpp) hides the details of the C time library and provides a convenient functional interface to callers. Unfortunately, as mentioned in Section |10.6| the functional approach has a serious limitation. The code in Listing |10.14| (timermodule.cpp) uses global variables to maintain the state of the timer. There is only one copy of each global variable. This means programmers using the timer functions cannot independently measure the elapsed time of overlapping events; for example, you cannot measure how long it takes for a function to execute and simultaneously measure how long a section of code within that function takes to execute.

A programmer could time multiple, simultaneous activites by using the raw C library clock function directly, but then we are back to where we began: messy, potentially error-prone code.

Objects provide a solution. Consider the following client code that uses a stopwatch object to keep track of the time:

Stopwatch timer; // Declare a stopwatch object timer.start(); // Start timing

©2018 Richard L. Halterman

Draft date: September 25, 2018

/*

* Do something here that you wish to time */

timer.stop(); // Stop the clock

std::cout << timer.elapsed() << " seconds\n";

This code using a Stopwatch object is as simple as the code that uses the timer functions from Listing 10.14 (timermodule.cpp). As an added benefit, a developer can think of a Stopwatch object as if it is a real physical stopwatch object: push a button to start the clock (call the start method), push a button to stop the clock (call the stop method), and then read the elapsed time (use the result of the elapsed method). What do you do if you need to time two different things at once? You use two stopwatches, of course, so a programmer would declare and use two Stopwatch objects. Since each object maintains its own instance variables, each Stopwatch object can keep track of its own elapsed time independently of all other active Stopwatch objects.

Programmers using a Stopwatch object in their code are much less likely to make a mistake because the details that make it work are hidden and inaccessible. With objects we can wrap all the messy details of the timing code into a convenient package. Given our experience designing our own types though C++ classes, we now are adequately equipped to implement such a Stopwatch class. Listing 16.2 (stopwatch.h) provides the header hie defining the structure and capabilities of our Stopwatch objects.

From this class declaration we see that when clients create a Stopwatch object a constructor is available to take care of any initialization details. Four methods are available to clients: sta rt, stop, reset, and elapsed. The reset method is included to set the clock back to zero to begin a new timing. Note that the “messy” detail of the clock_t variable is private and, therefore, clients cannot see or directly affect its value within a Stopwatch object.

This Stopwatch class (Listing 16.2 (stopwatch.h)) addresses the weaknesses of the non-object-oriented approach noted above:

©2018 Richard L. Halterman

Draft date: September 25, 2018

• The timing code can be implemented in methods of the Stopwatch class. Once the methods are correct, a programmer can use Stopwatch objects for timing the execution of sections of code without worrying about the details of how the timing is actually done. Client code cannot introduce errors in the timing code if the timing code is hidden within the Stopwatch class.

• The details of the timing code no longer intertwine with the code to be timed, since the timing code is located in the Stopwatch class. This makes it easier for programmers to maintain the code they are timing.

• The Stopwatch class provides a convenient interface for the programmer that replaces the lowerlevel details of calling system time functions.

Listing 16.3 (stopwatch.cpp) provides the Stopwatch implementation.

©2018 Richard L. Halterman

Draft date: September 25, 2018

return elapsed_time

+ static_cast<double> ((current_time - start_time))

/CLOCKS_PER_SEC;

}

else // Timer stopped; elapsed already computed in the stop method return elapsed_time;

}

// Returns the stopwatch's status (running or not) to the client.

// This method does not affect the state of the stopwatch, bool Stopwatch::is_running() const { return running;

}

// Resets the stopwatch so a subsequent start begins recording // a new time. Stops the stopwatch if it currently is running, void Stopwatch::reset() { running = false; elapsed_time = 0.0;

}

Note that our design allows a client to see the running time of a Stopwatch object without needing to stop it. An alternate design might print an error message and perhaps exit the program’s execution if a client attempts to see the elapsed time of a running stopwatch.

Some aspects of the Stopwatch class are notable:

• Stopwatch objects use three instance variables:

- The start_time instance variable records the time when the client last called the start method.

- The elapsed_time instance variable keeps track of the time since the latest call to the reset method.

- The runni ng Boolean instance variable indicates whether or not the clock is running.

• The constructor sets the initial values of the instance variables start_time, elapsed_time, and runni ng.

• The sta rt method notes the system time after the assignment to runni ng. If these two statements were reversed, the elapsed time would include the time to do the assignment to runni ng. The elapsed time should as closely as possible just include the statements in the client code between the start and stop method calls.

Notice that sta rt_ti me is not assigned if the stopwatch is running.

• In the stop method, the system time is noted before the assignment to runni ng so the elapsed time does not include the assignment to runni ng. This provides a more accurate accounting of the client code execution time.

The stop method computes the accumulated elapsed time. This design allows a client to stop the stopwatch and restart it later without losing an earlier segment of time.

• The elapsed method either returns the elapsed time computed by the stop method or computes the current running time without altering the elapsed_ti me variable. Clients should avoid calling elapsed when a Stopwatch object is running since doing so would interfere with the accurate timing of client code execution.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Compare the mai n function of Listing 12.5 (searchcompare.cpp) to that of Listing 16.4 (bettersearchcompare.cpp):

©2018 Richard L. Halterman

Draft date: September 25, 2018

Stopwatch timer;

// Ensure the elements are ordered low to high for (size_t i = 0; i < SIZE; i++) list[i] = i;

// Search for all the elements in list using linear search timer.start();

for (size_t i = 0; i < SIZE; i++) linear_search(list, i);

// Print the elapsed time timer.stop();

std::cout << "Linear elapsed: " << timer.elapsed() << " seconds\n"; // Prepare for a new timing timer. resetQ ;

// Search for all the elements in list using binary search timer.start() ;

for (size_t i = 0; i < SIZE; i++) binary_search(list, i);

// Print the elapsed time timer.stop();

std::cout << "Binary elapsed: " << timer.elapsed() << " seconds\n";

This new, object-oriented version is simpler and more readable.

The design of the Stopwatch class allows clients to create multiple Stopwatch instances, and each instance will keep track of its own time. In practice when profiling executing programs, such generality usually is unnecessary. Rarely do developers need to time overlapping code, so one timer object per program usually is enough. Multiple sections of code can be checked with the same Stopwatch object; simply start it, stop it, check the time, and then reset it and start it again when another section of code is to be timed.

16.3 Sorting with Logging

Section 12.2 shows how to use function pointers to customize the ordering that selection sort performs on a vector of integers. The selection_sort function in Listing 12.2 (flexibleintsort.cpp) accepts a function pointer parameter in addition to the vector. The function pointer points to a function that accepts two integer parameters and returns true or false. The function is supposed to use some kind of ordering rule to determine if its first integer parameter precedes its second integer parameter.

Suppose we wish to analyze the number of comparisons and the number of swaps the sort function performs on a given vector with a particular ordering strategy. One way to do this is have the sort function itself keep track of the number of times it calls the comparison function and swap function and return this information when it finishes. To do so we would have to define an object to hold the two pieces of data (comparisons and swaps) since a function can return only one value, not two. Also if we do this, we must significantly alter the code of the sort algorithm itself. We would prefer to keep the sort algorithm focused on its task of sorting and remain uncluttered from this additional logging code.

If instead of passing a function pointer to our sort function we pass a specially crafted object. We can design our object to do whatever we want; specifically, we can design our special object to perform the necessary comparisons and keep track of how many comparisons it performs. We could let the object do the swap, and it could log the swaps it performs.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing |T6T5| (loggingflexiblesort.cpp) is a variation of Listing |T2T2|[ (flexibleintsort.cpp) that uses a comparison object instead of a comparison function.

©2018 Richard L. Halterman

Draft date: September 25, 2018

return compare_count;

}

// Returns the number of swaps this object has // performed since it was created, int swaps() const {

return swap_count;

}

/*

* selection_sort(a, compare)

* Arranges the elements of vector a in an order determined

* by the compare object.

* a is a vector of ints.

* compare is a function that compares the ordering of

* two integers.

* The contents of a are physically rearranged.

*/

void selection_sort(std::vector<int>& a, Comparer& compare) { int n = a.size();

for (int i = 0; i < n - 1; i++){

// Note: i,small, and j represent positions within a // a[i], a[small], and a[j] represents the elements at // those positions.

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less // than a[i] int small = i ;

// See if a smaller value can be found later in the array for (int j = i + 1; j < n; j++)

if (compare.compare(a[j], a[small]))

small = j; // Found a smaller value // Swap a[i] and a[small], if a smaller value was found if (i != small)

compare.swap(a[i], a[small]);

}

}

/*

* print

* Prints the contents of an integer vector

* a is the vector to print.

* a is not modified.

*/

void print(const std::vector <i nt>& a) { int n = a.size(); std::cout << '{' ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a[i]; // Print the rest

}

std::cout << '}' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

bool less_than (i nt a, int b) { return a < b;

}

/*

* greater_than(a, b)

* Returns true if a > b; otherwise, returns

* false.

*/

bool greater_than (i nt a, int b) { return a > b;

}

int main() {

// Hake a vector of integers from an array

std::vector<i nt> original { 23, -3, 4, 215, 0, -3, 2, 23, 100, 88, -10 };

// Hake a working copy of the original vector

std::vector<i nt> working = original; std::cout << "Before: print(working); std::cout << 1 \n 1 ;

Comparer It(less_than), gt(greater_than); selection_sort(working, It); std::cout << "Ascending: "; print(working);

std::cout << " (" << It.comparisons() << " comparisons, "

<< It.swapsQ << " swaps)\n";

std: : cout << "-\n" ;

// Hake another copy of the original vector

working = original;

std::cout << "Before: ";

print(working);

std::cout << 1 \n 1 ;

selection_sort(working, gt);

std::cout << "Descending: ";

print(working);

std::cout << " (" << gt.comparisons() << " comparisons, "

<< gt.swapsQ << " swaps)\n";

std: : cout << "-\n" ;

// Sort a sorted vector std::cout << "Before: ";

print(working); std::cout << 1 \n 1 ;

// Reset the greater than comparer so we start counting at // zero gt.reset();

selection_sort(working, gt); std::cout << "Descending: ";

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

print(working);

std::cout << " (" << gt.comparisons() << " comparisons,

<< gt.swapsQ << " swaps)\n";

Notice that a Comparison object wraps a comparison function pointer, contains a swap method, and maintains two integer counters. The comparison object passed to the sort routine customizes the sort’s behavior (via its function pointer) and keeps track of the number of comparisons and swaps it performs (via its integer counters). As in Listing [l2.2| (flexibleintsort.cpp), the basic structure of the sorting algorithm remains the same regardless of the ordering determined by the comparison object.

Table captionThe output of Listingjjl6.5||(loggingflexiblesort.cpp) is

Before:

{23,-3,4,215,0,-3,2,23,100,88,-10}

Ascending:

{-10,-3,-3,0,2,4,23,23,88,100,215}

(55

comparisons,

7

swaps)

Before:

{23,-3,4,215,0,-3,2,23,100,88,-10}

Descending

: {215,100,88,23,23,4,2,0,-3,-3,-10}

(55

comparisons,

5

swaps)

Before:

{215,100,88,23,23,4,2,0,-3,-3,-10}

Descending

: {215,100,88,23,23,4,2,0,-3,-3,-10}

(55

comparisons,

0

swaps)

We see from the results that the number of comparisons is dictated by the algorithm itself, but the number of element swaps depends on the ordering of the elements and the nature of the comparison. Sorting an already sorted array with selection sort does not reduce the number of comparisons the function must perform, but, as we can see, it requires no swaps.

16.4 Automating Testing

We know that a clean compile does not imply that a program will work correctly. We can detect errors in our code as we interact with the executing program. The process of exercising code to reveal errors or demonstrate the lack thereof is called testing. The informal testing that we have done up to this point has been adequate, but serious software development demands a more formal approach. As you gain more experience developing software you will realize that good testing requires the same skills and creativity as programming itself.

Until recently testing was often an afterthought. Testing was not seen to be as glamorous as designing and coding. Poor testing led to buggy programs that frustrated users. Also, tests were written largely after the program’s design and coding were complete. The problem with this approach is major design flaws may not be revealed until late in the development cycle. Changes late in the development process are invariably more expensive and difficult to deal with than changes earlier in the process.

Weaknesses in the standard approach to testing led to a new strategy: test-driven development. In testdriven development the testing is automated, and the design and implementation of good tests is just as important as the design and development of the actual program. In pure TDD, developers write the tests before writing any application code and immediately test all application code they write.

Listing |16.6|(tester.h) defines the structure of a rudimentary test object.

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <vector>

#include <string>

class Tester {

int error_count; // Number of errors detected int total_count; // Number of tests executed

// Determines if double-precision floating-point // values dl and d2 are "equal."

// Returns true if their difference is less than tolerance, bool equals (double dl, double d2, double tolerance) const;

// Displays vector a in human-readable form

void print_vector (const std:: vector<int>& a); public :

// Initializes a Tester object Tester();

// Determines if an expected integer result (expected)

// matches the actual result (actual), msg is the message // that describes the test.

void check_equals (const std::string& msg, int expected, int actual);

// Determines if an expected double result (expected)

// matches the actual result (actual) or they differ by at // most tolerance, msg is the message that describes the test, void check_equals (const std::string& msg, double expected, double actual, double tolerance);

// Determines if an expected string result (expected)

// matches the actual result (actual), msg is the message

// that describes the test.

void check_equals (const std::string& msg,

const std:: vector<int>& expected, const std:: vector<int>& actual);

// Reports the final results: number of tests passed and // failed and the total number of tests run. void report_results() const;

};

#endif

A simple test object keeps track of the number of tests performed and the number of failures. The client uses the test object to check the results of a computation against a predicted result. Notice that the equals method, which checks for the equality of two double-precision floating-point numbers is private, as it is meant to be used internally by the other methods within the class. The equals method works the same way as the equals function we examined in Listing 9.17 (floatequals.cpp).

Listing fl677|(tester.cpp) implements the Tester methods.

Listing 16.7: tester. cpp

#include <iostream>

©2018 Richard L. Halterman

Draft date: September 25, 2018

ffinclude <cmath>

#include "tester.h"

Tester::Tester(): error_count(0), total_count(0) {

std::cout << " +- \n";

std::cout << "| Testing \n";

std::cout << " +- \n";

}

// dl and d2 are "equal" if their difference is less than // a specified tolerance

bool Tester::equals (double dl, double d2, double tolerance) const { return dl == d2 || abs(dl - d2) < tolerance;

}

// Prints the contents of a vector of integers.

void Tester: :print_vector(const std::vector <i nt>& a) { int n = a.size(); std::cout << ' { ' ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a [ i] ; // Print the rest

}

std::cout << ' } ' ;

}

// Compare integer outcomes

void Tester::check_equals(const std::string& msg, int expected,

int actual) {

std::cout << "[" << msg << "] total_count++; // Count this test

if (expected == actual) std::cout << "OK\n"; else {

error_count++; // Count this failed test

std::cout << "*** Failed! Expected: " << expected << ", actual: " << actual << '\n';

}

}

// Compare double-precision floating-point outcomes

void Tester::check_equals(const std::string& msg, double expected,

double actual, double tolerance) { std::cout << "[" << msg << "] total_count++; // Count this test

if (equals(expected, actual, tolerance)) std::cout << "OK\n"; else {

error_count++; // Count this failed test

std::cout << "*** Failed! Expected: " << expected << ", actual: " << actual << '\n';

}

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Compare vector outcomes

void Tester::check_equals(const std::string& msg,

const std::vector <i nt>& expected, const std::vector <i nt>& actual) { std::cout << "[" << msg << "] total_count++; // Count this test

if (expected == actual) std::cout << "0K\n"; else {

error_count++; // Count this failed test

std::cout << "*** Failed! Expected: print_vector(expected); std::cout << " Actual: print_vector(actual) ; std::cout << ' \n ' ;

}

}

// Display final test statistics

void Tester::report_results() const {

std:: cout << " +- \n";

std::cout << "| " << total_count << " tests run, "

<< total_count - error_count << " passed, "

<< error_count << " failed\n"; std:: cout << " +- \n";

©2018 Richard L. Halterman

Draft date: September 25, 2018

16.5. CONVENIENT HIGH-QUALITY PSEUDORANDOM NUMBERS

491

sort(vec);

t.check_equals( "Sort test #2", {2, 3, 4}, vec);

// Some test cases to test sum

t.check_equals( "Sum test #1", sum({0, 3, 4}), 7); t.check_equals( "Sum test #2", sum({-3, 0, 5}), 2);

Table captionThe program s output is

+

| Testing

[Sort test #1] *** Failed!

Expected: {2,3,4} Actual:

{4,2,3}

[Sort test #2] OK

[Sum test #1] OK

[Sum test #2] *** Failed!

Expected: 5, actual: 2

Notice that the sort function has yet to be implemented, but we can test it anyway. The first test is bound to fail. The second test checks to see if our sort function will not disturb an already sorted vector, and we pass this test with no problem. This is an example of coincidental correctness.

In the sum function, the programmer was careless and used 1 as the beginning index for the vector. Notice that the first test does not catch the error, since the element in the zeroth position (zero) does not affect the outcome. A tester must be creative and devious to try and force the code under test to demonstrate its errors.

16.5 Convenient High-quality Pseudorandom Numbers

In Section [13.5| we used some classes from the standard C++ library to generate high-quality pseudorandom numbers. Listing 13.11 (highqualityrandom.cpp) used three kinds of objects—random_device, mt!9937, and uni form_i nt_di stri buti on—to produce good pseudorandom sequences.

The C++ class construct allows us to creatively combine multiple sources of functionality into one convenient package. Listing 16.9 (uniformrandom.h) contains a custom Uni formRandomGenerator class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

16.5. CONVENIENT HIGH-QUALITY PSEUDORANDOM NUMBERS

492

// The largest pseudorandom number this generator can produce const int MAX;

// Create a pseudorandom number generator that produces values in // the range low...high

UniformRandomGenerator (int low, int high) : dist(low, high), mt(std::random_device()()),

MIN(low), MAX(high) {}

// Return a pseudorandom number in the range MIN...MAX int operator ()() { return dist(mt);

}

};

#endif

The Uni formRandomGenerator class provides a simplified interface to programmers who need access to high-quality pseudorandom numbers. Behind the scenes, every Uni formRandomGenerator object contains its own uni form_i nt_di stri bution object and mtl9937 object. The constructor accepts the minimum and maximum values in the range of pseudorandom numbers desired. The constructor uses this range to construct the appropriate uni form_i nt_di stri buti on object for this range. The constructor also initializes the mtl9937 object field. The Uni formRandomGenerator constructor passes to the constructor of the mtl9937 class a temporary random_devi ce object. Since a Uni formRandomGenerator object uses the random_devi ce only for creating its mtl9937 field and does not need it later. Uni formRandomGenerator objects do not contain a random_devi ce field.

To create a Uni formRandomGenerator object that produces pseudorandom integers in the range —100... 100, a client need only write

UniformRandomGenerator gen(-100, 100);

The Uni formRandomGenerator class also provides an operator() method. This allows a client to “call” an object as if it were a function. Given a Uni formRandomGenerator object named gen, we can assign a pseudorandom number to an integer variable x, with the statement

int x = gen();

This statement may appear to be calling a global function named gen; in fact, it is calling the operator() method of the Uni formRandomGenerator class on behalf of object gen. The expression gen() is syntactic sugar for gen. operator () (). The expression gen. operator () () may look unusual, but it simply is invoking the Uni formRandomGenerator: : operator () method on behalf of gen passing no arguments in the empty last pair of parentheses.

Listing jl6.10| (testuniformrandom.cpp) is a simplified remake of Listing |13.11|| (highqualityrandom.cpp). In Listing 16.10 (testuniformrandom.cpp) we see that with our Uni formRandomGenerator class we can generate high-quality pseudorandom numbers with a single object that is simple to use.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int main() {

// Pseudorandom number generator with range 0...9,999

UniformRandomGenerator rand(0, 9999);

// Total counts over all the runs.

// Make these double-precision floating-point numbers

// so the average computation at the end will use floating-point

// arithmetic.

double total5 = 0.0, total9995 = 0.0;

// Accumulate the results of 10 trials, with each trial // generating 1,000,000,000 pseudorandom numbers const int NUMBER_OF_TRIALS = 10;

for (int trial = 1; trial <= NUMBER_OF_TRIALS; trial++) {

// Initialize counts for this run of a billion trials int count5 = 0, count9995 = 0;

// Generate one billion pseudorandom numbers in the range // 0...9,999 and count the number of times 5 and 9,995 appear for (int i = 0; i < 1000000000; i++) {

// Generate a pseudorandom number in the range 0...9,999 int r = rand() ; if (r == 5)

count5++; // Number 5 generated, so count it

else if (r == 9995)

count9995++; // Number 9,995 generated, so count it

}

// Display the number of times the program generated 5 and 9,995

std::cout << "Trial #" << std::setw(2) << trial << " 5: "

<< std::setw(6) << count5

<< " 9995: " << std::setw(6) << count9995 << '\n';

total5 += count5; // Accumulate the counts to

total9995 += count9995; // average them at the end

}

std : : cout << "- \n" ;

std::cout << "Averages for " << NUMBER_OF_TRIALS << " trials: 5: " << std::setw(6) << total5 / NUMBER_OF_TRIALS << " 9995: " << std::setw(6) << total9995 / NUMBER_OF_TRIALS << 1 \n' ;

Note that in Listing 16.10 (testuniformrandom.cpp), the statement int r = rand();

is not a call to our familiar std : : rand function; rather, rand here is a Uni formRandomGenerator object, and the statement is invoking its operator () method.

16.6 Exercises

1. Create a large unsigned integer type named Bi gUnsi gned. Bi gUnsi gned objects represent unsigned integers with arbitrary precision; that is, unlike the standard C++ unsigned integer primitive types, a Bi gUnsi gned object can represent an unsigned integer as large as necessary. Unlike the floating-point types, a Bi gUnsi gned value retains all its digits of precision.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Internally, the Bi gUnsi gned class should hold a std : : vector of integers. Each integer in the vector is one of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. Each element in the vector represents a digit in a place value within the integer; for example, if the internal vector contains the following elements in the following order:

4,9,1,1,4,3,0,5

we would interpret the associated Bi gUnsi gned object as the mathematical nonnegative integer 49,114,305.

Your Bi gUnsi gned class implementation should provide the following features:

• The class should provide a constructor that accepts no arguments that initializes the Bi gUnsi gned object’s vector to contain a single element equal to zero.

• The class should provide a constructor that accepts a single unsigned integer. This constructor should populate its internal vector with the appropriate elements to correspond to the value of its parameter.

• The class should provide a constructor that accepts a Bi gUnsi gned argument. Clients use this constructor to create a new Bi gUnsi gned object from an exiting Bi gUnsi gned object.

• The class should provide a constructor that accepts a std : : st r i ng object representing an integer. Clients use this constructor when they need to create a large integer whose value exceeds the range of unsigned long long. The string argument should contain only digits.

• The class should provide access to a friend function named operator+ that adds two Bi gUnsi gned objects and returns the Bi gUnsi gned result.

• The class should provide access to a f ri end function named operator<< that allows clients to print a Bi gUnsi gned value as easily as a built-in integer type.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 17

Inheritance and Polymorphism

In Chapter^ we saw how it is possible to design classes from which clients can produce objects that exhibit somewhat sophisticated behavior. We built each of the classes from scratch. C++ provides a way to create a class from an existing class by a process known as inheritance. Through this process the new class inherits all the characteristics of the existing class, and the class developer can extend and customize the inherited functionality as well as add new features.

17.1 I/O Stream Inheritance

Recall from Section 13.3 that writing data to a file is almost as easy as printing it on the screen. Once a Std: : of stream object is set up, we can use the << operator in the same way we use it with the std : : cout object:

std::ofstream fout("myfile.dat") ; int x = 10;

if (fout.good()) { // Make sure the file was opened properly

fout << "x = " << x << '\n' ;

}

else

std::cout << "Unable to write to the file V'myfile.dat\"\n" ;

Section |15.7| showed how operator<< may be overloaded for a programmer-defined type. For a vector of integers we can write the function

ostream& operator<< (ostream& os, const std::vector<i nt>& vec) { os << ' { ' ; int n = vec.size();

if (n > 0) { // Is the vector non-empty?

os << vec[0]; // Send first element to the strean

for (int i = 1; i < n; i++)

os << << vec[i]; // Send remaining elements

}

os << '}' ; return os;

}

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Draft date: September 25, 2018

Can we easily adapt our << operator so that we can use it with std : : of stream objects as well?

The answer, perhaps surprisingly, is we do not have to adapt our operator<< function; it works as is with std: : of stream objects. How can this be, since the std: : cout object has type std : :ostream which is not the same class as std : : of stream?

C++ allows some automatic conversions among the built in numeric types; for example, an i nt is widened to a double, and a double is truncated to an i nt. bools and i nts are freely interconvertible. These types are built into the language, so standard conversions apply. When it comes to programmerdefined types, however, the compiler is unable to generate automatically code to convert from one type to another. Most of the time it would make no sense to do so—imagine attempting to convert an object of type Stopwatch (Listing 16.2 (stopwatch.h)) to an object of type Tester (Listing 16.6 (tester.h)).

So, how is it that an object of type std: : of stream can be converted automatically to an object of type ostream? You might think that it is because they are both part of the standard library, so the conversion has been programmed into them. The fact is, no conversion takes place! Any object of type std : : of st ream object is automatically treated as if it were an ostream object because the ostream and std : : of stream classes are related in a special way. The std : : of stream class is derived from the ostream class. We say that ostream is the base class and std : : of stream is the derived class. Sometimes the term superclass is used for the base class, in which case the derived class is called the subclass. The base/derived class terminology is used interchangeably with super/subclass, although the C++ community tends to prefer the terms base/derived class to super/subclass. The process is known as inheritance because the derived class inherits all the characteristics of its base class. The terms derivation, subclassing and specialization are sometimes used in place of the term inheritance.

As a consequence of the derivation process, an instance of the derived class can be treated as if it were an instance of the base class. Listing| [T7.lj |(printstreams.cpp) shows how a function can process instances of two different classes related by inheritance.

Observe that the pri nt function in Listing 17.1 (printstreams.cpp) expects a client to pass an ostream reference as the first parameter, but the mai n function can send it both ostream and std: : of stream object references with equal ease.

©2018 Richard L. Halterman

Draft date: September 25, 2018

This ability to allow a subclass object to be used in any context that expects a superclass object is known as the Liskov Substitution Principle, after computer scientist Barbara Liskov.

The term is a has a special meaning in the context of inheritance. Suppose we have class B and class D derived from B. B is the base class and D is the derived class. Since we can treat an instance of a derived class as if it were an instance of its base class, if we declared a D object as

Dd; // d is a D object we can say d is a D (as it is declared), and we also can say d is a B.

17.2 Inheritance Mechanics

The developers of the std: :ofstream class did not begin with a blank slate. The ost ream class existed first, and the developers specified the std : : of stream class in such a way so any std: : of stream object would be treated as a specific kind of ost ream. In this section we will examine a very simple example that illustrates the mechanics of class inheritance in C++.

Suppose we have class B defined as shown here: class B {

// Details omitted

};

To derive a new class D from B we use the following syntax:

class D: public B {

// Details omitted

};

Here B is the base class and D is the derived class. B is the pre-existing class, and D is the new class based

on B.

To see how inheritance works, consider classes B and D with additional detail: class B {

// Other details omitted public :

void f();

};

void B::f() {

std::cout << "In function 'f'\n";

}

class D: public B {

// Other details omitted public :

void g();

};

void D::g() {

std::cout << "In function 'g'\n";

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Draft date: September 25, 2018

}

The client code

B myB;

D myD; myB.f(); myD.f(); myD.g();

prints

In

function

1 f

In

function

' f

In

function

'g

Even though the source code for class D does not explicitly show the definition of a method named f, it has such a method that it inherits from class B.

Note that inheritiance works in one direction only. Class D inherits method f from class B, but class B cannot inherit D’s g method. Given the definitions of classes B and D above, the following code is illegal:

B myB;

myB.gO; // Illegal, a B object is NOT a D object

If we omit the word public from class D’s definition, as in

class D: B {

// Details omitted

};

all the public members of B inherited by D objects will be private by default; for example, if base class B looks like the following:

class B { public :

void f();

};

f() {

:cout <<

"In function

'f'\n";

the following code is not legal:

D myD;

myD.fQ; // Illegal, method f now is private!

This means a client may not treat a D object exacty as if it were a B object. This violates the Liskov Substitution Principle, and the is a relationship does not exist.

While this private inheritance is useful in rare situations, the majority of objectoriented software design uses public inheritance. C++ is one of the few objectoriented languages that supports private inheritance.

©2018 Richard L. Halterman

Draft date: September 25, 2018

There is no limit to the number of classes a developer may derive from a single base class. In the following code:

class Dl: public B { /* Details omitted */ };

class D2: public B { /* Details omitted */ };

class D3: public B { /* Details omitted */ };

the classes Dl, D2, and D3 are all derived from class B.

A developer may derive a class from more than one base class in a process known as multiple inheritance. In the following code:

class B1 { /* Details omitted */ }; class B2 { /* Details omitted */ };

class D: public Bl, public B2 { /* Details omitted */ };

Here class D has two base classes, Bl and B2. If a particular function or method expects a Bl object as

an argument, the caller may pass a D object; similarly, any context that requires a B2 object will accept a

D object. In object-oriented design, multiple inheritance is not as common as single inheritance (one base class).

The next section provides a simple example that shows how inheritance works.

17.3 Uses of Inheritance

Inheritance is a design tool that allows developers to take an existing class and produce a new class that provides enhanced behavior or different behavior. The enhanced or new behavior does not come at the expense of existing code; that is, when using inheritance programmers do not touch any source code in the base class. Also, developers can leverage existing code (in the base class) without duplicating it in the derived classes.

We can demonstrate the use of inheritance to enhance the behavior of a simple class. Listing ||17.2| (text.h) contains the declaration of a class named Text.

©2018 Richard L. Halterman

Draft date: September 25, 2018

virtual void append(const std::string& extra);

};

#endif

A Text object wraps a std : : stri ng object, and, since the string object is private to the Text class, clients cannot get to the string object directly. The clients may see the string via the get method, and can modify the wrapped string only in a limited way via the append method. Notice that the two methods, get and append, are marked vi rtual. The vi rtual keyword indicates that the designer of this Text class intends that classes derived from Text will be able to customize the behavior of their get and append methods.

The implementation of the Text methods as shown in Listing |T73](text.cpp) contains nothing unusual.

Next we introduce a new class, FancyText, derived from the Text class. Its interface appears in Listing [TT4] (fancytext.h)

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Allow clients to see the decorated text field std::string get() const override;

// Concatenate another string onto the

// back of the existing text, inserting the connector

// string

void append(const std::string& extra) override;

};

#endif

Observe that the declarations of the get and append methods include the override specifier. This keyword indicates that the FancyText class overrides, or provides custom behavior for, the methods declared vi rtual in its base class.

Listing|T731(fancytext.cpp) provides the implementation for the FancyText methods.

While the constructor for the Text class requires a single std::string parameter, the constructor for FancyT ext requires four string arguments:

FancyText::FancyText (const std::string& t, const std::string& left,

const std::string& right, const std::string& conn): Text(t), left_bracket(left), right_bracket(right), connector(conn) {}

The body of the constructor is empty, so all initialization happens in the constructor initialization list. We want to assign the constructor’s first parameter, t, to the inherited member text, but text is private in the base class. This means the FancyText constructor cannot initialize it directly. Since the constructor of its base class knows what to do with this parameter, the first expression in the constructor initialization list (the part between the : and the ):

... Text(t) . . .

©2018 Richard L. Halterman

Draft date: September 25, 2018

explicitly calls the base class constructor, passing it t. This base class initialization expression must be the first thing in the initialization list because C++ requires that the parts of an object inherited from its base class must be initialized before any new parts (added by the derived class) are initialized. The next three expressions in the initialization list:

... left_bracket(left), right_bracket(right), connector(conn) ...

initialize the left_bracket, ri ght_bracket, and connector fields of the FancyText object under construction. The body of the constructor is empty as no other initialization work is necessary.

The FancyText class alters the way get works. We say the FancyText class overrides its inherited get method. The keyword over ri de emphasizes the fact that the code in the get method in FancyText intends to do something differently from the code in Text’s get method. In this case the FancyText: : get method builds a string result by concatenating three other strings: the first string is a front bracketing string, the second is the wrapped string, and the third string is a trailing bracketing string. Notice that the second string is obtained with the expression

Text::get()

This calls the base class version of the get method. We say that the FancyT ext: : get method delegates some of its work to the base class version, Text : : get. Notice that the statement

return left_bracket + text + right_bracket; // Illegal

would be illegal because text is private to the base class. The member specifier p r i vate means inaccessible outside of the class, period. Derived classes have no special privilege in this regard. In order to perform the delegation we must use Text : : get () and not simply get (); the unqualified expression get ( ) is equivalent to thi s->get, which calls FancyText: :get. This means invoking the unqualified get within the definition of FancyT ext : : get is a recursive call, which is not what we want.

A method declared vi rtual in a base class is automatically virtual in its derived classes. You may repeat the vi rtual specifier in derived classes, but the use of over ri de makes this redundant.

The override keyword was added to the language in C++11. Prior to C++11 when a method in a derived class had the same signature as a virtual method in its base class, the method implicitly overrode its base class version. The problem was that a programmer could intend to override a method in the derived class but get the signature wrong. The resulting method overloaded the original method rather than overriding it. If a programmer uses the ove r r i de specifier and uses a signature that does not match the base class version, the compiler will report an error. The over ri de specifier provides a way for programmers to explicitly communicate their intentions.

For backwards compatibility the override keyword is optional. Its presence enables the compiler to verify that the method is actually overriding avi rtual method in the base class. Without it, the programmer must take care to faithfully reproduce the signature of the method to override.

The over ri de keyword is a context-sensitive keyword, meaning it is a keyword only when appearing as it does here in the declaration of a method header. In other contexts it behaves like an identifier.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The FancyText: : append method overrides the inherited append method by inserting a special separator string in between the existing wrapped text string and the string to append. Like FancyText: :get, the FancyText: : append method delegates the actual concatenation operation to its base class by calling Text: : append. Again, this is because code within the FancyText class cannot directly influence its text field.

The class FixedText, declared and defined in Listing 17.6 (fixedtext.h) and Listing 17.7|(fixedtext.cpp), is another class derived from Text.

The FixedText class is somewhat simpler than the FancyText class. It adds no fields and does not override the get method. Its constructor accepts no parameters because clients are not permitted to determine the contents of the wrapped string—the text field is always the word FIXED. It inherits the text field and get method (as is) from the Text class.

The FixedText constructor implementation invokes the base class constructor to assign the string "FIXED" to its inherited text field. The get method needs no customization. The custom append method does nothing, as clients are not allowed to add any extra text.

Listing T778j(testtext.cpp) exercises these classes.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 17.8: testtext.cpp

#include <iostream> #include "text.h" #include "fancytext.h" #include "fixedtext.h"

Table captionint main() {

Text tl("pla

in")

9

FancyText

t2

("fancy

II

9

"<<

", ">>", "***"

FixedText

t3

9

std::cout

<<

tl.

get

0

<<

' \n' ;

std::cout

<<

t2.

get

0

<<

' \n' ;

std::cout

<<

t3 .

get

0

<<

' \n' ;

std::cout

<<

II

tl.append(

"A

t2.append(

"A

t3.append(

"A

");

std::cout

<<

ti.

get

0

<<

' \n' ;

std: :cout

<<

t2.

get

0

<<

' \n' ;

std::cout

<<

t3 .

get

0

<<

' \n' ;

std::cout

<<

II

tl.append(

"B

t2.append(

"B

t3.append(

"B

");

std::cout

<<

ti.

get

0

<<

' \n' ;

std: :cout

<<

t2.

get

0

<<

' \n' ;

std::cout

<<

t3 .

get

0

<<

' \n' ;

The output of Listing ) 17.8|| (testtext.cpp) is

plain

<<fancy>>

FIXED

plainA

<<fancy***A>> FIXED

plainAB

<<fancy***A***B>>

FIXED

Given the Text and FancyText classes as declared in Listing ]! 7T2[ (text.h) and Listing ) 17T5| (fancytext.cpp), the following client code is legal:

Table captionText tl( "ABC" );

Table captionFancyText t2("XYZ",

std:

: cout

<< tl.get() << "

" << t2.get() <<

' \n' ;

tl =

t2;

std:

: cout

<< tl.get() << "

" << t2.get() <<

' \n' ;

Since t2’s declared type is FancyT ext, by virtue of inheritance, t2 is a T ext object as well. The above code fragment prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 17.1 Object slicing during assignment of a derived class instance to a base class variable

Text tl("plain") ;

FancyText t2("Fancy", "<<", ">>",

tl

text

t2

plain

text

fancy

left_bracket « right_bracket » connector "

>

Before Assignment

tl = t2; tl

text

text

left_bracket right_bracket connector

«

»

>

After Assignment

ABC <<XYZ>> XYZ <<XYZ>>

Notice that the assignment tl = t2;

copied into object tl only the fields that FancyText objects have in common with Text objects; that is, the text field. Since tl is a plain Text object, it does not have the left_b racket, right_bracket, and connector fields capable of storing the additional data contained in a FancyText object. This process of losing derived class data when assigning to a base class instance is known as object slicing. The parts that will not fit into the base class instance are “sliced” off. Figure j| 17.1 illustrates object slicing.

Note that the assignment in the other direction:

t2 = tl; // Illegal

is not possible; even though any FancyText object is a Text object, we cannot say any Text object is a FancyText object (it could be a FixedText object or just a Text object without any special decoration). Figure [T7l2| shows how such an attempted assignment would be meaningless because the base class instance has missing information needed by the derived class instance. Failure to properly assign all

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 17.2 Assigning a base class instance to a derived class variable is not possible and is illegal in C++

Text tl("plain"); FancyText t2("Fancy",

tl

text

plain

V

J

t2

text

left_bracket right_bracket connector

>

Before Assignment

the fields in the derived class instance would produce an object that is not well defined, so C++ does not allow the assignment.

Fi xedText class instances do not contain any additional data that plain Text instances do not have, but the assignment rules remain the same:

Table captionText tl( "ABC" );

FixedText

t3;

std:

: cout

<< tl.get() << "

" << t3.get() <<

' \n' ;

tl =

t3;

std:

: cout

<< tl.get() << "

" << t3.get() <<

' \n' ;

Table captionis legal and produces

ABC FIXED FIXED FIXED

but the statement t3 = tl; // Illegal

is illegal and will not compile.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 17.3 The Unified Modeling Language class hierarchy diagram for the family of text classes

It always is legal to assign a derived class instance to a variable of a base type. This is because a derived class instance is a specific kind of base class instance. In contrast, it is not legal to assign a base class instance to a variable of a derived type. This is because the is a relationship is only one directional, from a derived class to its base class.

The Text, FancyText, and FixedText classes form a small class hierarchy. We can represent the relationships in this class hierarchy in a graphical form using the Unified Modeling Language (UML). Figure 117.3| shows the UML diagram for our simple Text class hierarchy.

A rectangle represents a class. Text, the base class, appears at the top of the Figure [17.3} The two derived classes appear below Text. The inheritance arrow points from the derived classes to the base class. The arrow represents the is a relationship which flows upward. This visual layout and level of detail provided by the UML diagram more succinctly communicates the relationships amongst the classes than does the C++ source code.

The UML is a large, complex graphical language that may be used to model many facets of the software development process. More information about the UML is available at http : / /www .uml.org

17.4 Polymorphism

Recall the Text class hierarchy from Listing [TO] (text.h). Listing |~17~4| (fancytext.h), and Listing [T7761 (fixedtext.h) illustrated in Figure [TOj Consider the following client code fragment:

Text tl( "ABC" );

FancyText t2("XYZ",

std::cout << tl.getQ << " " << t2.get() << ' \ n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

What is the nature of the machine code generated by the expression tl. get () ? The compiler translates this higher-level expression into the machine language instmction that causes the program’s execution to jump to another part of the compiled code. Where does the program’s execution jump to? The variable tl’s declared type is T ext, the program’s execution jumps to the compiled Text: : get method (also the address of tl is passed as the implicit this parameter to the method so the compiled code can access tl’s text field).

For the expression t2 . get (), the program’s execution jumps to FancyT ext’s compiled get method, passing the address of object t2 as the implicit this parameter.

When the compiler can determine which method to execute based on the declared type of an object, the process is known as static binding or early binding. Static binding is used in all cases for non-virtual methods and in the cases we have seen so far for virtual methods.

The situation is different if we use pointers to objects instead of the objects themselves. Consider the following code:

Text tl( "ABC" );

FancyText t2("XYZ",

std::cout << tl.getQ << " " << t2.get() << ' \n' ;

Text *pl, *p2; pi = &tl; p2 = &t2;

The variables pi and p2 are declared to be pointers to Text objects. The variable tl is a Text object, so the assignment

pi = &tl;

makes perfect sense. The variable t2 has a declared type of FancyText, but a FancyText object is a Text object, so the assignment

p2 = &t2;

is legal since p2 is indeed pointing to a special kind of Text object.

What does the following code fragment print?

Text tl( "ABC" );

FancyText t2("XYZ",

std::cout << tl.getQ << " " << t2.get() << ' \n' ;

Text *pl, *p2; pi = &tl; p2 = &t2;

std::cout << pl->get() << " " << p2->get() << ' \n' ;

This code displays

ABC <<XYZ>> ABC <<XYZ>>

Even though p2’s declared type is “pointer to a Text object” not “pointer to a FancyText object,” the expression p2->get () calls FancyText: : get, not Text: : get. How does the compiler determine which method to call in this case? The answer may be surprising: The compiler does not determine which method to call!

©2018 Richard L. Halterman

Draft date: September 25, 2018

In the case of a virtual method invoked via a pointer, the running program, not the compiler, determines exactly which code to execute. The process is known as dynamic binding or late binding. Static binding is relatively easy to understand: the method to execute depends on the declared type of the variable upon which the method is invoked. The compiler keeps track of the declared type of every variable, so the choice is easy. Inheritance and the is a relationship make things more complicated. In the example above, p2’s declared type is ’’pointer to Text.” If the compiler were given the authority to select the method to call for the expression p2->get (), its only choice would be Text: : get; however, p2 actually is pointing to a FancyText object. How does the executing program know which code to execute?

We know that every instance of a class contains its own copy of the fields declared within the class. In the code

Text wordl("Wow") , word2( "Wee" );

the wordl object’s text field is the std : : stri ng object representing the string "Wow", and word2’s text field is "Wee". In reality, if a class contains at least one virtual method, all instances of that class will contain one extra “hidden” field, a pointer to an array of virtual method pointers. This array of method pointers commonly is called the vtable. One vtable exists for each class, but all instances of that class must store a pointer to that shared vtable. The compiler assigns an index to each virtual method in a class. In our example, the Text class contains two virtual methods, so the index of get might be 0, and the index of append might be 1.

Figure [IT4| illustrates a typical scenario with vtables. In this case the compiler translates the expression pl->get () into the machine language equivalent of pi ->vtable [0] (), which invokes the correct get method for the instance pointed to by pi. Similarly for the append method, pi->append ("suffix" ) internally becomes pl->vtable [1] ("suffix"). If pi points to a Text instance, pi- >vtable points to the vtable array for the Text class. If pi points instead to a FancyText instance, p 1 ->vtable points to the vtable array of the FancyT ext class. In either case the correct method is selected during the program’s execution.

You may argue that perhaps the compiler could be made to be able to determine in all situations which virtual method to call. In the code from above:

Text tl( "ABC" );

FancyText t2("XYZ",

std::cout << tl.getQ << " " << t2.get() << ' \ n' ;

Text *pl, *p2; pi = &tl; p2 = &t2;

std::cout << pl->get() << " " << p2->get() << '\n' ;

cannot the compiler deduce p2’s exact type since p2 is assigned to point to t2, and it knows t2’s type is FancyText?

Such extended analysis capabilities would further complicate the compiler, and C++ compilers are already very complicated pieces of software. Attempting to add this ability would prove futile anyway because the compiler cannot in general always determine which method to invoke. To see why, consider the following code fragment:

Text *p;

if (std::rand() % 2 == 0) p = new Text("ABC");

else

p = new FancyText("XYZ",

std::cout << p->get() << '\n ' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 17.4 Several objects and their associated vtables. You will not find any evidence in the C++ source code of the dashed pointers and vtables shown in this diagram. When virtual methods are involved the compiler produces executable code that builds these hidden data structures behind the scenes. When a client calls a virtual method via a pointer to an object, the run-time environment locates the exact method to execute by following the vtable pointer stored in the object itself. Observe that since the FixedText class does not override the inherited get method, its vtable references the same get code as that of Text’s vtable.

Text *pl, *p2, *p3, *p4; pi = new Text("ABC"); p2 = new FancyText( "XYZ" , p3 = new FixedText; p4 = new FancyText( "1" ,

©2018 Richard L. Halterman

Draft date: September 25, 2018

This code generates a pseudorandom number at run time. If it generates an even number, it directs p to point to a plain Text object; otherwise, it directs p to point to a FancyText object. Which method will this code call, T ext: : get or FancyT ext: : get? Since the code generates the pseudorandom number at run time, the compiler is powerless to determine the exact type of the object to which p points; thus, the compiler cannot determine which get method to call. The compiler can, however, generate code that jumps to the method found at the address stored in p’s associated vtable at the index corresponding to the get method.

Listing ||17.9| (vtablesize.cpp) demonstrates that the vtable pointer does occupy space within an object that contains a virtual method.

The output of Listing) 17.9|(vtablesize.cpp) is

no_vtable size = 4 has_vtable size = 8

A NoVTable object requires four bytes for its integer field, but a HasVTable object occupies eight bytes—four bytes for its integer field and four bytes for its secret vtable pointer.

Dynamic binding enables a powerful technique in object-oriented programming called polymorphism. A polymorphic method behaves differently depending on the actual type of object upon which it is invoked. Consider Listing! 17. lOl(polymorphicvector.cpp).

Listing 17.10: polymorphi cvector. cpp

ffinclude <string>

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Draft date: September 25, 2018

ffinclude <vector> #include <iostream> #include "fancytext.h" ffinclude "fixedtext.h"

int main() {

std::vector<Text *> texts { new Text("Wow"),

new FancyText( "Wee" , ,

new FixedText,

new FancyText( "Whoa" , };

for (auto t : texts)

std::cout << t->get() << '\n';

for (auto t : texts) { t->append( "A" ); t->append("B") ; t->append( "C" ) ;

}

for (auto t : texts)

std::cout << t->get() << '\n';

for (auto t : texts) delete t;

We know from Section[TTT||that a vector is a collection of homogeneous elements. Homogeneous means the elements in a vector must all be of the same type. Homogeneity takes on a deeper meaning when inheritance and the is a relationship is involved. In Listing 17.10 (polymorphicvector.cpp) the declared type of the texts vector is std : : vector <Text *>. With inheritance, not only can the texts vector hold pointers to simple Text objects, it also simultaneously can hold pointers to FixedText and FancyText objects. Listing||17.10|(polymorphicvector.cpp) prints

Wow

[Wee]

FIXED :Whoa:

WowABC

[Wee-A-B-C]

FIXED

:Whoa:A:B:C:

As we can see, the expression t->get () in the mai n function is polymorphic; the actual get method invoked— Text: : get, FancyText: : get, or FixedText: : get —depends on the exact type of the object to which t points. The append method is polymorphic as well. As t assumes the value of each element in the vector during the loop’s execution, the exact type of object that t points to varies. Even though all the elements of the texts vector are pointers to Text objects, only one of the elements points to a pure Text object; the rest of the elements point to FancyText or Fi xedText objects.

Why must we use pointers to objects rather than the objects themselves to achieve polymorphism? Remember that a pointer stores a memory address (see Section |T077| >. All pointers, no matter what type they point to, are all the same size (4 bytes on 32-bit systems and 8 bytes on 64-bit systems). Text objects and FancyText objects are not the same size (see Figure j 17.1 [ for a conceptual picture); FancyText objects are bigger, containing three extra string fields. All the elements of a vector must be the same size. If we made texts a vector of Text objects rather than a vector of pointers to Text objects, when we assign a FancyT ext object to an element in the texts vector, the assignment would slice the extra fields in the FancyText object. Pointer assignment avoids the slicing problem.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The main reason for using pointers is that C++ uses static binding for all methods (virtual and nonvirtual) invoked on behalf of an object; the compiler chooses the method based on the declared type of the object. In contrast, C++ uses dynamic binding for virtual method calls made via pointers to objects; the exact type of the object determines the method selection.

A polymorphic method in C++ requires four key ingredients:

1. The method must appear in a class that is part of an inheritance hierarchy.

2. The method must declared vi rtual in the base class at the top of the hierarchy.

3. Derived classes override the behavior of the inherited virtual methods as needed.

4. Clients must invoke the method via a pointer (or reference) to an object, not directly through the object itself.

In summary, polymorphism requires inheritance and the is a relationship. The base class defines the method signature, and the derived classes override the method with their own custom behavior.

17.5 Alternative to Inheritance and Polymorphism

Consider would life would be like without inheritance and polymorphism. Listing 17.11 (alttext.h) provides an alternative to the Text class hierarchy.

©2018 Richard L. Halterman

Draft date: September 25, 2018

#endif

Listing 17.12 (alttext.cpp) provides the method implementations for the AltText class.

Listing 17.13 (testalttext.cpp) tests the new AltText class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

for

(auto t :

std::cout

for

(auto& t

t.append(

t.append(

t.append(

}

for

(auto t :

std::cout

texts)

<< t.get() << : texts) { "A");

"B");

"C");

texts)

<< t.get() <<

{TextType: {TextType: {TextType:

' \n' ;

1 \n'

Fancy, "Wee", "[", "]",

Fixed},

Fancy, "Whoa", };

From the user’s perspective Listing p7’.T3| (testalttext.cpp) works exactly like Listing[T7TT0](polymorphicvector.cpp). From the programmer’s perspective, however, the two programs are very different. Listing [177l 3 (testalttext.cpp) packages within a single class all the functionality for the three different classes in Listing 177l0|(polymorphicvector.cpp). This non-polymorphic code differentiates among text objects with the TextType custom enumeration type. Note that each of the methods that were polymorphic in our earlier example now use conditional logic (a swi tch statement) to execute the code appropriate for actual kind of text object we wish to model.

This approach that avoids inheritance and polymorphism has several different issues:

1. Every Text object carries the burdens of every possible kind of text object. A plain text object holds the left bracket, right bracket and separator strings that fancy text objects require. The amount of memory a string occupies depends on its length (number of characters it holds), but even an empty std : st r"i ng object requires some memory. An application managing many mainly plain text objects could be consuming much more memory than it otherwise needs.

2. With inheritance, a developer can introduce a new text type without touching the code in existing text classes. A programmer wishing to introduce a new kind of text object in this example that avoids inheritance must make considerable changes to the code, involving the following:

• augmenting the enumeration type with a new element identifying the new kind of text object,

• adding new fields as may be needed by the new kind of text object, and

• augmenting the swi tch statement in every method that“ was polymorphic in the inheritance version, adding a case label that matches the new kind of text object.

This is not a small point. Modifying existing code can introduce errors. This can cause existing applications that depend on the Text class to fail. With inheritance, programmers add new classes without touching existing code. Pre-existing applications will continue to function as usual because they do not use the new code introduced via inheritance.

3. Without inheritance we need access to the original source code in order to augment the data type. If it is part of a pre-compiled library, we cannot make the necessary modifications. With inheritance, however, we can derive a new class from an existing class even if we do not have access to, or control over, the source code of its implementation.

To illustrate these issues, suppose we wish to add a new kind of text object that bounds the length of the text. Listing ?? (alttext2.h) augments the non-polymorphic Text class.

Listing 17.14: alttext2.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

#ifndef ALT_TEXT2_H_INCLUDED #define ALT_TEXT2_H_INCLUDED

#include <string>

// The kinds of text objects supported (added Bounded) enum class TextType { Plain, Fancy, Fixed, Bounded };

class AltText2 {

TextType type; std::string text; std::string left_bracket; std::string right_bracket; std::string connector;

size_t length_limit; // Maximum number of characters in the text public :

AltText2(TextType type, const std::string& t);

AltText2(TextType type, const std::string& t, const std::string& left, const std::string& right, const std::string& conn);

AltText2(TextType type);

// Constructor for a length-bounded text object

AltText2(TextType type, const std::string& t, size_t limit);

std::string get() const;

void append(const std::string& extra);

};

#endif

We extended the enumeration to include TextType: :Bounded. We added one more field (limit) to the T ext class, which means every T ext object will have a limit field whether they need it or not. We also added one more constructor overload to properly initialize a bounded text object.

Listing 17.14 (alttext2.cpp) implements the methods in the new Text class.

Listing 17.15: name.cpp

ttinclude "alttext2.h"

AltText2::AltText2(TextType type, const std::string& t): type(type), text(t) {}

AltText2::AltText2(TextType type, const std::string& t, const std::string& left const std::string& right, const std::string& conn): type(type), text(t), left_bracket(left), right_bracket(right), connector(conn) {}

AltText2::AltText2(TextType type): type(type), text("FIXED") {}

AltText2::AltText2(TextType type, const std::string& t, size_t limit): type(type) ,

text(t.substr(0, limit)), // Ensure text initially does not exceed bound length_limit(limit) {}

std::string AltText2::get() const { switch (type) {

case TextType::Plain:

©2018 Richard L. Halterman

Draft date: September 25, 2018

case TextType::Fixed: case TextType::Bounded:

return text; case TextType::Fancy:

return left_bracket + text + right_bracket; default :

return "UNKNOWN TYPE";

}

}

void AltText2::append (const std::string& extra) { switch (type) {

case TextType::Plain:

text += extra; // Just concatenate break ;

case TextType::Fancy:

text += connector + extra; // Join with connector break ;

case TextType::Fixed:

break; // Ignore attempt to append

case TextType::Bounded:

// Ensure the length does not exceed the established limit int avail = length_limit - text.length(); text += extra.substr(0, avail); break ;

}

}

Listing 17.16 (testalttext2.cpp) demonstrates that our new bounded text object does indeed limit the length of its enclosed string held.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

for (auto t : texts)

std::cout << t.get() << 1 \n' ;

cpp) displays

Wow

[Wee]

FIXED XYZ :Whoa:

WowABCDEF

[Wee-A-B-C-D-E-F]

FIXED

XYZAB

:Whoa:A:B:C:D:E:F:

Note that even though our new bounded text objects require no special get method, we still must add the case label to match the TextType: : Bounded type. Failure to add this case label would mean every bounded text object would respond with the "UNKNOWN TYPE" string. We definitely must add new code to the append to ensure the concatenation operation does not make bounded text objects too long.

Even if the get and append methods were known to work flawlessly before we introduced this new kind of text object, they now are suspect. Our act of modifying them could have introduced a subtle bug, and so they must be thoroughly retested.

Our non-polymorphic Text class is relatively small, containing only two methods. Consider a more substantial class that provides many more methods. The introduction of a variation of that type could require significant code modification.

Now suppose we do not have access the source code within Listing [17.14 (alttext2.cpp). It may be compiled and part of a library. In this case we cannot modify the Text class to introduce the custom behavior we need.

In contrast to these challenges, consider added a bounded text type to our polymorphic Text class hierarchy. Listing1 17.17|(boundedtext.h) provides the interface for our new class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

void append(const std::string& extra) override;

};

#endif

Listing 17.18 (boundedtext.cpp) implements the BoundedText constmctor and append method.

Listing 17.19 (testbounded.cpp) contains client code to exercise the new BoundedText class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

This BoundedText class addresses all the concerns we have about the non-polymorphic Text class:

1. A pure Text object will have a string field, period. A Fixed text object as well contains only a single string field. A FancyText object will contain four string fields, and each BoundedText object will maintain a string and integer value. Each particular type of text object will contain only the data it requires, not all the data that may be required for any possible kind of text object.

2. This derived class leaves the original code in the base class untouched. We can do nothing in our BoundedText class code to damage the Text, FancyText, or Fi xedText classes.

3. We can compile the code within Listing ! 17.17| (boundedtext.h) an d Listing [17.18| (boundedtext.cpp) and build an executable program using BoundedText objects without access to the source code in Listing 11773] (text.cpp). All we need is the header file Listing (T7.2|| (text, h) that specifies the interface of the Text class. This header must be available to any clients that wish to use a Text object, but the source code for the implementation of the Text class is not needed to compile client code that uses Text objects. The linker would need the compiled Listing [T7.3| (text.cpp) in order to link and produce an executable program, but at no point in the build process is the source code in Listing [T73] (text.cpp) necessary if its compiled code is available.

The inheritance with polymorphism approach is more modular; that is, if our BoundedText code does not work or is not as efficient as it could be, we or someone else easily can supply a different version to compile and link into an application. This modularity enables multiple programmers to work independently implementing separate classes without interfering with each other.

17.6 Adapter Design Pattern

Suppose a third-party library provides a class named Message that is similar to the classes in our Text hierarchy in Listing 17.10 (polymorphicvector.cpp). A Message object contains a pri vate piece of text and a method named text that reveals the text that it holds. The following code fragment:

Message msg("My message"); std::cout << msg.text() << ' \n' ;

would print

My message

In addition to revealing its contained text, each time a client calls a Message object’s text method the object records the access. A Message object thus keeps track of the number of times clients have called its text method. The Message class provides a method named access_count that returns the number

of text calls. The following code:

Message msg("My message

std:

: cout

<<

msg.text()

<<

' \n'

std:

: cout

<<

msg.text()

<<

' \n'

std:

: cout

<<

msg.text()

<<

' \n'

std:

: cout

<<

msg.access.

_count()

Table caption<< '\n'

Table captionwould print

©2018 Richard L. Halterman

Draft date: September 25, 2018

My message My message My message 3

We cannot modify the class Message, either because we do not have the source code to this library, or its license prohibits modifying or reverse engineering its code. This means we have no control over the Message class or how it works.

What if would like to maintain a collection of Text and Message objects, storing them all in a single vector? Is this possible? All of the elements in a particular C++ vector must all be of the same type. The Message class is not part of the Text class hierarchy, so no is a relationship exists between the two classes. Let us experiment with two possible solutions to this problem.

Make a copy of a Message object. We could try to simply copy the contents of a Message object to a Text object and put this new Text object into the vector. The following code illustrates:

// get_message is a function that provides a Message object Message msg = get_message();

// Put the text inside msg into a new Text object Text txt(msg.text()) ;

// Insert a pointer to the text object into vector

std::vector<Text *> texts;

texts.push_back(&txt);

std::cout << texts[0]->get() << '\n' ;

std::cout << texts[0]->get() << '\n' ;

std::cout << msg.access_count() << '\n' ;

The last line this code fragment prints is

1

We would rather it printed 2

because Text: :get is analogous to Message: :text, and the code calls the text method twice. Unfortunately as you may have noticed, the code calls text only once, when creating the txt object from the msg object. It is this single call that makes the access count become one. The subsequent calls to get are on a Text object, not a Message object. This means we really do not have a Message object in our vector, so none of the objects in our vector can take advantage of the services that a Message object provides.

Use inheritance and polymorphism to encapsulate Message objects within Text objects. We can

derive a new Text class in a clever way to allow us to place Message objects into a vector of Text objects. Consider the following new class:

class MessageText: public Text {

Message *msg; public :

MessageText(Message *m) : Text(""), msg(m) {} std::string get() const override { return msg->text();

}

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Draft date: September 25, 2018

};

Instances of this MessageText class wrap a pointer to a Message object. The constructor does not call the wrapped Message object’s text method, so making a MessageText object from a Message object does not artificially elevate the access count for the Message object. Further, any call to a MessageT ext object’s get method actually calls the text method of the Message object it is managing. The following code:

// get_message is a function that provides a Message object Message msg = get_message();

// Put the text inside msg into a new Text object //Text txt(msg.textQ) ;

MessageText txt(&msg);

// Insert a pointer to the text object into vector std::vector<Text *> texts; texts.push_back(&txt);

std:

: cout

<<

texts[0]->get() <<

' \n' ;

std:

: cout

<<

texts[0]->get() <<

' \n' ;

std:

: cout

<<

msg.access_count()

<< ' \n

Table captionbehaves exactly as desired, reporting

2

as the last line of its output. This proves that we really did sneak a Message object into our vector of Text objects.

This technique of adapting the interface of one class to that of another class has a name: the adapter design pattern. The adapter design pattern is useful when you have a class with properties similar to another class but with incompatible interfaces. You can use this technique of inheritance and polymorphism to derive a new class with the desired interface

Suppose you have class X and class Y that describe objects with similar functionality but different interfaces (different methods), and you need to treat a Y object as if it were an X object. You may be able to use the adapter design pattern as follows:

1. Derive a new class, Z, from X.

2. Store a pointer to the Y object in an instance of class Z.

3. Override methods in class Z to invoke the corresponding Y methods on the enclosed Y object.

17.7 Protected Members

As a more practical, yet still relatively simple example, suppose we need to model two-dimensional shape objects, such as rectangles, squares, triangles, ellipses, and circles. Our application will determine how to

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 17.5 Packing Two-dimensional Shapes into a Two-dimensional Container

pack parts into a containing area, so it is important to be able to determine an individual shape object’s area. Figure |[17.5|| illustrates packing some two-dimensional shapes into a two-dimensional container.

We thus want to determine the minimum area of the container that can hold a given collection of parts. A real-world application could be computing the size of the smallest circuit board that can hold a collection of electronic components. Our program will be much simpler and give us only a rough approximation; it does not take into account the geometry and orientation of the individual shapes but merely computes the total area of the components. The actual answer generally will be larger than the result computed by our program.

An interesting problem arises if a method in a derived class needs to use an inherited variable. If the variable is declared pri vate in the base class, a derived class method cannot access it. The pri vate specifier means “not available outside the class, period.” We know it is unwise in general to make instance variables public, since that breaks encapsulation. Since encapsulation is a desirable property, C++ provides a third level of access protection within a class— protected. A protected member, whether it be data or a method, is inaccessible to all code outside the class, except for code within a derived class. The use of protected is illustrated in the shapes code.

We begin by defining the base class for all shape objects: Shape. Listing 17.20 (shape.h) provides the code for Shape.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The “assignment to zero” of the two virtual methods in the Shape class make them special; they are called pure virtual methods or pure virtual functions. This special syntax signifies that these methods have no implementations. It is not possible to provide a body for these methods. A class that contains at least one pure virtual method is an abstract class. It is not possible to create an instance of an abstract class. The compiler enforces this restriction; the following statement;

Shape myShape; // Illegal

is illegal. A non-abstract class is called a concrete class. All the classes we have seen to this point except for Shape have been concrete classes.

An abstract class represents an abstract concept. Shape is an abstract concept. We can have circles, rectangles, and lots of other kinds of shapes, but can we have something that is “just a shape” without being a particular kind of shape? Even though we cannot create instances of abstract classes, abstract classes are useful for organizing a class hierarchy.

We can derive a concrete class from our Shape class as shown in Listing 17.21 (rectangle. h).

©2018 Richard L. Halterman

Draft date: September 25, 2018

#endif

Note the appearance of the protected access specifier. The methods in any class derived directly or indirectly from Rectangle will be able to access the length and wi dth fields. These fields will be inaccessible to code outside these classes. Listing [17.22[ (rectangle.cpp) provides the implementation of Rectangle’s methods.

From mathematics we know that a square is a special kind of rectangle, so Li sting [T7T23 1 ( square.h) and Listing [TL24| (square. cpp) specify a Square class.

Listing 17.24: square.cpp

// File square.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

ftinclude "square.h"

Table caption// Defer the work of initialization to the base class constructor Square::Square (double side): Rectangle(side, side) {}

Next, we add a triangle shape (Listing

17.25

(triangle.h) and Listing

17.26

1

(triangle.cpp)).

Listing 17.25: triangle.h

#ifndef TRIANGLE_H #define TRIANGLE_H

#include "shape.h"

class Triangle: public Shape { protected :

double sidel; // Triangles have three sides double side2; double side3; public :

Triangle (double si, double s2, double s3); double span() const override; double area() const override;

#endif

An ellipse is a simple curved shape that we can add to our class hierarchy. Listing [l7.27|| (ellipse.h) and Listing|ll7.28[(ellipse.cpp) define the ellipse class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table caption17.7. PROTECTED MEMBERS

Table caption527

Listing 17.27: elli pse. h

#ifndef ELLIPSE_H_

#define ELLIPSE_H_

ftinclude "shape, h"

class Ellipse: public Shape { protected :

double major_radius; // The double minor_radius; // The

public :

Ellipse (double major, double double span() const override; double area() const override;

};

longer radius of the ellipse shorter radius of the ellipse

mi nor);

#endif

A circle is just an ellipse with equal major and minor radii. Listing 17.29 (circle.h) and Listing 17.30 (circle.cpp) define the Ci rcle class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 17.6 Inheritance hierarchy of shape classes

// A circle is a special case of an ellipse

class Circle: public Ellipse { public :

// In a circle the major and minor radii are the same, so // we need specify only one value when creating a circle. Circle (double radius);

// Inherited methods work as is, no need to change their // behavior.

};

#endif

These shape classes form the class hierachy shown in Figure j 776.

Listing 17.31: testshapes. cpp

// File testshapes.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <iostream> #include <vector>

#include "rectangle.h" #include "triangle.h" #include "circle.h" #include "ellipse.h"

int main() {

Rectangle rect(3, 4);

Circle circ(4.5);

Triangle tri(3, 4, 5);

Ellipse elli (3, 4);

std::vector<Shape *> shape_list;

shape_list.push_back(&circ); shape_list.push_back(&tri); shape_list.push_back(&rect); shape_list.push_back(&elli);

int n = shape_list.size();

double area_total = 0.0, max_span = 0.0;

for (int i =0; i <n; i++) {

// Examine the area each shape

std::cout << "Area = " << shape_list[i]->area() << '\n'; // Accumulate the areas of all the shapes area_total += shape_list[i]->area() ;

// Account for the longest object if (max_span < shape_list[i]->span()) max_span = shape_list[i]->span();

}

// Report the total area of all the shapes combined

std::cout << "Total shape area is " << area_total << '\n';

// Report the minimum length of the container std::cout << "Longest shape is " << max_span << '\n';

Observe that neither Square nor Ci rcle needed access to the protected fields of their base classes. Consider Listing 17.32 (drawablerectangle.cpp) that derives a new class from Rectangle to allow clients to draw rectangle objects in a console window using text graphics.

Listing 17.32: drawablerectangle.cpp

#include <iostream>

#include "rectangle.h"

class DrawableRectangle: public Rectangle { public :

// Delegate construction to the base class

DrawableRectangle (double length, double width): Rectangle(length, width) {}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Draw a rectangle using text graphics void draw() const {

// Access the inherited protected fields int rows = static_cast<i nt> (length + 0.5), columns = static_cast<int> (width + 0.5); // Draw the rectangle for (int r = 0; r < rows; r++) {

for (int c = 0; c < columns; C++) std::cout << 1 # ' ; std :: cout << 1 \n ' ;

}

}

};

int main() {

DrawableRectangle recl(3, 2), rec2(10, 5), rec3 (4 , 8) ;

reel.

.draw();

std: :

:cout << "

- \n";

rec2.

.draw();

std: :

:cout << "

- \n";

rec3.

.draw();

.cpp) displays

##

##

##

#####

#####

#####

#####

#####

#####

#####

#####

#####

#####

########

########

########

########

The DrawableRectangle: : draw method needs access to the fields length and wi dth to be able to draw the rectangle. It is important to remember that every DrawableRectangle object contains these fields because it inherits them from Rectangle; however, if the length and wi dth fields were declared private instead of protected in Rectangle, DrawableRectangle: : d raw would not be able to access these fields.

©2018 Richard L. Halterman

Draft date: September 25, 2018

A class supports three levels of protection for its members:

1. private: This is the default. Private members are accessible to any code within the class itself but are inaccessible to code outside of the class.

2. protected: Protected members are accessible to code within the class itself and to code within derived classes that use public inheritance. Protected members are inaccessible to other (non-derived) classes.

3. public: Public members are accessible to code anywhere.

In sum, private means not accessible outside the class, period. Public means open to everyone. Protected means “public” to subclasses and “private” to all other classes.

17.8 Fine Tuning Inheritance

Recall the flexible sorting code found in Listing|T53j(loggingflexiblesort.cpp). It uses objects to enable the following functionality:

• The ordering imposed by a selection sort function can be varied by using custom comparison functions.

• The object used to determine the sort’s ordering collects data about the number of comparisons and element interchanges the sort function performs.

Listing [17.35| (polymorphicsort.cpp) provides a slight variation of Listing |16.5|[ (loggingflexiblesort.cpp). Besides splitting the code up into multiple source files, it adds two virtual methods that enable future developers to customize the compare and swap methods in derived classes.

Listing 17.33 (comparer.h) contains the declaration of the Comparer class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Function pointer directed to the function to // perform the comparison bool (*comp)(int, int);

protected :

// Method that actually performs the comparison // Derived classes may customize this method virtual bool compare_impl (i nt m, int n);

// Method that actually performs the swap // Derived classes may customize this method virtual void swap_impl (i nt& m, int& n);

public :

// The client must initialize a Comparer object with a // suitable comparison function.

Comparer (bool (*f)(int, int));

// Resets the counters to make ready for a new sort void reset() ;

// Method that performs the comparison. It delegates // the actual work to the function pointed to by comp. // This method logs each invocation, bool compare(int m, int n);

// Method that performs the swap.

// Interchange the values of // its parameters a and b which are // passed by reference.

// This method logs each invocation, void swap(int& m, int& n);

// Returns the number of comparisons this object has // performed since it was created, int comparisons() const;

// Returns the number of swaps this object has // performed since it was created, int swaps() const;

};

#endif

Listing 117.34 |(comparer.cpp) provides the implementation of the Comparer class methods.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Method that actually performs the swap // Derived classes may customize this method

void Comparer::swap_impl (i nt& m, int& n) { int temp = m; m = n; n = temp;

}

// The client must initialize a Comparer object with a // suitable comparison function.

Comparer::Comparer (bool (*f)(int, int)):

compare_count(0), swap_count(0), comp(f) {}

// Resets the counters to make ready for a new sort

void Comparer::reset() {

compare_count = swap_count = 0;

}

// Method that performs the comparison. It delegates // the actual work to the function pointed to by comp. // This method logs each invocation, bool Comparer::compare (i nt m, int n) { compare_count++; return compare_impl(m, n);

}

// Method that performs the swap.

// Interchange the values of // its parameters a and b which are // passed by reference.

// This method logs each invocation, void Comparer::swap (int& m, int& n) { swap_count++; swap_impl(m, n);

}

// Returns the number of comparisons this object has // performed since it was created.

int Comparer::comparisons() const { return compare_count;

}

// Returns the number of swaps this object has // performed since it was created, int Comparer::swaps() const { return swap_count;

}

Notice that even though the vi rtual keyword appears before the method declarations in comparer.h, it does not appear before the method implementations in comparer.cpp.

Listing [r7T35j (polymorphicsort.cpp) provides the client code that tests the new Comparer class.

Listing 17.35: polymorphicsort.cpp

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <iostream>

#include <vector>

#include "comparer.h"

/*

* select!on_sort(a, compare)

* Arranges the elements of vector a in an order determined

* by the compare object.

* a is a vector of ints.

* compare is a function that compares the ordering of

* two integers.

* The contents of a are physically rearranged.

*/

void selection_sort(std:: vector<int>& a, Comparer& compare) { int n = a.size();

for (int i = 0; i < n - 1; i++){

// Note: i,small, and j represent positions within a // a[i], a[small], and a[j] represents the elements at // those positions.

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less // than a[i] int small = i;

// See if a smaller value can be found later in the array for (int j = i + 1; j < n; j++)

if (compare.compare(a[j], a[small]))

small = j; // Found a smaller value // Swap a[i] and a[small], if a smaller value was found if (i != small)

compare.swap(a[i], a[small]);

}

}

/*

* print

* Prints the contents of an integer vector

* a is the vector to print.

* a is not modified.

*/

void print(const std::vector <i nt>& a) { int n = a.size(); std::cout << '{' ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a[i]; // Print the rest

}

std::cout << 1 } 1 ;

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

©2018 Richard L. Halterman

Draft date: September 25, 2018

bool less_than (i nt a, int b) { return a < b;

}

/*

* greater_than(a, b)

* Returns true if a > b; otherwise, returns

* false.

*/

bool greater_than (i nt a, int b) { return a > b;

}

int main() {

// Hake a vector of integers

std::vector<i nt> original { 23, -3, 4, 215, 0, -3, 2, 23, 100, 88, -10 };

}

// Hake a working copy of the original vector

std::vector<i nt> working = original; std::cout << "Before: print(working); std::cout << 1 \n 1 ;

Comparer It(less_than), gt(greater_than); selection_sort(working, It); std::cout << "Ascending: "; print(working);

std::cout << " (" << It.comparisons() << " comparisons, "

<< It.swapsQ << " swaps)\n";

std: : cout << "-\n" ;

// Hake another copy of the original vector

working = original;

std::cout << "Before: ";

print(working);

std::cout << 1 \n 1 ;

selection_sort(working, gt);

std::cout << "Descending: ";

print(working);

std::cout << " (" << gt.comparisons() << " comparisons, "

<< gt.swapsQ << " swaps)\n";

std: : cout << "-\n" ;

// Sort a sorted vector std::cout << "Before: ";

print(working); std::cout << 1 \n 1 ;

// Reset the greater than comparer so we start counting at // zero gt.reset();

selection_sort(working, gt); std::cout << "Descending: "; print(working);

std::cout << " (" << gt.comparisons() << " comparisons, "

<< gt.swapsQ << " swaps)\n";

©2018 Richard L. Halterman

Draft date: September 25, 2018

The functions in Listing |T7T35| (polymorphicsort.cpp) are identical to the functions in Listing|T675](loggingflexiblesort.cpp), and, not surprisingly, the output of Listing |l7T35( (polymorphicsort.cpp) is identical to the output of Listingjl6T5||(loggingflexiblesort.cpp):

Before:

{23,-3,4,215,0,-3,2,23,100,88,-10}

Ascending:

{-10,-3,-3,0,2,4,23,23,88,100,215}

(55

comparisons,

7

swaps)

Before:

{23,-3,4,215,0,-3,2,23,100,88,-10}

Descending

: {215,100,88,23,23,4,2,0,-3,-3,-10}

(55

comparisons,

5

swaps)

Before:

{215,100,88,23,23,4,2,0,-3,-3,-10}

Descend!ng

: {215,100,88,23,23,4,2,0,-3,-3,-10}

(55

comparisons,

0

swaps)

The question arises: What advantage does the new Compa re r class have over the original one?

The design of this new Comparer class is interesting:

• Since its counter fields are private, only methods in the Compa r e r class itself can access aComparer object’s data.

• The two virtual methods, compa re_i mpl and swap.! mpl, are protected, so clients cannot access them directly. Derived classes, however, can see them and override them. The suffix _ i m p l stands for “implementation,” so compare.i mpl represents the implementation details of the compare method and swap.! mpl represents the implementation details of the swap method.

• The public compare and swap methods both delegate part of their work to the protected compa re_i mpl and swap.impl methods.

• The compare and swap methods are not declared vi rtual, so derived classes cannot override them.

• The compare and swap methods manage the compa re_count and swap_count counter fields.

Since derived classes cannot see these fields, there is nothing that a designer of a derived class can do when overriding compa re_i mpl or swap.i mpl to disturb the correct accounting of the number of times a client calls compare or swap.

• The comparisons and swaps methods that report the results to the client are non-virtual, so derived classes may not override their behavior.

Observe that the designer of the Compa r e r class allows the nature of the comparisons and swaps in derived classes to be flexible, but it is rigid on the enforcement of how the accounting is performed and reported. The proper use of protected and pri vate specifiers in a base class as shown in Comparer affords class designers a great deal of control over exactly what derived class designers can do. Derived classes may adapt some behaviors, but other behaviors are non-negotiable.

What kind of customization would a programmer want to do to the Comparer class beyond changing how the comparison is performed? Consider the LogComparer class declared in Listing [I73 6| (logcomparer.h).

Listing 17.36: logcomparer.h

#ifndef LOGCOMPARER.H #define LOGCOMPARER.H

ffinclude <fstream>

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <string>

#include "comparer.h"

/*

* Comparer objects manage the comparisons and element

* interchanges on the selection sort function below.

*/

class LogComparer: public Comparer {

// Output stream to which logging messages are directed std::ofstream fout;

protected :

// Method that actually performs the comparison bool compare_impl(int m, int n) override;

// Method that actually performs the swap void swap_impl(int& m, int& n) override;

public :

// The client must initialize a LogComparer object with a // suitable comparison function and the file name of a text // file to which the object will direct logging messages LogComparer (bool (*f)(int, int), const std::string& filename);

// The destructor must close the log file ^LogComparer();

};

#endif

The LogComparer class overrides the compare_impl and swap_impl methods. Instances of the LogCompa rer class use a std : : ofstream object to record logging information to a text file.

The implementation of the LogCompa rer methods can be found in Listing 17.37 (logcomparer.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

// The client must initialize a LogComparer object with a // suitable comparison function and the file name of the // text file to receive logging messages.

LogComparer::LogComparer (bool (*f)(int, int), const std::string& filename): Comparer(f) { fout.open(filename); if (!fout.good()) {

std::cout << "Could not open log file " << filename << " for writing\n"; exit(l); // Terminate the program

}

// fout is an instance variable, not a local variable,

// so the file stays open when the constructor finishes

}

The constructor attempts to open a file output stream to write logging information to a text file. If the constructor cannot for any reason open the text file for writing, it terminates the program’s execution. The destructor closes the file stream object when the LogComparer object’s life is over.

The two overridden methods, compare_impl and swap_impl, write text to the log file. Both methods use the LogComparer object’s fout field rather than the std : : cout console output stream object.

Notice that even though the override keyword appears after the method declarations in logcomparer.h, it does not appear after the method implementations in logcomparer.cpp.

The client code in Listing ] 17.38 (loggingsort.cpp) uses a LogComparer object to create a text file named sort.log.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// See if a smaller value can be found later in the array for (int j = i + 1; j < n; j++)

if (compare.compare(a [j] , a[small]))

small = j; // Found a smaller value // Swap a[i] and a[small], if a smaller value was found if (i != small)

compare.swap(a[i], a[small]);

}

}

/*

* print

* Prints the contents of an integer vector

* a is the vector to print.

* a is not modified.

*/

void print(const std::vector <i nt>& a) { int n = a.size(); std::cout << ' { ' ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a [ i]; // Print the rest

}

std::cout << ' } ' ;

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

bool less_than (i nt a, int b) { return a < b;

}

int main() {

// Make a vector of integers from an array

int a[] = { 23, -3, 4, 215, 0, -3, 2 }; int len = (sizeof a)/(sizeof a[0]); std::vector<i nt> vec(a, a + len);

}

// Make a working copy of the original vector

std::cout << "Before: ";

print(vec);

std::cout << 1 \n 1 ;

LogComparer It(less_than, "sort.log"); selection_sort(vec, It); std::cout << "Ascending: "; print(vec);

std::cout << " (" << It.comparisons() << " comparisons,

<< It.swapsQ << " swaps)\n";

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing[17738] (loggingsort.cpp) prints to the console

Before: {23,-3,4,215,0,-3,2}

Ascending: {-3,-3,0,2,4,23,215} (21 comparisons, 4 swaps)

and writes the file sort.log the text

Comparing -3 to 23 Comparing 4 to -3 Comparing 215 to -3 Comparing 0 to -3 Comparing -3 to -3 Comparing 2 to -3 Swapping 23 and -3 Comparing 4 to 23 Comparing 215 to 4 Comparing 0 to 4 Comparing -3 to 0 Comparing 2 to -3 Swapping 23 and -3 Comparing 215 to 4 Comparing 0 to 4 Comparing 23 to 0 Comparing 2 to 0 Swapping 4 and 0 Comparing 4 to 215 Comparing 23 to 4 Comparing 2 to 4 Swapping 215 and 2 Comparing 23 to 4 Comparing 215 to 4 Comparing 215 to 23

If during development the selection sort function has a problem, the programmer can review the contents of the log file to examine how the sort progresses and perhaps determine where the problem lies.

The design of the Compa r e r class provides a overall structure that allows inheriting classes to fine tune the details without disturbing the overarching framework. Inheritance and polymorphism allow us to add functionality to an existing code base. Virtual methods provide extension points by which derived classes can add custom behavior.

17.9 Exercises

1. Consider the following C++ code:

class Widget { public :

virtual int f() { return 1; }

};

©2018 Richard L. Halterman

Draft date: September 25, 2018

class Gadget: public Widget { public :

virtual int f() { return 2; }

};

class Gizmo: public Widget { public :

virtual int f() { return 3; }

};

void do_it(Widget *w) {

std::cout << w->f() << "

}

int mainQ {

std::vector<Widget *> widgets;

Widget wid;

Gadget gad;

Gizmo giz;

widgets.push_back(&wid); widgets.push_back(&gad); widgets.push_back(&giz);

for (size_t i = 0; i < widgets.size(); i++) do_it(widgets[i]);

}

(a) What does the program print?

(b) Would the program still compile and run if the f method within the Widget class were a pure virtual function?

(c) How would the program run differently if the vi rtual keyword were removed from all the code?

(d) Would the program behave the same if the vi rtual keyword were removed from all the classes except for Wi dget?

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 18

Memory Management

1111111111 CAUTION! CHAPTER UNDER CONSTRUCTION 1111111111

The C++ programming language provides many options to programmers when it comes to managing the memory used by an executing program. This chapter explores some of these frequently used options and introduces modem techniques aimed at reducing the memory management problems that have plagued C++ projects in the past.

18.1 Memory Available to C++ Programs

A modern operating system reserves a section of memory for an executing program. This allows the operating system to manage multiple program executions simultaneously. Different operating systems layout the memory of executing programs in different ways, but the layout will include the following four sections:

• Code. The code section of memory holds the program’s compiled executable instructions. The contents of the code section should never change while the program executes, and the size of the code segment does not change during the program’s execution.

Data. The data section of memory contains global variables (see Section [l0.1| and persistent local variables (stati c locals, see Section 10.2). The variables in the data section exist for the life of the executing program, but, unless they are constants (see Section |3.6) , the executing program may freely change their values. Even though the values stored in the variables found in the data segment may change during the program’s execution, the size of the data segment does not change while the program executes. This is because the program’s source code precisely defines the number of global and stati c local variables. The compiler can compute the exact size of the data segment.

• Heap. The heap is where an executing program obtains dynamic memory. The new operator gets its memory from the heap, and delete returns previously allocated memory back to the heap. The size of the heap grows and shrinks during the program’s execution as the program allocates and deallocates dynamic memory using new and delete.

• Stack. The stack is where local variables and function parameters live. Space for local variables and parameters appears when a function is called and disappears when the function returns. The size of the stack grows and shrinks during the program’s execution as various functions execute.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Operating systems generally limit the size of the stack. Deep recursion can consume a considerable amount of stack space. An improperly written recursive function, for example one that omits the base case and thus exhibits “infinite” recursion, will consume all the space available on the stack. Such a situation is known as a stack overflow. Modern operating systems will terminate a process that consumes all of its stack space, but on some embedded systems this stack overflow may go undetected. Heap space typically is much more plentiful, and operating systems can use virtual memory to provide a executing program more space than is available in real memory. The extra space for virtual memory comes from a disk drive, and the operating system shuttles data from disk to real memory as needed by the executing program. Programs that use a lot of virtual memory run much slower than programs that use little virtual memory. Virtual memory is not unlimited, however, so a program with memory leaks eventually can run out of memory.

Because of the way function and method calls and their subsequent returns work, the stack grows and shrinks in a very regular fashion. It expands during a function call to make room for the executing function’s local variables and parameters (and it expands even more if that function calls other functions), and when the function returns, the stack contracts back to the original size it had before the function invocation. Variables are removed from the stack in the reverse order of their creation on the stack. The stack always consists of one contiguous chunk of memory with no areas of unused space within that chunk.

The heap grows and shrinks as the program executes new and delete, but its expansion and contraction is not regular. One function may allocate an object or dynamic array with new, and a different function may much later in the program’s execution deallocate the object or array with delete. An executing program may delete dynamically allocated memory in a very different order from its allocation. This means that memory allocated on the heap is not contiguous; that is, space for deallocated objects can be interspersed with space for allocated objects. The the available memory on the heap thus can become fragmented during the program’s execution.

Global variables and static local variables in the data segment live for the life of the executing program. The run-time environment initializes globals before main begins executing and cleans them up when mai n returns. The run-time environment initializes static locals during the function’s or method’s first invocation. Non-static local variables on the stack exist only when a function is executing. If a program calls and returns from the same function 20 times, that function’s local variables appear and disappear 20 times. An executing program can create dynamic memory as needed, hold onto it as long as necessary, and finally release it when it is no longer needed.

The quantity of global data is fixed when the program begins executing, and stack data is not persistent for the life of the executing program. This means an executing program that must manage a varying amount of data for an arbitrary amount of time must use the heap as a source of memory for that data. The runtime environment automatically manages global and local memory. Unfortunately, programmers must write code that manually manages heap data. The problem is this: Manual memory management in all but very simple systems turns out to be a difficult task. Development of large software systems with C++ in the early days often was a frustrating experience.

18.2 Manual Memory Management

Memory management issues with new and delete frequently are the source of difficult to find and fix logic errors. Programmers must adhere strictly to the following tenets:

• Every call to new should have an associated call to delete when the allocated memory is no longer needed. It sounds simple enough, but it is not always clear when delete should be used. The following function exhibits a memory leak:

void calc(int n) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.1 Memory leak

1. Before the call to calc, variable p does not exist

2. During the execution of calc, variable p is alive and points to dynamically allocated memory

0 12 3 4

3. After calc returns, variable p goes away, but the memory allocated on its behalf remains

// ...

// Do some stuff

// ...

int *p = new int [n];

// ...

// Do some stuff with p

// ...

// Exit function without deleting p's memory

}

If a program calls function calc enough times, the program will eventually run out of memory. Figure fl8Tlj shows how memory is stranded when local pointers go out of scope at the end of a function’s execution.

In the calc function p is a local variable. As such, p lives on the stack. When a particular call to calc completes, the function’s clean up code automatically releases the space help by the variable p. This is because all functions automatically manage the memory for their parameters and local variables. The problem is p is assigned via new to point to memory allocated from the heap, not the stack. Function executions manage the stack memory only. When the function’s execution completes, p is gone, and the memory to which p pointed is not deallocated automatically. Worse yet, the heap memory formerly referenced by the local variable p now is unreachable because no other variables that remain viable know anything about it.

A correctly written calc function has three options in this case:

1. free up p’s allocated memory with delete before returning,

2. assign a global or stati c local pointer to the allocated memory, or

©2018 Richard L. Halterman

Draft date: September 25, 2018

3. return p to the function’s caller and let the caller call delete when finished with the object calc created.

Option 1 is the easiest solution. The calc function needs a dynamically allocated array, creates it, uses it, and then deallocates it before returning. Within this single function definition we can see a new and later its corresponding delete — a perfect matched pair. Unfortunately, this is not a common case. If calc needs local working space, it is best handled on the stack through local variables. That way memory clean up is automatic.

Option 2 is possible only if callers invoke the calc function exactly once and, additionally in the case of a global pointer, invoke calc before attempting to use the global pointer.

Option[3]is the more common occurrence. The heap enables an executing program to add extra data at run time that persists across function calls. In theory the process is simple:

1. call calc to obtain a dynamically allocated object and

2. delete the object when finished with it.

The problem here is we cannot see the new paired with the delete. The new is hidden in calc, and the caller must exercise delete.

• The delete operator never should be used to free up memory that was not allocated by a previous call to new. This code fragment illustrates one such example:

int list[10], *p = list; // p points to list

// ...

// Do some stuff

// ...

delete [] p; // Logic error, attempt to deallocate p's memory

The space referenced by pointer p was not allocated by new, so delete should not be used to attempt to free up its memory.

Attempting to delete memory not allocated with new results in undefined behavior and represents a logic error.

• delete must not be used to deallocate the same memory more than once. This can happen when two pointers refer to the same memory. Such pointers are called aliases. The following code fragment illustrates the situation:

int *p = new int[10], *q = p; // q aliases p // •••

// Do some stuff with p and/or q

// ...

delete [] p; // Free up p's memory

// •••

// Do some other stuff

// ...

delete [] q; // Logic error, q's memory already freed!

Since pointer p and pointer q point to the same memory, they are aliases of each other. Deallocate the memory referenced by one of them, and the other’s memory is also deallocated, since it is the same memory.

Multiple deletes of the same memory results in undefined behavior and represents a logic error.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• Memory previously deallocated via delete should never be accessed. Attempting to access deleted memory results in undefined behavior and represents a logic error. The code fragment

int *list = new int[10];

// •••

// Use list, then

// ...

delete [] list; // Deallocate list's memory

// ...

// Sometime later

// ...

int x = list[2]; // Logic error, but sometimes works!

illustrates how such a situation can arise. For efficiency reasons the delete operator generally marks heap space as “available” without modifying the contents of that memory. Careless programmers can accidentally use the memory of a deleted pointer obliviously as if it were still live. The problem manifests itself when the freed up memory eventually gets reallocated elsewhere via a call to new. The result is that programs seem to “work” for a while and mysteriously fail at unpredictable times. Debugging such situations can be very difficult. The problem often happens because of aliasing:

int *list = new int [10];

// ...

int *arr = list; // arr aliases list

// ...

delete [] list; // Deallocate list's memory

// ...

// Sometime later

// ...

int x = arr[2]; // Same problem!

We deleted list’s memory, not arr’s memory, didn’t we? No, since arr is an alias for list, arr references memory previously deallocated with delete.

Aliasing is a problem because of our concept of variables. When we have two variables with different names it is natural to assume they represent two different objects. This is known as value semantics. Pointers and references introduce the possibility of aliasing; they use reference semantics. Reference semantics enable useful techniques such as call-by-reference and the traversal of dynamic data structures like linked lists, but reasoning about the identity of objects using reference semantics requires extra caution.

It seems simple enough to make sure every new has exactly one corresponding delete, but in practice it can be very difficult to determine exactly when to use delete. Suppose, for example, you obtain a dynamically allocated object from a function call, as in the following:

Widget *p = get_widget();

Quite possibly the get_wi dget function allocates a Wi dget object via new and simply returns a pointer to the object. In this case we can use

delete p;

when we are finished using the object to which p points. What if, however, the get_wi dget function is managing shared resources; that is, if get_wi dget already has created a Wi dget object with a particular

©2018 Richard L. Halterman

Draft date: September 25, 2018

value, it does not create a new Wi dget object. Instead it returns a pointer to the existing object it previously created. Listing118.1 (howtodelete.cpp) provides a rudimentary example.

Listing |18.1|| (howtodelete.cpp) prints

Entering main Creating node 23 Creating node 45 Creating node 16 Creating node 12 Creating node 3 Creating node 20 Creating node 10 Destroying node 45 Destroying node 16 Destroying node 12

©2018 Richard L. Halterman

Draft date: September 25, 2018

Destroying node 3 Destroying node 20 Destroying node 10 Destroying node 23 Destroying node 45 Destroying node 16 Destroying node 12 Leaving main

Observe widgets 45, 16, and 12 being destroyed twice. On some systems the program crashes before printing Leaving main. Double deletion is classified as undefined behavior, so it represents a bug in our program.

Before returning from process, how can you traverse the vector releasing the dynamically allocated memory and ensuring that you do not delete the same object more than once? The answer is that you cannot easily do so. Even if you are careful and account for each allocation of Widget objects of a particular value, you really do not know if the program elsewhere earlier called get_widget() and stored the result in a global variable that outlives this call to process. You would need to implement within your code a complex global accounting infrastructure that keeps track of all memory allocations.

18.3 Linked Lists

An object in C++ can hold just about any type of data, but there are some limitations. Consider the following struct definition:

struct Node { int data;

Node next; // Error, illegal self reference

};

(Here we use a struct instead of a class since we will consider a Node object a primitive data type that requires no special protection from clients.) How much space should the compiler set aside for a Node object? A Node contains an integer and a Node, but this contained Node field itself would contain an integer and a Node, and the nested containment would go on forever. Such a structure understandably is illegal in C++, and the compiler will issue an error. You are not allowed to have a class or struct field of the same type within the class or struct being defined.

Another object definition looks similar, but it is a legal structure:

struct Node { int data;

Node *next; // Self reference via pointer is legal

};

The reason this second version is legal is because the compiler now can compute the size of a Node object. A pointer is simply a memory address under the hood, so all pointer variables are the same size regardless of their declared type. The pointer solves the infinitely nested containment problem.

This ability of a object to refer to an object like itself is not merely an interesting curiosity; it has practical applications. Suppose we wish to implement a sequence structure like a vector. We can use the self-referential structure defined above to build a list of Node objects linked together via pointers. Listing [I8l2| (manuallinkedlist.cpp) builds a small linked list “by hand.”

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.2 A null-terminated linked list

nl

data

next

Listing |18.2| (manuallinkedlist.cpp) creates the null-terminated linked list illustrated in Figure 18.2| The program prints

23 10 0 3

In Figure [TO] the line in the next field of node n4 represents the null pointer.

Listing 18.2 (manuallinkedlist.cpp) augments the simple Node struct by adding a constructor. The program uses no dynamic memory (no calls to new); this is possible only because we know the nodes that are in the list ahead of time. The f o r loop uses a pointer named cu r so r to visit each node in the list. The cursor variable first points to node nl. The statement cursor = cursor->next reassigns cursor to point to the node that follows the current node. This enables cursor to visit nodes nl, n2, n3, and finally cursor will point to n4, the last node in the list. The next field of n4 is nullptr, so when the loop reassigns cursor to n4’s next field, cursor will be nullptr, and the loop will terminate.

The value nullptr in a Boolean context is considered false, so we can simplify the Boolean expression cursor ! = nullptr to just cursor; this allows us to simplify the loop somewhat, as

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Print the linked list built from the Node objects

for (Node ^cursor = &nl; cursor; cursor = cursor->next) std::cout << cursor->data << '

Since we hard-coded the four list nodes into the program’s source, the loop really is not necessary. The following statement:

std::cout << nl.data <<''<< n2.data <<''<< n3.data << n4.data << '\n' ;

is simpler, but why stop there? Since we know the nodes and their values ahead of time, the following statement is even simpler:

std::cout << "23 10 0 3\n";

The hard-coded list in Figure | T8l2| and Listing |T8l2j (manuallinkedlist.cpp) does not demonstrate the utility possible due to the dynamic nature of linked lists. It makes sense to use a linked list only when its elements are unknown ahead of time. We then can dynamically allocate space for the elements as they become available.

Armed with our knowledge of C++ classes, encapsulation, and methods, we can build a client-friendly, dynamic linked list type. The code found in Listing |18.3[ (intlistl ,h), Listing J18.4|(intlistl .cpp), and Listing j|18.5|| (listmain.cpp) demonstrates the power of linked lists. Listing [T~83] (intlist1 .h) is the header file for a simple integer linked list class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

/*

* The constructor makes an initially empty list */

IntListl();

/*

* insert(n)

* Inserts n onto the back of the list.

* n is the element to insert.

*/

void insert(int n);

/*

* print()

* Prints the contents of the linked list of integers. */

void printQ const;

/*

* Returns the length of the linked list.

*/

int lengthQ const;

/*

* clear()

* Removes all the elements in the linked list.

*/

void clear() ;

The Node struct is declared within the IntLi stl class. We say that Node is a nested struct. Since the declaration of Node appears in the private section oflntListl, Node is a type known only to code within the IntLi stl class. Because its declaration is nested within the IntLi stl class, the complete name of the Node type is IntLi stl: :Node. Recall that a struct is equivalent to a class, except the default access to its members is public. We can define nested a class in same manner as we defined our nested struct.

Notice that the IntLi stl class has several private methods in addition to its public methods. Code outside the class cannot execute these private methods directly. These private methods are helper methods that several of the public methods invoke to accomplish their tasks. We say that a public method delegates the work to its private helper methods. Why is this delegation necessary here? The private methods use recursion that requires a parameter of type IntListl: :Node which is unknown outside the IntLi stl class. A client is therefore unable to use the private methods directly, even it they were made public. The public methods do not expose to the client any details about the class’s implementation; specifically they keep the IntListl: : Node type and the head and tai l instance variables hidden from clients.

Observe that the overloaded length methods (both private and public) and print method of the IntListl class are declared const. Neither printing a list nor requesting its length should modify an IntListl object. Clients can, therefore, use the print and length methods with a constant IntListl object. An attempt to use insert or clear on a constant IntListl object will yield a compiler error. The error here makes sense because i nsert definitely will modify a list object, and clear potentially will modify a list object (we say potentially here because clear will not modify an empty list).

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 1 18.4| (intlistl .cpp) implements the methods declared in Listing jl8.3 |(intlist1 .h).

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

else // List is empty, so make head and tail point to new node

head = tail = new_node;

}

/*

* printQ

* Prints the contents of the linked list of integers.

*/

void IntListl::print() const {

for (auto cursor = head; cursor; cursor = cursor->next) std::cout << cursor->data << 1 '; std::cout << '\n 1 ;

}

/*

* Returns the length of the linked list.

*/

int IntListl::length() const {

return length(head); // Delegate work to private helper method

}

/*

* clearQ

* Removes all the elements in the linked list.

*/

void IntListl::clear() {

dispose(head); // Deallocate space for all the nodes

head = tail = nullptr; // Null head signifies list is empty

}

Since the code in Listing 18.4 (intlistl .cpp) appears outside of the class declaration, any use of the Node type requires its full name: IntListl: :Node. Note the : : use in the Node constructor:

IntListl::Node::Node (i nt n): data(n), next (nullptr) {}

The two private methods in Listing 18.4 (intlistl.cpp) (length and dispose) are recursive. The

insert method of the IntLi stl class uses new to dynamically allocate Node objects when adding elements to the collection. The clear method is responsible for deallocating the list nodes, effectively cleaning up the memory held by the list.

Listing prO| (listmain.cpp) provides some sample client code that exercises a linked list.

Listing 18.5: listmain.cpp

// list_main.cpp

ffinclude "intlistl.h" ffinclude <iostream>

int main() {

bool done = false; char command; int value;

IntListl list;

©2018 Richard L. Halterman

Draft date: September 25, 2018

while (Idone) {

std::cout << "I)nsert <item> P)rint L)ength E)rase Q)uit >>"; std::cin >> command; switch (command) {

case 'I': // Insert a new element into the list

case 1 i 1 :

if (std::cin >> value) list.insert(value);

else

done = true; break;

case 'P' : // Print the contents of the list

case 1 p 1 :

list.printQ ; break;

case 'L' : // Print the list's length

case 1 1 1 :

std::cout << "Number of elements: " << list.length() << 1 \n' ; break;

case 'E' : // Erase the list

case 1 e 1 :

list.clearQ ; break;

case 'Q 1 : // Exit the loop (and the program)

case 1 q 1 :

done = true; break;

}

}

list.clear(); // Free up the space held by the linked list

}

The client code in Listing [18.5[ (listmain.cpp) allows a user to interactively add items to a list, print the list, determine the list’s size, and clear the list. The following shows a sample run:

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>P

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>i

90

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>i

23

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>i

10

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>i

-4

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>P

90 23 10 -4

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>i

22

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>P

90 23 10 -4 22

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>1

Number of elements: 5

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>e

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>P

I)nsert <item>

P) ri nt

L)ength

E)rase

Q) ui t

>>q

Table captionFigure plO) visualizes the conceptual state of the linked list midway throught this sample run.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.3 Conceptual view of a typical IntLi stl object. The linked list object here is named li st.

Observe that the client code does not use pointers at all. All the pointer manipulations are hidden within the IntLi stl class. Pointer programming can be tricky, and it is easy to introduce subtle, hard to find bugs; thus, encapsulation once again results in easier and more robust application development. The Node struct itself is private within IntLi stl, out of the reach of programmers who use these linked lists.

As shown in the IntList: :dispose method, a pointer variable by itself can be used as a condition within a conditional statement or loop. A null pointer is interpreted as false, and any non-null pointer is true. This means if p is a pointer, the statement

if (P)

/* Do something */

is a shorthand for

if (p != nullptr)

/* Do something */

and the statement if (ip)

/* Do something */

is a shorthand for

if (p == nullptr)

/* Do something */

Most C++ programmers use the shorter syntax.

In order to better understand how the recursive methods work, think about the structure of a Node object with this interpretation: A Node object holds a data item and a pointer to rest of the list that follows. A pointer to a Node is either null or non-null. A null pointer represents the empty list. A non-null pointer represents a non-empty list consisting of two parts: the first element in the list and the rest of the list. If the next field of a Node object is null, the rest of the list is empty.

Armed with this view of lists we can now examine the behavior of the recursive linked list methods in more detail:

• length — Lists are either empty or non-empty. The length of the empty list is zero. The length of a non-empty list is at least one because a non-empty list contains at least one element. Symbolically

©2018 Richard L. Halterman

Draft date: September 25, 2018

(not in C++), we can let 0 stand for the empty list and x —> 0 stand for the list containing just the element x.

Writing a recursive list length method is as simple as this:

- If the list is empty, its length is zero. Symbolically, we can write length(0) = 0.

- If the list is non-empty, its length is one (counting its first element) plus the length of the rest of the list.

Symbolically, we can write length(x— >rest) = 1 + length(rest).

We can visualize the recursion process for determining the length of 2—>10—>7—>0 as:

length(2->lO->7->0)

1 + length(10—>7—>0) 1 + 1 + length(7—>0)

1 + 1 + 1 + length(0)

1 + 1 + 1+0

3

• dispose — The dispose method behaves similarly to length. Notice, however, that it makes the recursive call deleting the nodes in the rest of the list before it deletes the current node. An attempt to access data via a pointer after using delete to deallocate that data results in undefined behavior; therefore, it is a logic error to attempt to do so. This means the code in dispose should not be written as

if (p) { // Logic error! Do not do it this way!

delete p; // Deallocate this node first

dispose(p->next); // Then free up the rest of the list

}

Here we are attempting to use p->next, which itself uses p, after deleting p’s memory.

While the recursive methods provided a good review of recursion, recursion is not strictly necessary for these functions. We could instead express the public length and clear functions as shown in the following code snippets:

// Iterative versions of length and clear

int IntListl::length() const { int len = 0;

for (auto cursor = head; cursor; cursor = cursor->next) len++; return len;

}

void IntListl::clear() { auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next; delete temp;

}

head = tail = nullptr; // Null head signifies list is empty

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

As mentioned in Section |10.5[ given the same basic algorithm implemented recursively or iteratively, the iterative version will be more efficient. This is because each recursive call requires additional space on the stack to store fresh local variables (if any) and parameters. Not only does a recursive method or function require more memory, it takes more time to complete because the executing program must perform extra work to set up the new space needed by a recursive invocation and restore the context when a recursive invocation returns. If we build a very large linked list, a call to our recursive length or clear method could consume considerable space on the stack and impose a significant performance overhead. For future versions of our linked list code we will use the iterative version of the clear method.

To optimize the length method, we will choose a different route. If you have an application that manages rather large lists and makes frequent calls to the length method, even iteration can take considerable time. We can add an integer instance variable to the IntListl class that keeps track of the number of elements in the list. This new instance instance variable affects the rest of the class members as follows:

• The constructor would initialize this variable to zero.

• The insert method would increment this variable by one each time the client adds an element to the list.

• The clear method would reset this variable to zero.

• The length method would avoid the loop completely and simply return the value of this variable.

The time spent looping over all the elements in a list counting them can be considerable for large lists, so the additional space required by a single extra integer is a good trade off for speeding up the length method.

The IntLi stl class code as defined in Listing 18.3 (intlistl .h) and Listing 18.4 (intlistl .cpp) is useful for introducing the concepts of implementing linked data structures. Our IntLi stl class is, however, fundamentally different from all the earlier custom classes we examined in Section 16’ With the optimizations to length and clea r mentioned above, it may appear to be ready for clients to use as an alternative to std : : vector, but it has some servere limitations and pitfalls that make it practically useless for most applications. Section 18.4 exposes its weaknesses and introduces the modifications required to make it a viable, high-quality class worthy for use in any applications requiring a dynamic linked list data structure.

18.4 Resource Management

Section 18.3 provided our first attempt at a dynamic linked list class, IntLi stl, defined in Listing 18.3 (intlistl .h) and Listing 18.4 (intlistl .cpp). The IntLi stl: : i nsert method dynamically allocates memory for list elements from the heap. It is essential that the programmer intentionally call clear when finished with a linked list object. Consider the following function definition:

void f() {

IntListl my_list; // Constructor called here // Add some numbers to the list

my_list.insert(22); my_list.insert (5); my_list.insert (-44);

// Print the list

my_list.print();

} // Oops! Forgot to call my_list.clear!

©2018 Richard L. Halterman

Draft date: September 25, 2018

The variable my_li st is local to function f. When function f finishes executing the variable my_li st goes out of scope. At this point the space on the stack allocated for the local IntLi stl variable named my_li st is reclaimed; however, the space for the list’s heap-allocated elements remains. The only access the program could have to that memory is via my_li st. head (or my_li st .tail to the last element in the list), but my_li st no longer exists. This presents a classic memory leak.

Observe that none of the classes we have designed thus far except for IntLi stl have this potential problem.

Fortunately C++ provides a way for class designers to specify actions that must occur at the end of an object’s lifetime. Analogous to a constructor that executes code at the beginning of an object’s existence, a destructor is a special method that executes immediately before an object ceases to exist. A destructor has the same name as its class, with a tilde ~ prefix. A destructor accepts no arguments. Listing 118.6 | (intlist2.h) adds a destmctor to Listing [T83] (intlist1 .h) and also adds the previously suggested optimizations of the length and clear methods.

Listing 18.7 (intlist2.cpp) provides the implementation of the IntList2 class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 18.7: intl.-ist2.cpp

// intlist2.cpp

ttinclude "intlist2.h" ttinclude <iostream>

// Private IntList2 operations

// Node constructor

IntList2::Node::Node (i nt n): data(n), next(nullptr) {}

// The constructor makes an initially empty list.

// The list is empty when head and tail are null.

// The list's length initially is zero.

IntList2::IntList2(): head (nullptr) , tai1 (nullptr) , len(0) {}

// The destructor deallocates the memory held by the list IntList2::~IntList2() { clear();

}

// Inserts n onto the back of the list.

// n is the element to insert, void IntList2::insert (i nt n) {

// Make a node for the new element n IntList2::Node *new_node = new Node(n); if (tail) { // Is tail non-null?

tail->next = new_node; // Link the new node onto the back

tail = new_node; // The new node is the new tail of the list

}

else // List is empty, so make head and tail point to new node head = tail = new_node; len++; // List now has one more element

}

// Prints the contents of the linked list of integers.

void IntList2::print() const {

for (auto cursor = head; cursor; cursor = cursor->next) std::cout << cursor->data << 1 '; std::cout << '\n 1 ;

}

// Returns the length of the linked list, int IntList2::length() const { return len;

}

// Removes all the elements in the linked list.

void IntList2::clear() { auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next;

©2018 Richard L. Halterman

Draft date: September 25, 2018

delete temp;

}

head = tail = nullptr; // Null head signifies list is empty len = 0;

The destructor implementation:

IntList2::~IntList2() {

clearQ; // Free up the space held by the nodes in the list

}

simply invokes the services of the clea r method to deallocate the space held by the list.

When do constructors and destructors execute? A local or global object definition calls the class constructor to properly initialize the object; for example,

IntList2 seq;

defines the object seq. This definition invokes the IntLi st2 constructor to set both seq . head and seq . tai 1 to nullptr. If seq is a local variable, its destructor executes at the end of the function’s execution. If seq is global, its destructor executes when the program finishes.

A pointer is not an object; it points to an object. This means the definition

IntList2 *p;

does not invoke IntLi st2’s constructor. Given this definition of p, the statement p = new IntList2;

actually creates an IntLi st2 object and therefore calls the IntLi st2 constructor for the newly created object. The object to which p points is not destroyed until the programmer uses delete, as in

delete p;

It is at this point IntLi st2’s destructor executes for p’s object.

The addition of the destructor to IntList2 removes the memory leak from the f function we saw

earlier. Listing 18.8 (testf.cpp) is a complete program that uses IntLi st2 in function f.

Listing 18.8: testf.cpp

#include <iostream>

#include "intlist2.h"

void f() {

IntList2 my_list; // Constructor called here

// Add some numbers to the list

my_list.insert(22);

my_list.insert(5);

my_list.insert(-44);

// Print the list my_list.print() ;

} // my_list goes out of scope; destructor automatically frees its memory

int main() {

©2018 Richard L. Halterman

Draft date: September 25, 2018

f 0;

}

We can verify that our revised linked list class properly frees up its dynamic memory by augmenting the internal Node struct with a destructor, as shown here:

// This is the modified nested struct Node { int data;

Node *next;

Node (i nt d) ;

—Node();

};

private Node class

// A data element of the list

// The node that follows this one in the list

//

//

Constructor

Destructor

We also modify the constructor implementation and add the destructor implementation as shown here:

// Node constructor

IntList2::Node::Node (i nt n): data(n), next(nullptr) { std::cout << "Creating node " << data

<< " (" << reinterpret_cast<ui ntptr_t> (thi s) << ")\n";

}

// Node destructor

IntList2::NodeNode() {

std::cout << "Destroying node " << data

<< " (" << reinterpret_cast<ui ntptr_t> (thi s) << ")\n";

}

Listing 18.9 (intlist3.h) provides the header file updated with this modified Node nested class, and Listing ) 18. 10j| (intlist3.cpp) contains the implementation.

Listing 18.9: intlist3.h

// intlist3.h class IntList3 {

// The nested private Node class from before struct Node {

int data; // A data element of the list

Node *next; // The node that follows this one in the list

Node(int d); // Constructor

—Node(); // Destructor

};

Node *head; // Points to the first item in the list Node *tail; // Points to the last item in the list

int len; // Number of elements in the list

public :

// The constructor makes an initially empty list IntList3();

// The destructor that reclaims the list's memory

©2018 Richard L. Halterman

Draft date: September 25, 2018

~IntList3();

// Inserts n onto the back of the list, void insert(int n);

// Prints the contents of the linked list of integers, void printQ const;

// Returns the length of the linked list, int lengthQ const;

// Removes all the elements in the linked list, void clear() ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

head = tail = new_node; len++; // List now has one more element

}

// Prints the contents of the linked

void IntList3::print() const {

for (auto cursor = head; cursor;

std::cout << cursor->data << std::cout << '\n 1 ;

}

list of integers.

cursor = cursor->next)

I I .

// Returns the length of the linked list, int IntList3::length() const { return len;

}

// Removes all the elements in the linked list.

void IntList3::clear() { auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next; delete temp;

}

head = tail = nullptr; // Null head signifies list is empty len = 0;

Here we have the Node constructor identify which element it is creating by printing its data field and the address of where it resides in memory. C++ is very strict about conversions between pointer and non-pointer types—it is easy to do by mistake and almost never intended—so a simple stati c_cast will not work here. The rei nterpret_cast removes the safeguard and treats the bits that make up the pointer as a ui ntptr_t, an integer type guaranteed to represent the same range of values as a pointer. The destructor indicates when a Node object is destroyed. Listing 18.11 (testf2.cpp) is same program as Listing 18.8 (testf.cpp), except it uses an IntLi st3 object instead of an IntLi st2 object.

©2018 Richard L. Halterman

Draft date: September 25, 2018

If we remove the destructor from the IntLi st3 class, effectively making it the IntLi stl class without the enhanced Node struct. Listing 18.11 (testf2.cpp) will print the following:

Creating node 22 (16846704)

Creating node 5 (16823408)

Creating node -44 (16822992)

22 5 -44

(The actual memory addresses will vary from run to run, but the Node data values will be the same.) The function creates three nodes but deletes none of them. When this function returns, my_li st no longer exists, so we no longer can access the nodes it allocated. If we leave IntLi st3 as is. Listing 18.8 (testf.cpp) prints the following:

Creating node 22 (19337072)

Creating node 5 (19313328)

Creating node -44 (19313696)

22 5 -44

Destroying node -44 (19313696)

Destroying node 5 (19313328)

Destroying node 22 (19337072)

This shows that the IntLi st3 destructor properly deallocates the dynamic memory held by the linked list object. The Node constructor executes when declaring a Node object or when using new to create a Node object to assign to a Node pointer. The i nsert method uses new to create a Node object, so this invokes the constructor. The Node destructor executes when an object goes out of scope or when delete deallocates a dynamically-allocated object. The IntLi st2 destructor uses delete to free up each node in the list.

Consider the case of dynamically allocating the linked list itself, not just its nodes: void f2() {

IntList3 *lptr; // Pointer, constructor NOT called yet

Iptr = new IntList3; // Constructor called here

// Add some numbers to the list

lptr->insert(22);

lptr->insert(5) ;

lptr->insert(-44);

// Print the list lptr->print() ;

delete Iptr; // Destructor called here

}

In this f2 function Iptr is not an object; it is a pointer to an object. Declaring Iptr does not create an object, and, therefore, the IntLi st3 constructor does not execute. The statement

Iptr = new IntList3;

does create an object, and so the IntLi st3 constructor executes on behalf of the object to which Iptr points. When Iptr goes out of scope at the end of function f2’s execution, the stack variable Iptr goes away, but since it is a pointer, not an object, no destructor code executes. The client must explicitly free up memory with delete:

delete Iptr; // Destructor called here

©2018 Richard L. Halterman

Draft date: September 25, 2018

unless the programmer intends for the function to return the pointer to the client (in which case the client is responsible for calling delete when finished with the object).

As you can see, dynamically allocating the list itself (apart from the nodes that store its elements) brings us back to the situation we were in before: We must remember to do something when we are finished with the object. In this case we must remember to delete the list itself. A destructor cannot help us here. This is a good example that demonstrates that while dynamic memory enables us to do many interesting things, it is best to avoid it unless absolutely necessary to achieve the behavior we need.

A destructor performs the reverse role of a constructor: A constructor ensures that a new object begins its life in a well-defined state, while a destructor is responsible for performing actions required when an object’s life is over. A destructor is unnecessary for most classes. For a linked list object, however, a destructor is essential because the nodes that comprise the linked list are dynamically allocated with the new operator. Any memory allocated with new needs a corresponding call to delete when the memory no longer will be used. The clear method will take care of the memory deallocation, but, without a destructor, a programmer must remember to intentionally call clear when finished with a linked list object. The destructor relieves the programmer of this responsibility and removes the possibility of a memory leak. The destructor simply calls clea r to clean up the resources held by the list.

Listing 18.12 (testdestructors.cpp) demonstrates that executing program destroys local and global objects in the reverse order of their creation. For objects allocated via the new operator, as in the function test_wi dget_poi nters, destructors execute only when applying delete to the associated pointers.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Widget *pl = new Widget(10);

Widget *p2 = new Widget(20);

Widget *p3 = new Widget(30);

Widget *p4 = new Widget(40);

delete p2; delete pi; delete p4;

// Not deleting p3, introducing a memory leak std::cout << "Leaving test_widget_pointers" << '\n' ;

}

int mainQ {

std::cout << "Entering main" << '\n'; test_widget_objects() ; test_widget_pointers(); std::cout << "Leaving main" << '\n';

}

.cpp) prints the following:

Creating widget 100 (2707068)

Creating widget 200 (2707064)

Entering main

Entering test_widget_objects Creating widget 1 (14024180)

Creating widget 2 (14024184)

Creating widget 3 (14024188)

Creating widget 4 (14024192)

Leaving test_widget_objects Destroying widget 4 (14024192)

Destroying widget 3 (14024188)

Destroying widget 2 (14024184)

Destroying widget 1 (14024180)

Entering test_widget_pointers Creating widget 10 (14790752)

Creating widget 20 (14790816)

Creating widget 30 (14790832)

Creating widget 40 (14791760)

Destroying widget 20 (14790816)

Destroying widget 10 (14790752)

Destroying widget 40 (14791760)

Leaving test_widget_pointers Leaving main

Destroying widget 200 (2707064)

Destroying widget 100 (2707068)

Adding a destructor to the IntListl class is a significant step in correcting its deficiencies, but its successors, IntList2 and IntList3, still are not ready for general release. Consider Listing 18.13 (listassign.cpp) that uses the IntLi st3 class that properly automatically cleans up its memory.

©2018 Richard L. Halterman

Draft date: September 25, 2018

void f() {

IntList3 seql, seq2; // Create two empty integer linked lists

seql.insert(10); // Build the list [10]-->[-2]-->[8]

seql.insert(-2);

seql.insert(8); seql.print() ;

seq2.insert(5); seq2.insert(4); seq2.print() ;

std::cout <<

seql = seq2;

seql.print();

// Build the list [5]—>[4]

-\n";

// What does this do?

int main() {

f 0;

std::cout << "All done\n";

}

Listing 18.13 (listassign.cpp) builds two separate linked lists and then assigns one list to the other. On one system the program prints

Creating node 10

(14457304)

Creating node -2

(14457592)

Creating node 8

10 -2 8

(14456152)

Creating node 5

(14456200)

Creating node 4

5 4

(14456248)

5 4 1

Destroying node 4

(14456248)

Destroying node 5

(14456200)

Destroying node 4

(14456248)

Destroying node 5 All done

(14456200)

During this particular run the program ran to completion; however, sometimes the program will crash before printing All done. On some systems the program crashes before printing the last three lines of output.

During this run of Listing 18.13|| (listassign.cpp) the output shows that the program never destroys the nodes containing 10, —2, and 8. Further, the program destroys the nodes containing 4 and 5 twice! We can see the program deletes the same memory twice by comparing the memory addresses in parentheses. This undefined behavior of double deletion is what causes the program to crash at times.

The problem is in this statement:

seql = seq2;

What exactly does this statement do?

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.4 Conceptual view of IntLi st3 assignment. After the assignment the two linked list objects alias the same list of nodes, and seql’s original list becomes unreachable.

With no additional guidance from the programmer, the assignment operator for a programmer-defined type simply copies the bits in memory that make up the object to right of the assignment operator into the memory reserved for the object on the left side of the assignment operator. Under Visual C++producing a 32-bit executable, for example, an IntLi st3 object occupies 12 bytes of memory—four bytes for its head pointerplus four bytes for its tail pointerplus four bytes for ten. The actual size of an IntLi st3 object will vary from system to system and will be larger on 64-bit computers. You can verify the actual size ofanIntList3 object on your system by adding the following statement to Listing 18.13 (listassign.cpp):

std::cout << sizeof seql << '\ n ' ; // Prints 8 or 16 under Visual C++

The assignment seql = seq2;

simply copies seq2. head to seql. head and copies seq2. tail to seql. tai 1 and copies seq2. len to seql. len. This produces three undesirable results:

Aliasing. After the assignment the objects seql and seq2 refer to the same list of nodes. See Figure 18.4 for an illustration of the assignment process.

This means any actions to modify the list managed by seql will modify seq2 identically. The assignment operator does not make a copy of the contents of seq2. This means that our linked list objects behave differently than std : : vector objects with respect to assignment; assigning one vector to another makes a copy of the contained elements. Clients will expect our linked list objects to behave similarly. This aliasing problem, however, is the least of our problems.

©2018 Richard L. Halterman

Draft date: September 25, 2018

• Memory leak. Simply redirecting seql’s head and tai l pointers to seq2’s list renders the nodes in seql’s original list unreachable from any variables within the program. The program has no way to delete the nodes in seql’s original list. This constitutes a memory leak.

• Memory corruption. Both seql and seq2 are objects local to the mai n function. Based on their declaration order, seql’s constructor executes before seq2’s constructor. This means when mai n is finished executing seq2’s destructor will execute before seql’s destructor, as object destruction occurs in the reverse order of object construction for local objects. The destructor for seq2 will free up all the nodes in seq2’s list. Next, seql’s destructor will attempt to delete the memory occupied by its list. Unfortunately this involves referencing and deleting dynamic memory previously deleted by seq2. Any attempts to delete already deleted memory results in undefined behavior that usually results in memory corruption. That is why Listing [T8.13 ||(listassign.cpp) crashes during some runs.

Fortunately C++ provides a way for programmers to customize how assignment works for a custom type. Before we tackle assignment itself, we must distinguish between initialization and assignment. Consider the following statement:

int x = 3;

This statement defines and initializes the variable x to 3. This statement is fundamentally different from the following two statements:

int x;

x = 3;

For simple types like integers, floating-point numbers, and characters, this pair of statements on the surface behave identically to the single statement above. In fact, these two statements involve a declaration followed by assignment. Initialization and assignment are not the same thing. Recall from Section [3^2] the alternate syntax for initialization:

int x{3};

To the compiler, this statement is equivalent to the initialization statement above. Note, however, that the following code sequence is not legal:

int x;

x{3}; // Illegal

C++ gives programmers full control over initialization and assignment of custom types. We have seen how we can specify initialization via a constructor. In order to legitimize our linked list class and make it safe for clients to use, we need to provide an additional constructor, called the copy constructor, and define an assignment operator for the class.

The copy constructor for a class named X has the following form:

class X {

// Other stuff for class X

X::X(const X& other);

};

The parameter is a reference to an object of the same type.

To specify assignment, we supply an operator^ method of the form

©2018 Richard L. Halterman

Draft date: September 25, 2018

class X {

// Other stuff for class X X& operator^(const X& other);

};

Note that the assignment operator accepts a constant reference parameter of the type of the class and returns a reference to the type of the class.

Listing 18.14 (intlist4.h) extends Listing|[l8~l9|(intlist3.h) providing copy construction and assignment.

Listing 18.14: -intl-ist4.h

// intlist4.h

class IntList4 {

// The nested private struct Node {

int data;

//

Node *next;

//

Node (int d);

//

~Node();

//

};

Node class from before

A data element of the list

The node that follows this one in the list

Constructor

Destructor

Node *head; // Points to the first item in the list Node *tail; // Points to the last item in the list

int len; // Number of elements in the list

public :

// The constructor makes an initially empty list IntList4() ;

// The destructor that reclaims the list's memory ^IntList4();

// Copy constructor

IntList4 (const IntList4& other);

// Assignment operator

IntList4& operator=(const IntList4& other);

// Inserts n onto the back of the list, void insert(int n);

// Prints the contents of the linked list of integers, void printQ const;

// Returns the length of the linked list, int lengthQ const;

// Removes all the elements in the linked list, void clear() ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

The implementation of the copy constructor is straightforward:

IntList4::IntList4 (const IntList4& other):

// Walk through other's list inserting // into this list

for (auto cursor = other.head; cursor; insert(cursor->data) ;

}

IntList4() {

each of its elements

cursor = cursor->next)

The expression IntList4() in the constructor initialization list following the colon is calling the overloaded version of the constructor that accepts no arguments. This is known as constructor delegation. The no-argument constructor simply initializes head and tail to nullptr. We could have done the same thing here without calling the other constructor, but, in general, delegation is a good idea. Delegation can avoid code duplication, and while there currently is not much code in the no-argument constructor, we may decide to add more functionality in the future. By delegating, we can add the extra activity to the no-argument constructor without having to add it also to this copy constructor.

Constructors always begin with a brand new, non-preexisting object. In the case of our linked list objects, that means our constructor does not have to worry about cleaning up any preexisting list of nodes. All our copy constructor needs to do is ensure that head and tai l instance variables initially are null (the constructor delegation takes care of that) and then visit each node in the other list, inserting that node’s data value into its own list as it goes.

Next we will consider assignment. Suppose Istl and lst2 are two linked list objects. In the assignment

Istl = lst2;

we will refer to Istl as the assigned-to object and lst2 as the assigned-from object. Note that the syntactically desugared equivalent of this statement is

Istl. operator^ (lst2); // Same as Istl = lst2;

Unlike the copy constructor, the assignment operator works with a preexisting object. This means the assignment operator in the course of its operation must deallocate the original list of nodes, if any, managed by the assigned-to list. Failure to do so would introduce a memory leak. Also, the assignment operator must make a copy of all the values in the assigned-from list to avoid aliasing.

There are various ways we can implement the assignment operator to ensure it works correctly, but since assignment of this nature is such a common operation, C++ programmers have developed a standard idiom that guarantees the correctness of assignment. Best practices dictates that we implement our assignment as a process. This entails making a local temporary copy of the assigned-from list and swapping the list of nodes from the temporary list with list of nodes from the assigned-to list. Note that swapping the list of nodes simply requires swapping the head and tai l pointers between the two objects. This copy-and-swap process depends on a correctly implemented copy constructor and a correctly implemented destructor.

The following code provides the necessary assignment operator:

IntList4& IntList4:: operator^(const IntList4& other) {

// Make a local, temporary copy of other

IntList4 temp{other};

// Exchange the head and tail pointers and len from this list // with those of the new, temporary list std::swap(head, temp.head); std::swap(tail, temp.tail);

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::swap(Ten, temp.len);

// The temporary list now points to this list's original contents,

// and this list now points to the copy of other's list

// The temporary list will be destroyed when this constructor returns

return *this;

}

Surprising, perhaps, is what we do not see in this assignment operator:

• Missing is a loop or any indication of visiting each node in the assign-from list (other).

• Missing is any calls to delete to free up any preexisting list nodes in the assign-to list.

How does this assignment operator magically meet our requirements for a correct assignment? This is how it works:

• The first executable line:

IntList4 tempfother};

invokes the copy constructor to make a copy of the assign-from list (othe r) to a temporary list object (temp). Recall that the copy constructor uses a loop to traverse the assign-from list, making a copy of each node in that list. This solves the aliasing issue and explains how this assignment operator does actually visit every node in other’s list.

• The next two statements:

std::swap(head, temp.head); std::swap(tail, temp.tail); std::swap(len, temp.len);

exchange the head and tai l pointers and len between the assign-to list object and the temporary list object. This means the assign-to list object now holds the copy of the assi gn-f rom list, and the temporary list object holds the list originally managed by the assign-to list object.

• Since it is a local variable the temporary list object (temp) goes out of scope at the end of the function’s execution. The temp object’s destructor executes at this time. This temporary object now holds the assign-to object’s original list, so the destructor properly deallocates all the nodes in the assi gn-to object’s original list. The calls to delete to prevent the memory leak are found in the linked list class destructor.

Figure | 18.5| illustrates the copy-and-swap process of the assignment operator.

Our assignment operator leverages the code already written in the copy constructor and destructor. Any other implementation of assignment that correctly addresses the aliasing and memory management issues necessarily would duplicate the functionality of either the copy constructor or the destructor.

Note that the IntList4: :operator= method’s declaration indicates it returns a reference to an IntList4 object, and we see in the last line of IntList4: : operator=’s body that the method actually returns a reference to the object that appears on the left side of the assignment operator during its invocation. Recall that the thi s keyword represents a pointer to the object upon which the caller invoked the method (in this case the assign-to list object). If 1st 1 and lst2 are list objects, when executing the statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.5 The copy-and-swap process performed by the assignment operator

temp copy constructs from seq2

seql head g.

tail g

len |~3~|

data pTo~| data pi]

data g

data g data g

next next g

next g

next g^ ^ next g

temp

Table captionseq2

head

I-1

tai L

s

ten

0.

> I

temp and seql data [To] data g

swap lists next srl, next s

data g

data g data g

next g

next g^ next g

©2018 Richard L. Halterman Draft date: September 25, 2018

Istl = lst2; // Syntactic sugar for Istl.operator^(lst2);

the thi s pointer in points to Istl (and lst2 is the parameter named other).. The method must return an object reference , not a pointer to the object, so we must dereference it as *thi s. This is the typical C++ idiom used when defining operator^ for programmer-defined types.

We could instead define the ope rato r- method to return nothing (that is, declare its return type to be voi d). Instead we could define the method to return some type of object other than IntLi st4. If we do so, however, our IntLi st4 objects will not behavior properly with chained assignment (see Section 4.3). To illustrate, suppose Istl, lst2, and lst3 are all properly declared IntLi st4 objects. If we define the IntLi st4: : operator^ method to return voi d, the following statement:

Istl = lst2;

is perfectly acceptible and behaves as intended, but the compiler will not accept the following statement: Istl = lst2 = lst3;

This is because the assignment operator associates right-to-left; the compiler interprets the chained assignment statement above as if we had parentheses placed as shown in the following statement:

Istl = (lst2 = lst3);

If our assignment operator returns voi d, this statement produces a compile-time error because the subexpression (lst2 = lst3) would evaluate to voi d, and voi d is a degenerate type that we cannot assign to Istl.

If we use the original definition above of the IntLi st4: : operator^ method that returns a reference to the IntLi st4 object on the left side of the assignment operator (*thi s), the compiler does not complain and the chained assignment works flawlessly in the same manner as chained assignment involving the built-in numeric types; that is, after executing the chained assignment statement above, Istl and lst2 each will contain exact copies of the elements in lst3.

Listing 18.15 (intlist4.cpp) provides the complete implementation of our IntLi st4 class.

Listing 18.15: intlist4.cpp

// intlist4.cpp

ffinclude "intlist4.h"

#include <iostream>

#include <utility> // For std::swap // Private IntList4 operations // Node constructor

IntList4::Node::Node (i nt n): data(n), next(nullptr) { std::cout << "Creating node " << data

<< " (" << rei nterpret_cast<ui ntptr_t> (thi s) << ")\n";

}

IntList4::Node::~Node() {

std::cout << "Destroying node " << data

<< " (" << rei nterpret_cast<ui ntptr_t> (thi s) << ")\n";

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// The constructor makes an initially empty list.

// The list is empty when head and tail are null.

// The list's size initially is zero.

IntList4::IntList4(): head (nullptr) , tai1 (nullptr) , len(0) {}

// Copy constructor makes a copy of the other object's list IntList4::IntList4(const IntList4& other): IntList4() {

// Walk through other's list inserting each of its elements // into this list

for (auto cursor = other.head; cursor; cursor = cursor->next) insert(cursor->data);

}

// Assignment operator

IntList4& IntList4:: operator=(const IntList4& other) {

// Make a local, temporary copy of other

IntList4 temp{other};

// Exchange the head and tail pointers and len from this list

// with those of the new, temporary list

std::swap(head, temp.head);

std::swap(tail, temp.tail);

std::swap(len, temp.len);

// The temporary list now points to this list's original contents,

// and this list now points to the copy of other's list

// The temporary list will be destroyed when this constructor returns

return *this;

}

// The destructor deallocates the memory held by the list IntList4: :-~IntList4() { clearQ; }

// Inserts n onto the back of the list.

// n is the element to insert, void IntList4::insert (i nt n) {

// Make a node for the new element n IntList4::Node *new_node = new Node(n); if (tail) { // Is tail non-null?

tail->next = new_node; // Link the new node onto the back

tail = new_node; // The new node is the new tail of the list

}

else // List is empty, so make head and tail point to new node head = tail = new_node; len++; // List now has one more element

}

// Prints the contents of the linked

void IntList4::print() const {

for (auto cursor = head; cursor;

std::cout << cursor->data << std::cout << '\n' ;

}

list of integers.

cursor = cursor->next)

I I .

// Returns the length of the linked list, int IntList4::length() const { return len;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.6 An annotated output of Listing 18.13 (listassign.cpp) updated to use our IntLi st4 class. Examine carefully the node memory addresses (in parentheses) to convince yourself that the implementation of correct copy constructor, assignment operator, and destructor for the class solved the aliasing, memory leak, and undefined behavior problems.

Creating node 10 (17433976) ~1

Creating node -2 (17477728) Creating node 8 (17477744)

• Creating seql's original list

10 -2 8

Creating node 5 (17477760) ~| Creating node 4 (17478592) _J 5 4

• Creating seq 2's list

Creating node 5 (17478752)

Creating node 4 (17478560) _J

Destroying node 8 (17477744) ~jI

|- Creating a copy of seq2's list for seq 1

Destroying node -2 (17477728)

Destroying node 10 (17433976) _J

c A

» Destroying seql's original list

Destroying node 4 (17478592) ~|

Destroying node 5 (17477760) _J

1* Destroying seq2's list

Destroying node 4 (17478560) “] Destroying node 5 (17478752) _J All done

|- Destroying seql's list (the copy of seq2's list)

}

// Removes all the elements in the linked list.

void IntList4::clear() { auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next; delete temp;

}

head = tail = nullptr; // Null head signifies list is empty len = 0;

See Figure jl8,6|| provides an annotated output of Listing [18X3] (listassign.cpp) updated to use our IntLi st4 class.

The output demonstrates that assignment now works correctly for our linked list objects. Correctly implementing the copy constructor, assignment operator, and destructor for the IntList4 class solved the aliasing, memory leak, and undefined behavior concerns.

The copy constructor, assignment operator, and destructor have a special relationship in C++. These three methods are involved in the Rule of Three. The Rule of Three is this: If a class designer feels the need to add a copy constructor, assignment operator, and/or destructor to a class, the class should have all three

©2018 Richard L. Halterman

Draft date: September 25, 2018

methods. Said another way, it almost always is a mistake to have just one or two of these special methods defined for a class without including all three.

The Rule of Three is a design guideline; it is not requirement of the C++ language that the compiler enforces. Consider why the rule exists. If an object must be guaranteed to perform some action at the end of its existence and failure to do so would result in undesirable consequences as the program continues to execute, the object’s class must contain a destructor. This essential action usually involves some releasing some resource it owns. If the destructor is responsible for releasing a resource, the copy constructor must somehow acquire a resource that is in some way related to the resource of an existing object. The assignment operator must both release an owned resource and acquire a resource related to the resource of an existing object. What if you leave out one of the three?

• If you omit the destructor, the default destructor does no resource clean up. Objects can acquire resources through copy construction and assignment but cannot release them. Most resources (like memory) are finite, so lack of an appropriate destructor will limit the number objects available to the executing application.

• If you omit the copy constructor, the default copy constructor will copy the bits of the existing object into the new object. This means the copy-constructed object will have the exact resources managed by another object. The destruction of exactly one of the objects will release the resources held by the other object. The non-destroyed object then will not have access to the resources it needs to function.

• If you omit the assignment operator, the default assignment will copy the bits of one existing object into another existing object. This means the assigned object will have the exact resources managed by another object. It also means that the resources the assigned object originally held are not reclaimed. The destruction of exactly one of the objects will release the resources held by the other object. The non-destroyed object then will not have access to the resources it needs to function.

In sum, you should have a very good reason for designing a class that violates the Rule of Three.

18.5 Rvalue References

Consider the following code fragment:

int x = 5, y;

y = x + 2;

In the assignment statement

y = x + 2;

The variable y is known as an lvalue. The / in lvalue stands for left, as y can appear all by itself on the left side or right side of the assignment operator. The expression x + 2 is classified as an rvalue, since it can appear only on the right side of the assignment operator but cannot appear on the left side; for example, the following statement is illegal:

x + 2 = y; // Illegal!

The expression x + 2 represents a temporary value, as it has meaning and existence only during the execution of the statement in which it appears. The executing program stores the result of the computation of x + 2 temporarily in memory, but the program ordinarily cannot reference that memory after the statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

finishes. The term temporary is appropriate, as the program may reuse that same memory for other purposes after the statement executes.

Consider the following variable declarations:

i nt x = 5;

int& r = x + 3; // Illegal!

The second declaration is illegal; C++ does not allow us to assign a temporary to a reference variable. In this case the variable r would be an alias for a quantity that ceases to exist immediately after the statement executes. The variable r, however, would continue to exist, but it would not be aliasing any valid quantity.

C++ does permit us to make a const reference to a temporary. The following code fragment is legal:

i nt x = 5;

const int& cr = x + 3; // Legal

The const reference places the value of the temporary into a memory location referenced via cr. The temporary’s value persists until cr goes out of scope. In this case cr behaves as if it were simply a const int.

Next, consider the following function definition:

int f(int n) {

return 10 * n;

}

In the following statement: std::cout << f(x + 2) << '\n';

the actual parameter is a temporary value passed to the function f. Everything works as expected because the executing program copies the temporary’s value to the formal parameter n in this pass by value example.

Now consider a similar but slightly different function definition:

int g(int& n) {

return 10 * n;

}

The following statement is illegal: std::cout << g(x + 2) << '\n';

The function g accepts a reference to a variable, but the caller is attempting to pass a temporary. Once function g begins executing, the memory reserved for the original temporary is invalid, so the compiler rightly does not permit this.

As with the simple declarations we saw above, given function h:

int h (const int& n) { return 10 * n;

}

the following statement is perfectly acceptable: std::cout << h(x + 2) << '\n' ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

Since n is a const "i nt reference in h, the executing program will make a copy of the temporary’s value to send to h.

While these examples may seem a bit esoteric, we are paving the way for a more efficient linked list custom type. Consider Listing 18.16 (templist.cpp) which uses our IntList4 type from Listing 18.15 (intlist4.cpp) and Listing 18.15 (intlist4.cpp).

The output of Listing 18.16 (templist.cpp) indicates the creation and destruction of two Int Li st4 objects

when we would expect only one. Figure 118/71 annotates the output of Listingi 18.16 (templist.cpp) to explain the program’s behavior.

The statement

auto my_list = make_list(4);

invokes the IntLi st4 copy constructor. This statement is equivalent to auto my_list{make_list(4)};

Either way, the make_list(4) expression represents the Int Li st4 object returned by the make_li st function when passed the actual parameter 4. The expression make_li st (4) is an rvalue, a temporary, because it cannot appear on the left side of the assignment operator. Since the Int Li st4 copy constructor accepts a const IntLi st4& parameter, it will accept the temporary object, but it makes a copy of the temporary to send to the copy constructor.

If is wasteful to make a copy of this transient object. If the list object contained millions of nodes, this additional construction and destruction could be time consuming.

C++ does permit a special kind of reference for rvalues known as an rvalue reference. An rvalue reference enables programmers to alias a temporary without making a copy.

In the following code: int x = 5;

int&& r = x + 3; // Legal, note the two ampersands

std::cout << "x = " << x << " r = " << r << ' \n' ;

we see that variable r provides access to the temporary’s value.

We can use rvalue references as function parameters, as the following function demonstrates:

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 18.7 An annotated output of Listing 18.16 (templist.cpp). Examine carefully the node memory addresses (in parentheses). The executing program first creates the temporary IntLi st4 object returned by make_list. It the copy constructs the my_list object from the temporary and then destroys the temporary. After printing the linked list, the program finally destroys the my li st object.

Creating node 0 (18154856) ~'

Creating node 1 (18199696) _ . , i

creating node 2 (18199872) ’ Creating the temporary make_li st (5)

Creating node 3 (18199680) _

Creating node 0 (18199440) —

Creating node 1 (18199760)

Creating node 2 (18199808) ’ Copy constructing my_li st from the temporary

Creating node 3 (18199584) _

Destroying node 3 (18199680) —

Destroying node 2 (18199872) . ,

Destroying node l (18199696) ’ Destroying the temporary

Destroying node 0 (18154856) _

0 12 3

Destroying node 3 (18199584) ~

Destroying node 2 (18199808)

Destroying node 1 (18199760) ' Destroying my_ll st

Destroying node 0 (18199440) _

©2018 Richard L. Halterman

Draft date: September 25, 2018

int h(int&& n) { return 10 * n;

}

Given the definition of function h, the following invocation is legal: std::cout << h(x + 3) << '\n' ;

We can overload functions and methods to accept both normal references and rvalue references. The compiler can determine which overloaded function to invoke based on the actual parameters that the caller passes. Consider Listing| [T8.17 j|(rvalueparams.cpp).

Listing 18T7J (rvalueparams.cpp) prints

Calling with reference parameter, result is ==> 12 Calling with rvalue reference parameter, result is ==> 16 Calling with rvalue reference parameter, result is ==> 12

The expression twi ce ( x ) calls the twi ce function with an lvalue, so it calls the first version of twi ce. The expressions x + 2 and 2 are rvalues—neither can appear by itself on the left side of the assignment operator—so both twi ce ( x + 2) and twi ce ( 2 ) invoke the second version of the twi ce function.

These examples with integers we have seen so far help us better understand the mechanics of rvalue references, but, honestly, rvalue references offer little value to the simple types like integers. The C++ language designers introduced rvalue references into C++ for the specific purpose of making copy construction and assignment from temporaries more efficient. Rvalue references are exactly what we need to make our linked list of integers more efficient when dealing with temporary lists.

Listing 118.18[ (intlist5.h) declares the fifth generation of our integer linked list class. It contains a new constructor overload and adds an assignment operator overload, both of which accept rvalue references.

Listing 18.18: nntl-ist5.h

// intlist5.h

©2018 Richard L. Halterman

Draft date: September 25, 2018

class IntList5 {

// The nested private Node class from before struct Node {

int data; //A data element of the list

Node * *next; // The node that follows this one in the list

Node(int d); // Constructor

~Node(); // Destructor

};

Node *head; // Points to the first item in the list Node *tail; // Points to the last item in the list

int len; // Number the elements in the list

public :

// The constructor makes an initially empty list IntList5() ;

// The destructor that reclaims the list's memory ~IntList5();

// Copy constructor

IntList5 (const IntList5& other);

// Move constructor

IntList5(IntList5&& other);

// Assignment operator

IntList5& operator= (const IntList5& other);

// Move assignment operator

IntList5& operator= (IntList5&& other);

// Inserts n onto the back of the list, void insert(int n);

// Prints the contents of the linked list of integers, void printQ const;

// Returns the length of the linked list, int lengthQ const;

// Removes all the elements in the linked list, void clear() ;

Note 1

Note 2

©2018 Richard L. Halterman

Note 3

• If the caller passes an rvalue, the compiler generates code that invokes the move constructor or move assignment operator.

The purpose of move construction is to efficiently move the resources held by the temporary object into the new object being created. We want to avoid making a copy of the temporary. Similarly, the purpose of move assignment is to efficiently move the resources held by the temporary object into an existing object without creating a new object. The copy constructor and copy assignment operator are designed to make copies.

It is safe to “steal” the resources of the temporary object because a temporary object is transient and cannot be used later within the program. Even though temporary objects are transient, they nonetheless are real, nameless objects. If the class of the temporary has a destructor, the object’s destructor will execute when the temporary’s ephemeral life is over. This means that even though the move constructor and move assignment operator may move a temporary’s resources into another object, they must leave the temporary in a well-defined state so that the temporary’s destructor can do its job.

The following implements the move constructor for the IntLi st5 class:

// Move constructor takes possession of the temporary's list

IntList5:: IntList5(IntList5&& temp): IntList5() {

// Swap contents with the temporary

std::swap(head, temp.head); std::swap(tail, temp.tail); std::swap(len, temp.len);

}

This move constructor delegates to the constructor that accepts no arguments. This initializes the head and tail pointers of this new object to nullptr. Note that this represents an empty, but valid linked list object. The move constructor then exchanges the head and tail pointers of the object it is creating with those of the temporary. This effectively moves the temporary’s list of nodes to this object and moves the this object’s empty, but valid, list of nodes to the temporary. When this copy constructor finishes, the temporary’s life is over. Since the temporary still contains a valid list of nodes, its destructor can execute successfully. Observe that no where in this copy constructor did we traverse a list of nodes copying each element individually. This means move construction of a list with 1,000,000 nodes requires no more time than move constructing an empty list.

Note that the parameter to the move constructor is not declared const. If it were declared const, it would not be possible to swap its contents with new object being created.

The move assignment operator is similar to the move constructor, except assignment, of course, does not begin with an initially empty object. We must ensure our move assignment operator does not leak memory from any preexisting list of nodes the object may contain.

The implementation of the move constructor for the IntLi st5 class looks very similar to the move constructor:

// Move assignment operator

IntList5& IntList5:: operator^ (IntList5&& temp) {

// Exchange the head and tail pointers and len from this list

// with those of the new, temporary list

std::swap(head, temp.head);

std::swap(tail, temp.tail);

std::swap(len, temp.len);

// The temporary list now points to this list's original contents,

©2018 Richard L. Halterman

Draft date: September 25, 2018

// and this list now points to the temporary's list

// The temporary list will be destroyed since it is a temporary

return *this;

The only difference is the move constructor always will given the empty list to the temporary. The move assignment operator exchange the object’s list for the temporary’s list. The object’s list could be empty, but in general it will not be empty. When the move assignment operator returns, the temporary passed to it will cease to exist. The temporary’s destructor then will properly dispose of the object’s original list of nodes.

Listing 18.19 (intlist5.cpp) contains the complete implementation of the IntLi st5 class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

IntList5& IntList5:: operator=(const IntList5& other) {

// Make a local, temporary copy of other IntList5 temp{other};

// Exchange the head and tail pointers and len from this list

// with those of the new, temporary list

std::swap(head, temp.head);

std::swap(tail, temp.tail);

std::swap(len, temp.len);

// The temporary list now points to this list's original contents,

// and this list now points to the copy of other's list

// The temporary list will be destroyed since it is a temporary

return *this;

}

// Move assignment operator

IntList5& IntList5::operator=(IntList5&& temp) {

// Exchange the head and tail pointers and len from this list

// with those of the new, temporary list

std::swap(head, temp.head);

std::swap(tail, temp.tail);

std::swap(len, temp.len);

// The temporary list now points to this list's original contents,

// and this list now points to the temporary's list

// The temporary list will be destroyed since it is a temporary

return *this;

}

// The destructor deallocates the memory held by the list IntList5: :-~IntLi st5 () { clearQ; }

// Inserts n onto the back of the list.

// n is the element to insert, void IntList5::insert(i nt n) {

// Make a node for the new element n IntList5::Node *new_node = new Node(n); if (tail) { // Is tail non-null?

tail->next = new_node; // Link the new node onto the back

tail = new_node; // The new node is the new tail of the list

}

else // List is empty, so make head and tail point to new node head = tail = new_node; len++; // List now contains one more element

}

// Prints the contents of the linked list of integers.

void IntList5::print() const {

for (auto cursor = head; cursor; cursor = cursor->next) std::cout << cursor->data << ' '; std::cout << '\n' ;

}

// Returns the length of the linked list, int IntList5::length() const { return len;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Removes all the elements in the linked list.

void IntList5::clear() { auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next; delete temp;

}

head = tail = nullptr; // Null head signifies list is empty len = 0;

Listing |18.20| (templist2.cpp) is the same code as Listing ! 18.16| (templist.cpp), exce pt it uses the newest iteration of our integer linked list class.

The make_li st function creates the temporary object; this accounts for all statements that begin with Creating node.... The move constructor exchanges the temporary object’s list of nodes with the empty list found in the newly created my_list object. At this point my_list contains the temporary’s original list and the temporary contains the empty list. The temporary’s destructor executes but finds no nodes to destroy (head is null). At the end of the mai n function my_li st’s destructor delete’s all the nodes in my_li st.

©2018 Richard L. Halterman

Draft date: September 25, 2018

As an aside, note that the compiler can detect that the make_list function creates a local object (result) but merely returns it to the caller. The compiler can use return value optimization (see Section [1T7L4J to avoid creating an extra object within the function to return to the caller. Instead, the compiler generates code that enables the make_li st function to create the linked list object directly in the environment of the caller.

The addition of move construction and move assignment brings us to C++’s Rule of Five. The Rule of Five involves copy construction, move construction, destruction, copy assignment, and move assignment. If a programmer defines none of these special methods for a class, the compiler automatically will provide its own versions of each of them that work properly for classes that support value semantics; for example, all the classes in Chapter[TSjsupport value semantics. Classes that use value semantics avoid the memory management and aliasing issues we encountered with our linked list classes.

If the programmer defines one or more of a copy constructor, destructor, or copy assignment operator, the compiler will not automatically supply a move constructor or move assignment operator. This is not a problem as far as program correctness is concerned; move construction and move assignment merely provide an optimization that avoids the unnecessary creation of an extra object when constructing or assigning from a rvalue (temporary). A missing move constructor means a temporary is copied by the copy constructor, and a missing move assignment operator means a temporary is copied by the copy assignment operator.

The programmer can precisely control which of these special methods the compiler supplies by explicitly marking these methods with a default or delete label. We will not go into the details here, but merely provide a few examples.

Consider class XI:

class XI { public :

int data;

};

Class XI has no explicit constructor; therefore, the compiler will supply one that allows callers to create an XI object:

XI my_xl; // Okay; default constructed

std::cout << my_xl.data << '\n' ; // Prints some random integer value

In this case a client needs to reassign my_xl. data for the object to be remotely useful.

Next, consider class X2:

class X2 { public :

int data;

X2 (i nt n): data (n) {}

};

Here the programmer provides an explicit constructor, so the compiler will not generate a default constructor. This mean the following statement is illegal:

X2 my_x2; // Illegal; the client must provide an integer

If we really want a client to be able to create an object both with or without an integer argument, we can overload the constructor (provide our own default constructor) or force the compiler to generate one for us using the default label, as shown here:

©2018 Richard L. Halterman

Draft date: September 25, 2018

class X3 { public :

int data;

X3() = default; // Allow compiler to generate default constructor X3(int n): data(n) {} // and provide our own

};

This makes both of the following statements possible:

X3 my_x3a;

X3 my_x3b{4};

We can prevent the compiler from generating its default constructor by marking the default constructor it ordinarily would provide with the delete label, as in the following:

class X4 { public :

int data;

X4() = delete;

};

Did you notice that we violated the Rule of Three in our Node nested struct that we used in our linked list examples? We added a destructor but did not supply a copy constructor and did not define a copy assignment operator. How can we justify this decision?

In reality, the Node struct does not need a destructor. The linked list class will operate flawlessly with a Node inner struct that has no destructor. No code within the Node struct allocates any resources. The outer linked list class is responsible for allocating and deallocating memory resources. The linked list methods manipulate Node objects as passive data. We added the destructor only so we could see exactly when the program destroyed a Node object. This enabled us to detect memory leaks and multiple deletions and refine our linked list class into a robust useful type. The Node destructor cleans up no resources nor does anything else that would impact the work the compiler-generated copy constructor or the compiler-generated copy assignment operator would do. Remember, you should follow the Rule of Three unless you have a very good reason not to do so. In our case, our good reason is our destructor does nothing that would prompt us to write our own copy constructor and copy assignment operator to properly coordinate with destructor.

In order to emphasize our intentional decision to violate the Rule of Three, we can rewrite the Node struct as

struct Node {

int data; //

Node *next; //

Node (i nt d) ;

Node(const Node&) = default; Node(Node&&) = default;

—Node();

Node& operator^(const Node&) = Node& operator^ (Node&&) = defa

Table captionA data element of the list The node that follows this one

//

Constructor

//

Copy

constructor

//

Move

constructor

//

Destructor

default ;

//

Copy

assignment

It;

//

Move

assignment

};

By explicitly defaulting the copy constructor and copy assignment operator, we indicate that we did not omit them by accident. The inclusion of the destructor prevents the compiler from automatically generating a move constructor and move assignment operator. By declaring these two methods as default, the compiler will generate them for us.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Since our Node object contains only simple types (an i nt and a pointer) we can omit all the explicit defaulted methods in the declaration above, and nothing will be different. This is because C++ “moves” an integer merely by copying it. A simple integer has no resources we need to steal from a temporary; a simple assignment is all that is needed. Similarly, a pointer may refer to an elaborate object of some sort, but the pointer itself in simply an address. Copy and move construction is the same, and and copy and move assignment is handled the same as well.

Chapter Notes

The additional constructor is known as a move constructor, and the additional assignment operator is known as the move assignment operator. To make the discourse clearer, we will refer to the original assignment operator as copy assignment. The compiler can disambiguate between the overloaded methods by virtue of the actual parameters passed by the caller:

• If the caller passes an lvalue, the compiler generates code that invokes the copy constructor or copy assignment operator.

Draft date: September 25, 2018

18.6 Smart Pointers

C++ programmers that manually manage dynamic memory with new and delete follow a style inherited directly from the C programming language. Many modern programming languages like Python, Java, and C# manage dynamic memory through a technique called garbage collection. Garbage collection takes care of the accounting necessary to avoid multiple deletes and memory leaks. In garbage collected languages programmers need only call the equivalent of new; the garbage collector takes care of freeing up the space later when the executing program no longer uses the dynamically-allocated object. Garbage collection works well, but it does add some overhead to an executing program. This overhead consumes some extra memory and can affect a program’s run-time efficiency. C++ strives to be as efficient as possible, so it does not provide an automatic garbage collector. Garbage collected languages typically allocate all objects on the heap, thereby managing objects in a uniform manner. C++ supports statically-allocated and stack-allocated objects, as well as heap-allocated objects. Heap allocation is sightly slower, and heap fragmentation can further degrade program performance. C++ follows the mantra you only pay for what you use, meaning programs that do not need the heap do not incur the run-time cost of using the heap.

C++ provides the efficiency benefits of a non-garbage-collected language with the convenience of garbage collection when desired. C++ achieves this in various ways. One way we have seen and have been enjoying its benefits for some time. The std: :vector class manages a dynamic array, using new and delete behind the scenes. Software engineers implemented std : : vector carefully to do the right thing, avoiding aliasing, memory leaks, and multiple deletions.

Modern C++ makes it possible to write programs that manage dynamic memory using neither new nor delete directly. Such a style uses smart pointers', that is, pointers that “know” exactly when to deallocate the memory they reference.

C++ smart pointers eliminate the need for such manual intervention on the part of the programmer. A smart pointer automatically deletes its associated memory at the proper time. The std : : sha red_pt r type is one example of a standard C++ smart pointer.

Suppose we have the following Wi dget type:

struct Widget { int data;

Widget(int n): data(n) {}

};

The following code creates a Widget object on the heap and assigns it to a std : : shared_ptr object named p:

std::shared_ptr<Widget> p(new Widget(12));

The generic std: :make_shared function provides a more convenient way to make astd: :shared_ptr object:

std::shared_ptr<Widget> p = std::make_shared<Widget>(12);

©2018 Richard L. Halterman

Draft date: September 25, 2018

The std: :make_shared function eliminates the need of the new operator. It uses new behind the scenes to allocate the necessary memory for the object it creates, but the programmer does not see the new. On the other end of the object’s lifetime, programmers never call delete when using smart pointers; smart pointers automatically call delete at the proper time. The use of the std : : make_shared function enables programmers to work with dynamically-allocated memory without ever using new and delete directly. This removes the possibility of memory leaks and multiple deletions that haunt manual memory management.

We can use the type inference capabilities of auto to express smart pointer creation even more simply: auto p = std::make_shared<Widget>(12) ;

In the expression std : : make_sha red<Wi dget>(12) the name inside the angle brackets is the type of the object to create, and the value in the parentheses is the argument to pass to that type’s constructor. The compiler knows that the function will return type std: : shared_ptr<Widget>, so there is no need to spell out the exact type of p on the left side.

Once we have p defined in one of these ways we can treat it syntactically as if it were a raw pointer; for example:

// Make p point to a dynamically created a Widget object

auto p = std::make_shared<Widget> (12) ; std::cout << p->data << '\n' ; // Prints 12

p->data = 5;

std::cout << p->data << '\n' ; // Prints 5

Listing 18.21 (simplesharedptrtest.cpp) provides a program that performs some simple tests with std: :shared_ptr objects.

Listing 18.21: simplesharedptrtest.cpp

#include <iostream>

#include <string>

#include <memory>

struct Widget {

static unsigned id_source; // Source of unique IDs unsigned id;

WidgetQ: id (id_source++) {

std::cout << "Creating a widget #" << id << " ("

<< rei nterpret_cast<ui ntptr_t> (this)

<< ")\n";

}

~Widget() {

std::cout << "Destroying a widget #" << id << " (" << rei nterpret_cast<ui ntptr_t> (this)

<< ")\n";

}

};

unsigned Widget::id_source = 0;

// Global shared pointer

auto global_ptr = std::make_shared<Widget>(); std::shared_ptr<Widget> make_widget() {

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "- Entering make_widget - \n";

std::cout << "- Leaving make_widget - \n";

return std::make_shared<Widget>();

void testlQ {

std::cout << "- Entering Test 1 - \n";

// Make p point to a dynamically created a widget object auto p = std::make_shared<Widget>(); std::cout << p->id << '\n'; p->id = 25;

std::cout << p->id << '\n';

std::cout << "- Leaving Test 1 - \n";

void test2() {

std::cout << "- Entering Test 2 - \n";

// Make q point to a dynamically created a widget object

auto q = std::make_shared<Widget>();

std::cout << q->id << '\n';

q = nullptr; // Make q point to nothing

std::cout << "- Leaving Test 2 - \n";

Table captionvoid test3() {

Table captionstd::cout << "- Entering Test 3 - \n";

Table caption// Make p point to a dynamically created integer auto p = std::make_shared<i nt> (55);

std:

*p =

: cout

-4;

<< *p <<

' \n' ;

//

//

Prints 55 Reassign

std:

: cout

<< *p <<

' \n' ;

//

Prints -4

std:

: cout

<< "

Leaving Test

3 •

-\n" ;

void test4() {

std::cout << "- Entering Test 4 - \n";

static auto p = make_widget();

std::cout << p->id << '\n';

std::cout << "- Leaving Test 4 - \n";

void test5() {

std::cout << "- Entering Test 5 - \n";

auto p = make_widget();

std::cout << p->id << '\n';

std::cout << "- Leaving Test 5 - \n";

void test6() {

std::cout << "- Entering Test 6 - \n";

// Aliasing

auto q = std::make_shared<Widget>();

auto r = q; // r aliases q, no new memory allocated

auto s = q; // s aliases q, no new memory allocated

std::cout << q->id << 1 1

©2018 Richard L. Halterman

Draft date: September 25, 2018

<<

r->id

<<

1 1

<<

s->i d

<<

' \n 1 ;

q = nullptr; std::cout <<

r->i d

<<

1 1

<<

s->i d

<<

' \n' ;

r = nullptr; std :: cout <<

s->i d

<<

' \n' ;

s = nullptr;

//

Deallocates the widget object

std : :cout <<

II_

Leaving Test 6 - \n";

int main() {

std::cout << "- Entering main - \n";

testl (); test2 (); test3(); test4(); test5(); test6();

std::cout << "-Leaving main- \n";

}

The output of Listing |18.21} (simplesharedptrtest.cpp) shows chronologically when the program creates and destroys Wi dget objects:

Creating a widget #0 (18566044)

- Entering main

- Entering Test 1

Creating a widget #1 (18566092)

1

25

- Leaving Test 1

Destroying a widget #25 (18566092)

- Entering Test 2

Creating a widget #2 (18566380)

2

Destroying a widget #2 (18566380)

- Leaving Test 2

- Entering Test 3

55

-4

- Leaving Test 3

- Entering Test 4

- Entering make_widget

- Leaving make_widget

Creating a widget #3 (18566404)

3

- Leaving Test 4

- Entering Test 5

- Entering make_widget

- Leaving make_widget

Creating a widget #4 (18566092)

4

- Leaving Test 5

©2018 Richard L. Halterman

Draft date: September 25, 2018

Destroying a widget #4 (18566092)

- Entering Test 6

Creating a widget #5 (18566092)

5 5 5 5 5 5

Destroying a widget #5 (18566092)

- Leaving Test 6

- Leaving main

Destroying a widget #3 (18566404) Destroying a widget #0 (18566044)

The Wi dget constructor in Listing 18.21 (simplesharedptrtest.cpp) ensures that each widget object it creates has a unique id number. The first widget will have id 0, the second has id 1, etc.

The executing program initializes global objects before calling the mai n function. The first two lines of the program’s output:

Creating a widget #0 (18566044) - Entering main

shows the creation of the global object global_ptr. The next few lines:

- Entering Test 1

Creating a widget #1 (18566092)

1

25

- Leaving Test 1

Destroying a widget #25 (18566092)

show the creation of the local widget #1 in the testl function. The code in testl modifies the id value of the Wi dget object. (Recall that clients can freely modify fields of a struct.) At the end of the function’s execution the std : : shared_ptr object automatically destroys widget #1, now known as widget #25, as we can see the destructor’s output.

It is important to note that p is a local variable in testl, so the space for std: : shared_ptr p itself appears on the stack. The call to std : : make_sha red creates via new a widget object on the heap. When p goes out of scope at the end of testl’s execution, p’s desructor automatically calls delete to deallocate the widget from the heap. The usual function return mechanism automatically removes p from the stack.

The next few lines of output:

- Entering Test 2

Creating a widget #2 (18566380)

2

Destroying a widget #2 (18566380) - Leaving Test 2

shows that when a std: :shared_ptr previously assigned to a widget is reassigned, in this case to nullptr, the space for the original widget object is freed up (its destructor called) immediately; the object is cleaned up before reaching the end of the function.

In the next few lines of output:

©2018 Richard L. Halterman

Draft date: September 25, 2018

- Entering Test 3

55

-4

- Leaving Test 3

the test3 function does not reveal any clues about the automatic memory management ofstd:shared_pt as the i nt type has no constructors or destmctor that indicate the lifetime of the dynamically allocated i nt value. The program includes the test3 function simply to demonstrate that std : : sha red_pt r objects can manage the dynamic memory of simple types just as well as fancier types. The simple i nt type does not report its destruction when its memory is freed, but rest assured that the std : : shared_ptr object will deallocate its memory correctly.

In the next few lines of output:

- Entering Test 4

- Entering make_widget

- Leaving make_widget

Creating a widget #3 (18566404) 3

- Leaving Test 4

we see the creation of widget #3, but we do not see its destruction. This is because it is the first invocation of test4. The first call initializes the stati c local p, hence the construction of a std : : sha red_pt r and its associated Widget object. Since p is a static local variable it must survive between calls to test4; therefore, p cannot be deallocated until the program finishes executing (see below).

In the next few lines of output:

- Entering Test 5

- Entering make_widget

- Leaving make_widget

Creating a widget #4 (18566092)

4

- Leaving Test 5

Destroying a widget #4 (18566092)

we see the exact situation as in test4, except that p is not static. This means p destroys its widget object when the function returns.

In the output of the final test function, test6, we see

- Entering Test 6

Creating a widget #5 (18566092)

5 5 5 5 5 5

Destroying a widget #5 (18566092) - Leaving Test 6

The test6 function allocates just one Wi dget object. It assigns three std : : sha red_pt r objects to the same widget object. This provides a clear justification for the name shared_ptr —all three pointers share access to the same object. If p and q are std : : shared_ptrs of the same type, the statement

q = p;

©2018 Richard L. Halterman

Draft date: September 25, 2018

make p and q aliases to the same object. Regardless of the aliasing, the code within test6 allocates exactly one Widget object and deallocates that same Widget object when the function completes its execution.

The final lines in the program’s output:

- Leaving main

Destroying a widget #3 (18566404) Destroying a widget #0 (18566044)

show the destruction of test4’s static local std: :shared_ptr (widget #3) and global_ptr (widget #0).

If you analyze the output of Listingj 18.211 (simplesharedptrtest.cpp) carefully, you will see that every constructor call has an associated destructor call for the same object (remember testl renamed widget #1 to #25, so compare widget #1 ’s creation address with widget #25’s destruction address, and you will see they match). The heap provided all the space for Wi dget objects in Listing 18.21 (simplesharedptrtest.cpp), yet we see neither new nor delete anywhere in the code.

This ability to deallocate its referenced memory at the proper time is what makes a std : : sha red_pt r object a smart pointer.

Recall Listing 18.1j(howtodelete.cpp) that demonstrated the difficulty of managing dynamic memory manually. Listing l'8T22| (smartdelete.cpp) converts all the raw pointers of Listing fl8T] (howtodelete.cpp) into std : : sha red_pt rs. The result? We no longer need to worry about who “owns” the memory of the heap allocated objects; std : : shared_ptr objects manage all those details.

©2018 Richard L. Halterman

Draft date: September 25, 2018

while (n— > 0)

vec. push_back (get_widget());

// No need to clean up vector; smart pointers do it for us

}

int main() {

std::cout << "Entering main\n"; process(10);

std::cout << "Leaving main\n";

}

The output of Listing 18.22 (smartdelete.cpp) shows that the program destroys each Widget object it creates exactly once.

Entering Creatin Creatin Creatin Creatin Creatin Creatin Creatin Leaving Destroying widget 23 Destroying widget 45 Destroying widget Destroying widget Destroying widget 3 Destroying widget 20 Destroying widget

main

widget

23

widget

45

widget

16

widget

12

widget

3

widget

20

widget

10

mai n

16

12

10

How does a std : : shared_ptr smart pointer “know” when to call delete to free up its object? memory it manages by reference counting.

Given the following Widget type:

struct Widget { int value;

Widget(int value): value(value) {}

};

the following statement:

auto p = std::make_shared<Widget>(3) ;

creates a smart pointer referencing a Wi dget object containing the value 3. What happens to the object associated with p when we reassign the variable p? The following statement:

// p is the Widget object created above p = nullptr;

redirects p to point to nothing. At this point no variable references the Wi dget object created earlier. This means the object effectively is cut off from the remainder of the program’s execution. This abandoned object is classified as garbage. The term garbage is a technical term used in computer science that refers to memory allocated by an executing program that the program no longer can access. The std : : shared_ptr

©2018 Richard L. Halterman

Draft date: September 25, 2018

type uses a technique known as reference counting to automatically reclaim the space occupied by abandoned objects.

Reference counting garbage collection works as follows. All objects dynamically created via the std: :shared_ptr constructor or the std : : make_shared convenience function have an associated reference count. When the executing program creates a new object managed by a std : :shared_ptr object, it sets the shared pointer object’s reference count to 1. After executing the following statement:

auto p = std::make_shared<Widget>(3) ;

the reference count of p is 1. A reference count of 1 means that exactly one shared pointer object (in this case p) is assigned to the object. Making an alias, as in

q = p;

increments p’s reference count by one. Both p and q share the same object and share the same reference count. If we make another alias, as in

r = p;

the assignment statement increases the object’s reference count to 3. If reassign p, q, or r, as in q = std::make_shared<Widget>(22);

the reference count of the widget containing 3 decreases by one, and the reference count of the new widget object containing 22 becomes 1. If we then reassign p, for example:

p = nullptr;

this leaves only variable r referencing the widget containing 3, its reference count is 1. If we finally reassign r:

r = nullptr;

the reference count of the widget containing 3 drops to zero. The std : : sha red_pt r class has a custom assignment operator. The process of assignment alters the reference count for objects managed via these smart pointers. When an assignment would cause a shared pointer’s reference count for an object to become zero, the shared pointer can delete that object before attaching to the object being assigned. The assignment would increase the reference count of the object being assigned by one.

The std: :shared_ptr class has a method named use_count that returns the reference count for the current object managed by the shared pointer. Listing || T8.23|| (refcount.cpp) exploits this use_count method to demonstrate how reference counting garbage collection works.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Destroying a widget ("

<< rei nterpret_cast<ui ntptr_t> (this) << ")\n";

}

};

Table captionint main() {

Table captionauto p = std::make_shared<Widget>();

std::cout <<

p.use_count()

<<

' \n' ;

//

Prints

auto q = p; std::cout <<

p.use_count()

<<

' \n' ;

//

Prints

auto r = p; std::cout <<

p.use_count()

<<

' \n' ;

//

Prints

r = nullptr; std::cout <<

p.use_count()

<<

' \n' ;

//

Prints

q = nullptr; std::cout <<

p.use_count()

<<

' \n' ;

//

Prints

p = nullptr; std::cout <<

p.use_count()

<<

' \n' ;

//

Prints

Creating a 1 2 3 2 1

Destroying 0

.cpp) prints

widget (20338980)

a widget (20338980)

Observe how the object’s transition from a reference count of one to a reference count of zero automatically deletes the widget object, invoking its destructor.

In Listing 18.24 (intlist6.h) we retool our linked list class from Listing 18.18 fintlist5.h) to use std: :shared_ptr objects instead of raw pointers.

Listing 18.24: -intlist6.h

// intlist6.h

#include <memory> // For std::shared_ptr class IntList6 {

// The nested private Node class from before struct Node {

int data; // A data element of the list

std::shared_ptr<Node> next; // The node that follows this one Node(int d); // Constructor

Node(const Node&) = default; // Copy constructor

Node(Node&&) = default; // Move constructor

~Node(); // Destructor

Node& operator=(const Node&) = default; // Copy assignment

Node& operator= (Node&&) = default; // Move assignment

©2018 Richard L. Halterman

Draft date: September 25, 2018

};

// Points to the first item in the list // Points to the last item in the list

std::shared_ptr<Node> head; std::shared_ptr<Node> tail;

int len;

public :

// The constructor makes an IntList6();

// Number of elements in the list

initially empty list

// The destructor that reclaims the list's memory ~IntList6();

// Copy constructor

IntList6 (const IntList6& other);

// Move constructor

IntList6(IntList6&& other);

// Assignment operator

IntList6& operator=(const IntList6& other);

// Move assignment operator

IntList6& operator= (IntList6&& other);

// Inserts n onto the back of the list, void insert(int n);

// Prints the contents of the linked list of integers, void printQ const;

// Returns the length of the linked list, int lengthQ const;

// Removes all the elements in the linked list, void clear();

Listing |T8.25|(intlist6.cpp) implements methods declared in Listing p~8.24|(intlist6.h).

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

<< " (" << rei nterpret_cast<ui ntptr_t> (thi s) << ")\n";

IntList6 std:

}

:Node::~Node() {

cout << "Destroying node " << data

<< " (" << rei nterpret_cast<ui ntptr_t> (thi s)

<< ")\n";

// The constructor makes an initially empty list.

// The list is empty when head and tail are null.

IntList6::IntList6(): head (nullptr) , tai1 (nullptr) , len(0) {}

// Copy constructor makes a copy of the other object's list IntList6::IntList6(const IntList6& other): IntList6() {

// Walk through other's list inserting each of its elements // into this list

for (auto cursor = other.head; cursor; cursor = cursor->next) insert(cursor->data);

}

// Move constructor takes possession of the temporary's list

IntList6::IntList6(IntList6&& temp): IntList6() {

// Swap contents with the temporary std::swap(head, temp.head); std::swap(tail, temp.tail); std::swap(len, temp.len);

// Assignment operator

IntList6& IntList6:: operator=(const IntList6& other) {

// Make a local, temporary copy of other IntList6 temp{other};

// Exchange the head and tail pointers and len from this list

// with those of the new, temporary list

std::swap(head, temp.head);

std::swap(tail, temp.tail);

std::swap(len, temp.len);

// The temporary list now points to this list's original contents, // and this list now points to the copy of other's list // The temporary list will be destroyed since it is a temporary return *this;

}

// Move assignment operator

IntList6& IntList6::operator=(IntList6&& temp) {

// Exchange the head and tail pointers and len from this list

// with those of the new, temporary list

std::swap(head, temp.head);

std::swap(tail, temp.tail);

std::swap(len, temp.len);

// The temporary list now points to this list's original contents, // and this list now points to the temporary's list // The temporary list will be destroyed since it is a temporary return *this;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// The destructor deallocates the memory held by the list IntList6::~IntList6() { clearQ; }

// Inserts n onto the back of the list.

// n is the element to insert, void IntList6::insert (i nt n) {

// Make a node for the new element n

std::shared_ptr<IntList6::Node> new_node = std::make_shared<Node>(n); if (tail) { // Is tail non-null?

tail->next = new_node; // Link the new node onto the back

tail = new_node; // The new node is the new tail of the list

}

else // List is empty, so make head and tail point to new node head = tail = new_node; len++;

// Prints the contents of the linked list of integers.

void IntList6::print() const {

for (auto cursor = head; cursor; cursor = cursor->next) std::cout << cursor->data << 1 '; std::cout << '\n 1 ;

}

// Returns the length of the linked list, int IntList6::length() const { return len;

}

// Removes all the elements in

void IntList6::clear() { auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next; temp->next = nullptr;

head = tail = nullptr; // len = 0;

the linked list.

// Remember where we are

// Move next node

// Sever link from previous node

Null head signifies list is empty

Nowhere in the IntList6 class can we see the new or delete operators. The std : : make_shared function and std : : shared_ptr class hides those details from us.

We could have expressed the code within the clea r method as simply as the following:

void IntList6::clear() {

head = tail = nullptr; // Null head signifies list is empty len = 0;

}

Note that it uses no loop to iterate over the nodes of the list. When we set head, which points to the first element in the list, to nullptr, the reassignment automatically will destroy the first node on the list. This is because no other smart pointers currently point to that node. The destruction of the first node will destroy

©2018 Richard L. Halterman

Draft date: September 25, 2018

its next pointer that points to the second node on the list. This results in the destruction of the second node. The destruction of the second node destroys its next pointer which leads to the distruction of the third node, followed by the fourth node, etc. This cascading process ultimately destroys all the nodes in the list to which head points.

If this simple implementation of clea r achieves the same result as the more involved clear method in Listing 18.25 (intlist6.cpp) that uses a loop, why even consider the more complicated code? As it turns out, the simpler method has a problem with very long lists. To see how, suppose we have a long linked list. When the clear method sets the std: :shared_ptr head to null, no other smart pointers will be pointing to the first node. The smart pointer reassignment in this case calls a method behind the scenes to destroy the object to which it points (the object to which head points; that is, the first node in the list). This clean-up method does not return until the process is complete, and, for long lists, this process can be quite lengthy. The destruction of the first node requires the destruction of its next pointer, head->next. This head->next pointer points to the second node in the list. The destruction of this head->next pointer triggers the destruction of the second node because no other std: :shared_ptr objects point to it. This means that before head’s clean-up method returns, the chain of events it sets off must invoke the clean-up method of head->next which leads to the destruction of the second node. The destruction of the second node necessarily must destroy the next smart pointer of the second node (head->next->next). This in turn leads to the destruction of the object to which head->next->next points (that is, the third node in the list). By this same process, the destruction of the third node in the list leads to the destruction of the fourth node, and then the fifth node, etc. This cascade of method calls continue until it reaches the last node in the list. Two smart pointers point to the last node: the next pointer of the next-to-the-last node in the list and the tai l pointer of the Li nkedLi st object itself. The destruction of the next-to-the-last node removes one of the smart pointers but not the other. This means the clean-up method of the next-to-the-last node cannot destroy the last node. This turns out not to be a memory leak, however, as the clear method also sets tail to nullptr, so eventually the last node will be destroyed properly.

Everything appears to work perfectly—automatic resource management as advertised—so what is the problem for very long lists? We left the activity of the LinkedList: :clear method as the destruction of the next-to-the-next-to-last smart pointer’s clean-up method was destroying the next-to-the-last node in the list. The problem is this: The destruction of the first node of the list is not complete until the destruction of the second node is complete. The destruction of the second node is not complete until the destruction of the third node is complete, and so forth. This means the clean-up method destroying the first node does not do its job, return, and then clean up the node’s next pointer; it does not return until the second completes its clean up, which, of course, does not complete until the third node’s clean up is finished, etc. Theoretically, this chain of function calls eventually returns back to the action that initiated it—the reassignment of head to nullptr, and for lists that are not too long, this is the case. Each method invocation consumes some stack space, and for very long lists this call chain can be so deep so as to overflow the stack, causing the program to crash. The scenario is similar to a recursive function that recurses too deeply. On one system the program crashed when attempting to destroy a linked list containing 10,000 nodes.

The version of clear in Listing 18.25 (intlist6.cpp) iterates through the list setting the next pointers of the nodes it most recently visited to nullptr. On the very next iteration the temporary pointer temp destroys the node during its reassignment from cursor. This means it must destroy temp’s next smart pointer, but the previous iteration set this to null. This eliminates the chaining problem and allows the previous node to be destroyed with a single function call that returns immediately. This version deallocates the list through a series of separate, isolated function calls that return immediately rather than a chain of function invocations that potentially can overflow the stack.

Listing 18.26 (smartlist.cpp) exercises our IntLi st6 class, verifying that the smart pointers properly manage the dynamic memory.

©2018 Richard L. Halterman

Draft date: September 25, 2018

destructions. The std : : shared_ptr objects take care of all the heap management.

Our linked list class has an insert method that allows clients to add elements to the list, but it has no method that enables a client to remove a single element. In our most recent non-smart-pointer class, IntList5, we could add the following method:

// Removes the first occurrence of n from the list.

// Returns true if successful (found n and removed it).

// Returns false if n is not originally present in the list, bool IntList5::remove(int n) {

Node *cursor = head, // Start at head of list

*prev = head; // Keep track of previous node seen // Loop until we run off the end of the list or find n,

// whichever comes first

while (cursor && cursor->data != n) {

prev = cursor; // Remember previous node

cursor = cursor->next; // Move to next node

}

if (leursor) // Did we run off the end of the list

return false; // Indicate we did not find n

Table caption// Found n; cursor is pointing at the node containing n

if

(head == tail)

//

head = tail = nullptr;

//

else if (cursor == head)

//

head = head->next;

//

else

//

prev->next = cursor->next;

//

if

(cursor == tail)

//

tail = prev;

//

delete cursor;

//

len

3

//

n was the only element in the list cursor still points to node with n Is n the first element in the list Redirect head around n n is not the first element Redirect previous node around n Was n the last element in the list Update tail to new last element

Delete n's node

List size decreases by 1

Table caption©2018 Richard L. Halterman

Draft date: September 25, 2018

return true;

}

// We found n and deleted its node

The remove method is more complicated than the i nsert method because the i nsert method always adds new elements to the back end of the list. The remove method must be able to remove elements from anywhere in the list—front, back, and anywhere in between.

The remove method for our IntLi st6 smart list class would look like the following:

// Removes the first occurrence of n from the list.

// Returns true if successful (found n and removed it).

// Returns false if n is not originally present in the list, bool IntList6::remove (i nt n) {

auto cursor = head, // Start at head of list

prev = head; // Keep track of previous node seen

// Loop until we run off the end of the list or find n,

// whichever comes first

while (cursor && cursor->data != n) {

prev = cursor; // Remember previous node

cursor = cursor->next; // Move to next node

}

if (Icursor) // Did we run off the end of the list

return false; // Indicate we did not find n

// Found n; cursor is pointing

if (head == tail)

head = tail = nullptr; else if (cursor == head) head = head->next;

else

prev->next = cursor->next; if (cursor == tail) tail = prev;

// No delete is necessary len—;

return true;

at the node containing n // n was the only element in the list // cursor still points to node with n // Is n the first element in the list // Redirect head around n // n is not the first element // Redirect previous node around n // Was n the last element in the list // Update tail to new last element

// List size decreases by 1

// We found n and deleted its node

The IntLi st6: : remove method still needs to perform all the checks and properly redirect the pointers within the list, but it no longer needs to call delete explicitly.

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 19

Generic Programming

CAUTION! CHAPTER UNDER CONSTRUCTION

The flexible sorting examples in Listing [lX2| (flexibleintsort.cpp), Listing [T63] (loggingflexiblesort.cpp), and Listing 17.35|(polymorphicsort.cpp) allow us to arrange the elements in integer vectors in creative ways and perform other interesting activities such as logging. Those examples demonstrate the power of function pointers, inheritance, and polymorphism. As flexible and powerful as these techniques are, they all contain one major limitation: they deal with vectors of integers only. Consider the Comparer class from Listing 17.33 (comparer.h) and Listing 17.34 (comparer.cpp), and the “flexible” selecti on_sort function from Listing 17.38 (loggingsort.cpp). The selecti on_sort function accepts a vector of integers and a Comparer reference. What if we need to sort a vector of double-precision floating-point numbers or a vector of std : : stri ng objects? Unfortunately, all of this “flexible” code cannot handle this seemingly minor variation.

In this chapter we look at C++’s template mechanism that enables programmers to develop truly generic algorithms and data structures. We will see how the standard C++ library has embraced the template technology to provide a wealth of generic algorithms and data structures that greatly assist developers in the construction of quality software.

19.1 Function Templates

Consider the following comparison function found in Listings Listing [12,2| (flexibleintsort.cpp), Listing |[16.5|| (loggingflexiblesort.cpp), and Listing|l7?38|(loggingsort.cpp):

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

bool less_than (i nt a, int b) { return a < b;

}

Listing 19.1 (testlessthan.cpp) tests the less_than function with various arguments.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The compiler generates warnings for the last two statements. The less_than function expects two integer arguments, but the calling code sends two double-precision floating-point values. The automatic

conversion from double to i nt can lose information, hence the warnings. The output of Listing 19.1 (testlessthan.cpp) shows that we should take these warnings seriously:

Obviously 2 < 3 and 2.7 2.2, but 2.2 ^ 2.7? The automatic double to i nt conversion truncates, so

the less_than function treats both 2.2 and 2.7 as 2, and clearly 2-^2.

The situation is even worse for the following code:

std::string wordl = "ABC", word2 = "XYZ"; std::cout << (wordl < word2) << '\n' ; std::cout << (word2 < wordl) << '\n' ;

// The next statement will not compile //std::cout << less_than(wordl, word2) << '\n';

The C++ standard library provides a global operator< function that compares two std : : stri ng objects lexicographically. The first two std : : cout statements produce the expected output:

but the last line that is commented out will not compile if we remove the commenting symbols. This is because the C++ library does not provide a standard conversion from std: : string to int, and less_than requires two i nt parameters.

As another example, consider the following function that computes the sum of the elements in a vector of integers:

int sum(const std::vector<i nt>& v) { int result = 0; for (int elem : v)

©2018 Richard L. Halterman

Draft date: September 25, 2018

result += elem; return result;

}

The following client code works well:

std::vector'd' nt> v {10, 20, 30}; std::cout << sum(v) << ' \n' ;

It prints 60. The following code does not compile:

std:: vector<double> v {10, 20, 30}; std::cout << sum(v) << '\n' ;

The second code fragment attempts to pass a vector of double-precision floating-point values to the sum function. Unfortunately, the sum function accepts only vectors that contain integers. More precisely, sum accepts only arguments of type std: : vector<i nt>, and a std : : vector<double> object is not a std : : vector<i nt>. The solution is easy; just copy and paste the original sum function and change all the occurrences of “i nt” to “double,” creating an overloaded sum function:

double sum(const std:: vector<double>& v) { double result = 0; for (double elem : v) result += elem; return result;

}

This works, but the duplicated effort is unsatisfying. These two overloaded sum functions are identical except for the types involved. The actions of the two functions—the initialization, vector traversal and arithmetic—are essentially the same. In general, code duplication is undesirable. A programmer that discovers and repairs an error in one of the functions must remember to apply the corresponding correction to the function’s overloaded counterpart.

Both the less_than and sum functions share a common shortcoming: they are tied in some way to a particular data type. It would be convenient to be able to specify the common pattern and let the compiler fill in the types as required. In the case of less_than we would like to be able to write a function that can use the < operator on parameters of any type for which < is compatible. For sum, we would like to create a generic function that works for vectors containing any numeric type.

C++ enables programmers to write such generic functions via templates. A function template specifies a pattern of code, and either the programmer or the compiler supplies the exact type as needed. Listing [1972] (templatelessthan.cpp) uses C++’s template mechanism to create a generic less_than function.

©2018 Richard L. Halterman

Draft date: September 25, 2018

return a < b;

}

int main() {

std::cout << less_than(2, 3) << '\n'; std::cout << less_than(2.2, 2.7) << '\n ' ; std::cout << less_than(2.7, 2.2) << '\n';

std::string wordl = "ABC", word2 = "XYZ"; std::cout << less_than(wordl, word2) << '\n'; std::cout << less_than(word2, wordl) << ' \n';

}

In the less_than function definition:

template <typename T> bool less_than(T a, T b) { return a < b;

}

template and typename are reserved words, and T is a type parameter. The template keyword indicates that the function definition that follows is not a normal function definition but rather is a pattern or template from which the compiler can attempt to produce the correct function definition. A function template is also known as a generic function. The typename keyword indicates that the identifier that follows (in this case T) is a placeholder for a C++ type name. The type parameter T stands for an actual type to be determined elsewhere. T is an identifier and so can have any name legal for a variable, function, or class; some programmers prefer more descriptive names such as CompareType or TypeParam. Single capital letters such as T, S, U, and V are popular type parameter names among C++ programmers. Just as a regular parameter of a function or method represents a value, a template parameter represents a type.

You may use the reserved word class interchangeably with the keyword typename in this context:

template <class T> bool less_than(T a, T b) { return a < b;

}

In Listing 19.2 (templatelessthan.cpp) the compiler generates three different less_than functions: one that accepts two integers, one that accepts two double-precision floating-point values, and one the accepts two string objects. Although the programmer cannot see them in the source code, the compiler in effect creates the following literal function definitions:

bool less_than (i nt a, int b) { return a < b;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

bool less_than (double a, double b) { return a < b;

}

bool less_than(std::string a, std::string b) { return a < b;

}

When the compiler generates an actual function definition from a template function, the process is called template instantiation, not to be confused with an object instantiation from a class.

The compiler instantiates functions only as needed. If Listing [|T9T2| (templatelessthan.cpp) did not contain the std : : stri ng objects, when processing the source code the compiler would not instantiate the version of less_than that accepts two std : : stri ng objects.

For efficiency purposes, the better way to write less_thanis

template ctypename T>

bool less_than (const T& a, const T& b) { return a < b;

}

Notice that parameters a and b are passed by reference, not by value. This means the caller passes only the addresses of objects a and b and does not need to make copies to send to the function. This can make a big difference if T represents large objects. Since the parameters are const references, the function cannot change the state of the caller’s actual parameters; therefore, the function offers call-by-value safety without the overhead of copying the parameters.

If a caller attempts a statement such as

std::cout << less_than(2, 2.2) << '\n' ;

the compiler generates an error. This is because the template definition specifies that its two type parameters are identical. The literal 2 is an i nt, and the literal 2.2. is a double. The compiler can automatically instantiate less_than functions that accept two i nts or two doubles but not mixed types. In the expression

less_than(2, 2.2)

the compiler cannot know which instantiated version of the template to call.

One solution requires the programmer to explicitly instantiate the function a shown here: std::cout << less_than<i nt> (2, 2.2) << '\n' ;

This forces the compiler to instantiate and call the integer version. The compiler will issue a warning about truncating the 2.2. The statement

std::cout << less_than<double> (2, 2.2) << ' \n ' ;

would use the double-precision floating-point version of less_than, and it compiles cleanly with no warnings since widening the i nt 2 to a double is automatic.

We can rewrite the less_than template function to avoid the need for explicit instantiation. For the most flexibility, we can express the less_than template function as

©2018 Richard L. Halterman

Draft date: September 25, 2018

template ctypename T, typename V> bool less_than (const T& a, const V& b) { return a < b;

}

This version uses two type parameters, T and V, and they can represent different types. With this new definition all of the following statements are acceptable:

std::cout << less_than(2, 3) << '\n' ; std::cout << less_than(2.2, 2.7) << '\n' ; std::cout << less_than(2, 2.2) << '\n' ; std::cout << less_than(2.2, 2) << '\n' ;

No explicit template instantiation is necessary. Given this calling code, the compiler will automatically instantiate four overloaded less_than functions:

• less_than(2, 3) instantiates bool less_than (const i nt& a, const i nt& b)

• less_than (2.2, 2.7) instantiates bool less_than (const double& a, const double& b)

• less_than(2, 2.2) instantiates bool less_than (const int& a, const double& b)

• less_than (2.2, 2) instantiates bool less_than (const double& a, const i nt& b)

While this more flexible less_than template function allows us to compare mixed numeric expressions, in general it makes more sense to expect the two parameters to be the same type.

Returning to our vector summation function, we can express sum generically as

template ctypename T>

T sum(const std::vector<T>& v) {

T result = 0; for (T elem : v)

result += elem; return result;

}

As in the case of the generic less_than function, the keyword template introduces a template definition. The angle brackets (<>) that follow the template keyword contain declarations of template parameters.

When the compiler sees calling code like

std::vectorci nt> v {10, 20, 30}; std::cout << sum(v) << '\n' ;

it knows v’s declared type is std : : vectorci nt>; therefore, it uses the pattern in the template to instantiate an actual function that looks like the following:

// The compiler automatically generates this from the template: int sum(const std::vectorci nt>& v) { int result = 0; for (int elem : v) result += elem; return result;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

Notice how the compiler simply substitutes i nt for every occurrence of the type parameter T. If the compiler sees code like

std:: vector<double> v {10, 20, 30}; std::cout << sum(v) << '\n' ;

it again uses the template to instantiate the following function:

// The compiler automatically generates this:

double sum(const std:: vector<double>& v) { double result = 0; for (double elem : v) result += elem; return result;

}

Table captionIn a program that has code like

std:

: vector<double>

v {10, 20, 30};

std:

:vector<int> w

© i—1

'-v J

20, 30};

std:

:cout << sum(v)

<<

’\n* ;

std:

:cout << sum(w)

<<

1 \n ’ ;

the compiler will instantiate both versions of the sum function. The compiler generates these automatically and secretly. The programmer never sees these instantiated template functions because they do not appear in any source code. Unlike the preprocessor that sends a modified version of the source code to the compiler (see Section |1.2| to review the preprocessor’s role in the program’s build process), a modern C++ compiler generates the machine language versions of these instantiated functions directly from the programmer’s source code.

Recall our swap function from Listing 10.19 (swapwithreferences.cpp). Callers can use it to interchange the values of two integer variables. With our knowledge of C++ templates, we now can write a generic version that interchanges the values of two variables of any type:

/*

* swap(a, b)

* Interchanges the values of memory

* referenced by its parameters a and b.

* It effectively interchanges the values

* of variables in the caller's context. */

template <typename ElemType>

void swap(ElemType& a, ElemType& b) {

ElemType temp = a; a = b; b = temp;

The only restriction is the two parameters must be the same type. Here the type parameter’s name is ElemType. This swap function works fine, but we do not need to write such a function ourselves; the C++ standard library includes a std : : swap template function that does the same thing as our swap function shown above.

The following function will print the contents of a vector of any type:

©2018 Richard L. Halterman

Draft date: September 25, 2018

/*

* print

* Prints the contents of a vector

* a is the vector to print.

* a is not modified.

*/

template ctypename T> void print(const std::vector<T>& a) { int n = a.size(); std::cout << '{ 1 ; if (n > 0) {

std::cout << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a [ i ] ; // Print the rest

}

std::cout << ' } ' ;

}

The restriction here is that the elements in the vector must be printable to the std : : cout object using < <.

Listing 1 19.3] (templateflexsort.cpp) uses our new generic functions to increase the flexibility of our flexible sorting program from Listing|12.2|(flexibleintsort.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

* vec is a vector.

* compare is a function that compares the ordering of

* two types that support the < operator.

* The contents of vec are physically rearranged.

*/

template <typename T>

void selection_sort(std::vector<T>& vec,

bool (*compare) (const T&, const T&)) { int n = vec.size(); for (int i = 0; i < n - 1; i++){

// Note: i,small, and j represent positions within vec.

// vec[i], vec[small], and a [ j] represents the elements at // those positions.

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less // than vec[i] int small = i ;

// See if a smaller value can be found later in the vector for (int j = i + 1; j < n; j++)

if (compare(vec[j], vec[small]))

small = j; // Found a smaller value // Swap vec[i] and vec[small], if a smaller value was found if (i != small)

std::swap(vec[i], vec[small]); // Uses swap from <utility>

}

}

/*

* print

* Prints the contents of a vector

* vec is the vector to print.

* The function does not modify vec.

*/

template <typename T>

void print(const std::vector<T>& vec) { int n = vec.size(); std::cout << '{' ; if (n > 0) {

std::cout << vec[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << vec[i]; // Print the rest

}

std::cout << '}' ;

int main() {

std::vector<int> list{23, -3, 4, 215, 0, -3, 2, 23, 100, 88, -10};

std::cout << "Original: ";

print(list);

std::cout << 1 \n 1 ;

selection_sort(list, less_than<i nt> ); std::cout << "Ascending: "; print(list);

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << 1 \n 1 ;

selection_sort(list, greater_than<i nt>) ;

std::cout << "Descending:

print(list);

std::cout << 1 \n 1 ;

std: : cout << "-\n" ;

std::vector<std::string> words { "tree", "girl", "boy", "apple",

"dog", "cat", "bird" };

std::cout << "Original:

print(words);

std::cout << 1 \n 1 ;

selection_sort(words, less_than<std::string>);

std::cout << "Ascending:

print(words);

std::cout << 1 \n 1 ;

selection_sort(words, greater_than<std::string>);

std::cout << "Descending:

print(words);

std::cout << 1 \n 1 ;

Notice that all the functions except for mai n are generic functions. The selecti on_so rt function is the most interesting one. It accepts a generic array and a function pointer that accepts two generic parameters of the same type. In one of its invocations in mai n:

selection_sort(list, greater_than<i nt>) ;

the expression greater_than<i nt> is an explicit template instantiation, and it tells the compiler we want to send to the selection_sort function a pointer to the greater_than function instantiated with integer parameters. This explicit instantiation is required because the compiler cannot automatically instantiate the greater_than function without an actual call to the function passing real parameters, and a pointer to a function is not a function invocation. At this point in the program we are not calling the greater_than function but only passing a pointer to it. Calling it would provide the necessary type information to the compiler via the actual parameters used, but a pointer to a function does not contain parameter information. The compiler needs the assistance of this explicit template instantiation.

The call to swap within selection_sort is actually invoking the std : : swap function from the standard library. The #i nclude <uti li ty> directive brings in the declaration for std : : swap, which itself is a template function.

The compiler can instantiate an actual function from a template function only if the type substituted for the template parameter supports its use within the function. Consider the following code:

// Make two ofstream objects

std::ofstream foutl("filel.data") , fout2("file2.data") ;

// Compare them

if (less_than(foutl, fout2) // <-- Error!

std::cout << "foutl is less than fout2\n";

The expression less_than(foutl, fout2) is illegal because no operator< exists to compare two std : : ofstream objects; thus, the compiler cannot produce the machine language that represents the expression a < b when a and b are std : : of streams. Ultimately, therefore, the compiler cannot instantiate an actual less_than function that accepts two std : : ofstream objects.

©2018 Richard L. Halterman

Draft date: September 25, 2018

When programmers use templates incorrectly or construct incorrect template functions or classes, the compiler can detect and report the problems. All current C++ compilers share one weakness with template processing: poor human-readable error messages. The error messages the compiler produces in these situations tend to be lengthy and difficult to decipher even for experienced C++ programmers. This is because the compiler bases its error messages on its processing of the instantiated code, not the original un-instantiated code. Since programmers see only the un-instantiated source, deciphering the compiler’s template error messages tends to be more challenging than usual.

As Listing|19.4|(templatescale.cpp) shows, a template can accept non-type parameters.

Note that in Listing ||19.4| (templatescale.cpp) the typename keyword is missing, and in its place is the actual type i nt. This means parameter N is a non-type template parameter. The program prints

15

40

Listing fl93|(templatescale2.cpp) uses both a type-parameter and a non-type parameter.

Listing |T93|(templatescale2.cpp) displays the following during its execution:

15.9

40

The compiler will instantiate two scale functions:

// Instantiated by the compiler due to scale<double, 3>: double scale(const double& value) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

return value * 3;

}

and

// Instantiated by the compiler due to scale<int, 4>: int scale(const int& value) { return value * 4;

}

The types of non-type template parameters permitted by C++ are very limited. Integral types (i nt, unsi gned, long, etc.) are acceptable, as are pointers and references. Other types such as floating-point and programmer-defined types may not be non-type template parameters.

The C++ Standard Library contains many generic functions, some of which we have seen already:

• std : : max —computes the maximum of two values

• std : : mi n—computes the maximum of two values

• std : : swap —interchanges the values of two variables

19.2 Class Templates

Function templates (Section [19.1| enable us to build generic functions. C++ supports class templates as well. With class templates we can specify the pattern or structure of a class of objects in a type-independent way. The class template mechanism is a key tool for creating generic types.

As a simple example, consider a basic Point class that represents two-dimensional point objects. Mathematical point objects should have real-valued coordinates that we can approximate with doubleprecision floating-point values. A point on a graphical display, on the other hand, better uses integer coordinates because screen pixels have discrete, whole number locations.

Rather than providing two separate classes, we can write one class template let the compiler instantiate the coordinates as the particular program requires. Listing] 19.6[(genericpoint.h) contains the generic class.

If a client declares a Point object as Point<int> pixel(10, 10);

©2018 Richard L. Halterman

Draft date: September 25, 2018

the compiler will instantiate a Poi nt<~i nt> class that looks like

class Point { public: i nt x; int y;

Point(int x, int y): x(x), y(y) {}

};

If a client instead declares a Point object as Poi nt<double> pixel(10.0, 20.0);

the compiler will instantiate a Poi nt<double> class that looks like

class Point { public: double x; double y;

Point(double x, double y): x(x), y(y) {}

};

Neither of these instantiations appear in any source code, so a programmer will not see them. The compiler substitutes actual types (i nt or double) for the parameterized type (T).

As a more significant example. Listing 19.7 (genericcomparer.h) contains the declaration of a Comparer class that is the generic equivalent to Listing 17.33 (comparer.h).

Listing 19.7: genericcomparer.h

#ifndef GENERICCOMPARER_H_

#define GENERICCOMPARER_H_

/*

* Comparer objects manage the comparisons and element

* interchanges on the selection sort function below.

*/

template <typename T> class Comparer {

// The object's data is private, so it is inaccessible to // clients and derived classes

// Keeps track of the number of comparisons

// performed

int compare_count;

// Keeps track of the number of swaps performed

int swap_count;

// Function pointer directed to the function to

// perform the comparison

bool (*comp) (const T&, const T&);

protected :

// Method that actually performs the comparison // Derived classes may customize this method virtual bool compare_impl (const T& m, const T& n) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

return comp(m, n);

//

Method that actually performs the swap

Table caption// Derived classes may customize this method virtual void swap_impl(T& m, T& n) {

}

T temp = m; m = n; n = temp;

public

//

The client must initialize a Comparer object with a

// suitable comparison function.

Comparer (bool (*f) (const T&, const T&)):

compare_count(0), swap_count(0), comp(f) {}

Table caption// Resets the counters to make ready for a new sort void reset() {

}

compare_count = swap_count = 0;

//

//

Method that performs the comparison. It delegates the actual work to the function pointed to by comp.

Table caption// This method logs each invocation, bool compare (const T& m, const T& n) {

}

compare_count++;

return compare_impl(m, n) ;

//

//

//

//

Method that performs the swap.

Interchange the values of

its parameters a and b which are

passed by reference.

Table caption// This method logs each invocation void swap(T& m, T& n) {

}

swap_count++; swap_impl(m, n);

//

//

Returns the number of comparisons this object has performed since it was created.

Table captionint comparisons() const {

}

return compare_count;

//

//

Returns the number of swaps this object has performed since it was created.

Table captionint swaps() const {

}

};

return swap_count;

#endif

©2018 Richard L. Halterman

Draft date: September 25, 2018

As with Listing [|T7T33 (comparer.h), the Comparer objects specified in Listing jl977j (genericcomparer.h) compare and swap any types of values and are meant to be used in a vector or array sorting program. Given the function

bool less_than (i nt m, int n) { return m < n;

}

the following code fragment instantiates a Comparer template that works with integers:

Comparer comp(less_than); // Make an integer comparer object

Listing [19j8j(genericstatisticssort.cpp) provides the client code that tests the new Comparer class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

template <typename T>

std::ostream& operator<< (std::ostream& os, const std::vector<T>& a) { int n = a . size (); os << ;

if (n > 0) {

os << a[0]; // Print the first element

for (int i = 1; i < n; i++)

std::cout << << a [ i] ; // Print the rest

}

os << ' } ' ; return os;

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

template <typename T>

bool less_than (const T& a, const T& b) { return a < b;

}

/*

* greater_than(a, b)

* Returns true if a > b; otherwise, returns

* false.

*/

template <typename T>

bool greater_than (const T& a, const T& b) { return a > b;

}

int main() {

// Make a vector of integers

std::vector<i nt> original { 23, -3, 4, 215, 0, -3, 2, 23, 100, 88, -10 };

// Make a working copy of the original vector

std::vector<i nt> working = original; std::cout << "Before: ";

std::cout << working << '\n';

Comparer<i nt> It(less_than<i nt>) , gt(greater_than<int>); selection_sort(working, It); std::cout << "Ascending: "; std::cout << working << ' \n';

std::cout << " (" << It.comparisons() << " comparisons, "

<< It.swapsQ << " swaps)\n";

std: : cout << "-\n" ;

// Make another copy of the original vector

working = original;

std::cout << "Before: ";

std::cout << working << ' \n';

selection_sort(working, gt);

std::cout << "Descending: ";

std::cout << working << ' \n';

©2018 Richard L. Halterman

Draft date: September 25, 2018

Table captionstd::cout << " (" << gt.comparisons() << " comparisons,

Table caption<< gt.swaps() << " swaps)\n";

std

::cout << "

- \n" ;

//

Make a vector of strings

std

::vector<std::string> str_original

{ "tree",

"boy",

"apple"

"girl",

"dog" ,

"cat" }

//

Make a working copy of the original

vector

std

::vector<std::string> str_working =

str_original;

std

::cout << "Before: " ;

std

::cout << str_working << '\n';

Comparer<std::string> str_lt(less_than<std::string>),

str_gt(greater_than<std::string>); selection_sort(str_working, str_lt); std::cout << "Ascending: std::cout << str_working << '\n' ;

std::cout << " (" << str_lt.comparisons() << " comparisons,

<< str_lt.swaps() << " swaps)\n";

std: : cout << "-\n" ;

// Make another copy of the original vector

str_working = str_original;

std::cout << "Before:

std::cout << str_working << '\n' ;

selection_sort(str_working, str_gt) ;

std::cout << "Descending:

std::cout << str_working << '\n' ;

std::cout << " (" << str_gt.comparisons() << " comparisons,

<< str_gt.swaps() << " swaps)\n"; std: : cout << "-\n" ;

}

Listing |1978| (genericstatisticssort.cpp) demonstrates that the generic Comparer class works equally as well with integers and strings; the program’s output is

Before: {23,-3,4,215,0,-3,2,23,100,88,-10}

Ascending: {-10,-3,-3,0,2,4,23,23,88,100,215}

(55 comparisons, 7 swaps)

Before: {23,-3,4,215,0,-3,2,23,100,88,-10}

Descending: {215,100,88,23,23,4,2,0,-3,-3,-10} (55 comparisons, 5 swaps)

Before: {tree,boy,apple,girl,dog,cat}

Ascending: {apple,boy,cat,dog,girl,tree}

(15 comparisons, 3 swaps)

Before: {tree,boy,apple,girl,dog,cat}

Descending: {tree,girl,dog,cat,boy,apple} (15 comparisons, 4 swaps)

Recall theIntList5 linked list class from Listings Listing 18.18 (intlist5.h) and Listing 18.19 (intlist5.cpp). It implemented a linked list of integer elements. Suppose we instead want to make a linked list of std : : st r i ng

©2018 Richard L. Halterman

Draft date: September 25, 2018

objects. Without C++ templates, we would have to copy the IntLi st code and modify it so it works with st ri ng objects instead of integers. We could call this class St r i ngLi st. Note that the code in the IntLi st and Stri ngLi st classes would be almost identical; the only major difference would be the type of elements the list can hold. C++’s class template feature is ideal for designing generic container classes.

Listing 19.9 (linkedlist.h) defines a such a generic linked list in its Li nkedList class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Move constructor takes possession of the temporary's list

LinkedList(LinkedList&& temp): LinkedListQ {

// Swap contents with the temporary std::swap(head, temp.head); std::swap(tai1, temp.tail); std::swap(len, temp.len);

}

// Assignment operator

LinkedList& operator=(const LinkedList& other) {

// Make a local, temporary copy of other LinkedList temp{other};

// Exchange the head and tail pointers and len from this list // with those of the new, temporary list

std::swap(head, temp.head); std::swap(tai1, temp.tail); std::swap(len, temp.len);

// The other list now points to this list's original contents,

// and this list now points to the copy of other's list return *this;

}

// Move assignment operator

LinkedList& operator= (LinkedList&& temp) {

// Exchange the head and tail pointers and len from this list // with those of the new, temporary list

std::swap(head, temp.head); std::swap(tai1, temp.tail); std::swap(len, temp.len);

// The temporary list now points to this list's original contents,

// and this list now points to the temporary's list

// The temporary list will be destroyed since it is a temporary

return *this;

}

// The destructor deallocates the memory held by the list ~LinkedList() { clear();

}

// Inserts item onto the back of the list.

// item is the element to insert, void insert(const T& item) {

// Make a node for the new element n

auto new_node = std::make_shared<LinkedList::Node>(itern); if (tail) { // Is tail non-null?

tail->next = new_node; // Link the new node onto the back

tail = new_node; // The new node is the new tail of the list

}

else // List is empty, so make head and tail point to new node head = tail = new_node; len++;

}

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Removes the first occurrence of item from the list.

// Returns true if successful (found item and removed it).

// Returns false if item is not originally present in the list, bool remove(const T& item) {

auto cursor = head, // Start at head of list

prev = head; // Keep track of previous node seen

// Loop until we run off the end of the list or find n,

// whichever comes first

while (cursor && cursor->data != item) {

prev = cursor; // Remember previous node

cursor = cursor->next; // Move to next node

}

if (!cursor)

return false;

// Did we run off the end of the list? // Indicate we did not find n

// Found n; cursor is pointing

if (head == tail)

head = tail = nullptr; else if (cursor == head) head = head->next;

else

prev->next = cursor->next; if (cursor == tail) tail = prev;

at the node containing n // n was the only element in the list // cursor still points to node with n // Is n the first element in the list? // Redirect head around n // n is not the first element // Redirect previous node around n // Was n the last element in the list? // Update tail to new last element

// No need to delete node; shared_ptr takes care of it len--; // List size decreases by 1

return true; // We found n and deleted its node

// Prints the contents of the linked list of integers, void printQ const {

for (auto cursor = head; cursor; cursor = cursor->next) std::cout << cursor->data << 1 '; std::cout << ' \n 1 ;

}

// Returns the length of the linked list, int lengthQ const { return len;

}

// Removes all the elements in

void clearQ {

auto cursor = head; while (cursor) {

auto temp = cursor; cursor = cursor->next; temp->next = nullptr;

}

head = tail = nullptr; //

len = 0;

}

the linked list.

// Remember where we are

// Move next node

// Sever link from previous node

Null head signifies list is empty

// Provide a convenient way to print a linked list

©2018 Richard L. Halterman

Draft date: September 25, 2018

};

template <typename V>

friend std::ostream& operator<< (std::ostream& os,

const LinkedList<V>& list);

// Prints a linked list object to an output stream template <typename T>

std::ostream& operator<< (std::ostream& os, const LinkedList<T>& list) { os << ;

if (list.length() > 0) {

auto cursor = list.head; os << cursor->data; cursor = cursor->next; while (cursor) {

os << ", " << cursor->data; cursor = cursor->next;

}

}

os << ' } ' ; return os;

Notice that in Listing |19.9| (linkedlist.h) the linked list elements have the generic type T. Observe carefully where the T type parameter appears in the code.

Listing 19.10 (intlistmain.cpp) shows how a client can instantiate the LinkedList template for integer elements.

Listing 19.10: i ntli stmai n. cpp

// intlistmain.cpp

#include <iostream>

#include "linkedlist.h"

int main() {

bool done = false; char command; int value;

LinkedLi st<i nt> list; // Instantiated for integers

while (Idone) {

std::cout << "I)nsert <item> D)elete <item> P)rint L)ength E)rase Q) std::cin >> command; switch (command) {

case 'I': // Insert a new element into the list

case 1 i 1 :

if (std::cin >> value) list.insert(value);

else

done = true; break;

case 'D' : // Insert a new element into the list

case 1 d 1 :

if (std::cin >> value)

if (list.remove(value))

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

}

}

std::cout << value << " removed\n";

else

std::cout << value << " not found\n";

else

done = true; break;

case 'P' : // Print the contents of the list

case 1 p 1 :

list.printQ ; break;

case 1 L' : // Print the list's length

case 1 1 1 :

std::cout << "Number of elements: " << list.length() break;

case 'E' : // Erase the list

case 1 e 1 :

list.clearQ ; break;

case 'Q' : // Exit the loop (and the program)

case 1 q 1 :

done = true; break;

<<

\n 1

The statement

LinkedLi st<i nt> list;

instantiates an actual class where all the occurrences of T become i nt. It also declares li st to be an object of this instantiated class.

Table captionThe following shows a sample run of Listing 19.10 (intlistmain.cpp).

I)nsert <item> P)rint L)ength

D)elete

<item>

E)rase

Q)uit

>>P

I)nsert <item> P)rint L)ength Creating node 44 (16085084)

D)elete

<item>

E)rase

Q)uit

>>i

44

I)nsert <item> P)rint L)ength Creating node 23 (16084476)

D)elete

<item>

E)rase

Q)uit

>>i

23

I)nsert <item> P)rint L)ength Creating node 88 (16084380)

D)elete

<item>

E)rase

Q) ui t

>>i

88

I)nsert <item> P)rint L)ength Creating node 99 (16084668)

D)elete

<item>

E)rase

Q)uit

>>i

99

I)nsert <item> P)rint L)ength 44 23 88 99

D)elete

<item>

E)rase

Q)uit

>>P

I)nsert <item> P)rint L)ength Number of elements: 4

D)elete

<item>

E)rase

Q) ui t

>>1

I)nsert <item> P)rint L)ength Destroying node 44 (16085084)

44 removed

D)elete

<item>

E)rase

Q) ui t

>>d

44

I)nsert <item> P)rint L)ength Number of elements: 3

D)elete

<item>

E)rase

Q) ui t

>>1

I)nsert <item> P)rint L)ength 23 88 99

D)elete

<item>

E)rase

Q) ui t

>>P

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

I)nsert <item>

P)rint

L)ength

D)elete

<item>

E)rase

Q)uit

>>d 99

Destroying node

99 (16084668)

99 removed I)nsert <item> 23 88

P)rint

L)ength

D)elete

<item>

E)rase

Q) ui t

>>P

I)nsert <item>

P)rint

L)ength

D)elete

<item>

E)rase

Q)uit

>>1

Number of elements: 2

I)nsert <item>

P)rint

L)ength

D)elete

<item>

E)rase

Q) ui t

>>i 9

Creating node 9

(16085084)

I)nsert <item> 23 88 9

P)rint

L)ength

D)elete

<item>

E)rase

Q) ui t

>>P

I)nsert <item>

P) rint

L)ength

D)elete

<item>

E)rase

Q)uit

>>q

Table captionDestroying node 23 (16084476) Destroying node 88 (16084380) Destroying node 9 (16085084)

Listing 19.11 (stringlistmain.cpp) shows how a client can instantiate the Linked List template for std : : stri ng elements.

Listing 19.11: stringlistmain.cpp

// stringlistmain.cpp

#include <iostream>

#include <string>

#include "linkedlist.h"

int main() {

bool done = false; char command; std::string value;

LinkedList<std::string> list; // Instantiated for strings while (Idone) {

std::cout << "I)nsert <item> P)rint L)ength D)elete <item> E)rase Q) std::cin >> command; switch (command) {

case 'I': // Insert a new element into the list

case 1 i 1 :

if (std::cin >> value) list.insert(value);

else

done = true; break;

case 1 D' : // Insert a new element into the list

case 1 d 1 :

if (std::cin >> value)

if (list.remove(value))

std::cout << value << " removed\n";

else

std::cout << value << " not found\n";

else

done = true; break;

case 'P' : // Print the contents of the list

©2018 Richard L. Halterman

Draft date: September 25, 2018

case 1 p 1 :

list.printQ ; break;

case 'L 1 : // Print the list's length

case 1 l 1 :

std::cout << "Number of elements: " << list.length() << '\n'; break;

case 'E' : // Erase the list

case 1 e 1 :

list.clearQ ; break;

case 'Q 1 : // Exit the loop (and the program)

case 1 q 1 :

done = true; break;

}

}

}

Listing 19.11 (stringlistmain.cpp) adds the extra #i nclude directive for the string library, but observe that the only executable statements that differ from Listing 19.10 (intlistmain.cpp) are

std::string value;

LinkedList<std::string> list; // Instantiated for strings

int value;

LinkedList<i nt> list; // Instantiated for integers

All the other code in both programs is identical.

Just as we may instantiate function templates with multiple different types within the same program, we can do the same for class templates. The class template Li nkedLi st in Listing 19.9 (linkedlist.h) makes the following client code possible:

LinkedList<int> intlist;

LinkedList<std::string> strlist; intlist.insert(5); strlist.insert ("Wow") ; intlist.print() ; strlist.print() ;

This code fragment simultaneously manages lists of integers and lists of string objects.

Listing | T9. 121 (listoflists.cpp) shows how we can use our generic list to build a list of lists.

©2018 Richard L. Halterman

Draft date: September 25, 2018

intlistl.insert(i); for (int i = 100; i < 500; i += 100) intlist2.insert(i); for (int i = 5; i < 25; i += 5) intlist3.insert(i);

// Next build a list that contains lists of integers

LinkedList<LinkedLi st<int>> listoflists; listoflists.insert(intlistl); listoflists.insert(intlist2); listoflists.insert(intlist3);

std : : cout << "-\n" ;

std::cout << listoflists << 1 \n' ; std : : cout << "-\n" ;

By now you probably have a deduced the fact that std: :vectorisa class template. The std: : vector class template is much more sophisticated than our simple Li nkedList template, but the basic mechanism for its ability to store different types of elements, a class template, is the same.

19.3 Exercises

CAUTION! SECTION UNDER CONSTRUCTION

1. Write a generic function named is_ascending that accepts a std: :vector containing any elements comparable by o p e r a t o r <. The function should return t r u e if the elements in the vector appear in non-decreasing (or ascending) order; otherwise, the function should return false.

2. Write a generic function named is_member that accepts a argument of any type comparable by operator== and a second argument consisting of a std : : vector containing elements of same type as the first argument. The function should return true if the first argument is a member of the second argument; otherwise, the function should return false.

3. Augment Listing 19.9 (linkedlist.h) by adding a method named prepend that adds an element to the front of a generic linked list.

4. Augment Listing [T9T9| (linkedlist.h) by adding an operator== method that returns true if two generic linked list contain exactly the same elements in exactly the same order; otherwise, the method returns false. Also provide a one-line operator != method that utilizes your operator== method.

5. Augment Listing|T9T9](linkedlist.h) by adding an

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 20

The Standard Template Library

CAUTION! CHAPTER UNDER CONSTRUCTION

Chapter[l9]introduced the mechanics of generic programming with templates. The C++ standard library leverages templates to provide a rich collection of standard generic containers and algorithms to manipulate the containers and process the elements they contain. This part of the standard library commonly is known as the standard template library , or STL for short. As its name implies, the STL contains a number of generic functions and classes built with templates. We have seen the std : : vector class (Chapter 11)

and std : : swap function Section 12.1

The STL consists of four majors components:

• generic (that is, templated) containers for storing data, such as std: :vector,

• iterators for traversing containers,

• algorithms for processing the data within containers, and

• miscellaneous utility classes and functions, such as std : : swap and std : : max.

The design of the containers and their iterators make the STL’s generic algorithms possible. The algorithms provided by the STL are powerful and flexible, but they also are somewhat arcane and can be difficult to use for casual C++ programmers.

In this chapter we explore some of the features of the STL, providing examples that illustrate its capabilities.

20.1 Containers

We are familiar with one STL container: std : : vector. A vector object manages a primitive C array. C arrays come in two varieties: static and dynamic (see Section 11.2| . Vectors manage dynamicallyallocated arrays. A vector object can expand as needed the storage space for its low-level array. The STL provides an equivalent to a static array in its std : : array class. A programmer must specify the size of a std : : a r ray object when declaring it. The following code creates a std : : a r ray that can hold 10 integer values:

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::array<i nt , 10> a rr;

Note that the second template parameter is a non-type parameter (see Section |19Tl| specifying the size of the array. Besides not being able to modify the array’s size through methods such as push_back, std: :array objects work very much like std: :vectors. Array objects keep track of their size, unlike primitive C arrays.

In Listing 19.9 (linkedlist.h) we developed a generic linked list class named Li nkedLi st. That was good practice dealing with generic types, but our work really was re-inventing the wheel because the STL provides the generic std: :list class. The STL implements a linked list with pointers connecting a node to both its successor node and predecessor node. A list with both forward and backward pointers is known as doubly linked list. Listing 20.1 (stdlistmain.cpp) is the third and final variation of our list programs. Listing |18.5| (listmain.cpp) used a custom class to implement a singly linked list of integers

(forward pointers only). We used C++s template feature to build a type generic list class in Listing |19.10| (intlistmain.cpp). Listing 20.1 (stdlistmain.cpp) uses the std : : li st class provided by the STL.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

case 1 q 1 :

done = true; break;

}

}

Listingl20.1 (stdlistmain.cpp) contains all the code we need to write. The STL provides all of the linked list implementation code. Note that the differences between Listing [20.1 [ (stdlistmain.cpp) and Listing [19710| (intlistmain.cpp) are minimal.

A priority queue is a data structure that allows clients to store objects with various priorities or rankings.

Clients can insert the objects in any order, and the priority queue always will serve (remove) higher priority objects before lower priority objects. A properly designed priority queue supports very fast insertion and removal operations.

The C++standard library provides the std : : pri ori ty_queue class. Listing 20.2 (priorityqueuesimple.cpp) provides a simple example using a std : : pri ori ty_queue.

Listing 120.2[(priorityqueuesimple.cpp) displays the following:

15 15 11 7 4 4 2

Note that the priority queue serves larger values before smaller values regardless of their insertion order. It equates larger-valued numbers with a higher priority.

If we want to change the notion of priority so that lower-valued numbers are considered higher priority than larger numbers, the std: :priority_queue class provides the flexibility for us to do so. We must define a special class or struct that provides a public method named operator (). This method must return a Boolean result and accept two arguments of the same type as the elements held by the priority queue.

Consider the following Cmp type:

©2018 Richard L. Halterman

Draft date: September 25, 2018

struct Cmp {

bool operator () (int il, int i2) { return i2 < il;

}

};

This special method is the function invocation operator, ox function call operator. It enables any instance of the Cmp class to be used like a function. To see how this works, consider Listing|j20.3|(calloperator.cpp).

Listing|20.3|(calloperator.cpp) prints the following:

false

true

false

The first output line indicates it is false that 3 < 2. The second line reveals that it is true that 2 < 3, and in the last line we see that it is false that 3 < 3.

The expression op (2, 3) looks like a call to the function named op, but it really is just syntactic sugar for op.operator()(2, 3). We see that we really are invoking the method nameed operatorQ on behalf of the op object.

Listing j20~4| (reversepriority.cpp) provides the complete code for apriority queue that holds integers and recognizes lower-valued integers as higher priority than high-valued integers.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::priority_queue<int, std::vector<i nt> , Cmp> queue; //std::priority_queue<int> queue;

// Insert some integers into the priority queue

queue.push(3) ; queue.push(12); queue.push(55); queue.push(11); queue.push(2); queue.push(4);

// Serve items from the queue until it is empty while (Iqueue.emptyQ ) {

std::cout << queue.top() << 1 ' ; // See what's on top

queue.pop(); // Remove highest priority element

}

std::cout << 1 \n 1 ;

Note 1

Note 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

Note 9

Note 10

Note 11

Note 12

©2018 Richard L. Halterman

Note 13

double a = cl.real(), b = cl.imagO, c = c2.real(), d = c2.imag(); return sqrt((a*a + b*b) < (c*c + d*d));

}

};

With this our definition of complex number less than we overload operator< for complex numbers, as shown in Listing[203j(complexdiff.cpp).

If we want to prioritize complex numbers in a different way, we need only provide a different custom comparer type.

Custom comparer objects allow us to place items in a priority queue that inherently are not numerical themselves. Suppose we are writing part of a messaging system that processes text messages. In addition to the text in the message, each message has a integer priority in the range 1... 10. Lower numbered messages have priority over messages with higher numbers. Instances of the following struct model our simple messages:

©2018 Richard L. Halterman

Draft date: September 25, 2018

struct Message {

int rank; // Lower number = higher priority std::string text;

// Constructor

Message (const std::string& t, int rank): text(t), priority(rank) {}

};

The following shows how we can compare two message objects to give lower-numbered messages higher priority:

// Custom comparer object to properly prioritize Message objects struct Cmp {

bool operator ()(Message ml, Message m2) { return m2. rank < ml. rank;

}

};

Listing j2(L6| (messagepriority.cpp) provides the complete simple messaging example.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << '\n' ;

}

Listing |2Cf6j| (rnessagepriority.cpp) prints

Wi11 be late! : 1 Be there soon: 2

The project deadline is the first: 3 Gimme a few minutes: 3 I bought a new computer: 5 Have to work next week: 7

Vectors, arrays, lists, and priority queues are all sequence containers. This means their elements appear in a linear ordering from the beginning of the data structure to its end. The STL provides other kinds of containers that we will explore in Chapter |2lj

Chapter Notes

Listing |20.4[ (reversepriority.cpp) prints

2 3 4 11 12 55

Since we are providing a custom comparer class to modify the default priority queue ordering, the declaration of the std : : pri ori ty_queue object is a little more complicated:

std::priority_queue<i nt , std::vectorci nt> , Cmp> queue;

The template instantiation requires three type parameters:

• i nt is the type of items the priority queue holds.

• std : : vector<i nt> is the type of container that holds the items in the priority queue; programmers can specify a different type of container. The std : : pri ori ty_queue class serves as a wrapper around an exiting container type.

• Cmp is the type of comparer object that the priority queue will use to order its items.

Armed with the ability to precisely specify how the priority queue defines priorities, we can store any type of objects in a priority queue. By default, the std : : pri ori ty_queue class can store any type of objects that can be compared using the < operator. This includes the basic numeric types (i nt, double, unsigned, etc.) and std: : string objects. The std: : complex class (see Section 13.4) models mathematical complex numbers. The relational operators <, <, >, and > have no practical mathematical meaning in the context of complex numbers; therefore, C++ does not automatically support operator < comparison between two std : : complex objects. We can define our own ordering, however. Let a + bi and c + di be two complex numbers. We will define a + bi to have higher priority that c + di if the distance between a + bi and 0 on the complex plane is less than the distance between c + di and 0. The distance between a + bi and 0 is \/a 2 +b 2 , and the distance between c+di and 0 is \Jc 2 + d 2 . The following custom comparer class implements this notion of complex number priorities:

// Define priorities for complex numbers.

// If cl's distance to zero on the complex plain is less // than c2's distance to zero, cl has higher priority than c2. struct ComplexCompare {

bool operator ()(Complex cl, Complex c2) {

Draft date: September 25, 2018

20.2 Iterators

Section 11.2 demonstrates how we can use a pointer to access the elements within an array. A vector is an object that manages a primitive array, and the developers of the vector class designed vectors to look and feel as much as possible as arrays. They adopted the square bracket ([]) operator to access elements. They also devised a way for programmers to use pointer-like objects to access the elements within a vector. These pointer-like objects are called iterators.

An iterator is an object that allows a client to traverse and access elements of a data structure in an implementation independent way. C++ defines two global functions, std : : begi n and std : : end, that produce iterators to the front and back, respectively, of a data structure like a vector or static array. Containers defined int the STL provide begi n and end methods that serve the same purpose; for example, if v is a std: : vector, std : : begi n ( v) returns the same iterator as the call v . begi n (). Functions in the standard library that accept iterators as arguments rather than arrays or vectors work equally well with both vectors and arrays. Since they accept iterator arguments, these standard functions additionally are able to work with other, more sophisticated data structures. We will examine some of these standard functions later in this chapter.

In order to behave like a pointer, an iterator object provides the following methods:

• operator*: used to access the element at the itertator’s current position. The syntax is exactly like pointer dereferencing (see Section [l0.7] ).

• operator**: used to move the iterator to the next element within the data structure. The syntax is exactly like pointer arithmetic (see Section [LL2j).

• operator ! =: used to determine whether two iterator objects currently refer to different elements within the data structure.

Listing(2077j(simpleiterator.cpp) shows how to use these methods to manipulate an iterator object.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int main() {

// Make a simple integer vector

std::vector<i nt> vec {10, 20, 30, 40, 50};

// Direct an iterator to the vector's first element std::vector<i nt> ::iterator iter = std::begin(vec); // Print the element referenced by the iterator std::cout << *iter << '\n';

// Advance the iterator iter++;

// See where the iterator is now std::cout << *iter << '\n';

}

Listing |2077| (simpleiterator.cpp) prints

1 '

2 '

The statement

std::vectorci nt> ::iterator iter = std::begin(vec);

declares and initializes an iterator object, iter. The type of iter is std : : vectorci nt> : :iterator This complicated expression indicates that i terator is a type defined within the std : : vector<i nt> type. A shorter way to express this statement takes advantage of the compiler’s ability to infer the variable’s type from its context:

auto iter = std::begin(vec);

(Section 3.10 introduced C++’s type inference capabilities.) The compiler can deduce the type of iter based on the return type of the std: :begin function.

While the std: :begin function returns an iterator pointing to the first element in a data structure, the std : :end function returns an iterator pointing to the element just past the last element in the data structure. In the code fragment

std::vectorci nt> vec {10, 20, 30, 40, 50}; auto iter = std::end (vec) ;

the iterator object iter does not reference a viable element in the vector. As such, we never attempt to dereference the iterator; the expression *i ter in this case is undefined. We normally use the iterator returned by the std : : end function to test to see if we are past the end of our data structure. Listing 20.8 (iteratorloop.cpp) demonstrates.

Listing20.8: iteratorloop.cpp

#include <iostream>

#include <vector>

int main() {

// Make a simple integer vector

std::vector<i nt> vec {10, 20, 30, 40, 50};

// Print the contents of the vector

for (auto iter = std::begin(vec); iter != std::end(vec); iter++) std::cout << *iter << 1

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << '\n 1 ;

}

Listing pX8j (iteratorloop.cpp) prints

10 20 30 40 50

The expression

iter != std::end(vec)

checks each time through the loop to ensure the iterator object has not run off the back end of the vector.

We can use the vector methods begi n and end instead of the std : : begi n and std : : end functions. Listing |20.9| (iteratorloopmethods.cpp) is a modified version of Listing (2(T8| (iteratorloop.cpp) that uses the iterator methods.

The std : : begi n and std : : end functions are overloaded to work with vector objects, arrays, and other container classes found in the standard library. ListingpO.lO (iteratorlooparray.cpp) is the array version of Listing ||20.8|| (iteratorloop.cpp).

The output of Listing ||20.l0 j(iteratorlooparray.cpp) is identical to Listing]j20.8|[(iteratorloop.cpp):

10 20 30 40 50

Any type for which the std: :begin and std : : end functions have been overloaded may participate in a range-based for statement. In fact, the compiler internally transforms a range-based for construct into its equivalent std : : begi n/std : : end form during the compilation process. The following code

©2018 Richard L. Halterman

Draft date: September 25, 2018

for (auto i : vec)

std::cout << i <<

is short for (one possible internal compiler representation) for (auto _i = std::begin(vec); _i != std::end(vec) ;

(auto _i = std::cout

std::begin(vec) ;

<< * i << ' ' ;

-i++)

The STL supports various kinds of iterators. The kind of iterator available to std : : vector objects is known as a random access itertator. Random access iterators behave exactly like a pointers. Recall from

Section 11.2 that we can manipulate pointers with pointer arithmetic. If p points to the first element of an array, p + 5 points to the sixth element in the array (because p + 0 is the same as p). The expression p + + makes the p point to the next element in the array, while p-- moves p backwards one position. We can use similar arithmetic with iterators as Listing pOTl 1 [ (iterarith.cpp) illustrates.

Listing20.11: iterarith.cpp

#include <iostream>

#include <vector>

// Print the contents of vector v, traversing with a // caller supplied increment value (inc)

void print(const std::vector<int>& v, int inc) {

for (auto p = std::begin(v); p != std::end(v); p += inc) std::cout << *p << 1 1 ; std::cout << 1 \n 1 ;

}

// Print the contents of the vector v backwards,

// traversing with a caller supplied decrement value (dec)

void print_reverse(const std::vector<int>& v, int dec) { auto p = std::end(v); while (p != std::begin(v)) { p -= dec;

std::cout << *p << 1 1 ;

}

std::cout << 1 \n 1

}

int main() {

std::vector<i nt> vec(20); for (int i =0; i <20; i++) vec [i ] = i ;

print(vec, 1); print(vec, 2); print(vec, 4); print(vec, 5); print(vec, 10);

std::cout << 1 \n 1 ;

print_reverse(vec, 1); print_reverse(vec, 2); print_reverse(vec, 4);

©2018 Richard L. Halterman

Draft date: September 25, 2018

print_reverse(vec, 5); print_reverse(vec, 10);

Listing 20.11 (iterarith

.cpp) prints

0 12

3 4

5 6 7

8 9 10 11 12 13 14 15 16 17 18 19

0 2 4

6 8

10 12

14 16 18

0 4 8

12

16

0 5 10

15

0 10

19 18

17

16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

18 16

14

12 10 8

6 4 2 0

16 12

8 4

0

15 10

5 0

10 0

Some specialized data structures in the C++ standard library support specialized iterators that have some limits on the kinds of arithmetic they support; for example, some container types support forward but not backward traversal. Subtraction is not an option for these kinds of iterators.

20.3 Iterator Ranges

Iterators are valuable for specifying ranges over sequences (vectors and arrays). We can specify a range with a pair of iterators; one iterator points to the first element in the sequence, and the other iterator points to the position just past the end of the sequence. The global functions std : : begi n and std : : end fit well into this definition of range.

Suppose vec is a vector. The two iterators std : : begi n (vec) and std : : end (vec) span the complete range of values in vec. In the following statement:

auto b = std::begin(vec), e = b + 1;

the range of two iterators b and e includes just the first element in vec. Compare this range to the one represented by the following statement;

auto b = std::begin(vec), e = b + 10;

Here the range of two iterators b and e spans the first 10 elements of vec. The range of the iterators b and

e defined by the statement

auto e = std::end(vec), b = e - 5;

encompasses the last five elements of vec.

Section [ TL2| introduced a technique for traversing an array via a pointer range. Rather than passing an array (literally the address of the first element) and its size (number of elements) to a traversal function, the range-based approach passes the array (again, literally a pointer to the first element) and a pointer to the position just past the end of the array. Notice how the pointers in range-based array technique correspond directly to the iterator objects returned by the std : : begi n and std : : end functions. Since iterator objects behave like pointers, we can write truly generic code that can process both arrays and vectors.

The following function uses iterators to count the number of times a value appears within a vector:

©2018 Richard L. Halterman

Draft date: September 25, 2018

int count_value(std : :vector'd' nt> : : iterator iter_begin,

std::vector<i nt> ::iterator iter_end, int seek) {

int cnt = 0;

for (std::vector<i nt> ::iterator cursor = iter_begin; cursor != iter_end; iter++) if (*cursor == seek) cnt++; return cnt;

We can streamline its appearance using type aliasing: using Iter = std::vector<i nt> ::iterator;

int count_value(Iter iter_begin, Iter iter_end, int seek) { int cnt = 0;

for (Iter iter_begin; cursor != iter_end; iter++) if (*cursor == seek) cnt++; return cnt;

Listing[20. 12[(countitems.cpp) exercises the count function.

Listing [20.12|| |(countitems.cpp) prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

3

1

0

0

This is its expected output.

The program works as expected, but we can expand its capability greatly by making it generic, as Listing |20T3l(genericcount.cpp) shows.

Listing20.13: genernccount.cpp

#include <iostream>

#include <vector>

#include <array>

#include <list>

#include <string>

// Count the elements in a range that match seek.

// Type Iter is an iterator type working with a container that // contains elements of type T. Type T elements must be // comparable with operator==. template <typename Iter, typename T>

int count_value(Iter iter_begin, Iter iter_end, const T& seek) { int cnt = 0;

for (auto cursor = iter_begin; cursor != iter_end; cursor++) if (*cursor == seek) cnt++; return cnt;

}

int main() {

Table caption// Test with a vector of integers

Table captionstd::cout << "-Vector of integers- \n";

Table captionstd::vector<i nt> a {34, 5, 12, 5, 8, 5, 11, 2};

std::cout a = {};

<<

//

count_value(std::begin(a), std:

Try an empty vector

:end(a),

5)

<<

' \n

std:

: cout

<<

count_value(std:

:begin(a), std:

:end(a) ,

5)

<<

' \n

std:

: cout

<<

count_value(std:

:begin(a), std:

:end(a),

8)

<<

' \n

Table captionstd::cout << "-STL array of integers- \n";

Table caption// Test with a std::array of integers

Table captionstd:: array<int, 8> arr {34, 5, 12, 5, 8, 5, 11, 2};

std:

: cout

<<

count_value(std:

:begin(arr),

std:

: end(arr),

5)

<<

' \n' ;

arr

= {};

//

Try an empty array

std:

: cout

<<

count_value(std:

:begin(arr),

std:

: end(arr),

5)

<<

' \n' ;

std:

: cout

<<

count_value(std:

:begin(arr),

std:

: end(arr),

8)

<<

' \n' ;

std::cout << "-Primitive C array of integers- \n";

// Test with a primitive C array of integers int carr[] = {34, 5, 12, 5, 8, 5, 11, 2};

std::cout << count_value(std::begin(carr), std::end (carr), 5) << 1 \n ' ; std::cout << count_value(std::begin(carr), std::end(carr), 8) << 1 \n ' ;

std::cout << "-Vector of strings- \n";

// Test with a vector of strings

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::vector<std::string> b {"mae", "al", "pat", "mel", "al",

"ray", "al"};

std::cout << count_value(std::begin(b), std::end(b), "al") << '\n'; b = {};

std::cout << count_value(std::begin(b), std::end(b), "al") << '\n'; std::cout << count_value(std::begin(b), std::end(b), "pat") << '\n';

}

Table captionstd::cout << "-Linked list of strings- \n";

Table caption// Test with a linked list of strings

Table captionstd::list<std::string> 1st {"mae", "al", "pat", "mel", "al",

Table caption"ray", "al"};

std:

: cout

<<

count_value(std:

:begin(lst),

std:

: end(1st),

"al")

<<

1 \n 1 ;

1st

= O;

std:

: cout

<<

count_value(std:

:begin(lst),

std:

: end(1st),

"al")

<<

1 \n 1 ;

std:

: cout

<<

count_value(std:

:begin(lst),

std:

: end(1st),

"pat")

<<

1 \n * 1 * 3

std:

: cout

<<

"-Primitive C

array of Points—

- \n" ;

struct Point { int x; int y;

bool operator==(const Point& other) {

return x == other.x && y == other.y;

}

};

// Test with a primitive array of Point objects

Point pts[] = {{5, 3}, {0, 0}, {5, 3}, {3, 5}, {2, 1}};

std::cout << count_value(std::begin(pts), std::end(pts), Point{5, 3}) « ' \n' ;

std::cout << count_value(std::begin(pts), std::end(pts), Point{3, 5}) « ' \n' ;

std::cout << count_value(std::begin(pts), std::end(pts), Point{2, 3}) « ' \n' ;

.cpp) prints

Note 1

Note 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

Note 9

Note 10

Note 11

Note 12

Note 13

Note 14

Note 15

Note 16

Note 17

Note 18

©2018 Richard L. Halterman

Note 19

0

-Primitive C array of Points

2

1

0

As we can see. Listing 20.13 (genericcount.cpp) can count the number of occurrences of any type that supports testing for equality using the == operator in a container that supports iterators.

Listing 20.14| i(genericloggingflexiblesort.cpp) uses template functions and template classes to make our logging flexible sort code truly generic. It also uses inheritance to derive a class from a template class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

void reset();

// Method that performs the comparison. It delegates // the actual work to the function pointed to by comp. // This method logs each invocation, bool compare (const T& m, const T& n);

// Method that performs the swap.

// Interchange the values of // its parameters a and b which are // passed by reference.

// This method logs each invocation, void swap(T& m, T& n);

// Returns the number of comparisons this object has // performed since it was created, int comparisons() const;

// Returns the number of swaps this object has // performed since it was created, int swaps() const;

// Method that actually performs the comparison // Derived classes may override this method template <typename T>

bool Comparer<T>::compare_impl(const T& m, const T& n) { return comp(m, n);

}

// Method that actually performs the swap // Derived classes may override this method template <typename T>

void Comparer<T>::swap_impl(T& m, T& n) {

T temp = m; m = n; n = temp;

}

// The client must initialize a Comparer object with a // suitable comparison function, template <typename T>

Comparer<T>::Comparer (bool (*f) (const T&, const T&)): compare_count(0), swap_count(0), comp(f) {}

// Resets the counters to make ready for a new sort

template <typename T> void Comparer<T>::reset() {

compare_count = swap_count = 0;

}

// Method that performs the comparison. It delegates // the actual work to the function pointed to by comp. // This method logs each invocation.

©2018 Richard L. Halterman

Draft date: September 25, 2018

template <typename T>

bool Comparer<T>::compare(const T& m, const T& n) { compare_count++; return compare_impl(m, n);

}

// Method that performs the swap.

// Interchange the values of // its parameters a and b which are // passed by reference.

// This method logs each invocation, so // we do not use std::swap here, template <typename T> void Comparer<T>::swap(T& m, T& n) { swap_count++; swap_impl(m, n);

}

// Returns the number of comparisons this object has // performed since it was created, template <typename T>

int Comparer<T>::comparisons() const { return compare_count;

}

// Returns the number of swaps this object has // performed since it was created, template <typename T> int Comparer<T>::swaps() const { return swap_count;

}

/*

* selection_sort(a, compare)

* Arranges the elements of a sequence in an order determined

* by the compare object.

* begin points to the beginning of the sequence.

* end points to the imaginary element just past the last

* element of the sequence.

* compare is an object that compares the ordering of two

* elements and records the actions it performs.

* The function physically rearranges the contents of the

* sequence.

*/

template <typename T, typename V>

void selection_sort (const T begin, const T end, Comparer<V>& compare) { for (auto i = begin; i != end - 1; i++) {

// Note: i, small, and j represent positions within the // sequence.

// a [i], a[small], and a[j] represents the elements at // those positions.

// small is the position of the smallest value we've seen // so far; we use it to find the smallest value less // than a[i]

©2018 Richard L. Halterman

Draft date: September 25, 2018

auto small = i;

// See if a smaller value can be found later in the sequence for (auto j = i + 1; j != end; j++) if (compare.compare(*j, *small))

small = j; // Found a smaller value // Swap a[i] and a[small], if a smaller value was found if (i != small)

compare.swap(*i, *small);

}

}

/*

* print

* Prints the contents of a sequence

* begin points to the beginning of the sequence.

* end points to the imaginary element just past the last.

* The function does not modify the sequence.

*/

template <typename T>

void print(const T begin, const T end) { std::cout << '{' ; if (begin != end) {

T iter = begin;

std::cout << *iter; // Print the first element iter++; // Move to next element

while (iter != end) { // Print the rest

std::cout << << *iter;

iter++; // Move to next element

}

}

std::cout << 1 } 1 ;

/*

* less_than(a, b)

* Returns true if a < b; otherwise, returns

* false.

*/

template <typename T>

bool less_than (const T& a, const T& b) { return a < b;

}

/*

* greater_than(a, b)

* Returns true if a > b; otherwise, returns

* false.

*/

template <typename T>

bool greater_than (const T& a, const T& b) { return a > b;

}

/*

©2018 Richard L. Halterman

Draft date: September 25, 2018

* Comparer objects manage the comparisons and element

* interchanges on the selection sort function below.

*/

template <typename T>

class LogComparer: public Comparer<T> {

// Output stream to which logging messages are directed std::ofstream fout;

protected :

// Method that actually performs the comparison

bool compare_impl (const T& m, const T& n) override;

// Method that actually performs the swap

void swap_impl(T& m, T& n) override;

public :

// The client must initialize a LogComparer object with a // suitable comparison function and the file name of a text // file to which the object will direct logging messages LogComparer (bool (*f) (const T&, const T&),

const std::string& filename);

// The destructor must close the log file ^LogComparer();

};

// Method that actually performs the comparison // Derived classes may override this method template <typename T>

bool LogComparer<T>::compare_impl (const T& m, const T& n) { fout << "Comparing " << m << " to " << n << '\n' ;

// Base class method does the comparision return Comparer<T>::compare_impl(m, n);

}

// Method that actually performs the swap // Derived classes may override this method template <typename T>

void LogComparer<T>::swap_impl(T& m, T& n) {

fout << "Swapping " << m << " and " << n << '\n' ;

//T temp = m;

//m = n;

//n = temp;

// Base class method does the swap

Comparer<T>::swap_impl(m, n) ;

}

// The client must initialize a LogComparer object with a // suitable comparison function and the file name of the // text file to receive logging messages, template <typename T>

LogComparer<T>::LogComparer (bool (*f) (const T&, const T&),

const std::string& filename): Comparer<T>(f) {

fout.open(filename); if (!fout.good()) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Could not open log file " << filename << " for writing\n"; exit(l); // Terminate the program

}

// fout is an instance variable, not a local variable, // so the file stays open when the constructor finishes

int main() {

// Make a vector of integers

std::vector<i nt> vec = { 23, -3, 10, 4, 215, 0, -3, 2 }; std::cout << "Before:

print(std::begin(vec), std::end(vec)); std::cout << 1 \n 1 ;

LogComparer<i nt> It(less_than<i nt> , "upsort.log"); selection_sort(std::begin(vec), std::end(vec), It); std::cout << "Ascending: print(std::begin(vec), std::end(vec));

std::cout << " (" << It.comparisons() << " comparisons, "

<< It.swapsQ << " swaps)\n";

LogComparer<i nt> gt(greater_than<i nt> , "downsort.log"); selection_sort(std::begin(vec), std::end(vec), gt); std::cout << "Descending: print(std::begin(vec), std::end(vec));

std::cout << " (" << gt.comparisons() << " comparisons, "

<< gt.swapsQ << " swaps)\n";

std: : cout << "-\n" ;

// Make a vector of string objects

std::vector<std::string> words{"tree" , "girl", "boy", "dog",

"cat", "girl", "bird"};

// Make a working copy of the original vector

std::cout << "Before: ";

print(std::begin(words), std::end(words));

std::cout << 1 \n 1 ;

LogComparer<std::string> wit(less_than<std::string>, "upwords.log" ); selection_sort(std::begin(words), std::end(words), wit); std::cout << "Ascending: "; print(std::begin(words), std::end(words));

std::cout << " (" << wit.comparisons() << " comparisons, "

<< wlt.swaps() << " swaps)\n";

LogComparer<std::string> wgt(greater_than<std::string>, "downwords.log" );

selection_sort(std::begin(words), std::end(words), wgt);

std::cout << "Descending: ";

print(std::begin(words), std::end(words));

std::cout << " (" << wgt.comparisons() << " comparisons, "

<< wgt.swaps() << " swaps)\n";

std: : cout << "-\n" ;

// Make an array of integers

©2018 Richard L. Halterman

Draft date: September 25, 2018

int arr[] = { 23, -3, 10, 4, 215, 0, -3, 2 };

std::cout << "Before: print(arr, arr + 8); std::cout << 1 \n 1 ;

LogComparer <int> lt2(less_than<int> , "upsort2.log"); selection_sort(arr, arr + 8, lt2); std::cout << "Ascending: print(arr, arr + 8);

std::cout << " (" << lt2.comparisons()

<< It.swapsQ << " swaps)\n";

LogComparer <int> gt2(greater _than<i nt> , selection_sort(arr, arr + 8, gt2); std::cout << "Descending: print(arr, arr + 8);

std::cout << " (" << gt2.comparisons()

<< gt.swapsQ << " swaps)\n";

<< " comparisons, "downsort2.log") ;

<< " comparisons,

Observe that the selecti on_sort function in Listing 20.14 (genericloggingflexiblesort.cpp) does not restrict the sequence it can process to be a vector or an array. The first two parameters of selecti on_so rt are generic, and the code within the function treats these two parameters as if they are pointers. Since iterator objects behave exactly like pointers to the extent exercised within selecti on_sort, the compiler can instantiate the template to accept pointer or iterator arguments. Similarly, the pri nt function works equally well with both pointer ranges for arrays and iterators for vectors. The main function demonstrates the flexibility of print and selection_sort functions by sending them both array pointer ranges and vector iterators. Behind the scenes the compiler will automatically instantiate two overloaded pri nt functions and two overloaded selecti on sort functions.

During its execution Listing|20.14| (genericloggingflexiblesort.cpp) produces the following output:

Before: {23,-3,10,4,215,0,-3,2}

Ascending: {-3,-3,0,2,4,10,23,215} (28 comparisons, 5 swaps)

Descending: {215,23,10,4,2,0,-3,-3} (28 comparisons, 4 swaps)

Before: {tree,girl,boy,dog,cat,girl,bird}

Ascending: {bird,boy,cat,dog,girl,girl,tree} (21 comparisons, 3 swaps) Descending: {tree,girl,girl,dog,cat,boy,bird} (21 comparisons, 4 swaps)

Before: {23,-3,10,4,215,0,-3,2}

Ascending: {-3,-3,0,2,4,10,23,215} (28 comparisons, 5 swaps)

Descending: {215,23,10,4,2,0,-3,-3} (28 comparisons, 4 swaps)

The code in Listing |20.14 (genericloggingflexiblesort.cpp) truly is generic:

• Clients may use vectors, arrays, and any sequence type that overloads the begi n and end functions.

• Clients may work with sequences that contain elements of any type that supports the < and = operators.

• Clients may customize the element ordering.

• Clients may customize the behavior of the comparison and swapping procedures.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter Notes

-Vector of integers

3

0

0

-STL array of integers

3

0

0

-Primitive C array of integers

3

1

-Vector of strings

3

0

0

-Linked list of strings

3

0

Draft date: September 25, 2018

20.4 Lambda Functions

CAUTION! SECTION UNDER CONSTRUCTION

One of the primary benefits of functions is that we can write a function’s code once and invoke it from many different places within the program (and even invoke it from other programs). Ordinarily, in order to call a function, we must know its name. Almost all the examples we have seen have invoked a function via its name. Listing 10.20 (arithmeticeval.cpp) in Section 10.10 provided examples of invoking functions without using their names directly. There we saw a function named evaluate that accepts a function as a parameter:

int evaluate (int (*f)(int, int), int x, int y) { return f(x, y);

}

The evaluate function calls f . The question is, what function does evaluate call? The name f refers

to one of evaluate’s parameters; there is no separate function named f defined within Listing 10.20

(arithmeticeval.cpp). The answer, of course, is that evaluate invokes the function passed in from the caller. The function mai n in Listing 10.20 (arithmeticeval.cpp) calls evaluate passing the add function on one occasion and the multi ply function on another.

The code in the evaluate function demands that callers send a function as the first parameter. Does this mean we have to write a separate function with a name in order to call evaluate? Once we create a function with a name it is available to be called from anywhere within the program after its definition or declaration. What if we want to ensure that our function will execute exactly one time and only when invoked by evaluate?

C++ supports the definition of anonymous functions via lambda expressions. The general form of a lambda expression is

jj^ capture list

parameter list

return type

{

statements

}

where:

• capture list specifies the calling context to which the function has access (more on this follows)

• parameter list is a comma-separated list of parameters as you would find in any function definition

• return type is the type of the result the function returns

• statements are the statements as you would find in any function definition.

The term lambda comes from lambda calculus (see http://en.wi ki pedia.org/wiki/Lambda_ calculus), a function-based mathematical system developed by Alonzo Church in the 1930s. Concepts from lambda calculus led to the development of the modern computer. The lambda calculus is the basis for modern functional languages like Haskell and F#.

We can use a lambda function in a call to the evaluate function:

int val = evaluate([] (i nt x, int y)->int { return x * y; }, 2, 3);

©2018 Richard L. Halterman

Draft date: September 25, 2018

The [ ...]( ...){ ...} construct identifies a lambda function; thus, the first argument being passed to evaluate is indeed a function that takes two integer parameters. Notice that result of passing the lambda function here is the same as passing the multi ply function fromListing 10.20 (arithmeticeval.cpp) —both compute the product of the two parameters.

When the compiler can deduce the type of the result of a lambda function, we can omit the return type: int val = evaluate([] (i nt x, int y) { return x * y; }, 2, 3);

Here the compiler can deduce that an integer times an integer is an integer.

Given the evaluate function as before, the expression evaluate([] (i nt x, int y) { return 3*x + y; }, 10, 2);

evaluates to 32. The statement

[](int x, int y) { std::cout << x << " " << y << '\ n ' ; } (10, 20);

prints

10 20

Observe that this statement defines the lambda function and explicitly invokes it.

The following two statements:

auto f = [](int x) { return 5*x; }; std::cout << f(10) << '\n' ;

show how we can assign a lambda function to a variable and invoke it through that variable at a later time.

One interesting aspect of lambda functions is that they can be used to create closures. A closure is a unit of code (in this case a function-like object) that can capture variables from its surrounding context. These captured variables then can be used outside of their original context. In order to demonstrate closure, we first must explore function objects.

A std : : f uncti on object works like a function pointer (see Section 10.10). The std : : f uncti on class is a generic class parameterized by a function’s type specifications. A function object representing a function that accepts two integer parameters and returns an integer result can be declared as

std::function<i nt (i nt , int)> f;

Note the type parameter i nt ( i nt , int) inside the angle brackets. The first i nt represents the function’s return type. The two i nts inside the parentheses specify the function’s parameters. Function objects take the place of function pointers. Function pointers are available in C as well as C++, but C does not provide function objects. Function objects provide capabilities above simple function pointers, including the ability to manage closures.

Listing 20.15 (closurein.cpp) demonstrates a simple closure.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

int main() { i nt a;

std::cout << "Enter an integer: std::cin >> a;

std::cout << evaluate2([a] (int x, int y) {

if (x == a) x = 0;

else

}

y + + ;

return x + y; }, 2, 3) « 1 \n 1 ;

Note that mai n creates a function via the lambda expression that it passes to evaluate2. The variable a appears within the capture square brackets. This makes a’s value available to whatever code invokes the lambda function. In this case the evaluate2 function can see a’s value even though a is local to mai n and is not passed to evaluate2 as an explicit parameter.

We say the lambda function captures the variable a. When evaluate2 invokes the function sent by the caller, evaluate2 has no access to a variable named a. The a involved in the conditional expression is captured from mai n. This is an example of a closure transporting a captured variable into a function call.

For an example of a closure transporting a captured local variable out of a function, consider Listing (20U6j(makeadder.cpp) which includes a function that returns a lambda function to its caller.

Ordinarily when a function returns, all of its local variables disappear. This means that after the following statement in the main function executes:

auto f = make_adder();

make_adder’s loc_var local variable should no longer exist. The function that make_adder returns, however, uses loc_var in its computation. This means the function that make_adder returns

forms a closure that captures make_adder’s local variable loc_var. In the output of Listing 20.16 (makeadder.cpp) we can see that function f still has knowledge of loc_val’s value:

12

4

©2018 Richard L. Halterman

Draft date: September 25, 2018

C++’s lambda capture mechanism provides capabilities that go beyond the examples shown here; for example, the expression &a within the square brackets would capture variable a by reference, allowing an external context to modify the variable. Note that when a closure captures a variable by reference, that variable must exist in its original context as long as the closure is viable. This means you should not attempt to capture a local non-stati c variable of a function by reference by a closure to be returned by that function. The local variables disappear when the function returns, and so the references will refer to garbage values.

We can assign a variable to a lambda function; the following code fragment:

auto f = [](int x) { return 2*x; }; std::cout << f(10) << '\n' ;

will print 20. This gives the function a name, so the statement auto f = [](int x) { return 2*x; };

is roughly equivalent to the function definition

int f(int x) { return 2*x;

}

While not a particularly useful application of lambda function, to demonstrate the regularity of the C++ language, we can define an anonymous function and invoke it immediately; for example, the statement

std::cout << [](int x, int y) { return x * y; }(2, 3);

prints 6. In this case the statement std::cout << 2*3 << '\n ' ;

or, even better,

std::cout << 6 << '\n' ;

produces the same result much more simply.

As a more practical example using a lambda function and a closure, consider the calculation of a derivative. Those familiar with basic calculus will recall the derivative of a function / at a is defined to be

/(«)

lim

0

f(a + h)-f(a) h

If you are unfamiliar with calculus, all you need to know is that the derivative of a function is itself a function; the above formula shows how to transform a function into its derivative. The process of computing a derivative is known as differentiation. The lim/,_,o notation indicates that the answer becomes more precise as the value h gets closer to zero. Letting h be exactly zero would result in division by zero, which is undefined. The trick is to make h as small as possible, keeping in mind that the computer’s floating-point values have limitations.

Based on the mathematical definition we can define a C++ function that computes the derivative of another function, as shown here:

std:: functiorKdouble (double) > derivative(std::functi on<double (double) > f,

double h) {

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Capture function f and h value and return the function's derivative return [f, h] (double x) { return (f(x + h) - f(x)) / h; };

Note that the derivative function returns a function, as a lambda expression is a simple function definition. The function that derivative returns is a closure because it captures the function parameters f and h.

Our deri vati ve function allows us to compute the derivative of a function at a given value. This is known as numerical differentiation. Another approach (the one emphasized in calculus courses) uses symbolic differentiation. Symbolic differentiation transforms the formula for a function into a different formula. The details of symbolic differentiation are beyond the scope of this text, but we will use one of its results for a particular function to check our computed numerical results.

A particular function / is defined as follows:

f(x) = 3x 2 + 5

If you have studied calculus, you can confirm that /’s derivative, /', is:

f'{x) = 6x

Without a knowledge of calculus, simplyjust accept this as the correct answer so we can test our de ri vati ve function.

Listing

20.17

(derivative. cpp) uses the derivative function on f{x) = 3x 2 + 5 and compares its

results with the known solution, f (x) = 6x.

Listing20.17: derivative.cpp

#include <iostream>

#include <iomanip> ffinclude <functional>

// Approximates the derivative of function f given an h value.

// The closer h is to zero, the better the estimate.

std:: function<double(double) > derivative(std::functi on<double(double) > f,

double h) {

// Capture function f and h value

return [f, h] (double x) { return (f(x + h) - f(x)) / h; };

}

double fun(double x) { // The function we wish to differentiate

return 3*x*x + 5;

}

double ans(double x) { // The known derivative of function fun

return 6*x;

}

int main() {

// Difference: Approximation better as h -> 0 double h = 0.0000001;

// Compute the function representing an approximation // of the derivative of function fun

©2018 Richard L. Halterman

Draft date: September 25, 2018

auto der = derivative(fun, h);

// Compare the computed derivative to the exact derivative // derived symbolically double x = 5.0;

std : : cout << "-\n" ;

std::cout << " Approx. Actual \n";

std::cout << " x f(x) h f\'(x) f\'(x)\n";

std : : cout << "-\n" ;

while (x < 5.1) {

std::cout << std::fixed << std::showpoint << std::setprecision(5); std::cout << x << " " << fun(x) << " " << h << " " << der(x)

<< " " << ans(x) << ' \n 1 ;

x += 0.01;

}

}

Table captionWith h = 0.0000001, Listing 20.17 (derivative. cpp) produces good results to the fifth decimal place:

Approx.

Actual

X

f(x)

h

f' (x)

f' (x)

5.00000

80.00000

0.00000

30.00000

30.00000

5.01000

80.30030

0.00000

30.06000

30.06000

5.02000

80.60120

0.00000

30.12000

30.12000

5.03000

80.90270

0.00000

30.18000

30.18000

5.04000

81.20480

0.00000

30.24000

30.24000

5.05000

81.50750

0.00000

30.30000

30.30000

5.06000

81.81080

0.00000

30.36000

30.36000

5.07000

82.11470

0.00000

30.42000

30.42000

5.08000

82.41920

0.00000

30.48000

30.48000

5.09000

82.72430

0.00000

30.54000

30.54000

5.10000

83.03000

0.00000

30.60000

30.60000

Even with h as large as 0.01, the results are not too bad:

Approx.

Actual

X

f(x)

h

f' (x)

f' (x)

5.00000

80.00000

0.01000

30.03000

30.00000

5.01000

80.30030

0.01000

30.09000

30.06000

5.02000

80.60120

0.01000

30.15000

30.12000

5.03000

80.90270

0.01000

30.21000

30.18000

5.04000

81.20480

0.01000

30.27000

30.24000

5.05000

81.50750

0.01000

30.33000

30.30000

5.06000

81.81080

0.01000

30.39000

30.36000

5.07000

82.11470

0.01000

30.45000

30.42000

5.08000

82.41920

0.01000

30.51000

30.48000

5.09000

82.72430

0.01000

30.57000

30.54000

5.10000

83.03000

0.01000

30.63000

30.60000

Table captionIn Listing(20.17 (derivative.cpp), the statement

©2018 Richard L. Halterman

Draft date: September 25, 2018

auto der = derivative(fun, h);

assigns der to the function returned by derivative; thus, der (x) returns the value of the derivative of fun at x. In order for der to compute its answer, it must have access to function fun. It has this access because der is a lambda function that captured fun and h during the call to derivative.

20.5 Algorithms in the Standard Library

CAUTION! SECTION UNDER CONSTRUCTION

The flexible design of the STL containers and their iterators make possible the STL’s generic algorithms. The algorithms provided by the STL are powerful and flexible, but they also are somewhat arcane and can be difficult to use for casual C++ programmers. The STL algorithms are best viewed as the building blocks for more specific tasks required by applications.

In order to use the STL algorithms you must include the following preprocessor directive:

ffinclude <algorithm>

One relatively simple algorithm is std : : for_each. The for_each function applies a unary function to each element in the container. Like the other algorithms we will see, f o r_each uses an iterator to drive a loop behind the scenes. The following statement prints out each element in a std : : Ti st object called seq holding integers:

std::for_each(std::begin(seq), std::end(seq),

[](int x) { std::cout << x << ' '; });

If sec were instead a std : : vector of integers, this statement will work equally well with no changes. That is the beauty of the STL algorithms: many of them work seamlessly on a variety of the different containers provided by the STL.

Listing 20.18 (incelements.cpp) increases by one the value of every element in a list.

Listing20.18: incelements.cpp

ffinclude <iostream> ffinclude <list> ffinclude <algorithm>

int main() {

// Make a list of integers

std::li st<i nt> seq{5, 22, 6, -3, 8, 4};

// Display the vector

std::for_each(std::begin(seq), std::end(seq),

[](int x) { std::cout << x << 1 1 ; }) ; std::cout << '\n 1 ;

// Increase each element in the vector by 1

std::for_each(std::begin(seq), std : :end(seq),

[] (int& x) { x++; });

// Redisplay the vector

std::for_each(std::begin(seq), std::end(seq),

[](int x) { std::cout << x << 1 1 ; }) ; std::cout << '\n 1 ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

Table captionListing [20718[|(incelements.cpp) prints the following:

5

22

6

-3

8

4

6

23

7

-2

9

5

In the statement

std::for_each(std::begin(seq) , std : : end(seq) , [](int& x) { x++; }) ;

note that the lambda function passes the parameter x by reference; this allows the function to modify each element in the sequence.

We can use lambda capture to compute the sum of the elements in a sequence, as shown in Listing 20.19 (sumvec.cpp).

The lambda capture of sum by reference allows the for_each function to modify sum as it iterates over the vector vec.

The std : : iota function, delared in the <numerics> header, is a simple but handy function that fills a container with ascending numbers. The std : : i ota function allows us to replace the following code:

// Make a vector to hold 1,000 elements std::vector<i nt> seq(1000);

// Populate the vector with 0, 1, 2, 3, 999

int count = 0; for (auto& elem : seq) elem = count++;

with

// Make a vector to hold 1,000 elements std::vector<i nt> seq(1000);

// Populate the vector with 0, 1, 2, 3, ..., 999 std::iota(std::begin(seq), std::end(seq), 0);

©2018 Richard L. Halterman

Draft date: September 25, 2018

(The function’s non-descriptive name comes from the Greek letter i, a function from the APL programming language that fills a vector with ascending numbers.)

The std: :find algorithm locates an element within a container. Given a range within a container specified with iterators, the fi nd function returns an iterator to the sought object. If the object is not present

in the container, the function returns the iterator object just past the end of the container. Listing 20.20 (testfind.cpp) tests the find function.

Listing |20i20] (testf ind.cpp) prints

678 is present -200 is NOT present

The std : : copy function copies the elements from one container to another. The std : : transform function works like std : : copy except it expects a function that that can modify the copied elements. Both functions require the begin and end iterators from the source container and the begin iterator of the destination container. Listing 20.21 (testtransform.cpp) illustrates the use of std : copy and std: :transform.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int main() {

const int SIZE = 20;

// Make a vector of SIZE integers

std::vector<i nt> seq(SIZE);

// Populate the vector with 0, 1, 2, 3, SIZE - 1

std::iota(std::begin(seq), std::end(seq), 0);

// Display the vector

std::for_each(std::begin(seq), std::end(seq),

[](int x) { std::cout << x << 1 1 ; }) ; std::cout << '\n 1 ;

// Make a vector large enough to hold the copied values std::vector<i nt> seq2(SIZE);

// Copy the seq to seq2

std::copy(std::begin(seq), std::end(seq), std::begin(seq2));

// Display seq2

std::for_each(std::begin(seq2), std::end(seq2),

[](int x) { std::cout << x << 1 1 ; }) ; std::cout << '\n 1 ;

// Make a vector large enough to hold the transformed values std::vector<i nt> seq3(SIZE);

// Copy the seq to seq3

std::transform(std::begin(seq), std::end(seq), std::begin(seq3), [] (int n) { return 2*n; });

// Display seq3

std::for_each(std::begin(seq3), std::end(seq3),

[](int x) { std::cout << x << 1 1 ; }); std::cout << '\n 1 ;

}

Table captionListing 20.21 (testtransform.cpp) prints

0

1

2

3

4

5 6

7

8 9

10

11

12

13

14

15

16

17

18

19

0

1

2

3

4

5 6

7

8 9

10

11

12

13

14

15

16

17

18

19

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34 36 38

The std: : copy function may seem superfluous since operator^ for vectors also performs a vector copy. With direct assignment there is no need to ensure the receiving vector has enough space; the assignment operator takes care of this detail. The std : : copy function, however, is much more flexible than operators as Listing |20.22|(trimvector.cpp) illustrates.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Make a vector of SIZE integers

std::vector<i nt> seq { 2, 3, 4, 5, 6 };

// Display seq

std::for_each(std::begin(seq) , std::end(seq) ,

[](int x) { std::cout << x << 1 ' ; }) ; std::cout << '\n 1 ;

// Make a copy of vec with the first and last element trimmed off if (seq.sizeQ >= 2) {

// Make a vector large enough to hold trimmed values

std::vector <i nt> seq2(seq.size() - 2); std::copy(std::begin(seq) + 1, std::end(seq) - 1, std::begin(seq2));

// Display seq2

std::for_each(std::begin(seq2), std::end(seq2),

[](int x) { std::cout << x << 1 });

std::cout << '\n ' ;

}

}

Listing 20.22 (trimvector.cpp) makes a copy of a vector with the first and last elements trimmed off, as shown in its output:

2 3 4 5 6

3 4 5

Note how Listing [20.22| (trimvector.cpp) advances the begin iterator of the source vector and decreases the end iterator to restrict the range of values it copies.

The std : : transform function is handy for capitalizing all the letters in a std : : stri ng. List

©2018 Richard L. Halterman

Draft date: September 25, 2018

Before: Fred abcDEF-GFII j kl345qw After : FRED ABCDEF-GHIJKL345QW

The standard library provides an special iterator, std: : ost ream_ite rato r, that enables the std : : copy

function to copy the contents of a container to an output stream instead of another container. Listing |20.24j (copytostream.cpp) shows how this special iterator works.

Listing |20.24 ||j(copytostream.cpp) prints the following to the console:

10 20 30 35 40 45 50 55

Note that std : : ostream_iterator is a generic class parameterized by the type of object the output stream is to receive.

Listing 20.25 (copytofile.cpp) shows how we can use std : : copy to just as easily save the contents of a container to a text file.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Note that the two statements

auto strm = std::ostream_iterator<i nt> (fout, " "); std::copy(std::begin(vec), std::end(vec), strm);

may be colapsed into a single statement, as

std::copy(std::begin(vec) , std::end(vec),

std::ostream_iterator<i nt> (fout, " "));

thus avoiding the extra variable.

The std : : count serves the role of our count_value function from Listing 20.13 (genericcount.cpp). A similar function, std : : count_i f, counts the number of elements in a container that possess a certain property; for example, the following code will print the number of values in vec that are even:

// vec is a vector of integers

std::cout << std::count_if(std::begin(vec), std :: end(vec) ,

[](int n) { return n ?6 2 -- 0; }) ;

The last argument to std: :count_ifisa function that accepts a single value of the type the container is declared to hold. The function returns true or false. A function that returns a Boolean result is known as a predicate. Some STL algorithms, like std : : count_i f, expect a predicate to allow them to process only elements that satisfy the predicate. As another example, the std : : copy_i f function copies only elements from one container to another that satisfy a given predicate. Listing 20.26| (copyevens.cpp) uses std : : count_i f and std : : copy_i f to copy relevant portions of vectors.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

Listing 2Q.26| (copyevens.cpp) prints

2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12

Observe that in Listing 20.26 (copyevens.cpp) we assigned the lambda functions to the variables pri nt and i s_even. This is so we did not have to write the same lambda expressions twice, for printing seq and seq2 and for testing evenness in for count_~i f and copy_~i f. Predicates do not have to be lambda functions—they can be global named functions as well, but lambda function often are more convenient.

In Section 12.4 we wrote a function to randomly permute a vector. The STL provides a function that

does the work for us. Listing 20.27 (testshuffle.cpp) shows how to permute a vector using std : : shuffle.

Listing ||2CL27[| (testshuffle.cpp) prints the vector before and after its permutation. The following shows the output of one run of Listing 207271 (testshuffle.cpp):

0

12 3 4

5 6 7

8 9

10

11

12

13

14 15 16

17 18 19

5

18 8 13

10 16

14 0

15

2

6

11

19 9 12 3

1 17 4 7

Table captionNote that the std : : shuffle function applies only tocontainers that support random access. Thestd: :Tist

©2018 Richard L. Halterman

Draft date: September 25, 2018

class, for example, has no operator [] method and does not support random access. This means you cannot permute the elements inastd: :list object using std : : shuffle.

We can use the std : : generate function to populate a container based on a generating function. A generating function typically returns a different value each time it is called. Listingf20.28 (testgenerate.cpp) uses std : : generate to

1. fill a container with identical values,

2. fill a container with a sequence produced from a formula, and

3. fill a container with pseudorandom values.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

One run of Listing |20.28|| (testgenerate.cpp) produces the following output:

22222222222222222222

10 15 16 17 18 19 20 25 26 27 28 29 30 35 36 37 38 39 40 45 59 55 55 40 53 1 48 91 10 13 65 78 52 28 17 23 30 12 0 20

The first two lines of the output will always be the same, but the last line will vary from one run to the next.

The std: :accumulate function applies a binary operation to all the elements of a container to produce a single value. (A binary operation is an operator or function that expects two arguments.) One example of its use is adding up the elements in a numeric list. Listing 20.29 (testaccumulate.cpp) shows the std: :accumulate function in action.

One run of Listing |20.29|(testaccumulate.cpp) produces the following output:

©2018 Richard L. Halterman

Draft date: September 25, 2018

13

48

This is the expected output, since 2+1+3 +4 + 1+2=13, and 2xlx3x4xlx2 = 48.

It is possible to use std : : accumulate on containers holding nonnumeric values; for example, the following code

std::vector<std::string> words { "fred", "ella", "jo", "sam", "pat" }; std::copy(std::begin(words), std::end(words),

std::ostream_iterator<std::string>(std::cout, " ")); std::cout << '\n' ;

// Concatenate the elements

std::cout << std::accumulate(std::begin(words), std::end(words),

std::string(""),

[](std::string a, std::string b) { return a + b; })

« '\n' ;

will concatenate all the strings in the vector to produce the following output:

fred ella jo sam pat fredellajosampat

While it may seem good in theory, this approach is not efficient and should be avoided. Each application of the operator+ concatenation operator creates a new std : : stri ng object from two existing std: : string objects. Especially for longer lists, this repeated string creation process unnecessarily wastes time and space. For a container that contains n strings, the std : : accumulate function will create n — 1 new string objects on its way to produce the final accumulated string result. Numeric arithmetic does not create new objects, and so std: accumulate is best used on containers holding numbers. (That is why its declaration appears in the <numeri c> header.)

It you need to concatenate the strings in a container to make one big string, you should use operator+=. This operator appends characters onto the end of an existing string object, thus avoiding the creation of new string objects. In this case a simple familiar for loop is preferable to a sophisticated STL algorithm. The following code illustrates a more efficient solution:

std::vector<std::string> words { "fred", "ella", "jo", "sam", "pat" }; std::copy(std::begin(words), std::end(words),

std::ostream_iterator<std::string>(std::cout, " ")); std::cout << '\n' ;

// Concatenate the elements std::string joined = for (const std::string& word : words) joined += word; std::cout << joined << '\n' ;

This version produces the same results, but it executes faster and uses less memory. If the number of strings is small, it does not make much difference. It is only when the collection of strings to concatenate becomes large that we will detect a performance difference. Listing 20.30 (teststrconcat.cpp) tests the two algorithms.

Listing 20.30: teststrconcat.cpp

ffinclude <iostream>

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <vector>

#include <string>

#include <algorithm>

#include <numeric>

#include <iterator>

#include <random>

#include <ctime>

// Uniform pseudorandom number generator from an earlier chapter

#include "uniformrandom.h"

// Some global resources // Valid characters in our words

const std::string character_set = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" ;

// Our words will contain 1-8 letters

UniformRandomGenerator word_len_gen(1, 8);

// We will select from a random index in character_set UniformRandomGenerator char_chooser_gen(0, 25);

std::string make_random_string() { std::string result =

int size = word_len_gen(); // Length of this word

for (int i = 0; i < size; i++)

result += character_set[char_chooser_gen()]; return result;

}

std::vector<std::string> make_random_string_vector (int size) { std::vector<std::string> result(size); for (auto& elem : result)

elem = make_random_string(); return result;

}

std::string concatl (const std::vector<std::string>& words) { return std::accumulate(std::begin(words), std::end(words), std::string( "" ),

[](std::string a, std::string b) { return a + b; });

}

std::string concat2 (const std::vector<std::string>& words) { std::string joined = for (const std::string& word : words) joined += word; return joined;

}

int main() {

auto words = make_random_string_vector(25);

copy(std::begin(words), std::end(words),

std::ostream_iterator<std::string>(std::cout, " ")); std::cout << '\n 1 ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << " ========================\n" ;

clock_t start_time, stop_time; start_time = clockQ ; auto s = concatl(words); std::cout << s << 1 \n' ; stop_time = clock();

std::cout << "Accumulate: " << stop_time - start_time << " msec\n";

std : : cout << "-\n" ;

start_time = clockQ ; s = concat2(words); std::cout << s << 1 \n' ; stop_time = clockQ;

std::cout << "for loop: " << stop_time - start_time << " msec\n";

Listing 20.30 (teststrconcat.cpp) compares the two algorithms on a vector containing 25 strings generated at random with lengths ranging from 1 to 8 letters. Its output on one run is

IQW WOP V WVAQZGNG M BGMBBIM T GS HBIPVLUU ZAIN NODPNQDR TO SUHV QY K M 0 LAY

IQWWOPVWVAQZGNGMBOMBBIMTGSHBIPVLUUZAINNODPNQDRTOSUHVQYKMOLAYDOPKQHDWOAEVFZGBG Accumulate: 2 msec

IQWWOPVWVAQZGNGMBOMBBIMTGSHBIPVLUUZAINNODPNQDRTOSUHVQYKMOLAYDOPKQHDWOAEVFZGBG for loop: 1 msec

Some runs show std : : accumulate to be faster, but the differences are usually single-digit milliseconds. If crank up the size of the vector to 200,000 and comment out the statements that print the strings, we see a more significant difference:

Accumulate: 55805 msec

for loop: 34 msec

Here std: :accumulate requires almost one minute to build the string .while the for loop with o p e r a t o r + takes less than one-tenth of a second.

The std: :partition function reorders the elements in a container so that all the elements that

satisfy a predicate will appear before the elements that do not meet satisfy the predicate. Listing }20.31

(testpartition.cpp) rearranges the elements in a vector of integers so that all the even numbers appear before any odd number. It also partitions a list of strings so that words that contain more than three letters appear before any word with three or fewer letters.

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include "uniformrandom.h" int main() {

std::vector<i nt> nums(25);

UniformRandomGenerator gen(0, 100);

auto int_output = std::ostream_iterator <i nt> (std::cout, " ");

// Populate the vector with pseudorandom // integers in the range 0, 1, 100

std::generate(std::begin(nums), std::end(nums), gen);

std::cout << "Original sequence\n";

std::copy(std::begin(nums), std::end(nums), int_output); std::cout << '\n 1 ;

std : : cout << "-\n" ;

std::cout << "Partitioned sequence\n";

std::partition(std::begin(nums), std::end(nums),

[] (int n) { return n % 2 == 0; }); std::copy(std::begin(nums), std::end(nums), int_output); std::cout << '\n 1 ;

std::cout << "=================\n\n" ;

auto string_output = std::ostream_iterator<std::string>(std::cout, " "); std::vector<std::string> words { "fred", "ella", "adam", "jo",

"pat", "mel", "anna", "ed",

"oscar", "will", "tom", "ingrid" }; std::cout << "Original sequence\n";

std::copy(std::begin(words), std::end(words), string_output); std::cout << '\n 1 ;

std : : cout << "-\n" ;

std::cout << "Partitioned sequence" << '\n';

std::partition(std::begin(words), std::end(words),

[] (const std::string& w ) { return w.lengthQ >3; }) ; std::copy(std::begin(words), std::end(words), string_output); std::cout << '\n 1 ;

Table captionListing [20.31|(testpartition.cpp) prints

Original sequence

81 80 2 63 13 25 12 7

8 16

84

91

56 91 56 7

59 94 18 68

68

71

78

66

60

Partitioned sequence

60 80 2 66 78 68 12 68 8 16

84

18

56 94 56 7

59 91 91 7

25

71

13

63

81

Original sequence

fred ella adam jo pat

mel anna

ed

oscar will

tom ingrid

Partitioned sequence

fred ella adam ingrid

wi 11

oscar

anna ed mel

pat tom jo

Table captionNote that std : : pa rti ti on does not attempt to preserve the original relative order of elements within a

©2018 Richard L. Halterman

Draft date: September 25, 2018

partition. Also, std : : pa rti ti on does not make any new string objects. It simply moves existing string around within the container. This makes it as efficient for strings as for simple numbers.

The std: :merge function merges two ordered containers into a third container. The resulting container will be ordered. Listing[207321 (testmerge.cpp) shows an example of testmerge. cpp.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << '\n' ;

}

Table captionOne run of Listing 20.32 (testmerge.cpp) prints the following:

Original sequences

8 26 8

17 26 23

31

7

16 30 5 21

37

20

4

29 0 22

32 18 4

36

26

38

21 14

34

32

Sorted

sequences

4 5 7 8

8 16 17

20

21

23

26 26

30

31

37

0 4 14

18 21 22

26

29

32

32 34

36

38

Merged

sequence

0 4 4 5

7 8 8 14

16

; 17 18

20 21

21

22

23 26 26 26 29 30 31 32 32 34 36 37 38

We can use the std : : remove and std : : remove_i f functions to remove elements from a container. Unlike the other algorithms we have seen so far, these functions work in an unexpected way given their names. Neither remove nor remove_i f by themselves achieve the results we generally desire.

Listing 20.33 (removeonly.cpp) shows what happens when we attempt to use remove or remove, in isolation.

if

©2018 Richard L. Halterman

Draft date: September 25, 2018

copy(std::begin(nums), std::end(nums), output); std::cout << '\n 1 ;

The output of Listing 20.33 (removeonly.cpp) is surprising to those unfamiliar with std : : remove and std:: remove if:

0

1

2

3

4

5 6

7

8 9

10

11

12

13

14

15

16

17

18

19

0

1

2

3

4

5 6

7

8 9

11

12

13

14

15

16

17

18

19

19

1

3

5

7

9

11

13

15

17

19

19

12

13

14

15

16

17

18 19 19

The first line shows the contents of the original vector. The second line shows the modified vector with 10 removed. Element 10 definitely is gone, but the vector contains the same number of elements as before! A closer inspection reveals that all the elements that followed 10 in the original vector have been shifted forward one position. It is as if the removal of 10 left a hole in the vector that the following elements had to shift forward to fill. That would be fine, but the last element, 19, was copied forward and remains the last element in the vector.

In the last line we see that all the evens are missing in the front of the vector, but, again, some unusual shifting and copying occurred to keep the vector the same size.

In order to actually remove the elements and make the resulting container smaller, we must couple remove or remove_i f with the container’s erase method. The erase method accepts two iterators establishing a range of elements to delete from the container. Listing 20.34 (vectorerase.cpp) shows how to remove a section of a vector using the std : : vector <T> : : erase method.

Table captionListing [20.34j| (vectorerase.cpp) prints

10

20

30

40

50 60 70 80 90 100

10

20

30

90

100

The remove and remove_i f functions return an iterator that points to the first element in the container that was not removed. Recall the output of Listing 20.33 (removeonly.cpp), reproduced here:

©2018 Richard L. Halterman

Draft date: September 25, 2018

0

1

2

3

4

5 6

7

8 9

10

11

12

13

14

15

16

17

18 19

0

1

2

3

4

5 6

7

8 9

11

12

13

14

15

16

17

18

19 19

1

3

5

7

9

11

13

15

17

19

19

12

13

14

15

16

17 18 19 19

The return value of the call to remove returns an iterator pointing to the second occurrence of 19 in the second line of output. In the third line of output the call to remove_i f returns a pointer to second occurrence of 19 as well. Note that in both cases the iterators point to the first element in the remaining values that ought to be erased from the vector.

Listing 20.35 (testremove.cpp) combines the vector’s erase method and the remove function to achieve the desired results.

Listing 20.35 (testremove.cpp) prints the expected results:

0

1

2

3

4

5 6 7

8 9 10 11

12

13

14

15

16

17

18 19

0

1

2

3

4

5 6 7

8 9 11 12

13

14

15

16

17

18

19

1

3

5

7

9

11 13

15 17 19

Table caption©2018 Richard L. Halterman

Table captionDraft date: September 25, 2018

The combination of std : : vector <T> : : erase and std : : remove is known in the C++ community as the erase-remove idiom.

The STL contains a number of other algorithms to process generic containers. Some examples include

• std:: reverse reverses the elements of a container,

• std : : all_of returns true if all the elements in a container satisfy a predicate,

• std::any_of returns true if at least one of the elements in a container satisfy a predicate,

• std : : none_of returns true if none of the elements in a container satisfy a predicate,

• std::find_if returns an iterator to the first element in a container that satisfies a predicate.

20.6 Namespaces

In Section 2.3 we reviewed the various approaches for using names from the std namespace. We have been avoiding the blanket using directive:

using namespace std;

claiming that its disadvantages outweight its occasional convenience.

We now are creating our own names for functions and types within the programs we write. Using the blanket usi ng directive can present problems at times because the std namespace contains hundreds of type and function names, and it is too easy for a programmer to accidentally reuse for another purpose a name already claimed by the std namespace. Such name conflicts lead to problems during software development, and since the development process generally has enough other challenges to address, it is best practice to avoid the blanket usi ng directive.

Listing 20.36 (maxvector.cpp) defines a max function that computes the number of times the maximum value appears in a vector of integers. The is_sorted function determines if all the elements in a vector appear in nondecreasing order. The mai n function tries out the function on a sample vector.

Listing20.36: maxvector.cpp

#include <iostream>

#include <vector>

using namespace std;

// Counts the number of occurrences of the maximum value in

// a nonempty vector vec

int max(const vector<int>& vec) {

auto p = std::begin(vec) ; // p points to the first element

// Determine maximum value

int m = *p++; // Set m to the first element and move p

while (p != std::end(vec)) { if (* p > m )

m = *p; // Found a reason to update m

p++;

}

// Count the number of times the maximum appears

©2018 Richard L. Halterman

Draft date: September 25, 2018

int count = 0; for (auto elem : vec) if (elem == m) count++; return count;

Table caption// Returns true if all the elements in vector vec appear // in nondecreasing order; otherwise, returns false, bool is_sorted (const vector<int>& vec) {

for (unsigned i

= 0; i

< vec.size() - 1;

i++)

if (vec[i]

V

<

fD

n

i — i

—i.

+ 1])

return

false ;

// Found elements

out of order

return true;

main()

{

cout

<<

boolalpha << is_sorted({l, 2,

3,

4,

5})

<<

' \n

cout

<<

boolalpha << is_sorted({5, 4,

3,

2,

1})

<<

' \n

cout

<<

boolalpha << is_sorted({5, 5,

5,

5,

5})

<<

' \n

cout

<<

"-\n" ;

cout

<<

max({1, 2, 3, 4, 5}) << '\n' ;

cout

<<

max({5, 4, 3, 2, 1}) << '\n' ;

cout

<<

max({3, 4, 5, 2, 1}) << 1 \n' ;

cout

<<

max({5, 2, 3, 4, 5}) << '\n' ;

cout

<<

max({5, 4, 5, 2, 5}) << 1 \n' ;

cout

<<

max({5}) << ' \n 1 ;

cout

<<

max({5, 5, 5, 5, 5}) << '\n';

}

Notice the blanket usi ng namespace std directive that makes all the function and type names in the std namespace available to this program. This has not been our common practice so far, but you frequently will encounter this approach in published C++ code. This program works correctly, however, as it prints the following:

The C++ standard library contains a function named i s_sorted, declared in the <algori thm> header. The standard is_sorted performs the same task as this is_sorted, except that the standard function, striving to be as generic as possible, accepts two iterators instead of the container itself. In preparation to replace our i s_sorted function with the standard i s_sorted function, we add the following directive to the top of the code with the other #i includes:

#include <algorithm>

©2018 Richard L. Halterman

Draft date: September 25, 2018

If we compile and run our program with this addition, we get no errors or warnings, and the program prints the following:

Observe that our max function behaves very differently after this slight change. In fact, the code that executes for the max invocations is not the code in Listing[20.36 (maxvector.cpp) but rather the max function in the standard library! This is because a call such as

max({1, 2, 3, 4, 5})

passes an initializer list to max, not an actual vector object. Before the inclusion of <algorithm>, the only max the compiler knew of was the one defined in Listing 20.36 (maxvector.cpp). This max function expects a reference to a std : : vector object. The std : : vector class contains a constructor that accepts an initializer list. The compiler, therefore, automatically can create a vector from an initializer list. The compiler automatically uses the initializer list to create a vector object and sends it off the max function for processing.

The inclusion of the <algorithm> header provides the declaration of std: :max that accepts, among other arguments, an initializer list. When the compiler matches a function call to its corresponding definition, it always seeks the best match for the arguments passed. Since the std : : max accepts an initializer list, it better matches the calls in the mai n function.

Remember, our purpose for including the <algori thm> header was to gain access to i s_sorted, and we had no intention of changing our max implementation. Unfortunately, the compiler, following a well-established and sensible algorithm, silently (no warnings or errors) substituted a different function to change the behavior of our program. This is prime example of why the blanket using namespace std directive can be dangerous.

To avoid the danger, avoid the usi ng directive, as shown in Listing 20.37 (bettermaxvector.cpp)

©2018 Richard L. Halterman

Draft date: September 25, 2018

p + +;

}

// Count the number of times the maximum appears

int count = 0; for (auto elem : vec) if (elem == m) count++; return count;

// Returns true if all the elements in vector vec appear // in nondecreasing order; otherwise, returns false, bool is_sorted (const std:: vector<int>& vec) {

for (unsigned i = 0; i < vec.sizeQ - 1; i++) if (vec[i] > vec[i + 1])

return false; // Found elements out of order

return true;

main() {

std:

: cout

<<

std::boolalpha <<

i s_

sorted({1,

2, 3,

4, 5})

<<

' \n

std:

: cout

<<

std::boolalpha <<

i s_

sorted({5,

00

2, 1})

<<

' \n

std:

: cout

<<

std::boolalpha <<

i s_

sorted({5,

5, 5,

5, 5})

<<

' \n

std:

: cout

<<

II

-\n";

std:

: cout

<<

max({l, 2, 3, 4,

5})

<<

1 \n 1

5

std:

: cout

<<

max({5, 4, 3, 2,

1})

<<

1 \n 1

?

std:

: cout

<<

max({3, 4, 5, 2,

1})

<<

1 \n 1

?

std:

: cout

<<

max({5, 2, 3, 4,

5})

<<

1 \n 1

?

std:

: cout

<<

max({5, 4, 5, 2,

5})

<<

1 \n 1

5

std:

: cout

<<

max({5}) << '\n 1 ;

std:

: cout

<<

max({5, 5, 5, 5,

5})

<<

1 \n 1

5

}

In Listing 20.37 (bettermaxvector.cpp) because of the missing std : : prefixes the compiler knows that the calls to max cannot be the calls to std : : max.

Identifiers (variable names, function names, and type names) should be meaningful, clearly communicating their intent. Well-chosen English words or simple variations of common words are ideal. This means it is quite likely that a library developed by a team of developers would contain function names and type names that also appear in a different library developed by a different team of programmers. Each library used separately is not a problem, but issues can arise when building a software system atop multiple libraries; for example, consider the task of building a program that models and visualizes the spread of an infectious agent. Such a system could make good use of the following libraries:

• a 3-D graphics library that defines a mathematical vector class, used for a number computer graphics rendering processes, such as scene orientation and light intensities,

• an epidemiology modeling library with a vector type that represents the means of transmission of a disease, such as a mosquito or tick, and

• the C++ standard library which includes a vector generic class used to store sequences of any type.

The name vector has a different meaning in each of these contexts. C++ namespaces allow us to manage simultaneously and effectively all of these vector types within a single software system.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Ideally, any code meant for widespread use should be part of a namespace. A company developing libraries for internal use could place them in a namespace based on the company name. Components intended for public consumption could be placed in a namespace with a different name.

In C++ it is easy to put the functions and types we develop into custom namespaces. Suppose we wish to make the functions from Listing 120.37 (bettermaxvector.cpp) available to a wider audience. Listing 20.38 (vectutils.h) and Listing 20.39 (vectutils.cpp) package the two functions into a namespace named vectuti Is. Listing 20.38 (vectutils.h) provides the function declarations, and Listing 20.39 (vectutils.cpp) contains the function definitions.

©2018 Richard L. Halterman

Draft date: September 25, 2018

return false; // Found elements out of order return true;

}

} // End vecutils namespace

The general form of a namespace declaration is

namespace name {

The name of a namespace is an identifier; therefore, the same rules governing variable names, function names, and type names apply equally to namespace names.

Listing 20.38 (vectutils.h) and Listing|20.39 (vectutils.cpp) demonstrate that namespace declarations can span multiple files. The components of the std namespace are scattered over many different files.

Listing 20.40|(testns.cpp) tests the functions in our new namespace.

Listing20.40: testns.cpp

ffinclude <iostream> ffinclude "vectutils.h"

int main() {

std:

: cout

<<

std::boolalpha <<

vecutiIs

: : is_

sorted({1,

2, 3,

4, 5})

<<

1 \n 1

std:

: cout

<<

std::boolalpha <<

vecutiIs

: : is_

sorted({5,

4 , 3 ,

2, 1})

<<

1 \n 1

std:

: cout

<<

std::boolalpha <<

vecutiIs

: : i s_

sorted({5,

5, 5,

5, 5})

<<

1 \n 1

std:

: cout

<<

II

-\n

i .

5

std:

: cout

<<

vecutiIs:

:max({1,

2, 3,

4,

5})

<<

1 \n

5

std:

: cout

<<

vecutiIs:

:max({5,

4, 3,

2,

1})

<<

1 \n

?

std:

: cout

<<

vecutiIs:

:max({3 ,

4, 5,

2,

1})

<<

1 \n

?

std :

: cout

<<

vecutiIs :

:max({5,

2, 3,

4,

5})

<<

1 \n

?

std :

: cout

<<

vecutiIs :

: max({5 ,

4, 5,

2,

5})

<<

1 \n

5

std :

: cout

<<

vecutiIs :

:max({5})

<< 1

\n 1

5

std :

: cout

<<

vecutiIs :

: max({5 ,

5, 5,

5,

5})

<<

' \n

5

}

Note that instead of using the long names for vecutils: :is_sorted and vecutils: :max, we could have used the focused using declarations:

using vecutiIs::is_sorted; using vecutiIs::max;

We also could us the blanket using directive using namespace vecutils;

©2018 Richard L. Halterman

Draft date: September 25, 2018

but this introduces the possibility of name clashes, especially with the similar-named functions from the std namespace declared in the <algori thm> header. Just as with the std namespace, it is best to avoid blanket usi ng directives for custom namespaces.

C++ permits namespaces to be nested, as in

namespace utils {

namespace graphics { namespace math {

double f(double v) { /* Details omitted ...*/}

}

}

}

Absent of any using directives, we would call function f as std::cout << utiIs::graphics::math::f(9.4) << '\n' ;

Since nested namespace names can become quite lengthy, C++ supports namespace aliases, as in namespace ugm = utiIs::graphics::math;

This namespace alias makes it possible for us to call f with the more compact statement std::cout << ugm::f(9.4) << '\n' ;

Nesting allows developers to organize better the components within libraries; for example, a company may have an outer namespace derived from the company’s name and nested namespaces that correspond to departments or divisions within the company.

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 21

Associative Containers

21.1 Associative Containers

Chapter [TTj introduced the vector and array data types. Both of these data structures represent linear sequences of elements. Vectors and arrays are convenient for storing collections of data, but they have some limitations. For one, we locate an element within a vector or array based on its position (index). To retrieve a specific element we must supply its index. While this approach is fine for many applications, in other situations this access-by-index approach is awkward or inefficient.

In contrast, an associative container permits access based on a key, rather than an index. Unlike an index, a key is not restricted to an integer expression. The C++ standard library supports three kinds of associative containers: set, map, and unordered_map. Here we will examine each of these types in some detail.

21.2 The std :: set Data Type

C++ provides a data structure that models to some extent a mathematical set. Unlike C++ vectors, arrays, and lists, mathematical sets are unordered and may contain no duplicate elements. The C++ std: : set container, like mathematical sets, ignores any attempts to include duplicate elements; however, std : : set objects do order their elements internally in a particular way. This ordering permits very fast access to elements. Listingpl.l|(seffest.cpp) demonstrates these properties.

©2018 Richard L. Halterman

Draft date: September 25, 2018

return a.data < b.data;

}

// Define this operator so output streams can print // instances of our custom type.

std::ostream& operator<< (std::ostream& os, const MyClass& obj) { os << obj.data; return os;

}

int main() {

// Attempt to add duplicates

std:: set<i nt> S {10, 3, 7, 2, 7, 11, 3}; for (auto elem : S)

std::cout << elem << 1 std::cout << '\n 1 ;

std:: set<i nt> T {5, 4, 5, 2, 4, 9}; for (auto elem : T)

std::cout << elem << 1 std::cout << '\n 1 ;

// Make a set of our custom types

std::set<MyClass> U {MyClass(10), MyClass(3), MyClass(7), MyClass(2)}; for (auto& elem : U)

std::cout << elem << 1 std::cout << '\n 1 ;

}

The output of Listingj2~I7T|(settest.cpp) is

2 3 7 10 11 2 4 5 9 2 3 7 10

Note the element ordering in the initializer list for the set constructor is different from the order of the printed elements when traversed via a for loop. The order actually is ascending order in all of our tests in Listing j21.11| (settest.cpp), and this is not a coincidence. Also observe that sets do not admit duplicate elements.

The implementation of the std : : set class on all the major C++ libraries use a red-black tree (see https://en.wikipedia.org/wiki/RedUblack_tree) as the internal data structure. The ordering imposed by this internal data structure enables very fast access to the set’s elements. A red-black tree permits binary search (see Section; 12.3.2). A set determines the order of its elements via operators The < operator works with all the primitive numeric types (int, double, float, unsigned, etc.). The operator< is defined for std: :stri ng class instances to compare two string objects lexicographically. Instances of any type we wish to store in a std : : set must support the < operator.

In Listing 21.1 (settest.cpp) we define a new custom type, MyClass. We must ensure that it is possible to compare two MyClass instances using the < operator in order to put MyClass objects in a set. To achieve this, we define operator< as a global function that compares two MyClass objects. This allows us to create a set of MyClass objects.

We can make a set out of a vector using the set constructor that accepts a pair of iterators to another container:

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::vector<i nt> vec {40, 10, 20, 50, 10, 30}; set<int> my_set(std::begin(vec), std::end(vec)); for (auto elem : my_set) std::cout << elem << ' std::cout << '\n' ;

As with an initializer list, this construction from a vector will not preserve the original ordering found in the vector. Also, any duplicate elements in the vector will appear only once in the set object.

Unlike in mathematics, all sets in C++ must be finite.

Listing 21.2 (setoutput.h) provides a convenient function that prints a std : : set in familiar humanreadable form.

Listing [2L2] (setoutput.h) enables us to write code such as

std::set<i nt> S = {20, 40, 60, 80}; std::cout << S << '\n' ;

which prints

{20, 40, 60, 80}

just like the set would appear in a mathematics book. We will include this header file in subsequent programs that use std : : set so we easily can display a set’s contents.

C++ supports the standard mathematical set operations of intersection, union, set difference, and symmetric difference. These functions are part of the algorithms library, and thus they are designed to work with as wide an array of containers as possible. The downside of this flexibility is they are somewhat arcane and awkward to use, as Listing f2Q (setopsbuiltin.cpp) shows.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing 21.3: setopsbunltnn.cpp

#include #include #include #include #include

<iostream> <set> <vector> <algorithm> <iterator>

#include "setoutput.h"

int main() {

// Compute the intersection and union of two sets std:: set<i nt> sl{l, 2, 3, 4, 5, 6}; std:: set<i nt> s2{2, 5, 7, 9, 10}; std:: set<i nt> sl_inter_s2;

std::set_intersection(std::begin(si), std::end(si),

std::begin(s2), std::end(s2),

std::inserter(sl_inter_s2, std::end(sl_inter_s2))) ; std::cout << "Intersection of " << si << " and " << s2 << " = " << sl_inter_s2 << '\n' ;

std::cout << "\n- \n";

std:: set<i nt> sl_union_s2;

std::set_union(std::begin(si), std::end(si), std::begin(s2), std::end(s2),

std::inserter(sl_union_s2, std::end(sl_union_s2))); std::cout << "Union of " << si << " and " << s2 << " = " << sl_union_s2 << '\n' ;

std::cout << "\n- \n";

std:: vector<i nt> vl{l, 2, 3, 4, 5, 6}; std:: vector<i nt> v2{2, 5, 7, 9, 10};

// Note: vl and v2 both must be sorted for this to work

// Since we created them sorted the next two statements are not

// technically necessary, but we include them here to emphasize

// the fact that the vectors must be sorted to compute their

// intersection and union in this manner. Sets are inherently

// sorted, and so need no such preprocessing.

sort(std::begin(vl), std::end(vl)) ;

sort(std::begin(v2), std::end(v2));

std: :vector<int> vl_intersection_v2;

std:: vector<i nt> vl_union_v2;

std::set_intersection(std::begin(vl), std::end(vl),

std::begin(v2), std::end(v2), std::back_inserter(vl_intersection_v2)); std::set_union(std::begin(vl), std::end(vl), std::begin(v2), std::end(v2), std::back_inserter(vl_union_v2)); for (auto elem : vl_intersection_v2) std::cout << elem << 1 '; std::cout << '\n 1 ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

for (auto elem : vl_union_v2) std::cout << elem << 1 std::cout << '\n 1 ;

Listing pT31 (setopsbuiltin.cpp) shows how the intersection and union functions work for vectors as well as sets. The catch is that the elements in the containers must be ordered for these functions to work properly. We saw that std : : set objects are ordered automatically. Since std : : vector objects do not impose an order on their elements, we must first sort any vectors we wish to send to the standard intersection and union functions.

Listing 21.4 (setops.cpp) implements operators* and operator | to work with set objects to provide a more convenient interface to programmers. The & operator represents set intersection, and | represents set union.

If we did a lot of programming with mathematical sets, we probably would add these two functions to our header file that overloads operator<< to print set objects.

©2018 Richard L. Halterman

Draft date: September 25, 2018

The real value of the set class comes from the speed of access it provides to its elements. As an associative container, we do not access an element via an index as we do with a vector or array. In fact, std : : set does not even provide operator [] . We want to place an item into a set and retrieve it later without regard to its location within its internal data structure.

Recall the std: :find algorithm provided by the STL (see Section 20.5). Given an iterator to the beginning of the container, an iterator just past the end of the container, and an item to find, std : :find returns an iterator that points to the sought element within the container. If the container does not contain the sought element, std : : find returns the iterator that equals the just-past-the-end iterator.

The std : : find function works with a std: : set object just as it does with other containers, but the std : : set class provides its own find method that exploits the structure of the data within the set object to locate elements very quickly. Listing 21.5 (setvsvector.cpp) illustrates the use the std: : set: : find method, comparing the time to locate an element in a vector versus the time to locate the same element in a set containing the exact elements contained in the vector.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::cout << "Vector time: " << stop_time - start_time << '\n' ;

start_time = clockQ ; for (int i = 0; i < SIZE; i++) { int seek = search_values[i]; s.find(seek);

}

stop_time = clockQ;

std::cout << "Set time: " << stop_time - start_time << '\n';

The vector and set objects within Listing [2T3) (setvsvector.cpp) each contain the integers 0,1,..., 249,000. Note that the vector contains the elements in ascending order. We then create a vector containing pseudorandom values in the range 0,1,... ,249,000. The program will search for these random values within each container. The program measures the time it takes to complete the searches.

The output Listing |21,5| (setvsvector.cpp) reveals the dramatic difference in performance between the std : : find function on a vector and the std : : set: : find method with a set:

Vector time: 84044 msec Set time: 234 msec

We see on this particular run that the vector search required almost one and a half minutes to complete, while the set search took only about a quarter of a second. While the exact numbers will vary from run to run and be higher or lower depending on the host machine, the disparity of times will be consistent. The two data structure contain exactly the same elements, and program uses the exact same search values. The std : : set’s search is so much quicker because std : : set: : fi nd performs binary search on its internal data structure, while std : : find uses linear search (see Section 12.3.2).

21.3 Tuples

In C++ a function can return only one thing. That one thing might be an integer or a single object like a vector or an instance of some other class, but it must be just one thing. What if we need a function to return more than one thing? We could put the desired return values into a vector and return the vector. The caller then would extract the components from the vector upon the function’s return. Unfortunately, this will not work if the multiple elements to return have different types. The container types we have examined thus far—vectors, arrays, lists, and sets—have been homogeneous; that is, their elements all have the same type.

We could define a struct or class that has fields of different types, but this creates a new, named, custom type. In a large program we may need many different structs to cover all the combinations of multiple-valued return types we need. Providing a named struct or class introduces a new type into the system, thereby increasing the system’s complexity.

All we want is to be able to package multiple elements together for some simple purpose, without needing to create a new custom type. Fortunately, C++ provides the std: :tuple generic class in its standard library. Listing[2L6|(simpletuples.cpp) shows how to use tuples in a C++ program.

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <cmath> // For sqrt int main() {

// Declare some local variables

std::string word; int number; double quantity;

// Construct a tuple directly with some literal values std::tuple<std::string, int, double> tl {"Bob", 4, 9.5}; // Unpack the tuple's components std::tie(word, number, quantity) = tl;

// Print the results

std::cout << "word = " << word << ", number = " << number << ", quantity = " << quantity << '\n' ;

// Use std::make_tuple convenience function auto t2 = std::make_tuple( "Eve" , 22, 8.3);

// Unpack the tuple's components std::tie(word, number, quantity) = t2;

// Print the results

std::cout << "word = " << word << ", number = " << number << ", quantity = " << quantity << '\n' ;

}

// Declare some variables

std::string name = "dan";

int age = 12;

double amount = 50.2;

// Build a tuple from more general expressions

auto t3 = std::make_tuple(name, age * 2, std::sqrt(amount));

// Unpack the tuple's components one at a time

word = std::get<0>(t3); // 1st component is at index 0

number = std::get<l>(t3); // 2nd component is at index 1

quantity = std::get<2>(t3); // 3rd component is at index 2

// Print the results

std::cout << "word = " << word << ", number = " << number << ", quantity = " << quantity << '\n' ;

When compiled and executed. Listing |21.6j| (simpletuples.cpp) prints

word = Bob, number = 4, quantity = 9.5 word = Eve, number = 22, quantity = 8.3 word = dan, number = 24, quantity = 7.0852

As the program shows, we can construct astd: :tuple directly, as in the case of tl, but the std : : make_ tuple function results in simpler code. The arguments used when making a tuple can consist of literals, variables, and other more complex expressions.

Extracting the components of a tuple is known as unpacking. Listing |21.6| (simpletuples.cpp) shows how to use the std : : ti e function to assign the components of a tuple to individual variables in one statement.

The std : : ti e function is a generic function that works with any types storable within a tuple. If we wish to extract just one element from a tuple, we can use the std : : get generic function. The generic std : : get function is parameterized by an integer that serves as an index into the tuple. As with vectors.

©2018 Richard L. Halterman

Draft date: September 25, 2018

the first element of the tuple is found at index zero.

C++ supports another way of unpacking tuples. Structured binding is similar to std : : ti e but can be used only when declaring the variables used to represent the components of a tuple. With structured binding we can rewrite the following code:

std::string word, name = "Jan";

int number, age = 25;

double quantity, amount = 50.2;

auto t = std::make_tuple(name, age, amount);

// Unpack the tuple's components

std::tie(word, number, quantity) = tl;

as

std::string name = "Jan";

int age = 25;

double amount = 50.2;

auto t = std::make_tuple(name, age, amount);

// Unpack the tuple's components auto [word, number, quantity] = t;

The statement

auto [word, number, quantity] = t;

constitutes the structured binding. Note that we can use this special syntax only when declaring the variables to be bound to the components of the tuple. This copies the components of the tuple into the newly declared variables. Specifically, the following statement:

[word, number, quantity] = t; // Illegal, not a declaration

is illegal, even if the variables word, number, and quantity are properly declared before the this statement.

We can specify that the structured binding be done by reference, as in the following: auto& [word, number, quantity] = t;

In this case each name within the binding becomes an alias to a component of the tuple. In the previous code fragment above, reassigning number will similarly modify the second component of tuple t.

Structured binding is especially convenient when processing tuples within loops. Listing ||21.7| (tupleloop.cpp) uses structured bindings by reference to reassign the elements in a vector of tuples. The program then uses structured bindings to extract the components of each tuple to print them out.

©2018 Richard L. Halterman

Draft date: September 25, 2018

int count = 1; double quant = 10.0;

// Populate the vector

for (auto& [s, i, d] : vec) {

s = "Item #" + std::to_string(count); i = count++; d = quant; quant += 10;

}

// Print the contents of the vector for (auto [s, i, d] : vec)

std::cout << "[" << s << ", " << i << ", " << d << "]\n";

Table captionListing |2T77|(tupleloop.cpp) prints the following:

[Item

#1,

1,

10]

[Item

#2,

2,

20]

[Item

#3,

3,

30]

[Item

#4,

4,

40]

[Item

#5,

5,

50]

[Item

#6,

6,

60]

[Item

#7,

7 ,

70]

[Item

#8,

8,

80]

[Item

#9,

9,

90]

[Item

#10

, 10, 100]

The C++ standard library supports a special case of std: : tuple called std: :pair. While a std : : tuple supports zero or more components, each std : : pai r object must contain exactly two components. Listing 21.8 (pairtest.cpp) shows std : : pai r in action.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Print the results

std::cout << "word = " << word << ", number = " << number << '\n' ;

// Declare some variables

std::string name = "do"; int age = 12;

// Build a pair from more general expressions auto t3 = std::make_pair(name + "-ann", 2* age);

// Unpack the tuple's using first and second fields word = t3.first; // 1st component

number = t3.second; // 2nd component // Print the results

std::cout << "word = " << word << ", number = " << number << '\n' ;

// Use structured binding to extract compoents auto [wrd, nbr] = t3;

// Print the results

std::cout << "word = " << wrd << ", number = " << nbr << '\n' ;

As Listing 21.8 (pairtest.cpp) shows, we can use std: :tie, std: :get, and structured binding with a std : : pai r object, and they work exactly as they do with std : : tuple. Since pair objects always contain exactly two elements the std : : pai r class provides the public fields fi rst and second through which we can unpack a pair using simpler syntax.

Neither std: : tuple nor std : : pai r are associative containers. The std : : pai r class is used by the two associative containers we will consider next: std: : map and std : : unordered_map.

21.4 The std :: map Data Type

The std : : ma p data structure is another example of a C++ associative container. In order to use a std : : ma p object within a program we must use the appropriate #i nclude directive:

#include <map>

The std : : ma p class is a template class, so when declaring an instance we must supply type parameters within angle brackets as shown in the following example:

std::map<std::string, int> my_map;

Here the my_map variable refers to an associative container that holds std : : pai r objects, each of which consist of a string key and an integer value. We say each integer in the map object has an associated stri ng key. In the expression std : : map<std : : stri ng , i nt> the first template argument (here std: : stri ng) indicates the map’s key type, and the second template argument indicates the type of values stored in the map (here i nt). Listing 21.9 (simplemap.cpp) provides a simple example that uses a C++ map object.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::map<std::string, int> container;

container ["Fred"] = 22; container ["Ella"] = 21; container ["Owen"] = 34; container ["Zoe"] = 29;

std::cout << container ["Ella"] << '\n' ; std::cout << container ["Zoe"] << '\n';

Note that in this case we access an element in a map object via operator [] with a string “index” rather than a nonnegative integer index as we would in a vector. In Listing |21.9| (simplemap.cpp) the statement

container ["Fred"] = 22;

associates the value 22 with the key "Fred". Keys must be unique; that is, no two values in an unordered map can have the same key. Duplicate values are allowed; that is, two different keys can have the same value, but two different values cannot have the same key. This is similar to a vector or array, in that the same value may be stored at different indices, but only one value may be associated with a particular index.

One big difference between a map and vector is a vector of size n allows any index in the range 0... n — 1, while a map contains a key only when the programmer specifically uses it with the unordered map. Consider the statement

container ["Fred"] = 22;

if the key within the square brackets ("Fred") does not exist in the map before this statement executes, the statement adds the key to the map and pairs it with the value on the right of the assignment operator. If the key already exists in the map, the statement replaces the value previously associated with the key with the new value on the right of the assignment operator.

Consider accessing a value with a given key rather than assigning the value; the statement

std::cout << container["Fred"] << ' \n' ;

prints the value associated with the key "Fred". If "Fred" is not currently a key in the map, this statement will add the key "Fred" with the default value for the type of value declared for the map. For integers, the default value is 0. As other examples, the default floating-point value is 0.0, the default string value is the empty string, " ", and the default bool value is false.

You should use a map object when you need fast and convenient access to an element of a collection based on a search key rather than an index. Consider the problem of implementing a simple telephone contact list. Most people are very familiar with the names of their friends, family, and business contacts but can remember only a handful of telephone numbers. A contact list associates a name with a telephone number.

It would be inappropriate to place the names in a vector, for example, and locate a name using the associated phone number as an index into the vector. This look-up method is backwards—we do not want to find a name given a phone number; we want to look up a number based on a name. Besides, each phone number contains many digits, and we would not need or want to have a vector with indices that large—most of the space in the data structure would be unused.

In our situation a person or company’s name is a unique identifier for that contact. In this case the name is a key to that contact. A map is an ideal data structure for mapping keys to values. It allows for the fast

©2018 Richard L. Halterman

Draft date: September 25, 2018

retrieval of a value given its associated key. Listing 21.10 (phonelist.cpp) uses a C++ map to implement a simple telephone contact database with a rudimentary command line interface.

The following shows a sample run of Listing 21.10 (phonelist.cpp):

©2018 Richard L. Halterman

Draft date: September 25, 2018

A)dd

L)ook

up

Q)uit:

a

Fred 5550134

A)dd

L)ook

up

Q)uit:

d

FRED

5550134

A)dd

L)ook

up

Q)uit:

a

Ella 5559921

A)dd

L)ook

up

Q)uit:

1

Ella

ELLA

5559921

A)dd

L)ook

up

Q)uit:

1

Fred

FRED

5550134

A)dd

L)ook

up

Q)uit:

d

ELLA

5559921

FRED

5550134

A)dd

L)ook

up

Q)uit:

q

Listing [|21.10|| (phonelist.cpp) contains a secret “dump” command that prints out the contents of the map object. This command executes the following loop:

for (auto& elem : contacts)

std::cout << elem.first << " " << elem.second << '\n' ;

This code reveals the fact that std : : map objects store their elements as std: : pai r objects.

Note that we are storing a phone number as an integer, but values within a map object are not limited to integers.

To further motivate maps, consider Listing 21.11 (translateif.cpp) which uses conditional logic to translate some Spanish words into English.

Listing 21.11: translateif.cpp

#include <iostream>

#include <string>

int main() {

std::string word = // Initial word to ensure loop entry

while (word != "quit") { // Loop until user presses return by itself

// Obtain word from the user std::cout << "Enter Spanish word: std::cin >> word;

if (word == "i

jno'

")

std::cout

<<

"one\n" ;

else if (word

==

"dos")

std::cout

<<

"two\n" ;

else if (word

==

"tres")

std: : cout

<<

"three\n"

else if (word

==

"cuatro" )

std: : cout

<<

"four\n" ;

else if (word

==

"cinco")

std: : cout

<<

"five\n" ;

else if (word

==

"seis" )

std::cout

<<

"six\n" ;

else if (word

==

"siete")

std::cout

<<

"seven\n"

else if (word

==

"ocho" )

std: : cout

<<

"eight\n"

Table captionelse // Unknown word std::cout << "???\n";

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing [21.11 (translateif.cpp) can successfully translate eight Spanish words into English. If we wish to increase the program’s vocabulary, we must modify the program’s logic by adding another else if block for each new word. Listing |21.12[ (translatemap.cpp) provides a better approach; it uses a map to assist the translation.

Note that Listing 21.12 ftranslatemap.cpp) uses a map in which both the keys and values are strings. Listing 21.12| (translatemap.cpp) in conjunction with the text file engspanwords.txt containing the following data:

uno one dos two tres three

©2018 Richard L. Halterman

Draft date: September 25, 2018

cuatro four cinco five sens six siete seven ocho eight

translates the same words as Listing 2TTTT](translateif.cpp), but we do not need to touch the program’s logic at all to expand the program’s vocabulary; all we need do is add the appropriate words to our text file. The words will become the key and value items in our map when the program runs. This is a significant difference if wish to include enough words to make the program practical.

Like std : : set, the major C++ platforms use a red-black tree (see https: //en .wi ki pedia . org/wi ki /Red-black_tree) as the underlying data structure for the std: : map class. The nature of this data structure makes key lookup within a map object very fast.

21.5 The std : : unordered_map Data Type

The std : :u no rdered_map type is another example of a C++associative container. A std : : unordered_ma object works like a std: :map object, but they each use a different underlying data structure. Most std : : map implementations use a red-black tree (see https://en.wi kipedia.org/wiki/Red-bIack_ tree) to store the map’s elements, while an unordered map uses a hash table (see https://en. wi ki pedi a . org/wi ki /Hash_table ). This difference makes an unordered map faster in general than a map for accessing an element via its key. Map objects trade raw speed for the ability to access efficiently elements in order based on their keys. Unordered map objects truly are unordered; they provide no efficient way for clients to traverse their key-value pairs by order of their keys.

In order to use a std: :unordered_map object within a program we must use the appropriate #include directive:

ttinclude <unordered_map>

Like the std : : map class, the std : : unordered_map class is a template class, so when declaring an instance we must supply type parameters within angle brackets as shown in the following example:

std::unordered_map<std::string, int> my_map;

Here each integer in the map object has an associated string key.

Listing 21.13 (ordvsunord.cpp) adds in the same order equal strings to both a map object and an unordered map object. It then iterates over each container, printing each element as visited by the iterator.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Add some names in random order

m["fred"] = um["fred"] = 23; m["adam"] = um["adam"] = 99; m["cathy"] = um["cathy"] = 2; m["wilma"] = um["wilma"] = 50; m["betty"] = um["betty"] = 19; m["roger"] = um["roger"] = 44; m["kim"] = um["kim"] = 7; m["doug"] = um["doug"] = 10; m["zach"] = um["zach"] = 5; m["tom"] = um["tom"] = 34;

// Print the names in each container for (auto& p : m)

std::cout << p.first << << p.second << " "

std::cout << 1 \n 1 ;

std : : cout << "- \n" ;

for (auto& p : urn)

std::cout << p.first << << p.second << " "

std::cout << 1 \n 1 ;

std::cout << "===================\n" ;

// Add some more names to each container

m["tammy"] = um["tammy"] = 80; m["joey"] = um["joey"] = 80; m["abby"] = um["abby"] = 80;

// Again, print the names in each container for (auto& p : m)

std::cout << p.first << << p.second << " "

std::cout << 1 \n 1 ;

std : : cout << "- \n" ;

for (auto& p : urn)

std::cout << p.first << << p.second << " "

std::cout << 1 \n 1 ;

Table captionA run of Listing |21.13i [(ordvsunord.cpp) on one system prints

adam:99

betty:19

cathy: 2

doug:

10 fred:23 kim:7

roger:44

tom:34

wiIma:50

zach:5

f red: 23

roger:44

adam:99

kirn: 7

doug:10 cathy:2

wiIma:50

betty:19 zach:5

tom:34

abby:80

adam:99

betty:19

cathy

:2 doug:10 fred:23

1 joey:80

kirn: 7

roger:44

tammy:80

tom:34

wilma:50 zach:5

f red: 23

roger:44

adam:99

kirn: 7

doug:10 cathy:2

wiIma:50

abby:80

betty:19

zach: 5

tom:34

tammy:80 joey:80

The output shows that we can iterate over the elements of a map object in the order of their keys. String keys are ordered lexicographically. The ordering of the unordered map appears random.

Listing I2L13 (ordvsunord.cpp) adds a few additional elements to both map objects. The insertions do

©2018 Richard L. Halterman

Draft date: September 25, 2018

not disturb the lexicographical key order of the map object, but note that the insertions appear in seemingly random locations in the unordered map.

The ordering of the elements in an unordered map is not really random; a special function known as a hash function determines their position within the unordered map at the time of their insertion. This hashing process makes unordered maps slightly faster than regular map objects. If the speed of access is critical and accessing the elements in order is not necessary, a C++ std : : unordered_map is the better choice.

21.6 Counting with Associative Containers

Associative containers are useful for counting things. We have experience using variables to count; recall Listing [Oj (countup.cpp) and Listing [6.211 (startree.cpp). These programs counted one thing at a time, so they each use just one counter variable. In general, we need to use a separate variable for each count we manage. Listing 21.14 (countnegnonneg.cpp) uses a function to count the number of negative and nonnegative numbers in a vector of integers and returns a Std : : pai r with the results:

Since we needed to count two different kinds of things, we had to use two separate counters. In this case we used neg_count and nonneg_count to serve the role of counter variables.

As an aside, consider a variation of Listing 21.14 (countnegnonneg.cpp), shown in Listing 21.15 (countnegnonneg2.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

IntPair count_neg_nonneg (const std::vectorcint>& nums) { // Initialize counters int neg_count = 0, nonneg_count = 0; for (int num : nums) if (num < 0)

neg_count++;

else

nonneg_count++;

return {neg_count, nonneg_count}; //std::make_pair(neg_count, nonneg_count)

}

int main() {

auto counts = count_neg_nonneg({8, -3, -1, 7, 7, -2, 0, 3}); std::cout << counts.first << " " << counts.second << '\n';

}

Note that we created a type alias (IntPai r) for the more complicated type (std : : pai r<i nt , i nt>). This is not particularly helpful in this simple program (we only use the type in one place), but it illustrates that we can use the usi ng statement for type aliasing std: : pai r as easily as with std: : vector or any other more complicated looking type name. We also simplified the return statement at the end of the count_neg_nonneg function. The compiler knows the return type of the function (declared as IntPai r —a pair of integers), so it must return a pair object. The curly brace notation without any other verbiage indicates the arguments to the std::pair<int, int> class constructor that it should use when creating the object to return. The compiler automatically generates the machine code to call the pair constructor with the arguments within the curly braces.

Suppose we wish to keep track of the quantity of each letter that appears in a text file. There are 26 letters in the alphabet, so we would need 26 counter variables. Managing 26 different counter variables is inconvenient, so we could use a vector containing 26 integers. The element at index 0 could store the number of As, the element at index 1 could keep track of the number of /is, etc. An associative container may be useful but is not necessary to solve our problem. Listing [21.16|| (lettercount.cpp) provides one implementation.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::vector <int> counters(26, 0); std::ifstream fin(filename);

if (fin.good()) { // Open the file for reading

char ch;

while (fin >> ch) {

// Capitalize the letter ch = static_cast<char> (toupper(ch)); if (isalpha(ch)) // Only count alphabetic characters // Compute offset into counter vector counters[ch - 'A'] ++ ;

}

// Report the counts for each letter

ch = 'A' ;

for (auto count : counters)

std::cout << ch++ << " << count << ' \n';

}

else

std::cout << "Cannot open file for reading\n";

}

}

The following paragraph appears in the Declaration of Independence of the United States (for simplicity all punctuation has been removed):

When in the Course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth the separate and equal station to which the Laws of Nature and of Nature's God entitle them a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation

©2018 Richard L. Halterman

Draft date: September 25, 2018

In this case we knew we needed to count 26 different things (letters), so we were prepared with 26 counters (26 vector elements). The number of letters in the English alphabet does not change, so this approach works well.

So far so good, but what if we face a situation in which we must count multiple kinds of things, and we cannot know ahead of time how many kinds of things there will be to count? How can we determine how many counter variables to use in a program that attempts to solve such a problem?

The answer is this: We cannot know how many counter variables we will need, so we must use a different approach. With an associative container we can use the items we wish to count as the keys.

(wordcount.cpp) reads the content of a text file containing words. After reading the file the program prints a count of each word. To simplify things, the text file contains only words with no punctuation. The user supplies the file name on the command line when launching the program (see Section )l 1T277| .

The value associated with a key will be the count of that item. As a concrete example. Listing 121.17

If we send to Listing ||21.17 1 ( wordcount.cpp) the same excerpt as before from the Declaration of Independence of the United States it prints the following:

©2018 Richard L. Halterman

Draft date: September 25, 2018

A: 1

AMONG: 1 AND: 3 ANOTHER:1 ASSUME:1 BANDS:1 BECOMES:1 CAUSES:1 CONNECTED:1 COURSE: 1 DECENT:1 DECLARE:1 DISSOLVE:1 EARTH:1 ENTITLE:1 EQUAL:1 EVENTS:1 FOR: 1 GOD: 1 HAVE: 1 HUMAN: 1 IMPEL:1 IN: 1 IT: 1 LAWS: 1 MANKIND:1 NATURE:1 NATURE'S:1 NECESSARY:1 OF: 5 ONE: 1

OPINIONS:1 PEOPLE: 1 POLITICAL:1 POWERS:1 REQUIRES: 1 RESPECT:1 SEPARATE:1 SEPARATION:1 SHOULD: 1 STATION:1 THAT: 1 THE: 9 THEM: 3 THEY: 1 TO: 5 WHEN: 1 WHICH:3 WITH: 1

In Listing 21.17 (wordcount.cpp), since we cannot predict what words will appear in a document, we cannot use a separate variable for each counter. Instead, we use the document’s words as keys in a map object. For each key in the map we associate an integer value that keeps track of the number of times the word appears in the file. We use a map instead of an unordered_map so that we can list the words and their counts in

©2018 Richard L. Halterman

Draft date: September 25, 2018

lexicographical order.

In Listing| [2LT7 ||(wordcount.cpp) the statement counters[word]++;

increments the integer mapped to the string word. If the map currently holds the string word, the expression simply adds one to the integer value; it the string word does not appear in the counters map object, the statement first inserts the string word with an associated value of 0 and then immediately increments it to 1. This is the exact behavior we need for our word counting program.

21.7 Grouping with Associative Containers

Associative containers are useful for grouping items. Like Listing 21.17 (wordcount.cpp). Listing 21.18

(groupwords.cpp) reads in the contents of a text file. Instead of counting the words, Listing 21.18 f groupwords.cpp)

groups the words into sets based on the number of letters in the word. All the words containing only one letter are in one set, all the words containing two letters are in another set, etc.

Listing 21.18: groupwords.cpp

// Uses a map to group words in a document by their length.

ffinclude <iostream>

ffinclude <fstream>

ffinclude <string>

ffinclude <map>

ffinclude <set>

ffinclude <algorithm>

ffinclude <cctype> // For toupper

// Conveniently send to an output stream a set of any printable type template<typename T>

std::ostream& operator<< (std::ostream& os, const std::set<T>& s) { os << '{' ;

auto iter = std::begin(s); // iter points to first element initially

const auto iend = std::end(s); // iend always points just past the end

if (iter != iend) os << *iter++; while (iter != iend)

os << ", " << *iter++; os << 1 } 1 ; return os;

// Set empty?

// No? Print first element // More left?

// Print element, comma, move to next element

}

int main(int argc, char *argv[]) { if (argc < 2) {

std::cout << "Usage: wordgroup <filename>\n" ;

std::cout << " where <filename> is the name of a text file.\n";

}

else { // User provided file name

std::string filename = argv[l];

// Make a grouping map of sets

std::map<int, std::set<std::string>> groups; std::ifstream fin(filename);

©2018 Richard L. Halterman

Draft date: September 25, 2018

if (fin.good()) { // Open the file for reading

std::string word; while (fin >> word) {

// Capitalize all the letters in the word

transform(std::begin(word), std::end(word), std::begin(word), toupper);

// Add word to appropriate set based on the word's length

groups[word.length()].insert(word);

}

// Report the counts for each word for (auto item : groups)

std::cout << item.first << << item.second << '\n';

}

else

std::cout << "Cannot open file for reading\n";

}

}

The following shows a sample run of Listing 21.18j (groupwords.cpp) on our snippet from the Declaration of Independence'.

1: {A}

2: {IN, IT, OF, TO}

3:{AND, FOR, GOD, ONE, THE}

4:{HAVE, LAWS, THAT, THEM, THEY, WHEN, WITH}

5:{AMONG, BANDS, EARTH, EQUAL, HUMAN, IMPEL, WHICH}

6:{ASSUME, CAUSES, COURSE, DECENT, EVENTS, NATURE, PEOPLE, POWERS, SHOULD} 7:{ANOTHER, BECOMES, DECLARE, ENTITLE, MANKIND, RESPECT, STATION}

8:{DISSOLVE, NATURE'S, OPINIONS, REQUIRES, SEPARATE}

9:{CONNECTED, NECESSARY, POLITICAL}

10:{SEPARATION}

Each integer key represents the length of all the strings in the set it oversees.

In this example the need for a map object is not as compelling as in Listing ||2 1,1 7 (wordcount.cpp), because in practice the length of English words is limited. We could instead use a vector of 50 sets. Only rarely used, highly technical words exceed 50 letters. We could handle these “too-long” words in a special way, perhaps storing them in the set in the last position in the vector with other words of more than 49 letters. Our program could use special processing for this set of long words if it ever becomes nonempty. This approach under typical circumstances would result in a number of empty sets at higher indices because most English text contains words of at most about 20 letters. The advantage of a map is that it stores only what it needs. Listing 21.19| (groupwordsvector.cpp) is close transliteration of Listing [21.181 (groupwords.cpp) that uses a vector in place of a map.

Listing 21.19: groupwordsvector. cpp

// Uses a vector to group words in a document by their length.

#include <iostream>

#include <fstream>

#include <string>

#include <vector>

#include <set>

#include <algorithm>

#include <cctype>

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Conveniently send to an output stream a set of any printable type template<typename T>

std::ostream& operator<< (std::ostream& os, const std::set<T>& s) { os << ' { ' ;

auto iter = std::begin(s); // iter points to first element initially

const auto iend = std::end(s); // iend always points just past the end if (iter != iend) // Set empty?

os << *iter++; // No? Print first element

while (iter != iend) // More left?

os << ", " << *iter++; // Print element, comma, move to next element os << ' } ' ; return os;

}

const size_t MAX_WORD_LENGTH = 20;

int main(int argc, char *argv[]) { if (argc < 2) {

std::cout << "Usage: wordgroup <filename>\n" ;

std::cout << " where <filename> is the name of a text file.\n";

}

else { // User provided file name

std::string filename = argv[l];

// Make a grouping map of sets

std::vector<std::set<std::string>> groups(MAX_WORD_LENGTH); std::ifstream fin(filename);

if (fin.good()) { // Open the file for reading

std::string word; while (fin >> word) {

// Capitalize all the letters in the word

std::transform(std::begin(word), std::end(word), std::begin(word), toupper);

// Add word to appropriate et based on the word's length

if (word.length() > MAX_WORD_LENGTH)

std::cout << "Ignoring word, too long\n" ; groups[word.length()].insert(word);

}

// Report the counts for each word

for (size_t i = 1; i < groups.size(); i++)

std::cout << i << << groups[i] << '\n' ;

}

else

std::cout << "Cannot open file for reading\n";

}

}

We can see the unused space in the output o

1: {A}

2: {IN, IT, OF, TO}

3:{AND, FOR, GOD, ONE, THE}

4:{HAVE, LAWS, THAT, THEM, THEY, WHEN, WITH}

5:{AMONG, BANDS, EARTH, EQUAL, HUMAN, IMPEL, WHICH}

©2018 Richard L. Halterman

Draft date: September 25, 2018

6:{ASSUME, CAUSES, COURSE, DECENT, EVENTS, NATURE, PEOPLE, POWERS, SHOULD} 7:{ANOTHER, BECOMES, DECLARE, ENTITLE, MANKIND, RESPECT, STATION}

8:{DISSOLVE, NATURE'S, OPINIONS, REQUIRES, SEPARATE}

9:{CONNECTED, NECESSARY, POLITICAL}

10:{SEPARATION}

11 : {}

12 : {}

13: {}

14: {}

15: {}

16: {}

17: {}

18: {}

19: {}

In a different document there could be empty sets in the groups representing the words with fewer than 11 letters.

21.8 Memoization

We know a program can use variables to remember values as it executes. A programmer must be able to predict the number of values the program must manage in order to write enough variables in the code. An associative container provides an opportunity to create an arbitrary amount of new storage during a program’s execution. We will consider a simple problem that demonstrates the value of the dynamic storage provided by unordered_map objects.

Section[103]introduced the Fibonacci number sequence. That section provided a function to compute the n th Fibonacci number, reproduced here:

// Returns the nth Fibonacci number

int fibonacci (int n) { if (n <= 0) return 0; else if (n == 1) return 1;

else

return fibonacci(n - 2) + fibonacci(n - 1);

}

This fibonacci function is correct, but it does not scale well—its execution time grows significantly as its parameter, n, increases. The problem is this: when computing a solution for a particular Fibonacci number the function can repeat exactly the same work multiple times. Figure) 10.2 illustrates the repetitive work performed by the call fibonacci (5) . As we can see from the figure, the function’s recursive execution calls fibonacci (1) five times during the computation of fibonacci (5). We can verify the results shown in Figure 10.2 by augmenting our fibonacci function with a global map that counts function calls.

Listing|2l.20|(fibonacciinstrumented.cpp).

Listing 21.20: fibonacci i nstrumented. cpp

#include <iostream> #include <map>

©2018 Richard L. Halterman

Draft date: September 25, 2018

// This associative container will keep track of the number of // calls to the fibonacci function, std::map<i nt , int> call_counter;

// Returns the nth Fibonacci number int fibonacci (int n) {

// Count the call

call_counter [n]+ +;

if (n <= 0) return 0; else if (n == 1) return 1;

else

return fibonacci(n - 2) + fibonacci(n - 1);

int main() {

// Call fibonacci(5)

std::cout << "fibonacci(5) = " << fibonacci(5) << "\n\n";

}

// Report the total number of calls to the fibonacci function

std::cout << "Argument Calls" << '\n';

std : : cout << "- \n" ;

for (auto& counts: call_counter)

std::cout << " " << counts.first << " "

<< counts.second << '\n' ;

Listing pi .20} (fibonacci instrumented, cpp) prints

fibonacci (5)

= 5

Argument

Calls

0

3

1

5

2

3

3

2

4

1

5

1

Note the results that Listing 21.20 (fibonacciinstrumented.cpp) prints agree exactly with the call count

shown in Figure 10.2[ As we compute larger Fibonacci numbers, the amount of repeated work worsens

quickly; for example, the call fibonacci (20) recursively calls fibonacci (1) 6,765 times! For additional emphasis, the call fibonacci (35) recursively calls fibonacci (1), fibonacci (2), fibonacci (3), fibonacci (4), and fibonacci (5) over one million times each ! We may be tempted to care less about the program’s repeated work—after all, it is the computer doing the work, not us. Unfortunately, the computer, even though it is very fast, requires some amount of time to perform any task. As we multiply the number of tasks a program must do to solve a problem, the time to compute the solution increases, and, in the case of the fibonacci function, the time increases dramatically.

We can improve the performance of our fibonacci function using a technique known as memoization

©2018 Richard L. Halterman

Draft date: September 25, 2018

(not to be confused with the word memorization which means to commit something to memory). Memoization is an algorithm design technique that records the result of a specific computation so that result can be used as needed at a later time during the algorithm’s execution. It is as if the executing program “makes a note to itself” or “stores the result in a memo.” When the program needs the result of an identical computation in the future, if simply reads the memo with the answer it stored earlier. In this way the program avoids repeating the work. Memoization is especially useful for problems that consist of subproblems that overlap and appear to require multiple computations with identical input.

The following function uses an unordered map object to cache previously computed Fibonacci numbers:

// Returns the nth Fibonacci number. Caches a // recursively computed result to be used when needed // in the future. Provides a huge performance improvement // over the recursive version, int fibonacci2 (i nt n) {

// Map for caching the results of the fib function // ans is declared static so it retains its value between // calls to fibonacci2.

// Precomputes the results for 0 and 1.

static unordered_map<i nt , int> ans {{0, 0}, { 1 , 1}};

if (n > 1 && ans[n] == 0) // Need to compute?

ans[n] = fibonacci2(n - 2) + fibonacci2(n - 1); return ans[n] ;

}

The fibonacci 2 function uses an unordered map as a cache of stored values that persist for the duration of the program’s execution. Since the ans local variable is stati c, the run-time environment creates and initializes it with keys 0 and 1 before executing the mai n function. When a caller invokes fibonacci 2, if the answer is not in ans, it computes the result and stores the result in ans for future use. This not only helps future calls to the function from the outside, but it also speeds up recursive invocations that must perform the same work.

Listing 21.21 (fibonacci.h) declares the interfaces for fibonacci and fibonacci 2, two functions that compute the n th Fibonacci number.

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Draft date: September 25, 2018

The Fibonacci numbers grow very quickly, so the functions in Listing 21.21 (fibonacci.h) return unsigned long long values. For convenience it introduces the type alias Integer for unsigned long long to simplify the code. Under Visual C++, for example, this type supports values in the range 0... 18,446,744,073,709,551,615, inclusive. Listing[21.22[(fibonacci.cpp) provides the implementations for the two functions.

When compiled and linked with the code in Listing 21.22 (fibonacci.cpp). Listing 21.23 (testfib.cpp) verifies that the fibonacci2 function produces the same results as the fibonacci function when given the same arguments. It tests unsi gned values up to 50. You will observe that as the arguments become larger, the program takes longer to print the results.

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Draft date: September 25, 2018

0 : 0 0 1 : 1 1 2 : 1 1 3:2 2 4 : 3 3 5 : 5 5 6 : 8 8 7 : 13 13 8: 21 21 9 : 34 34 10 : 55 55 11 : 89 89 12 : 144 144 13 : 233 233 14 : 377 377 15 : 610 610 16 : 987 987 17 : 1597 1597 18 : 2584 2584 19 : 4181 4181 20 : 6765 6765

In total, all 50 lines match, and that gives us confidence that our memoized version is correct.

Listing 21.24 (timefib.cpp) reveals just much faster the memoized function executes compared to the non-memoized version.

One run of Listing 21.24 (timefib.cpp) prints

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 21.1 The hierarchy of recursive function calls that result from the call fibonacci2(5). Note that the calls of fibonacci (2) and fibonacci (3) on the right side of the tree need no recursive calls; this is because their earlier calls on the left side of the tree stored their results in the map for instant retrieval.

Caller

I *

5 5

Time: fibonacci = 111430 msec, fibonacci2 = 1 msec

The original recursive version requires over 111 seconds (almost two minutes), while the memoized recursive version takes only 1 millisecond. During this run the memoized version was over 100,000 times faster. The fibonacci 2 function is so fast because it avoids all the redundant recursive calls the fibonacci function must compute.

Listing 21.24 (timefib.cpp) provides an honest test, as it forces fibonacci 2 to compute the 50 th Fibonacci number right away with no previous fibonacci 2 invocations. Once completing a call of fibonacci 2 («), all of the Fibonacci numbers from 0...« will be present in the function’s unordered_ma cache of precomputed values. This means future invocations involving any values in that range will be very fast. Any program that must compute Fibonacci numbers multiple times during their execution will especially benefit from the memoized version.

Figure |21,l [ shows the recursion tree for our memoized Fibonacci function computing the fifth Fibonacci number. The figure shows only nine invocations of fibonacci 2, compared to 15 invocations of the nonmemoized fibonacci function. If you add the function call counting instrumentation used in Listing 21.20 (fibonacciinstrumented.cpp) to fibonacci 2, you will find the numbers it reports agrees with Figure 21.1

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Chapter 22

Handling Exceptions

1111111111 CAUTION! CHAPTER UNDER CONSTRUCTION 1111111111

In our programming experience so far we have encountered several kinds of run-time errors. To this point, all of our run-time errors have resulted in the executing program’s termination. C++ provides an exception handling framework that allows programmers to deal with certain kinds of run-time errors. Rather than always terminating the program’s execution, the exception handling infrastructure enables programmers to detect a problem and execute code to correct the issue or manage it in other ways. This chapter explores C++’s exception handling mechanism.

22.1 Motivation

Algorithm design can be tricky because the details are crucial. It may be straightforward to write an algorithm to solve a problem in the general case, but there may be a number of special cases that must all be addressed within the algorithm for the algorithm to be correct. Some of these special cases might occur rarely under the most extraordinary circumstances. For the code implementing the algorithm to be robust, these exceptional cases must be handled properly; however, adding the necessary details to the algorithm may render it overly complex and difficult to construct correctly. Such an overly complex algorithm would be difficult for others to read and understand, and it would be harder to debug and extend.

Ideally, a developer would express the algorithm in its general form including any common special cases. Exceptional situations that should arise rarely, along with a strategy to handle them, could appear elsewhere, perhaps as an annotation to the algorithm. Thus, the algorithm is kept focused on solving the problem at hand, and measures to deal with exceptional cases are handled elsewhere.

C++’s exception handling infrastructure allows programmers to cleanly separate the code that implements the focused algorithm from the code that deals with exceptional situations that the algorithm may face. This approach is more modular and encourages the development of code that is cleaner and easier to maintain and debug.

An exception is an exceptional event that occurs during a program’s execution. An exception always is possible, but it should be a relatively rare event. If it were not rare, it would be a customary or expected event, and the program should handle it as part of its normal processing.

An exception almost always represents a problem, usually some sort of run-time error. Suppose we have

©2018 Richard L. Halterman

Draft date: September 25, 2018

a vector named v and an integer i. Unless 0 < i < v . si ze (), the expression v [i ] attempts to access an element outside the vector’s bounds. The operator [] method performs no bounds checking; thus, an executing program using the expression v [ i ] would represent undefined behavior. Consider instead the expression v . at (i ). The at method works just like ope rato r [], except at does check the vector’s bounds. If i > v . si ze () or i <0, the expression v . at ( i ) represents an exceptional situation, and we say the vector’s at method throws , or raises, an exception.

Without taking advantage of C++’s exception handling infrastructure, the following statement: v.at(i) = 4;

could terminate the program with an error message. While this is better than undefined behavior, it is not ideal. The program crashes. When a real application crashes the user may lose unsaved data. Badly behaving programs terminate unexpectedly. It would be better to defend against the out-of-bounds index and keep the program alive.

An algorithm could handle many potential problems itself. For example, a programmer can use an i f statement to test to see if a vector’s index is within the proper bounds:

if (0 <= i && i < v.sizeQ) // Ensure i is in range v.at(i) = 4;

However, if the programmer accesses a vector in several different locations within a given function or method and the index variable can vary from place to place, the number of i f statements necessary to ensure safe vector access might obscure the overall logic of the function or method.

22.2 Exception Examples

Consider Listing [22711 (vectorboundscrash.cpp). The program crashes whenever the user enters a value equal to an index outside the range of vector nums.

Listing 22.1: vectorboundscrash.cpp

#include

<iostream>

#include

<vector>

int main() {

std:

: vector<double> nums { 1.0,

2.0, 3.0 };

int

input;

std:

:cout << "Enter an index: "

5

std:

:cin >> input;

std:

:cout << nums.at(input) <<

' \n' ;

}

The at method guarantees that an illegal access will not go undetected. To intercept the problem at run time and prevent the program from terminating due to an error, we use a try/catch block, which consists of two parts: a try block and a catch block. To form a try/catch block we

1. wrap the code that has the potential to throw an exception in a t ry block, and

2. provide code to execute only in the event of an exception in a catch block.

Listing [2Z2| (vectorboundsexcept.cpp) adds the exception handling code to Listing |22.l| (vectorboundscrash.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

If a user enters a value less than zero or greater than two when executing Listing |2Z2] (vectorboundsexcept.cpp), the program will print an error message and technically terminate successfully instead of crashing.

Both try and catch are keywords in C++. Unlike the bodies of the structured statements such as i f and whi le, the statements within a try block and statements within a catch block must appear within curly braces, even if only one statement appears in the section.

Every try block or catch block must surround its statements with curly braces—even if it contains just one statement.

The variable e within the catch block of Listing 22.2 (vectorboundsexcept.cpp) is a reference to an exception object. The exception class is part of the standard C++ library and is the base class for all the standard exceptions. The exception class provides a what method that returns a string. The excepti on : : what method’s string is a message containing information about the exception. The C++ standard does not specify the exact message, but at the very least the exception: :what method indicates the kind of exception caught. The following shows what the program reports under Visual C++ when the user enters the value 3:

Enter an index: 3

invalid std::vector<T> subscript

While Listing |[22.21 (vectorboundsexcept.cpp) does not technically crash, its behavior is not much different from an actual abnormal program termination. Listing ||223| (betterboundsexcept.cpp) provides a more practical example. This improved version uses a loop to continuously request integer values until the user supplies one that does not throw an exception.

Listing 22.3: betterboundsexcept.cpp

#include <iostream> #include <vector>

©2018 Richard L. Halterman

Draft date: September 25, 2018

int main() {

std:: vector<double> nums { 1.0, 2.0, 3.0 }; int input; while (true) {

std::cout << "Enter an index: std::cin >> input; try {

std::cout << nums.at(input) << '\n';

break; // Printed successfully, so break out of loop

}

catch (std::exception&) {

std::cout << "Index is out of range. Please try again. \n";

}

}

}

What makes the exception code try {

std::cout << nums.at(input) << ' \n ' ;

}

catch (std::exception& e) {

std::cout << e.whatQ << ' \ n' ;

}

better than the conditional code

if (0 <= input && input < nums.size()) { std::cout << nums.at(input) << '\n' ;

}

else {

std::cout << "Vector out of bounds exception\n" ;

}

is not immediately obvious from this simple example. To see the real capability of exceptions, consider Listing j22(4] (callchainexception.cpp).

©2018 Richard L. Halterman

Draft date: September 25, 2018

bool find(const std:: vector<int>& v, int lower, int upper) {

std::cout << "-[Entering find]- \n";

Tracker obj("find"); // Local tracking object bool result = false; // Not there by default int seek; // What to look for

std::cout << "Enter item to locate: "; std::cin >> seek;

for (int i = lower; i < upper; i++) if (v.at(i) == seek) {

result = true; // Found it break;

}

std::cout << "-[Leaving find]- \n";

return result;

void process (const std:: vector<int>& v) {

std::cout << "-[Entering process]- \n";

Tracker obj( "process") ; // Local tracking object

int low, high;

std::cout << "Enter a range: "; std::cin >> low >> high; if (find(v, low, high))

std::cout << "Found it\n";

else

std::cout << "Not there\n"; std::cout << "-[Leaving process]- \n";

// Global tracking object

Tracker obj( "global") ;

int main() {

std::cout << "-[Entering main]- \n";

Tracker obj ("main"); // Local tracking object

std::vector<i nt> nums { 11, 42, 23 }; try {

process(nums);

}

catch (std::exception& e) {

std::cout << "nums vector bounds exceeded\n";

}

std::cout << "-[Leaving main]- \n";

Listing |2Z4| (callchainexception.cpp) is specially crafted to provide insight into the program’s exact execution path. Each function prints a message at its beginning and end so we can see when the code within a function is active. Each function also declares a local Tracker object which is identified by the name of that function. An executing function constructs a local object at its point of declaration and automatically destroys the object when the function returns to its caller. These local objects, therefore, have a lifetime that mirrors the lifetime of the function that manages them. Finally, Listing |22.4| (callchainexception.cpp) declares a global T racker object. An executing program creates global objects before it calls man n and

©2018 Richard L. Halterman

Draft date: September 25, 2018

automatically destroys them after main completes.

In Listing 22.4 (callchainexception.cpp) the vector nums, declared in mai n, holds three elements. The main function passes its nums vector to process. During its call to process, the main function has no control over the process function’s attempts to access an element outside the range of nums. The process function, however, does not itself attempt to access any elements within the vector that mai n supplies. Instead, process passes the vector on to the find function. It is in find where problems may arise because find calls the vector’s at method. If the find function calls the vector’s at method with an out-of-bounds index, at will throw an exception. Observe that unlike in Listing [22.2| (vectorboundsexcept.cpp), the method that calls std: : vector<i nt> : :at does not do so within a try/catch block. This means find cannot catch any exceptions that std : : vectorci nt> : ratmight throw.

The following shows a sample run of Listing|22i4j(callchainexception.cpp):

Creating Tracker (global)

-[Entering main]

Creating Tracker (main)

-[Entering process]

Creating Tracker (process) Enter a range: 0 2

-[Entering find]

Creating Tracker (find)

Enter item to locate: 4

-[Leaving find]

Destroying Tracker (find)

Not there

-[Leaving process]

Destroying Tracker (process)

-[Leaving main]

Destroying Tracker (main) Destroying Tracker (global)

In this output of Listing [22]4||| (callchainexception.cpp) we see the following sequence of events:

1. The program creates the global Tracker object.

2. The program calls main.

3. The mai n function creates its Tracker object.

4. mai n calls process.

5. The process function creates its Tracker object.

6. The process function obtains the user’s input for range values. Here the users entered the range

0 ... 2 .

7. The process function calls find.

8. The find function creates its Tracker object.

9. The find function obtains the user’s input for the element to seek. Here the user enters 4 (which is not present in the vector).

10. The find function executes its last statement.

11. When find returns to process, the program destroys find’s local Tracker object.

12. process uses find’s result to print the message that the element sought is not present in the vector.

13. The process function executes its last statement.

14. When process returns to main, the program destroys process’s local T racker object.

15. The main function executes its last statement.

16. When mai n returns, the program destroys mai n’s local Tracker object.

17. When the program terminates it destroys the global Tracker object.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 22.1 Function call chain without an exception. The std: :vector<int>: :at method, the fi n d function, and the process function all complete their work and return as usual to their callers.

Program Execution Timeline

mai n _

▲

nums

▼_

process (

l 0 ' 2 1

Tals

I f i nd

v,i

1

i

L

v.at(i)

vectorcint>::at

Figure [22T| provides a more graphical representation of this process.

In this case the user did not enter a range in the process function that would cause a problem in find, so no exceptions arise. Since the program’s execution produced no exceptions, it did not execute the printing statement in the catch block.

To see what happens during an exception consider the following sample run of Listing )22.4i| (callchainexception.cpp):

Creating Tracker (global)

-[Entering main]

Creating Tracker (main)

-[Entering process]

Creating Tracker (process) Enter a range: 10 20

-[Entering find]

Creating Tracker (find)

Enter item to locate: 4 Destroying Tracker (find) Destroying Tracker (process) nums vector bounds exceeded

-[Leaving main]

Destroying Tracker (main) Destroying Tracker (global)

The user supplied range of 10.. .20 definitely is outside the bounds of mai n’s nums vector. Because the program does not print find’s exit message we know the find function does not complete its execution as usual. This is because the std : : vector<i nt> : : at method called by find throws an exception. Furthermore, it does not appear that find returns normally to process, since process does not print its exit message either. We do see, though, that the program does properly destroy the the local Tracker

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 22.2 Function call chain interrupted by an exception. Neither the std : : vector <i nt> : : at method, the find function, nor the process function completes its work and returns as usual to its caller. Control passes back to the catch block associated with the nearest try block in the call chain.

Program Execution Timeline

mai n

nums

F

process

/

j

f

find /

ception

v,i

J ex

vector<i nt> :^t|

objects owned by find and process. The program’s execution path lands immediately back in mai n, which we see does exit normally after executing the statement in its catch block. The program finishes

by destroying mai n’s T racker object followed by destroying the global T racker object. Figure 22.2 better illustrates the program’s execution.

Listing j22i4[ (calIchainexception.cpp) demonstrates that exceptions have the potential to radically alter the normal function call and return pathways. In one sense an exception works like a “super goto” statement. The program’s execution jumps back to a previous point in its execution sequence, bypassing all functions in the call chain in between. Recall Section 6.3.2 discouraged the use of the goto statement except for it use to exit from within a nested loop. This is because the logic in code that uses indiscriminate gotos instead of the structured branching and looping constructs such as i f/else, swi tch, whi le, and for tends to be obscure and difficult to extend and maintain. C++’s exception mechanism is different than a “super goto” in several important ways:

• A goto statement cannot jump to code outside of the function in which it appears. Exceptions have no such limitation.

• The programmer must specify a destination (label) for a goto statement. In the case of Listing |22.4| (callchainexception.cpp), the std: : vector<i nt> : :at method throws the exception. We can call at from many different functions within a single program and use at in many different programs. The code within the at method cannot possibly know where to go if it encounters an exceptional situation. An exception simply redirects the program’s execution to the most recent try/catch block in the call chain that can handle the exception.

Listing [223| (badinput.cpp) follows.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Listing [22.6|[ (strboundsexcept.cpp) follows.

Listingf2277](filereadexcept.cpp) follows.

©2018 Richard L. Halterman

Draft date: September 25, 2018

std::ifstream fin( "data.dat" ); if (fin.good()) { i nt n;

fin >> n; // Size of dataset std::vectorci nt> data(n); // Allocate vector for (int i = 0; i <= n; i++ ) { // Error: should be < int value; fin >> value; data.at(i) = value;

}

// Print the values

for (auto value : data)

std::cout << value << 1 '; std::cout << '\n ' ;

}

else

std::cout << "File does not exist\n";

}

catch (std::exception& e) {

std::cout << e.whatQ << '\n';

}

22.3 Custom Exceptions

The standard C++ library has a limited number of standard exceptions. We can create our own custom exceptions for specialized error handling that our applications may require. Listing [22.8j (customfilereadexcept.cpp) defines a custom exception class, FileNot Found Exception, derived from the standard std: :exception class.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Creates and returns a vector of integers from data stored // in a text file.

// filename: the name of the text file containing the data // Returns a vector containing the data in the file, if possible std::vector<i nt> load_vector (const std::string& filename) {

std::ifstream fin(filename); if (fin.good()) {

std::vector <int> result; i nt n; fin >> n;

for (int i = 0; i < n; i int value; fin >> value; result.push_back(val

}

return result;

}

else // Could not open the

throw FileNotFoundExcept

}

int main() { try {

std::vector <int> numbers for (int value : numbers std::cout << value < std::cout << '\n' ;

}

catch (std::exception& e) {

std::cout << e.whatQ << '\n'

}

}

// Open the text file for reading // Did the file open successfully? // Initially empty vector

// Size of data set

{

// Read in a data value // Append it to the vector

// Return the populated vector

text file

on(filename);

= load_vector( "values.data" );

If we execute Listing |22.81 (customfilereadexcept.cpp) in a directory that does not contain a text file named values.data, it displays

File "values.data" not found

Since we derived the FileNotFoundException class from std: :exception, any FileNotFoundExcepti on object also is a std : : excepti on object (see Section 17.1). This enables the main function to catch a Fi leNotFoundExcepti on object in its catch body even though it is declared to catch std : : excepti on objects.

The C++ standard library provides a number of exception classes, all derived from std : : excepti on.

The vector out-of-bounds exception objects thrown by the at method are instances of the standard std: :out_of_ range class. The std: : out_of_range class is derived from the standard logic_error class which itself is derived from the standard std : : excepti on class. Figure 22.3 shows the relationship among these exception classes.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure 22.3 The relationship among the exception classes involved in Listing 22.8 (customfilereadexcept.cpp). The classes exception, logic_error, and out_of_range are standard exception classes, Fi TeNotFoundExcepti on is our custom exception class.

22.4 Catching Multiple Exceptions

Listing f22!9](filereadmultiexcept1 .cpp) has the potential to throw more than one type of exception.

©2018 Richard L. Halterman

Draft date: September 25, 2018

// Returns a vector containing the data in the file, if possible std::vector<i nt> load_vector (const std::string& filename) {

std::ifstream fin(filename); if (fin.good()) { //

i nt n;

fin >> n; //

std::vector<i nt> result(n); int value, i = 0; while (fin >> value)

result.at(i++) = value; // return result; //

}

else // Could not open the text file

throw FileNotFoundException(filename);

// Open the text file for reading Did the file open successfully?

Size of data set

// Allocate space for the vector

Insert it into the vector Return the populated vector

int main() { try {

std::vector <i nt> numbers = load_vector( "values.data" ); for (int value : numbers)

std::cout << value << * 1 2 '; std::cout << '\n' ;

}

catch (std::exception& e) {

std::cout << e.whatQ << '\n';

}

}

Note 1

Note 2

Note 3

Note 4

Note 5

Note 6

Note 7

Note 8

©2018 Richard L. Halterman

Note 9

20

30

40

50

theload_vector function will throw the standard std: :out_of_range exception.

Listing 22.10 (filereadmultiexcept2.cpp) uses two catch blocks to print different messages depending

on the exact type of exception object thrown by a load_vector.

Listing 22.10: filereadmultiexcept2. cpp

#include <iostream>

#include <fstream>

#include <vector>

#include <string>

// Exception object to thrown when a client attempts to // open a text file via a name that does correspond to a // file in the current working directory, class FileNotFoundException : public std::exception {

std::string message; // Identifies the exception and filename public :

// Constructor establishes the exception object's message

FileNotFoundException(const std::string& fname): message("File \"" + fname + "\" not found") {}

// Reveal message to clients const char *what() const { return message.c_str();

}

};

// Creates and returns a vector of integers from data stored // in a text file.

// filename: the name of the text file containing the data // Returns a vector containing the data in the file, if possible std::vector<i nt> load_vector (const std::string& filename) {

//

std::ifstream fin(filename); if (fin.good()) { i nt n; fin >> n;

std::vector<i nt> result(n); int value, i = 0; while (fin >> value)

result.at(i++) = value; return result;

}

else // Could not open the text file

throw FileNotFoundException(filename);

// Open the text file for reading // Did the file open successfully?

Size of data set

// Allocate space for the vector

// Append it to the vector // Return the populated vector

}

int main() { try {

std::vector <int> numbers = load_vector("values.data") ;

©2018 Richard L. Halterman

Draft date: September 25, 2018

for (int value : numbers) std::cout << value << 1 std::cout << '\n' ;

}

catch (std::out_of_range& e) {

std::cout << "Error: vector bounds exceeded\n"; std::cout << e.what() << '\n';

}

catch (FileNotFoundException& e) {

std::cout << "Error: cannot open file\n"; std::cout << e.what() << '\n';

}

}

22.5 Exception Mechanics

An exception handler within a catch block may take a few steps to handle the exception and then re-throw the exception or throw a completely different exception.

©2018 Richard L. Halterman

Draft date: September 25, 2018

}

produces the following output:

•k-k-k-k-k'k-k-k-k-k'k-k-k-k-k-k-k-k-k'k'k'k-k-k'k-k-k-k-k'k-k-k

* For loop terminated prematurely

* when i = 5

********************************

Caught an exception: invalid std::vector<T> subscript Program finished

Notice that in Listing |22.1 l|| (rethrow.cpp) the compute function does not create a new exception object; it simply re-throws the same exception object that it caught. This concept of intermediate exception handlers is important since a function invocation has complete knowledge of it own local context such as its local variables. This means that an intermediate function (or method) in the call chain has access to information that may be unavailable to all other functions (or methods) within that call chain. The catch block in the compute function of Listing 22.11 (rethrow.cpp) involves only local variables. The catch block within the mai n function cannot know the subscript that caused compute’s failure since i is local to compute. Some general exception guidelines include:

• Handle exceptions as close (up the call chain) as possible to the code that throws the exception.

• Use local information where applicable to correct as much of the problem as possible within that local context:

- Local information which may be important for recovering from the exceptional situation is available; this local information is unavailable to functions or methods up the call chain.

- The lower-level functions/methods that are prone to exceptions may be called by many different higher-level functions/methods. If the lower-level functions/methods are responsible for their own exception handling, then the higher-level functions/methods may be able to dispense with exception handling altogether making the lower-level methods more robust units of reuse.

- The lower-level functions/methods may handle many different kinds of exceptions, do any local clean up they can based on the type of exception thrown, and then throw a different type of exception up to the higher-level methods. The higher-level method may just need to know there was a problem without needing to know exactly what the problem was. For example, in Listing 22.11 (rethrow.cpp), the compute function could throw a custom ComputeExcepti on object whenever filter throws its std : : out_of_range instead of just passing up the call chain the std: : out_of_range object it receives.

If total recovery is not possible or desirable at the lower levels of the call chain, re-throw the exception so an exception handler up the call chain can take steps to recover from the problem in a manner that makes sense in its context.

When a section of code throws an exception, the catch blocks within the nearest exception handler are checked in the order they appear in the C++ source code. The first catch block that matches the type of the exception thrown is the one executed. For example. Listing 22.12 (multipleexceptions.cpp) expects two types of exceptions, and it uses the catch-all exception in case any unexpected exceptions arise.

Listing 22.12: multi pleexcepti ons. cpp

#include <iostream> ttinclude <fstream>

©2018 Richard L. Halterman

Draft date: September 25, 2018

#include <vector>

#include <string>

// Get an integer from the user. Note that std::stoi can // throw a std::invalid_argument exception if the user's // input is not an integer, and it can throw std::out_of_range // if the string is a valid integer but outside the range of // a C++ int on this platform, int get_int() {

std::string input; std::cin >> input; int result = stoi(input); return result;

}

int main() {

std::vector<i nt> a { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }; try { // What possibly could go wrong?

int n = a.sizeQ ;

std::cout << "Enter index in the range 0..." << n - 1 << ": "

// Will user enter a valid integer value? int i = get_int();

std::cout << "Index entered: " << i << ' \n';

// Will the user's index be in the range of valid indices? std::cout << "a[" << i << "] = " << a.at(i) << ' \n' ;

}

catch (std::out_of_range&) {

std::cout << "Index provided is out of range\n";

}

catch (std::invalid_argument&) {

std::cout << "Index provided is not an integer\n";

}

catch (...) { // What have we forgotten?

std::cout << "Unknown error\n";

}

}

When an exception is caught, its type is first compared to std: : out_of_range. If it matches, the std: :out_of_range catch block is executed. If not, the exception’s type is then compared to i nvalid_argument. The i nvalid_argument catch block is executed in the case of a match. If neither of the two types match, the catch-all code is executed.

When inheritance is involved, the situation becomes more interesting. The comparison performed in each catch block is a test for assignment compatibility. A reference or a pointer to an instance of a derived class can be assigned to a variable declared to be a reference a pointer to a base class. This upcasting operation is always legal because of the is a relationship between a derived class and its base class. This means an exception object of type std: :out_of_range is assignment compatible with both std: :out_of_range variables and std: :exception variables. Since the catch blocks are checked in the order they appear in the source code, the following code would have a problem:

try {

// Execute some code that can throw an // out_of_range exception

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}

catch (std::exception& e) {

// Do something here

}

catch (std::out_of_range& e) { // Error, this can never be reached

// Do something else here

}

The std : : out_of_range catch block will never execute since a std : : out_of_range object is an excepti on instance also. For this reason it is illegal for a more specific type to follow a more general type in a sequence of catch blocks. The above code fragment will not compile in any context. Thus, in a sequence of catch blocks, list the more specific exceptions first followed by the more general exceptions.

All C++ standard exception classes have std : : excepti on as their direct or indirect base class. C++ does not require exception objects to be derived from excepti on; in fact, primitive types such as i nt and char can be thrown and caught as well. Because of this, the “catch all” exception clause is

catch (...) {

// Catches any exceptions not caught by more specific // catch blocks in this try/catch block

}

The ellipses (...) stand for an exception of any type.

Any function or method can throw an exception object. Given an exception of type E, the statement to do so is:

throw E();

22.6 Using Exceptions

Exceptions should be reserved for uncommon errors. For example, the following code adds up all the elements in an integer vector named vec:

int sum = 0, n = vec.sizeQ; for (int i = 0; i < n; i++) { sum += vec[i];

}

std::cout << "Sum = " << sum << ' \n' ;

This loop is fairly typical. Another approach uses exceptions:

sum = 0; int i = 0; try {

while (true)

sum += vec.at(i++);

}

catch (std::out_of_range&) {} std::cout << "Sum = " << sum << ' \n' ;

Both approaches compute the same result. The second approach terminates the loop when the array access is out of bounds. It interrupts the statement

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sum += vec.at(i++);

in midstream, so it does not incorrectly modify sum’s value. The second approach, however, always throws and catches an exception. The exception definitely is not an uncommon occurrence.

You should not use exceptions to dictate normal logical flow. While very useful for its intended purpose, the exception mechanism adds some overhead to program execution, especially when an exception is thrown. This overhead is reasonable when exceptions are rare but not when exceptions are part of the program’s normal execution.

Sometimes it is not clear when an exception is appropriate. Consider a function that returns the position of an element within a vector. The straightforward approach that does not use exceptions could be written:

int find(const std::vector<i nt>& a, int elem) { int n = a.sizeQ ; for (int i = 0; i < n; i++)

if (list[i] == elem)

return i; // Found it at position i

return -1; // Element not present

}

Here a return value of — 1 indicates that the element sought is not present in the array. Should an exception be thrown if the element is not present? The following code illustrates:

int find(const std::vector<i nt>& a, int elem) { int n = a.sizeQ ; for (int i = 0; i < n; i++)

if (list[i] == elem)

return i; // Found it at position i

// Element not there; throw an exception throw ElementNotPresentException();

}

In the first approach, an unwary programmer may not check the result and blindly use — 1 as a valid position. The exception code would not allow this to happen. However, the first approach is useful for determining if an element is present in the vector. If find (x) returns —1, then x is not in the vector; otherwise, it is in the vector. If the exception approach is used, a client programmer cannot determine if an element is present without the risk of throwing an exception. Since exceptions should be rare, the second approach appears to be less than ideal. In sum,

• The first approach is more useful, but clients need to remember to properly check the result.

• The second approach provides an exception safety net, but an exception always will be thrown when searching for missing elements.

Which approach is ultimately better? The first version uses a common programming idiom and is the better approach for most programming situations. The exception version is a poorer choice since it is not uncommon to attempt to look for an element missing from a vector; exceptions should be reserved for uncommon error situations.

©2018 Richard L. Halterman

Draft date: September 25, 2018

©2018 Richard L. Halterman

Draft date: September 25, 2018

Appendices

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Draft date: September 25, 2018

Appendix A

Chapter Notes

The text file containing the integers to load into the vector has a specific format. The first integer read from the file is not a data element; instead, it specifies the number of integers that follow. This gives us two options for creating and populating the vector:

1. Create the vector with sufficient size up front and then use a loop to place to individual elements in their proper places.

2. Create an empty vector and then use a loop to push_back the individual elements.

Option 1 is more efficient than Option |2] Successive calls to std: : vectorci nt> : : push_back must reallocate and copy elements multiple times. Option[2|is safer than Option|T]because the number of elements specified at the start may not agree with the actual number of data elements in the file. If the specified number is too small, the function will attempt to overrun the bounds of the vector.

Listingj|22.9|(filereadmultiexcept1 .cpp) opts for efficiency at the expense of safety. This means it depends on a correctly created data hie. If the hie does not exist, load_vector will throw our Fi leNotFoundExcepti on custom exception:

File "values.data" not found

If the hie exists and contains 3

10

Draft date: September 25, 2018

Using Visual Studio 2015 to Develop C++ Programs

This appendix describes the task of C++ software development under Visual Studio:

• To begin creating a C++ program, you must first launch Visual Studio 2015 from the Windows start screen or other relevant shortcut. Figure |A.1| shows the appropriate application tile to activate.

You soon should see a splash screen similar to the one shown in Figure [A72|

If you have never before used the Visual Studio application, you must wait a few moments while it configures the development environment for you. At this point you will indicate that Visual C++ is your preferred development language. You also may select a color scheme. The figures shown here reflect the blue color scheme.

Figure jA3| shows what Visual Studio looks like when it is fully loaded and ready to use.

• After Visual Studio has started, you begin the process of developing a C++ program by creating a new project. As Figure |A!4j shows, you can create a new project by following the menu sequence: File^New^Project

• In the dialog that results, shown on the right of Figure |A~4] you should choose the project type to be Visual C++ in the left pane, and use the Win32 Console Application option in the center pane. In the name field near the bottom of the dialog, enter a name for the project; we will use the name simple. You may change the location to a different folder if you like, or even a different drive (such as a USB pen drive). In this example, we chose to not change the default location provided by Visual Studio.

• When you select OK on the project creation dialog, a Win32 Application Wizard as shown on the left of Figure |A3| appears. At this point, the instructions in the dialog say “Click Finish from any window to accept the current settings.” Do not select Finish; instead, select Next to continue. We have one more key step to complete so our project is set up correctly.

Figure A.l Visual Studio application tile

Visual Studio 2015

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Figure A.2 Visual Studio Splashscreen

* Visual Studio

Community 2015

in Help/About

Figure A.3 Visual Studio Ready for Use

^ Start Page-Microsoft Visual Studio V & Q uick Launch (Ctrl.Q) P _ n X

File Edit View Debug Team Tools Test Analyte Window Help sign in H

• I S3 - SO J* ' ' ► Attach- * 0

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Figure A.5 Configuring the New Project

n

Win32 Application Wizard - simple

Welcome to the Win32 Application Wizard

These are the current project set

Win32 Application Wizard - simple

Application Settings

Application Settings

CSdc Finish from any window to accept the current settings.

OStatlc library Additional options: 0 Empty project

Zl Security Development Lifecyde (SDL)

H^7-ir^rir^n

| |[ Neo liquid._J| Caned

In the subsequent Applications Settings dialog (see the right image in Figu re [AT5) , select the Empty project checkbox. The dialog should look like the right image in Figure A.5 before you proceed. Choose Finish when you are ready to continue.

At this point, the Solution Explorer panel shows the structure of the newly created, albeit empty, project. The left image in Figure A.6| shows the newly populated Solution Explorer pane.

• Right click oil the simple element in the Solution Explorer. As shown on the right of in Figure [A.6[ select Add and New Item from the resulting pop-up menu.

• In the Add New Item dialog box, shown on the left in Figure A.7 select C++File (.cpp) and enter a name for the C++ file in the text field at the bottom. You need not add .cpp to the end of the name, as Visual Studio will do that for you. The file here will be named simple.cpp. Press Add when done.

• As shown on the right in Figure A.7 the Solution Explorer pane now shows the file si mple. cpp, and the large editor pane is ready for you to type in the source code for the program. The new source file is initially empty.

• In the editor pane with the simple.cpp tab at the top, type in the source code for our simple C++ program. Figure||A.8||shows the completed code.

You may save the sou rce file at th is point by selecting Save from the File menu or by pressing pressing at the same time the keys. If you do not save your program. Visual Studio will prompt

you to do so before it builds and runs your program.

To run the program, select Debug—?Start Without Debugging , as shown on the left of Figure |A.9[

(You also may use the

Ctrl I F5

key sequence to build and run the program.) Visual Studio will

attempt to build the executable program. It will prompt you to save your file if you have not saved it

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure A.6 Adding a C++ Source File

Search Inctalled Templates (Ctrl*- E) ft

Figure A.7 Ready to Edit the C++ Source File

* simple - Microsoft Visual Studio

or have made changes since the last time you saved it. The progress of the build process is displayed is in the Output panel in the bottom window. One of the lines has

l>Compiling. . .

and another later has

l>Linking. . .

The last few lines are very important:

l>Build succeeded.

1 >

l>Time Elapsed 00:00:02.98

========= Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ===

These lines indicate the build was successful.

• A console window appears with the output of your program. The right image in Figure j[A.9| shows this text window. You can press any key on the keyboard to close the window. If the console window does not appear, you have typographical errors in your program; return to the editor, fix the errors, and try to run the program again.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure A.8 Editor Pane

t>4 simple - Microsoft Visual Studio • 7 l Quidl Laurlch (Qrl-Q)

Figure A.9 Building and Running the Program

When you are finished with Visual Studio, select the File^-Exit menu items as shown in Figure A. 10

These are the steps for writing a basic C++ program in Visual Studio 2015. While the steps initially may seem complex and tedious, they will become natural after you have written a few C++ programs.

When the program was run, the Visual Studio environment created a console window in which to run the program.

This is a simple C++ program! Press any key to continue . . .

The first line of the output was printed by the program. The second line prompting the user to press any key to continue is added by the Visual C++ run-time environment so the console window stays visible long enough for the user to see the output. If you run the program from a the standard Windows command shell (CMD.EXE, usually found in the Start menu under Accessories and named Command Prompt), only the program’s output will appear and the “Press any key to continue . . .” message will not appear.

The following summarizes the steps you should follow when writing a C++ program using the Visual Studio IDE:

1. In the main menu:

File—>New—^Project (or

2. Select “Win32 Console Project” and click “Next” to set the “Empty Project” option

©2018 Richard L. Halterman

Draft date: September 25, 2018

Figure A.10 Exiting Visual Studio

3. In the Solution Explorer pane right click on “Source Files” and select Add—KNew Item...

4.

5.

6 .

Select C++ File (.cpp) and enter the name of your file Type in the source code for your program in the editor panel

Save your file:

File—>-Sa ve filename (or

Ctrl

7.

In the main menu:

Debug—^Start Without Debugging (or

Ctrl I F5

It is possible to develop C++ programs without using Visual Studio’s integrated development environment. Visual Studio comes with some additional tools for command-line development. Appendix |Bjdescribes how you can edit the C++ source code with a standalone text editor and compile and run the program from the Windows command prompt (CMD.EXE). Command-line development under Linux and macOS is covered in[B| Some programmers prefer the freedom of using their favorite editor, a standalone compiler, and scripts to automate the build process.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Appendix B

Command Line Development

An integrated development environment (IDE) like Visual Studio combines all the tools a developer needs into one comprehensive application. While this approach works well for most programmers, some developers prefer a less centralized approach, using instead command line tools to manage the development process. Command line tools are focused and fast, and each tool itself is fairly simple compared to a fullfeatured IDE. A developers may prefer a different editor to one provided by the IDE. Developers can build scripts to around command line tools to automate the building and testing process.

There are a few commands that are essential for working within the command-line environment. These center around manipulating and using files and folders. Our discussion assumes the Windows CMD.EXE shell, and we will note differences with macOS and Linux as needed. Linux and macOS are both Unix-like operating systems.

When you run CMD.EXE in Windows, the Terminal application on a Mac, or a bash terminal in Linux, the operating system presents a text-based console window. You type commands into this window and receive text feedback. Most of the commands are programs that you launch by typing their name. The following lists common commands useful for using the command-line;

•dir

When the command line interface starts it locates you in a particular folder, or directory, in the file system managed by the operating system. Your location is known as the current working directory. The command dir prints a list of the files in your current working directory. On Unix-like machine the Is -l command performs similar work. The command dir /w displays a wide listing of the hies with fewer details; the Is command is the equivalent on Unix-like systems.

• mkdi rname

Creates a new subdirectory (subfolder) named name in the current directory. Subdirectories allow you to better organize your hies.

• cd name

Changes you current directory to be that specihed by name. Some examples of its use include - cd Code

Changes the current working directory to be the subdirectory named Code. Here the name is relative to the current directory. It is an error to provide a name that does not correspond to a subdirectory of the current directory.

©2018 Richard L. Halterman

Draft date: September 25, 2018

- cd . .

Changes the current working directory to its parent directory. Said another way, the current working directory is itself a subdirectory of some other directory. This command makes this other (parent) directory the current working directory. The . . means “parent directory” or “parent folder.”

- cd C:\Users\rick\Documents\Code

Changes the current working directory to the completely specified one. The name here is known as a full-path name. The name is an absolute location; it is not relative to the current working directory. Unix-like systems do not have a drive letter (C:), and the backslashes (\) would be forward slashes (/).

- cd .

Changes the current working directory to itself, which effectively does nothing! This command does no useful work. The dot (.) in this context means “current working directory.”

• del name

Deletes the file named name. Use this command carefully. Unix-like systems use the rm command in its place.

• ren namel name2

Renames the file namel to name2. The move command does the same thing, and Unix-like systems use the mv command to rename files.

In preparation for our programming, we can create a new directory for our code and make that new directory our current working directory with the commands:

mkdir Code cd Code

We can edit our source code with a simple text editor such as Notepad or Wordpad for Windows, TextEdit on the Mac, or gEdit on Linux systems. More powerful programming editors such as Notepad++ ( http : / / notepad-plus. sourceforge. net ) (Windows) and Vim (http://www.vim.org) (Windows, Mac, and Linux) make editing source code more convenient.

B.0.1 Visual Studio Command Line Tools

Visual Studio provides a number of command line tools as an alternative to its integrated development environment.

To use the command line tools, select the Visual Studio Command Prompt from the Start menu. A command console appears similar to the console that the IDE provides when executing a program (see Section \2.2) . Instead of selecting menu items and interacting with dialog boxes, you type commands into the console window to build and run your program. To edit your program you can use the editor from the IDE, or you can use a standalone editor such as Notepad-H- ( http : / /www. notepad- plus . sourceforge. net ) or Vim (http : //www. vi m. org). Both Notepad++ and Vim provide color syntax highlighting and folding like the built-in Visual Studio editor.

In order to use the command prompt version of Visual Studio, it is convenient to first create a folder in which you will place all your development files; for example, you could create a folder named Code under your Documents folder. Suppose the full path to this folder is

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Draft date: September 25, 2018

C:\Users\rick\Documents\Code

Once your development folder is created, you can launch the Visual Studio Command Prompt. The first command you should issue in the console window is

C

to ensure you are working on the correct drive. Next issue

cd \Users\rick\Documents\Code

The cd command means “change directory.” This command sets the console’s working directory to the development folder you previously created. If you are working in another folder, you can adjust the path given in the cd command to your work area.

You are ready to edit your code. If your environment is set up so that your editor program is in the system path, you can type

notepad++ simple.cpp

to launch the Visual Studio editor.

Within the editor type in your program and then save it to a file.

When you have finished creating the source hie, we will need to build the executable program. Switch back to the Visual Studio Command Prompt window, and issue the command

cl /W3 /EHsc simple.cpp

The cl (“cee elle”, not “cee one”) command, which stands for compile and link, preprocesses, compiles, and links the program. The /W3 switch uses the Level 3 warning level. Level 3 warnings provide more thorough analysis of your source code and can detect more programming mistakes. If you omit the /W3 switch, by default the compiler operates at warning level 1. Warning level 1 is insufficient for catching many mistakes made by both beginning and experienced C++ programmers. By default the IDE compiler uses warning level 3, and the warning level can be changed by adjusting the project’s properties. On the command line, specifying /W4 (the highest warning level) is just as easy as specifying /W3. It is better to use /W4 so the compiler can do a more thorough check for potential programmer mistakes. The / EHsc is required for all the C++ programs we write.

If want to reduce the level of detail in the output produced by the compiler and linker, you can add the additional switch / nologo:

cl /W4 /EHsc /nologo simple.cpp

Notice that we used the enhanced warning level (/W4) here. To see the complete list of compiler options, many more than you probably will ever need, type

©2018 Richard L. Halterman

Draft date: September 25, 2018

In C++ programs consisting of a single source file, the compiler produces an executable file with the same base name as the source file (simple, in our example), with an exe extension.

Once the program has been compiled successfully, you can run the program by entering the name of the executable produced. In our example, we would issue the command

simple

The program runs in the same window; no new console window is produced. When the program is finished executing, no “Press any key to continue” message is printed; you get simply a command prompt ready for you to enter your next command.

If you modify your source code in your editor, you must remember to recompile your code before you run it again. In the IDE, if you modify your code, the environment will suggest that you rebuild the project before running the program.

If the program consists of multiple source files, list all the required files on the command line. The exe file will be named after the first file listed; for example, the command

cl /W4 /EHsc /nologo app.cpp list.cpp util.cpp

compiles the three C++ sources files and links the compiled code together to produce app.exe.

In the Visual Studio command prompt program you can enter the Visual Studio IDE at any time with the command

devenv

(devenv stands for “development environment.”) If you started Visual Studio in the IDE, not the command prompt, you can open a command prompt console window at any time by selecting the Command Prompt item under the Tools menu.

B.0.2 Developing C++ Programs with the GNU Tools

The tools provided in the GNU Compiler Collection ( http : //gcc . gnu .org), orGCC for short, include one of the most up-to-date standards compliant C++ compilers available. The GNU tools are free and are available for the major computing platforms:

• Microsoft Windows XP-Windows 10

Windows-based GCC tools can be found at the MinGW website http : / /www. mi ngw .org The Nuwen site (www. nuwen .org) offers an easy to install custom distribution of MinGW with a number of additional useful C++ libraries.

• Apple macOS

The Homebrew (http://brew.sh) and MacPorts (http: / /www.macports. org /) projects bring the GCC toolset to Mac developers. Mac users also may use the clang++ compiler that comes with Xcode.

• Linux

©2018 Richard L. Halterman

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Linux-based GCC tools are readily available for all the major Linux distributions. To get them, simply install the g++ development packages.

The name of the GNU C++ compiler is g++. It is a command-line tool, which means it is launched from a command shell— CMD.EXE in Windows or bash in the Mac and Linux environments.

To see how the GNU C++ buld system works, we will consider Listing [271 [ (simple.cpp) from Chapter[2] Use an editor to create a text file containing the code for Listing j2T] (simple.cpp), and save the file with the name simple.cpp. In Windows, if notepad++ is installed and set up properly, in the command shell you can type

notepad++ simple.cpp

This command brings up a separate window with an editor. We can type the source code for Listing (2TTj (simple.cpp) and save the file.

To create the executable program with GNU C++, back in our command-line window we issue the command

g++ -Wall -std=c++14 -o simple simple.cpp This command has five parts:

• g++ -Wall

g++ invokes the GCC C++ build process. This one command runs the preprocessor, followed by the compiler, and finally the linker to produce the executable program. Even though the preprocessor and linker are also involved here, we generally simply say we are "compiling the program."

• g+- -Wall

-Wall stands for “warn all” and directs the compiler to be very strict when it is compiling the source code. It goes beyond checking that the program is well-formed C++ it also warns about code constructs that many programmers consider questionable because code of that nature often contains errors. The -Wall component can be interpreted to mean "warn about as many possible problems as possible." You should compile all C++ programs with this directive because it enables the compiler to catch many careless programmer mistakes that otherwise might go unnoticed. Use of the -Wall directive is desirable for all C++ programmers from novice to expert.

The C++ standards committee is responsible for defining the C++ language. The committee refines the language specification over time. In addition to adding new features to the language, the committee also addresses shortcomings in existing language features. As a result of the committee’s work newer compilers can check more thoroughly the validity of C++ programs. Modern compilers do a better job of catching common programming errors.

The -Wall directive is optional because sometimes developers must work with older C++ source code. The code was written originally under more relaxed C++ language rules, but it may not be worthwhile to rewrite the code to bring it up to modern standards. If this older code has proven to be reliable, it may be compiled without the more stringent checks. All new code, however, should take advantage of the newer, better checking capabilities of the most up-to-date C++ compiler; therefore, always use -Wall on the compiler command line for code that you write.

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• g+ + -Wall -std=c++14

The -std = c+ + 14 option directs the compiler to process the C++ source code according to the rules of the C++14 standard which the International Standards Organization (ISO) adopted in 2014. Since this standard is relatively new, if you omit this part of the command, g++ assumes the programmer is writing the source code under the rules of the older, 1998 ISO C++ standard, usually referred to as C++98.

The code in this book is based on the C++11 standard.

• -o simple

The -o simple part of the command specifies the name of the executable program. The desired name appears after the -o part, so our executable program will be named simple.exe on Microsoft Windows systems. On Mac and Linux platforms the name of the executable file produced will be just simple (no exe name extension). If the C++ source code code contains no errors, the compiler will produce the executable file named simple.exe (or simple). On a Windows Machine we can run the compiled program from the command line by typing the command

simple

(We also can use the full name, simple.exe.) On a Unix-ike system (macOS or Linux), we instead would type

. /simple

to execute the program.

• -Wall -std=c++14 -o simple simple.cpp

si mple . cpp specifies the name of the C++ source file we wish to compile. Here the file simple.cpp must reside in our current working directory for the compiler to process it.

The general form of the command to compile a C++ source file, therefore, is

g++ -Wall -std=c++14 -o executable source

where source is the name of the file containing the C++ source code, and executable is the name of the executable program the build process generates.

When you are finished with the executable file simple.exe, you can delete it with the following command:

del simple.exe

We can reconstruct the executable file whenever we like by simply recompiling the source file. Be careful not to delete accidentally the source file, or you have no choice but to type it in again.

©2018 Richard L. Halterman

Draft date: September 25, 2018

Index

abstract class, l|524|| actual parameter, ||208[ adapter design pattern, ||522| alias, [326||

aliasing, pointer, |546|[ and, bitwise, [72] and, logical, [97] argument.

array, [3TT| array slice, |322|| assignment, p~9] associative container, [587] associativity, operator, |44| attributes, |409| auxiliary methods, |428|

bias in pseudorandom number generation,

binary search, 359||688|

bitwise and, 72]

bitwise exclusive or, [73]

bitwise left shift, f74|

bitwise negation, [73]

bitwise operators, [72]

bitwise or, [73]

bitwise right shift, [74]

bitwise shift operators, |73j

bitwise xor,j73)

block, |92j

bottom-checking loop, 165 break statement, jl40 | buffer overrun, p34[ buffering, 395

C string. |333| call by reference, |274|| call by value,] caller, fl82j carriage return,[17] case label in a switch statement, ||162|| catch block, ;720[ class derivation, ][496]

class templates, [618] client, [384! closure, [656)

coincidental correctness, [4911 command line, |9j command-line arguments, |337| compiler, [2] concrete class, ||524| constructor, |422|| constructor delegation, |572| constructor initialization list, ij423| copy assignment,: copy constructor.

583

570

copy-and-swap, 572

CR,jT7]

current working directory, 747

data members, [409] default argument, 2: default constructor, default parameter, |252[ delegation, method, |50! delimit, [TT| derivation, class, |496] derivative, [638] destructor, [559] differentiation, |658[ dot operator (.), pH f|[ doubly linked list,|634 dynamic binding, 509]

early binding, 508

encapsulation, 430

enumerated type,: enumeration classes, [3T| enumeration type,pT| erase-remove idiom, [679] escape sequence,p0| evaluation, [38]

exception, 719

class specialization, 496]

exception handling, 719 exclusive or, bitwise, [73

©2018 Richard L. Halterman

Draft date: September 25, 2018

explicit template instantiation, [611 616 expressions, |37]

Fibonacci sequence, 260 fields, |409| for statment, |l67| foreach, |298|

fragmentation, memory, 544] f ri end, [466] full-path name,||748| function call, 182

function call operator, j636 function declaration, |23T|| function definition, |2031 function invocation, |Y82I| function invocation operator, |636[ function objects, [656]

function overloading, 251

function pointers, 1278

garbage, |597| garbage collection, [590] generating function, 669 generic function, 610 goto statement, 141

hash function, 704 hash table, |702) heap fragmentation, 544| helper methods, |428| hiding variables, [420

higher-order function, 278

homogeneous, 291

if statement.

inheritance, 496

initialization, [20} |570[ initializer list, |68~l| instance, ■

instance variables.

is-a relationship, 497 iteration, |123| iterators

key, 687

lambda calculus, 655

lambda expressions, 655

late binding, 509 left shift, [74]

LF, [17] line feed, [T7]

linear ordering, [2911 linear search, [359| linker, [5]

Liskov Substitution Principle, 497

logical and, 97

logical negation,'

logical not, 97 logical or, 97

loop, 123

loop unrolling, 372 lvalue, 578

mask, [75] matrix, [507] member data, j409|j member function, [4191 member functions, [2991 [417] members, |409] memoization, [7131| memory fragmentation, j|544| memory leak, ||326| [4411|

Mersenne Twister pseudorandom number generator, j403l

method delegation, |502]

methods, 299 417

move assignment, 5831 move constructor, jp83| multiple inheritance, j]499

negation, bitwise, [73] negation, logical, [97] nested loop, 133

newline, [10] non-type parameters, template, |617| non-type template parameters, 617

not, logical, 97

numerical differentiation, 659

object slicing, [505] operator associativity,]44| operator precedence. 44 or, logical, [97] overflow, [64] overloaded function, [25T|| override, [502]

:ieter, 182

teter, actual, 208 ly reference, 274 ty value, |215|

©2018 Richard L. Halterman

Draft date: September 25, 2018

pointer, 267

pointer aliasing, |546[ polymorphism, [51 f| precedence, operator, ■

predicate, 667

pretty printer, 50 priority queue,]635

ice,g98j

s,|418|

private inheritance, private members, profiler, [5] protected member, |523|| pure virtual methods, [524|

Table captionrandom access itertator, [6431 range-based for, [298| ranges, |644| rational number, | 425| re-throw,

Table captionreference counting, 597 [598

Table captionreference semantics, 547

reference variable, [2711[

relational operators, |86|

return statement, [2071

return value optimization, 306 588

right shift, |74f

Rule of Five, j588|

Rule of Three, [577 [ rvalue reference, 580

scoped enumerations, [3T| sequence, |290| shift, bitwise, [74] short-circuit evaluation, [99] slice, array, |322j smart pointer;[590 source code formatting, 47| specialization, class, [496) stack overflow, |544| standard namespace, [9]

standard template library, 633

static binding, 508

387

steam manipulator, 129 STL, [633]

string concatenation, string objects, |384| struct, [465| structured binding, 6'

subclassing, 496]

switch statement,1 159 | symbolic differentiation, |65~9| symmetric, <

template instantiation, 611

template type parameter, 610{ template value parameters, 617 templates, 609 temporary, 579 this, [442 throws, j|720[

transitive, [4681 try block, [720 try/catch block, 720 tuple unpacking, [694 two’s complements^

Table captiontwo-dimensional array, 330 two-dimensional vector, 307

re-throwing an exception, 734

type alias, 308

real number, [64|

type parameter.

610

red-black tree, 688| [702[

typedef, 309

undefined behavior, |297| underflow, [64]

unordered_map, 702 unpacking tuples, 61

unscoped enumeration, 31

unsigned, 24

usi ng type alias, 308

value parameters, template, 617 value semantics, 115471

variable aliasing with references, 271 variable hiding, [420|| vector, |29T|

vector initializer list, [292] virtual memory, 544 vtable, 15091

while statement, [124] xor, bitwise, [73]

©2018 Richard L. Halterman

Draft date: September 25, 2018