lab a and lab b

Sam1

c_for_everyone_2nd_edition_horstmann_wiley_plus_textbook.pdf

Home >Computer Science homework help >lab a and lab b

This page intentionally left blank

C + + f o r E v E r y o n E

cfe2_fm_pi_xxvi.indd 1 10/28/10 5:08 PM

This page intentionally left blank

C + + f o r E v E r y o n E

S e c o n d e d i t i o n

cay Horstmann San Jose State University

John Wiley & Sons, Inc.

cfe2_fm_pi_xxvi.indd 3 10/28/10 5:08 PM

VICE PRESIDENT AND EXECUTIVE PUBLISHER Don Fowley EXECUTIVE EDITOR Beth Lang Golub EDITORIAL PROGRAM ASSISTANT Michael Berlin PRODUCTION SERVICES MANAGER Dorothy Sinclair SENIOR PRODUCTION EDITOR Janet Foxman EXECUTIVE MARKETING MANAGER Christopher Ruel MARKETING ASSISTANT Diana Smith CREATIVE DIRECTOR Harry Nolan SENIOR PHOTO EDITOR Lisa Gee SENIOR DESIGNER Madelyn Lesure EXECUTIVE MEDIA EDITOR Tom Kulesa PRODUCTION SERVICES Cindy Johnson COVER PHOTO © Ricardo Azoury/iStockphoto

This book was set in Stempel Garamond by Publishing Services, and printed and bound by RRD Jefferson City. The cover was printed by RRD Jefferson City.

This book is printed on acid-free paper. ∞

Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work. In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business. Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support. For more information, please visit our website: www.wiley.com/go/ citizenship.

Copyright © 2012, 2009 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be re- produced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, pho- tocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Dan- vers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748- 6011, fax (201) 748-6008, website www.wiley.com/go/permissions.

Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instruc- tions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel. Outside of the United States, please contact your local representative.

Library of Congress Cataloging in Publication Data: Horstmann, Cay S., 1959- C++ for everyone / Cay S. Horstmann. -- 2nd ed. p. cm. Includes index. ISBN 978-0-470-92713-7 (pbk.) 1. C++ (Computer program language) I. Title. QA76.73.C153H6685 2010 005.13'3--dc22 2010039907

ISBN 978-0-470-92713-7 (Main Book) ISBN 978-0-470-92092-3 (Binder-Ready Version)

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

cfe2_fm_pi_xxvi.indd 4 10/28/10 5:08 PM

www.copyright.com

www.wiley.com/go/citizenship

www.wiley.com/go/permissions

www.wiley.com/go/returnlabel

P r E fa C E

This book is an introduction to C++ and computer programming that focuses on the essentials—and on effective learning. The book is designed to serve a wide range of student interests and abilities and is suitable for a first course in programming for computer scientists, engineers, and students in other disciplines. No prior program- ming experience is required, and only a modest amount of high school algebra is needed. Here are the key features of this book:

Guidance and worked examples help students succeed. Beginning programmers often ask “How do I start? Now what do I do?” Of course, an activity as complex as programming cannot be reduced to cookbook-style instruc- tions. However, step-by-step guidance is immensely helpful for building confidence and providing an outline for the task at hand. “Problem Solving” sections stress the importance of design and planning. “How To” guides help students with common programming tasks. Additional Worked Examples are available online.

Practice makes perfect. Of course, programming students need to be able to implement nontrivial programs, but they first need to have the confidence that they can succeed. This book contains a substantial number of self-check questions at the end of each section. “Practice It” pointers suggest exercises to try after each section. At the end of each chapter, you will find a great variety of programming assignments, ranging from simple practice problems to realistic applications.

teach computer science principles, not just c++ or object-orientation. This book uses the C++ programming language as a vehicle for introducing com- puter sci ence concepts. A substantial subset of the C++ language is covered, focusing on the modern features of standard C++ that make students productive. The book takes a traditional route, stressing control structures, procedural decomposition, and array algorithms, before turning to the design of classes in the final chapters.

A visual approach motivates the reader and eases navigation. Photographs present visual analogies that explain the nature and behavior of computer concepts. Step-by- step figures illustrate complex program operations. Syntax boxes and example tables present a variety of typical and special cases in a compact format. It is easy to get the “lay of the land” by browsing the visuals, before focusing on the textual material.

Focus on the essentials while being technically accurate. An encyclopedic coverage is not helpful for a begin- ning programmer, but neither is the opposite— reducing the material to a list of simplistic bullet points. In this book, the essentials are presented in digestible chunks, with separate notes that go deeper into good prac- tices or language features when the reader is ready for the additional information. You will not find artificial over-simplifications that give an illusion of knowledge.

Visual features help the reader with navigation.

cfe2_fm_pi_xxvi.indd 5 10/28/10 5:08 PM

vi Preface

new to This Edition Problem Solving Strategies This edition adds practical, step-by-step illustrations of techniques that can help stu- dents devise and evaluate solutions to programming problems. Introduced where they are most relevant, these strategies address barriers to success for many students. Strategies included are:

• Algorithm Design (with pseudocode) • First Do It By Hand (doing sample

calculations by hand) • Flowcharts • Test Cases • Hand-Tracing • Storyboards • Reusable Functions

• Stepwise Refinement • Adapting Algorithms • Discover Algorithms by Manipulat-

ing Physical Objects • Draw a Picture (pointer diagrams) • Tracing Objects (identifying state and

behavior) • Discovering Classes

optional Engineering Exercises End-of-chapter exercises have been enhanced with problems from scientific and engineering domains. Geared to students learning C++ for a technical major, the exercises are designed to illustrate the value of programming in those fields. Addi- tional exercises are available on the book’s companion web site.

new and reorganized Topics All chapters were revised and enhanced to respond to user feedback and improve the flow of topics. Loop algorithms are now introduced explicitly in Chapter 4. Debug- ging is now introduced in a lengthy Worked Example in Chapter 5. Arrays are cov- ered before vectors are introduced in Chapter 6, and a new section on vector algo- rithms builds on the array algorithms presented earlier in the chapter. A new optional section on structure types is now in Chapter 7. New example tables, photos, and exercises appear throughout the book.

a Tour of the Book The core material of the book is:

Chapter 1. Introduction Chapter 2. Fundamental Data Types Chapter 3. Decisions Chapter 4. Loops Chapter 5. Functions Chapter 6. Arrays and Vectors

In a course for engineers with a need for systems and embedded programming, you will want to cover Chapter 7 on pointers. Sections 7.1 and 7.4 are sufficient for using pointers with polymorphism in Chapter 10.

cfe2_fm_pi_xxvi.indd 6 10/28/10 5:08 PM

Preface vii

File processing is the subject of Chapter 8. Section 8.1 can be covered sooner for an intro duction to reading and writing text files. The remainder of the chapter gives addi tional material for practical applications.

Chapters 9 and 10 introduce the object-oriented features of C++. Chapter 9 introduces class design and implementation. Chapter 10 covers inheritance and polymorphism.

Four additional chapters are available on the Web. They can be used individu- ally for a capstone chapter, or they can be combined for teaching a two-semester course. (They can also be incorporated into a custom print version of the text; ask your Wiley sales representative for details.)

Chapter 11. Recursion Chapter 12. Sorting and Searching Chapter 13. Lists, Stacks, and Queues Chapter 14. Sets, Maps, and Priority Queues

Figure 1 shows the dependencies between the chapters.

Figure 1 Chapter Dependencies

Section 8.1 contains the core

material

Sections 7.1 and 7.4 are

required

A gentle introduction to recursion

is optional

1. Introduction

2. Fundamental Data Types

3. Decisions

4. Loops

5. Functions

6. Arrays and Vectors

9. Classes 11. Recursion 12. Sorting and Searching

8. Streams

13. Lists, Stacks, and Queues

14. Sets, Maps, Priority Queues

7. Pointers

10. Inheritance

Fundamentals

Online

cfe2_fm_pi_xxvi.indd 7 10/28/10 5:08 PM

viii Walkthrough

a Walkthrough of the Learning aids The pedagogical elements in this book work together to focus on and reinforce key concepts and fundamental principles of programming, with additional tips and detail organized to support and deepen these fundamentals. In addition to traditional fea- tures, such as chapter objectives and a wealth of exercises, each chapter contains ele- ments geared to today’s visual learner.

4.3 The for Loop 143

4.4 The for Loop It often happens that you want to execute a sequence of statements a given number of times. You can use a while loop that is controlled by a counter, as in the following example:

counter = 1; // Initialize the counter while (counter <= 10) // Check the counter { cout << counter << endl; counter++; // Update the counter }

Because this loop type is so common, there is a special form for it, called the for loop (see Syntax 4.2).

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Some people call this loop count-controlled. In contrast, the while loop of the preceding section can be called an event-controlled loop because it executes until an event occurs (for example, when the balance reaches the target). Another commonly-used term for a count-controlled loop is definite. You know from the outset that the loop body will be executed a definite number of times––ten times in our example. In contrast, you do not know how many iterations it takes to accumulate a target balance. Such a loop is called indefinite.

The for loop neatly groups the initialization, condi- tion, and update expressions together. However, it is important to realize that these expressions are not exe- cuted together (see Figure 3).

The for loop is used when a value runs from a starting point to an ending point with a constant increment or decrement.

You can visualize the for loop as an orderly sequence of steps.

Syntax 4.2 for Statement

for (int i = 5; i <= 10; i++) { sum = sum + i; }

This loop executes 6 times. See page 147.

These three expressions should be related.

See page 147.

This initialization happens once before the loop starts.

The loop is executed while this condition is true.

This update is executed after each iteration.

The variable i is defined only in this for loop.

See page 144.

Annotations explain required components and point to more information on common errors or best practices associated with the syntax.

Throughout each chapter, margin notes show where new concepts are introduced and provide an outline of key ideas.

Annotated syntax boxes provide a quick, visual overview of new language constructs.

Like a variable in a computer program, a parking space has an identifier and a contents.

Analogies to everyday objects are used to explain the nature and behavior of concepts such as variables, data types, loops, and more.

cfe2_fm_pi_xxvi.indd 8 10/28/10 5:08 PM

Walkthrough ix

6.5 Problem Solving: Discovering Algorithms by Manipulating Physical Objects 277

Now how does that help us with our problem, switching the first and the second half of the array?

Let’s put the first coin into place, by swapping it with the fifth coin. However, as C++ programmers, we will say that we swap the coins in positions 0 and 4:

Table 3 Variable Names in C++

Variable Name Comment

can_volume1 Variable names consist of letters, numbers, and the underscore character.

x In mathematics, you use short variable names such as x or y. This is legal in C++, but not very common, because it can make programs harder to understand (see Programming Tip 2.1 on page 38).

! Can_volume Caution: Variable names are case-sensitive. This variable name is different from can_volume.

6pack Error: Variable names cannot start with a number.

can volume Error: Variable names cannot contain spaces.

double Error: You cannot use a reserved word as a variable name.

ltr/fl.oz Error: You cannot use symbols such as / or.

Step 1 Determine the inputs and outputs.

In our sample problem, we have these inputs: • purchase price1 and fuel efficiency1, the price and fuel efficiency (in mpg) of the first car • purchase price2 and fuel efficiency2, the price and fuel efficiency of the second car We simply want to know which car is the better buy. That is the desired output.

H O W T O 1 . 1 Describing an Algorithm with Pseudocode

Before you are ready to write a program in C++, you need to develop an algorithm—a method for arriving at a solution for a particular problem. Describe the algorithm in pseudocode: a sequence of precise steps formulated in English.

For example, consider this problem: You have the choice of buying two cars. One is more fuel efficient than the other, but also more expensive. You know the price and fuel efficiency (in miles per gallon, mpg) of both cars. You plan to keep the car for ten years. Assume a price of $4 per gallon of gas and usage of 15,000 miles per year. You will pay cash for the car and not worry about financing costs. Which car is the better deal?

WO R K E D E X A M P L E 1 . 1 Writing an Algorithm for Tiling a Floor

This Worked Example shows how to develop an algorithm for laying tile in an alternating pattern of colors.

Memorable photos reinforce analogies and help students remember the concepts.

Example tables support beginners with multiple, concrete examples. These tables point out common errors and present another quick reference to the section’s topic.

Problem Solving sections teach techniques for generating ideas and evaluating proposed solutions, often using pencil and paper or other artifacts. These sections emphasize that most of the planning and problem solving that makes students successful happens away from the computer.

How To guides give step-by-step guidance for common programming tasks, emphasizing planning and testing. They answer the beginner’s question, “Now what do I do?” and integrate key concepts into a problem-solving sequence.

Worked Examples apply the steps in the How To to a different example, showing how they can be used to plan, implement, and test a solution to another programming problem.

A recipe for a fruit pie may say to use any kind of fruit. Here, “fruit” is an example of a parameter variable. Apples and cherries are examples of arguments.

pie(fruit) pie(fruit)

Next, we swap the coins in positions 1 and 5:

cfe2_fm_pi_xxvi.indd 9 10/28/10 5:08 PM

x Walkthrough

•

Figure 3 Parameter Passing

1 Function call result1 =

side_length =

2 Initializing function parameter variable result1 =

side_length = 2

3 About to return to the caller result1 =

side_length =

volume = 8

4 After function call result1 = 8

double result1 = cube_volume(2);

double volume = side_length * side_length * side_length; return volume;

double result1 = cube_volume(2);

The parameter variable side_length of the cube_volume function is created. 1 • The parameter variable is initialized with the value of the argument that was

passed in the call. In our case, side_length is set to 2. 2 • The function computes the expression side_length * side_length * side_length,

which has the value 8. That value is stored in the variable volume. 3 • The function returns. All of its variables are removed. The return value is trans-

ferred to the caller, that is, the function calling the cube_volume function. 4

11. Write the for loop of the invtable.cpp program as a while loop. 12. How many numbers does this loop print?

for (int n = 10; n >= 0; n--) { cout << n << endl; }

13. Write a for loop that prints all even numbers between 10 and 20 (inclusive). 14. Write a for loop that computes the sum of the integers from 1 to n. 15. How would you modify the for loop of the invtable.cpp program to print all bal-

ances until the invest ment has doubled?

Practice It Now you can try these exercises at the end of the chapter: R4.2, R4.7, P4.12.

S E L F C H E C K

ch05/cube.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 /** 6 Computes the volume of a cube. 7 @param side_length the side length of the cube 8 @return the volume 9 */

10 double cube_volume(double side_length) 11 { 12 double volume = side_length * side_length * side_length; 13 return volume; 14 } 15 16 int main() 17 { 18 double result1 = cube_volume(2); 19 double result2 = cube_volume(10); 20 cout << "A cube with side length 2 has volume " << result1 << endl; 21 cout << "A cube with side length 10 has volume " << result2 << endl; 22 23 return 0; 24 }

Program Run

A cube with side length 2 has volume 8 A cube with side length 10 has volume 1000

Figure 3 Execution of a for Loop

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Initialize counter1

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Check condition2

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Execute loop body3

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Update counter4

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Check condition again5

counter = 1

counter = 2

Progressive figures trace code segments to help students visualize the program flow. Color is used consistently to make variables and other elements easily recognizable.

Optional engineering exercises engage students with applications from technical fields.

Program listings are carefully designed for easy reading, going well beyond simple color coding. Functions are set off by a subtle outline.

Self-check exercises at the end of each section are designed to make students think through the new material—and can spark discussion in lecture.

Engineering P7.20 Write a program that simulates the control software for a “people mover” system, a set of driverless trains that move in two concentric circular tracks. A set of switches allows trains to switch tracks. In your program, the outer and inner tracks should each be divided into ten segments. Each track segment can contain a train that moves either clockwise or counterclockwise. A train moves to an adjacent segment in its track or, if that segment is occupied, to the adjacent segment in the other track. Define a Segment structure. Each segment has a pointer to the next and previous segments in its track, a pointer to the next and previous seg ments in the other track,

cfe2_fm_pi_xxvi.indd 10 10/28/10 5:08 PM

Walkthrough xi

Hand-Tracing

A very useful technique for understanding whether a program works correctly is called hand-tracing. You simulate the pro- gram’s activity on a sheet of paper. You can use this method with pseudocode or C++ code.

Get an index card, a cocktail napkin, or whatever sheet of paper is within reach. Make a column for each variable. Have the program code ready. Use a marker, such as a paper clip, to mark the current statement. In your mind, execute statements one at a time. Every time the value of a variable changes, cross out the old value and write the new value below the old one.

For example, let’s trace the tax program with the data from the program run on page 95. In lines 13 and 14, tax1 and tax2 are initial- ized to 0.

6 int main() 7 { 8 const double RATE1 = 0.10; 9 const double RATE2 = 0.25;

10 const double RATE1_SINGLE_LIMIT = 32000; 11 const double RATE1_MARRIED_LIMIT = 64000; 12 13 double tax1 = 0; 14 double tax2 = 0; 15

In lines 18 and 22, income and marital_status are initialized by input statements.

16 double income; 17 cout << "Please enter your income: "; 18 cin >> income; 19 20 cout << "Please enter s for single, m for married: "; 21 string marital_status; 22 cin >> marital_status; 23

Because marital_status is not "s", we move to the else branch of the outer if statement (line 36).

Programming Tip 3.6

Hand-tracing helps you understand whether a program works correctly.

marital tax1 tax2 income status

0 0

marital tax1 tax2 income status

0 0 80000 m

Using Undefined Variables

You must define a variable before you use it for the first time. For example, the following sequence of statements would not be legal:

double can_volume = 12 * liter_per_ounce; double liter_per_ounce = 0.0296;

In your program, the statements are compiled in order. When the compiler reaches the first statement, it does not know that liter_per_ounce will be defined in the next line, and it reports an error.

Common Error 2.1

Random Facts provide historical and social information on computing—for interest and to fulfill the “historical and social context” requirements of the ACM/IEEE curriculum guidelines.

According to legend, the first bug was

found in the Mark II, a huge electrome- chanical computer at Harvard Univer- sity. It really was caused by a bug—a moth was trapped in a relay switch.

Actually, from the note that the operator left in the log book next to the moth (see the photo), it appears as if the term “bug” had already been in active use at the time.

The First Bug

The pioneering computer scientist Maurice Wilkes wrote, “Somehow, at the Moore School and afterwards, one had always assumed there would be no particular difficulty in getting pro-

grams right. I can remember the exact instant in time at which it dawned on me that a great part of my future life would be spent finding mistakes in my own programs.”

Random Fact 4.1 The First Bug

A Sorting Algorithm

A sorting algorithm rearranges the elements of a sequence so that they are stored in sorted order. Here is a simple sorting algorithm, called selection sort. Consider sorting the following array values:

[0] [1] [2] [3] [4]

11 9 17 5 12

An obvious first step is to find the smallest element. In this case the smallest element is 5, stored in values[3]. You should move the 5 to the beginning of the array. Of course, there is already an element stored in values[0], namely 11. Therefore you cannot simply move val- ues[3] into values[0] without moving the 11 somewhere else. You don’t yet know where the 11 should end up, but you know for certain that it should not be in values[0]. Simply get it out of the way by swapping it with values[3]:

5 9 17 11 12

Now the first element is in the correct place. In the foregoing figure, the darker color indicates the portion of the array that is already sorted.

Next take the minimum of the remaining entries values[1]...values[4]. That minimum value, 9, is already in the correct place. You don’t need to do anything in this case, simply extend the sorted area by one to the right:

5 9 17 11 12

Repeat the process. The minimum value of the unsorted region is 11, which needs to be swapped with the first value of the unsorted region, 17:

5 9 11 17 12

Special Topic 6.2

Special Topics present optional topics and provide additional explanation of others.

Common Errors describe the kinds of errors that students often make, with an explanation of why the errors occur, and what to do about them.

Programming Tips explain good programming practices, and encourage students to be more productive with tips and techniques such as hand-tracing.

cfe2_fm_pi_xxvi.indd 11 10/28/10 5:09 PM

xii Preface

appendices Appendix A contains a programming style guide. Using a style guide for program- ming assignments benefits students by directing them toward good habits and reduc- ing gratuitous choice. The style guide is available in electronic form so that instruc- tors can modify it to reflect their preferred style.

Appendices B and C summarize C++ reserved words and operators. Appendix D lists character escape sequences and ASCII character code values. Appendix E docu- ments all of the library functions and classes used in this book.

Additional appendices available from the book’s companion web site include an expanded version of Appendix E that includes the functions and classes used in the four optional chapters, 11–14, plus appendices that cover number systems, bit and shift operations, and a comparison of C++ and Java.

Student and Instructor resources The following resources for students and instructors can be obtained by visiting www.wiley.com/college/horstmann. Two companion web sites accompany the book— one for students, and a password-protected site for instructors only.

• Additional exercises geared to the scientific and engineering problem domains • Worked Examples that apply the problem-solving steps in the book to other

realistic examples (identified in the book by an icon, ) • Source code for all examples in the book • Solutions to all review and programming exercises (for instructors only) • Lecture presentation slides (in PowerPoint format) that summarize each chapter

and include code listings and figures from the book (for instructors only) • A test bank that focuses on skills, not just terminology (for instructors only) • Four additional chapters on recursion, sorting and searching, and data structures • The programming style guide in electronic form

W O R K E D E X A M P L E 2 . 1 Computing Travel Time

In this Worked Example, we develop a hand calculation to compute the time that a robot requires to retrieve an item from rocky terrain.

Pointers in the book describe what students will find on the Web.

Visit the C++ for Everyone companion web sites at www.wiley.com/college/horstmann.

cfe2_fm_pi_xxvi.indd 12 10/28/10 5:09 PM

www.wiley.com/college/horstmann

acknowledgments xiii

acknowledgments Many thanks to Beth Golub, Tom Kulesa, Andre Legaspi, Elizabeth Mills, Michael Berlin, and Lisa Gee at John Wiley & Sons, and to the team at Publishing Services for their hard work and sup port for this book project. An especially deep acknowledg- ment and thanks to Cindy Johnson, who, through enormous patience and attention to detail, made this book a reality. We would also like to thank Jonathan Tolstedt, North Dakota State University, for his high-quality solutions; Brent Seales, Univer- sity of Kentucky, for revising and enhancing the test bank; and to Evan Gallagher, Polytechnic Institute of New York University, for his creative PowerPoint slides.

We are very grateful to the many individuals who reviewed and/or class tested this and the first edition of the book. We value their many valuable suggestions for improvement. They include:

Charles D. Allison, Utah Valley State College Fred Annexstein, University of Cincinnati Stefano Basagni, Northeastern University Noah D. Barnette, Virginia Tech Susan Bickford, Tallahassee Community College Ronald D. Bowman, University of Alabama, Huntsville Peter Breznay, University of Wisconsin, Green Bay Richard Cacace, Pensacola Junior College, Pensacola Kuang-Nan Chang, Eastern Kentucky University Joseph DeLibero, Arizona State University Subramaniam Dharmarajan, Arizona State University Mary Dorf, University of Michigan Marty Dulberg, North Carolina State University William E. Duncan, Louisiana State University John Estell, Ohio Northern University Waleed Farag, Indiana University of Pennsylvania Stephen Gilbert, Orange Coast Community College Kenneth Gitlitz, New Hampshire Technical Institute Daniel Grigoletti, DeVry Institute of Technology, Tinley Park Barbara Guillott, Louisiana State University Charles Halsey, Richland College Jon Hanrath, Illinois Institute of Technology Neil Harrison, Utah Valley University Jurgen Hecht, University of Ontario Steve Hodges, Cabrillo College Jackie Jarboe, Boise State University Debbie Kaneko, Old Dominion University Mir Behrad Khamesee, University of Waterloo Sung-Sik Kwon, North Carolina Central University

cfe2_fm_pi_xxvi.indd 13 10/28/10 5:09 PM

xiv acknowledgments

Lorrie Lehman, University of North Carolina, Charlotte Cynthia Lester, Tuskegee University Yanjun Li, Fordham University W. James MacLean, University of Toronto LindaLee Massoud, Mott Community College Charles W. Mellard, DeVry Institute of Technology, Irving Ethan V. Munson, University of Wisconsin, Milwaukee Philip Regalbuto, Trident Technical College Don Retzlaff, University of North Texas Jeff Ringenberg, University of Michigan, Ann Arbor John P. Russo, Wentworth Institute of Technology Kurt Schmidt, Drexel University Brent Seales, University of Kentucky William Shay, University of Wisconsin, Green Bay Michele A. Starkey, Mount Saint Mary College William Stockwell, University of Central Oklahoma Jonathan Tolstedt, North Dakota State University Boyd Trolinger, Butte College Muharrem Uyar, City College of New York Mahendra Velauthapillai, Georgetown University Kerstin Voigt, California State University, San Bernardino David P. Voorhees, Le Moyne College Salih Yurttas, Texas A&M University

A special thank you to all of our class testers:

Pani Chakrapani and the students of the University of Redlands Jim Mackowiak and the students of Long Beach City College, LAC Suresh Muknahallipatna and the students of the University of Wyoming Murlidharan Nair and the students of the Indiana University of South Bend Harriette Roadman and the students of New River Community College David Topham and the students of Ohlone College Dennie Van Tassel and the students of Gavilan College

cfe2_fm_pi_xxvi.indd 14 10/28/10 5:09 PM

C o n T E n T S

PrEfaCE v

SPECIaL fEaTurES xx

InTroDuCTIon 1

1.1 What is Programming 2

1.2 The anatomy of a Computer 3

1.3 Machine Code and Programming Languages 6

1.4 Becoming familiar with your Programming Environment 7

1.5 analyzing your first Program 11

1.6 Errors 15

1.7 Problem Solving: algorithm Design 17

funDaMEnTaL DaTa TyPES 29

2.1 variables 30

2.2 arithmetic 40

2.3 Input and output 48

2.4 Problem Solving: first Do It By Hand 52

2.5 Strings 56

DECISIonS 75

3.1 The if Statement 76

3.2 Comparing numbers and Strings 82

3.3 Multiple alternatives 90

3.4 nested Branches 94

3.5 Problem Solving: flowcharts 99

3.6 Problem Solving: Test Cases 102

3.7 Boolean variables and operators 103

3.8 application: Input validation 109

LooPS 131

4.1 The while Loop 132

4.2 Problem Solving: Hand-Tracing 139

4.3 The for Loop 142

4.4 The do Loop 148

4.5 Processing Input 150

cHAPter 1

cHAPter 2

cHAPter 3

cHAPter 4

cfe2_fm_pi_xxvi.indd 15 10/28/10 5:09 PM

xvi Contents

4.6 Problem Solving: Storyboards 154

4.7 Common Loop algorithms 157

4.8 nested Loops 165

4.9 random numbers and Simulations 168

funCTIonS 193

5.1 functions as Black Boxes 194

5.2 Implementing functions 196

5.3 Parameter Passing 199

5.4 return values 202

5.5 functions Without return values 206

5.6 Problem Solving: reusable functions 208

5.7 Problem Solving: Stepwise refinement 210

5.8 variable Scope and Global variables 218

5.9 reference Parameters 220

5.10 recursive functions (optional) 226

arrayS anD vECTorS 249

6.1 arrays 250

6.2 Common array algorithms 256

6.3 arrays and functions 265

6.4 Problem Solving: adapting algorithms 269

6.5 Problem Solving: Discovering algorithms by Manipulating

Physical objects 274

6.6 Two-Dimensional arrays 278

6.7 vectors 284

PoInTErS 307

7.1 Defining and using Pointers 308

7.2 arrays and Pointers 314

7.3 C and C++ Strings 320

7.4 Dynamic Memory allocation 325

7.5 arrays and vectors of Pointers 329

7.6 Problem Solving: Draw a Picture 332

7.7 Structures and Pointers (optional) 336

STrEaMS 351

8.1 reading and Writing Text files 352

8.2 reading Text Input 358

cHAPter 5

cHAPter 6

cHAPter 7

cHAPter 8

cfe2_fm_pi_xxvi.indd 16 10/28/10 5:09 PM

Contents xvii

Available online at www.wiley.com/college/horstmann.

8.3 Writing Text output 361

8.4 String Streams 363

8.5 Command Line arguments 365

8.6 random access and Binary files 372

CLaSSES 389

9.1 object-oriented Programming 390

9.2 Specifying the Public Interface of a Class 392

9.3 Data Members 395

9.4 Member functions 397

9.5 Constructors 403

9.6 Problem Solving: Tracing objects 407

9.7 Problem Solving: Discovering Classes 414

9.8 Separate Compilation 417

9.9 Pointers to objects 422

InHErITanCE 441

10.1 Inheritance Hierarchies 442

10.2 Implementing Derived Classes 446

10.3 overriding Member functions 451

10.4 virtual functions and Polymorphism 455

rECurSIon (WEB onLy)

11.1 Triangle numbers

11.2 Thinking recursively

11.3 recursive Helper functions

11.4 The Efficiency of recursion

11.5 Permutations

11.6 Mutual recursion

SorTInG anD SEarCHInG (WEB onLy)

12.1 Selection Sort

12.2 Profiling the Selection Sort algorithm

12.3 analyzing the Performance of the Selection Sort algorithm

12.4 Merge Sort

12.5 analyzing the Merge Sort algorithm

12.6 Searching

cHAPter 9

cHAPter 10

cHAPter 11

cHAPter 12

cfe2_fm_pi_xxvi.indd 17 10/28/10 5:09 PM

www.wiley.com/college/horstmann

xviii Contents

Available online at www.wiley.com/college/horstmann.

LISTS, STaCkS, anD QuEuES (WEB onLy)

13.1 using Linked Lists

13.2 Implementing Linked Lists

13.3 The Efficiency of List, array, and vector operations

13.4 Stacks and Queues

SETS, MaPS, anD PrIorITy QuEuES (WEB onLy)

14.1 Sets

14.2 Binary Search Trees

14.3 Maps

14.4 Priority Queues

14.5 Heaps

aPPEnDIx a C++ LanGuaGE CoDInG GuIDELInES 481

aPPEnDIx B rESErvED WorD SuMMary 489

aPPEnDIx C oPEraTor SuMMary 491

aPPEnDIx D CHaraCTEr CoDES 493

aPPEnDIx E C++ LIBrary SuMMary 495

aPPEnDIx f nuMBEr SySTEMS (WEB onLy) aPPEnDIx G BIT anD SHIfT oPEraTIonS (WEB onLy) aPPEnDIx H a C++ / Java CoMParISon (WEB onLy)

GLoSSary 499

InDEx 507

CrEDITS 529

cHAPter 13

cHAPter 14

APPendiceS

cfe2_fm_pi_xxvi.indd 18 10/28/10 5:09 PM

www.wiley.com/college/horstmann

Contents xix

SynTax BoxES

assignment 34

C++ Program 12 Class Definition 393 Comparisons 83 Constructor with Base-Class Initializer 451

Defining an array 251 Defining a vector 285 Derived-Class Definition 448 Dynamic Memory allocation 325

for Statement 144 function Definition 197

if Statement 78 Input Statement 48

Member function Definition 400

output Statement 13

Pointer Syntax 310

Two-Dimensional array Definition 279

variable Definition 31

while Statement 133 Working with file Streams 354

AlPHAbeticAl liSt oF

cfe2_fm_pi_xxvi.indd 19 10/28/10 5:09 PM

xx Special features

C H a P T E r

Available online at www.wiley.com/college/horstmann.

Programming Tips

Special Topics random facts

Backup Copies 11 Escape Sequences 14 The EnIaC and the Dawn of Computing 5

Standards organizations 7

Choose Descriptive variable names 38

Do not use Magic numbers 39 Spaces in Expressions 46

numeric Types in C++ 38 numeric ranges and

Precisions 39 Casts 46 Combining assignment

and arithmetic 47

The Pentium floating-Point Bug 47

International alphabets and unicode 61

Brace Layout 79 always use Braces 80 Tabs 81 avoid Duplication in Branches 82 Compile With Zero Warnings 85 Hand-Tracing 97 Make a Schedule and

Make Time for unexpected Problems 103

The Selection operator 81 Lexicographic ordering

of Strings 86 The switch Statement 93 Short-Circuit Evaluation

of Boolean operators 108 De Morgan’s Law 108

The Denver airport Luggage Handling System 89

artificial Intelligence 112

use for Loops for Their Intended Purpose only 147

Choose Loop Bounds That Match your Task 147

Count Iterations 147 flowcharts for Loops 149

Clearing the failure State 153 The Loop-and-a-Half Problem

and the break Statement 153 redirection of Input and

output 154

The first Bug 138 Software Piracy 172

function Comments 199 Don’t Modify Parameter

variables 201 keep functions Short 216 Tracing functions 216 Stubs 217 avoid Global variables 220 Prefer return values to

reference Parameters 225

function Declarations 203 Constant references 225

The Explosive Growth of Personal Computers 230

Common Errors

How Tos and Worked Examples

1 Introduction omitting Semicolons 14 Misspelling Words 16

Describing an algorithm with Pseudocode 20

Writing an algorithm for Tiling a floor

2 fundamental Data Types

using undefined variables 37 using uninitialized variables 37 unintended Integer Division 43 unbalanced Parentheses 44 forgetting Header files 45 roundoff Errors 45

Computing Travel Time Carrying out Computations 54 Computing the Cost

of Stamps

3 Decisions a Semicolon after the if Condition 80

Confusing = and == 85 Exact Comparison of floating-

Point numbers 86 The Dangling else Problem 98 Combining Multiple

relational operators 107 Confusing && and ||

Conditions 107

Implementing an if Statement 87

Extracting the Middle

4 Loops Infinite Loops 136 Don’t Think “are We

There yet?” 137 off-by-one Errors 137

Writing a Loop 162 Credit Card Processing

5 functions Missing return value 203

Implementing a function 204 Matching and replacing Parts

of a String using a Debugger Calculating a Course Grade Thinking recursively 229

cfe2_fm_pi_xxvi.indd 20 10/28/10 5:09 PM

www.wiley.com/college/horstmann

Special Features xxi

Available online at www.wiley.com/college/horstmann.

Programming Tips

Special Topics Random Facts

Backup Copies 11 Escape Sequences 14 The ENIAC and the Dawn of Computing 5

Standards Organizations 7

Choose Descriptive Variable Names 38

Do Not Use Magic Numbers 39 Spaces in Expressions 46

Numeric Types in C++ 38 Numeric Ranges and

Precisions 39 Casts 46 Combining Assignment

and Arithmetic 47

The Pentium Floating-Point Bug 47

International Alphabets and Unicode 61

Brace Layout 79 Always Use Braces 80 Tabs 81 Avoid Duplication in Branches 82 Compile With Zero Warnings 85 Hand-Tracing 97 Make a Schedule and

Make Time for Unexpected Problems 103

The Selection Operator 81 Lexicographic Ordering

of Strings 86 The switch Statement 93 Short-Circuit Evaluation

of Boolean Operators 108 De Morgan’s Law 108

The Denver Airport Luggage Handling System 89

Artificial Intelligence 112

Use for Loops for Their Intended Purpose Only 147

Choose Loop Bounds That Match Your Task 147

Count Iterations 147 Flowcharts for Loops 149

Clearing the Failure State 153 The Loop-and-a-Half Problem

and the break Statement 153 Redirection of Input and

Output 154

The First Bug 138 Software Piracy 172

Function Comments 199 Don’t Modify Parameter

Variables 201 Keep Functions Short 216 Tracing Functions 216 Stubs 217 Avoid Global Variables 220 Prefer Return Values to

Reference Parameters 225

Function Declarations 203 Constant References 225

The Explosive Growth of Personal Computers 230

Common Errors

How Tos and Worked Examples

1 Introduction Omitting Semicolons 14 Misspelling Words 16

Describing an Algorithm with Pseudocode 20

Writing an Algorithm for Tiling a Floor

2 Fundamental Data Types

Using Undefined Variables 37 Using Uninitialized Variables 37 Unintended Integer Division 43 Unbalanced Parentheses 44 Forgetting Header Files 45 Roundoff Errors 45

Computing Travel Time Carrying out Computations 54 Computing the Cost

of Stamps

3 Decisions A Semicolon After the if Condition 80

Confusing = and == 85 Exact Comparison of Floating-

Point Numbers 86 The Dangling else Problem 98 Combining Multiple

Relational Operators 107 Confusing && and ||

Conditions 107

Implementing an if Statement 87

Extracting the Middle

4 Loops Infinite Loops 136 Don’t Think “Are We

There Yet?” 137 Off-by-One Errors 137

Writing a Loop 162 Credit Card Processing

5 Functions Missing Return Value 203

Implementing a Function 204 Matching and Replacing Parts

of a String Using a Debugger Calculating a Course Grade Thinking Recursively 229

cfe2_fm_pi_xxvi.indd 21 11/9/10 9:55 AM

www.wiley.com/college/horstmann

xxii Special features

C H a P T E r

Available online at www.wiley.com/college/horstmann.

Programming Tips

Special Topics random facts

use arrays for Sequences of related values 255

Prefer vectors over arrays 289

Sorting with the C++ Library 263 a Sorting algorithm 263 Binary Search 264 Constant array Parameters 269

an Early Internet Worm 255 The first Programmer 290

use a Separate Definition for Each Pointer variable 313

Program Clearly, not Cleverly 319

Pointers and references 314 using a Pointer to Step

Through an array 318 Constant Pointers 320 Working with C Strings 323

Embedded Systems 336

Encryption algorithms 368 Databases and Privacy 377

all Data Members Should Be Private; Most Member functions Should Be Public 402

const Correctness 402 Make Parallel vectors into

vectors of objects 416

Initializer Lists 405 overloading 406 Destructors and resource

Management 424

Electronic voting Machines 412 open Source and

free Software 426

use a Single Class for variation in values, Inheritance for variation in Behavior 450

Don’t use Type Tags 462

Calling the Base-Class Constructor 451

virtual Self-Calls 463

The Limits of Computation 469

Common Errors

How Tos and Worked Examples

6 arrays and vectors Bounds Errors 254 omitting the Column

Size of a Two- Dimensional array Parameter 284

Working with arrays 271 rolling the Dice a World Population Table

7 Pointers Confusing Pointers with the Data to Which They Point 313

returning a Pointer to a Local variable 319

Dangling Pointers 328 Memory Leaks 328

Working with Pointers 334 Producing a Mass Mailing

8 Streams Processing Text files 369 Looking for for

Duplicates

9 Classes forgetting a Semicolon 395 Trying to Call a Constructor 405

Implementing a Class 409 Implementing a

Bank account Class

10 Inheritance Private Inheritance 449 replicating Base-Class

Members 450 forgetting the Base-

Class name 455 Slicing an object 462

Developing an Inheritance Hierarchy 464

Implementing an Employee Hierarchy for Payroll Processing

cfe2_fm_pi_xxvi.indd 22 10/28/10 5:09 PM

www.wiley.com/college/horstmann

Special Features xxiii

Available online at www.wiley.com/college/horstmann.

Programming Tips

Special Topics Random Facts

Use Arrays for Sequences of Related Values 255

Prefer Vectors over Arrays 289

Sorting with the C++ Library 263 A Sorting Algorithm 263 Binary Search 264 Constant Array Parameters 269

An Early Internet Worm 255 The First Programmer 290

Use a Separate Definition for Each Pointer Variable 313

Program Clearly, Not Cleverly 319

Pointers and References 314 Using a Pointer to Step

Through an Array 318 Constant Pointers 320 Working with C Strings 323

Embedded Systems 336

Encryption Algorithms 368 Databases and Privacy 377

All Data Members Should Be Private; Most Member Functions Should Be Public 402

const Correctness 402 Make Parallel Vectors into

Vectors of Objects 416

Initializer Lists 405 Overloading 406 Destructors and Resource

Management 424

Electronic Voting Machines 412 Open Source and

Free Software 426

Use a Single Class for Variation in Values, Inheritance for Variation in Behavior 450

Don’t Use Type Tags 462

Calling the Base-Class Constructor 451

Virtual Self-Calls 463

The Limits of Computation 469

Common Errors

How Tos and Worked Examples

6 Arrays and Vectors Bounds Errors 254 Omitting the Column

Size of a Two- Dimensional Array Parameter 284

Working with Arrays 271 Rolling the Dice A World Population Table

7 Pointers Confusing Pointers with the Data to Which They Point 313

Returning a Pointer to a Local Variable 319

Dangling Pointers 328 Memory Leaks 328

Working with Pointers 334 Producing a Mass Mailing

8 Streams Processing Text Files 369 Looking for for

Duplicates

9 Classes Forgetting a Semicolon 395 Trying to Call a Constructor 405

Implementing a Class 409 Implementing a

Bank Account Class

10 Inheritance Private Inheritance 449 Replicating Base-Class

Members 450 Forgetting the Base-

Class Name 455 Slicing an Object 462

Developing an Inheritance Hierarchy 464

Implementing an Employee Hierarchy for Payroll Processing

cfe2_fm_pi_xxvi.indd 23 11/9/10 9:55 AM

www.wiley.com/college/horstmann

xxiv Special features

C H a P T E r

Available online at www.wiley.com/college/horstmann.

Programming Tips

Special Topics random facts

Library functions for Sorting and Binary Search

The Quicksort algorithm Defining an ordering for

Sorting objects

Cataloging your necktie Collection

reverse Polish notation

Defining an ordering for Container Elements

Constant Iterators Discrete Event Simulations

Common Errors

How Tos and Worked Examples

11 recursion (WEB onLy) Infinite recursion Tracing Through recursive

functions

12 Sorting and Searching (WEB onLy)

13 Lists, Stacks, and Queues (WEB onLy)

14 Sets, Maps, and Priority Queues (WEB onLy)

cfe2_fm_pi_xxvi.indd 24 10/28/10 5:09 PM

www.wiley.com/college/horstmann

Special Features xxv

Available online at www.wiley.com/college/horstmann.

Programming Tips

Special Topics Random Facts

Library Functions for Sorting and Binary Search

The Quicksort Algorithm Defining an Ordering for

Sorting Objects

Cataloging Your Necktie Collection

Reverse Polish Notation

Defining an Ordering for Container Elements

Constant Iterators Discrete Event Simulations

Common Errors

How Tos and Worked Examples

11 Recursion (WEB ONLY) Infinite Recursion Tracing Through Recursive

Functions

12 Sorting and Searching (WEB ONLY)

13 Lists, Stacks, and Queues (WEB ONLY)

14 Sets, Maps, and Priority Queues (WEB ONLY)

cfe2_fm_pi_xxvi.indd 25 11/9/10 9:56 AM

www.wiley.com/college/horstmann

This page intentionally left blank

1C h a p t e r

I n t r o d u C t I o n

to learn about the architecture of computers

to learn about machine languages and higher-level programming languages

to become familiar with your compiler

to compile and run your first C++ program

to recognize compile-time and run-time errors

to describe an algorithm with pseudocode

to understand the activity of programming

C h a p t e r G o a l s

C h a p t e r C o n t e n t s

1.1 What Is ProgrammIng? 2

1.2 the anatomy of a ComPuter 3

Random Fact 1.1: the enIaC and the dawn of Computing 5

1.3 maChIne Code and ProgrammIng Languages 6

Random Fact 1.2: standards organizations 7

1.4 BeComIng famILIar WIth your ProgrammIng envIronment 7

Programming Tip 1.1: Backup Copies 11

1.5 anaLyzIng your fIrst Program 11

Syntax 1.1: C++ program 12 Syntax 1.2: output statement 13

Common Error 1.1: omitting semicolons 14 Special Topic 1.1: escape sequences 14

1.6 errors 15

Common Error 1.2: Misspelling Words 16

1.7 ProBLem soLvIng: aLgorIthm desIgn 17

How To 1.1: describing an algorithm with pseudocode 20

Worked Example 1.1: Writing an algorithm for tiling a Floor

cfe2_ch01_p1_28.indd 1 10/25/10 1:03 PM

Just as you gather tools, study a project, and make a plan for tackling it, in this chapter you will gather up the basics you need to start learning to program. after a brief introduction to computer hardware, software, and programming in general, you will learn how to write and run your first C++ program. You will also learn how to diagnose and fix programming errors, and how to use pseudocode to describe an algorithm—a step-by-step description of how to solve a problem—as you plan your programs.

1.1 What Is programming? You have probably used a computer for work or fun. Many people use computers for everyday tasks such as electronic banking or writing a term paper. Computers are good for such tasks. They can handle repetitive chores, such as totaling up numbers or placing words on a page, without getting bored or exhausted.

The flexibility of a computer is quite an amazing phenomenon. The same machine can balance your checkbook, print your term paper, and play a game. In contrast, other machines carry out a much nar rower range of tasks; a car drives and a toaster toasts. Computers can carry out a wide range of tasks because they execute different programs, each of which directs the computer to work on a specific task.

The computer itself is a machine that stores data (numbers, words, pictures), inter- acts with devices (the monitor, the sound system, the printer), and executes programs. A computer program tells a computer, in minute detail, the sequence of steps that are needed to fulfill a task. The physical computer and peripheral devices are collectively called the hardware. The programs the computer executes are called the software.

Today’s computer programs are so sophisticated that it is hard to believe that they are composed of extremely primitive operations. A typical operation may be one of the following:

• Put a red dot at this screen position. • Add up these two numbers. • If this value is negative, continue the program at a certain instruction.

The computer user has the illusion of smooth interaction because a program contains a huge number of such operations, and because the computer can execute them at great speed.

The act of designing and implementing computer programs is called program- ming. In this book, you will learn how to program a computer—that is, how to direct the computer to execute tasks.

To write a computer game with motion and sound effects or a word processor that supports fancy fonts and pictures is a complex task that requires a team of many highly skilled programmers. Your first programming efforts will be more mundane. The concepts and skills you learn in this book form an important foundation, and you should not be disappointed if your first programs do not rival the sophis ticated software that is familiar to you. Actually, you will find that there is an immense thrill even in sim ple programming tasks. It is an amazing experience to see the computer precisely and quickly carry out a task that would take you hours of drudgery, to

Computers execute very basic instructions in rapid succession.

a computer program is a sequence of instructions and decisions.

programming is the act of designing and implementing computer programs.

make small changes in a program that lead to immediate improvements, and to see the computer become an extension of your mental powers.

1. What is required to play music on a computer? 2. Why is a CD player less flexible than a computer? 3. What does a computer user need to know about programming in order to play a

video game?

Practice It Now you can try these exercises at the end of the chapter: R1.1, R1.4.

1.2 the anatomy of a Computer To understand the programming process, you need to have a rudimentary under- standing of the building blocks that make up a computer. We will look at a personal computer. Larger computers have faster, larger, or more powerful components, but they have fundamentally the same design.

At the heart of the computer lies the central processing unit (CPU) (see Figure 1). It consists of a sin gle chip, or a small number of chips. A computer chip (integrated circuit) is a component with a plastic or metal housing, metal connectors, and inside wiring made principally from silicon. For a CPU chip, the inside wiring is enor- mously complicated. For example, the Pentium chip (a popular CPU for personal computers at the time of this writing) is composed of several million structural ele- ments, called transistors.

The CPU performs program control and data processing. That is, the CPU locates and executes the program instructions; it carries out arithmetic operations such as addition, subtraction, multiplication, and division; it fetches data from external mem- ory or devices and stores data back.

The computer stores data and programs. There are two kinds of storage. Primary storage is made from memory chips: electronic circuits that can store data, provided they are supplied with electric power. Secondary storage, usually a hard disk, pro- vides less expensive storage that persists without elec tricity. A hard disk consists of rotating platters, which are coated with a magnetic material, and read/write heads, which can detect and change the magnetic flux on the platters (see Figure 2).

s e L f C h e C k

the central processing unit (Cpu) performs program control and data processing.

storage devices include memory and secondary storage.

figure 1 Central processing unit

cfe2_ch01_p1_28.indd 2 10/25/10 1:03 PM

1.2 the anatomy of a Computer 3

make small changes in a program that lead to immediate improvements, and to see the computer become an extension of your mental powers.

1. What is required to play music on a computer? 2. Why is a CD player less flexible than a computer? 3. What does a computer user need to know about programming in order to play a

video game?

Practice It Now you can try these exercises at the end of the chapter: R1.1, R1.4.

s e L f C h e C k

the central processing unit (Cpu) performs program control and data processing.

storage devices include memory and secondary storage.

figure 1 Central processing unit

cfe2_ch01_p1_28.indd 3 10/25/10 1:03 PM

4 Chapter 1 Introduction

figure 2 a hard disk

Programs and data are typically stored on the hard disk and loaded into memory when the program starts. The program then updates the data in memory and writes the modified data back to the hard disk.

To interact with a human user, a computer requires peripheral devices. The com- puter transmits infor mation (called output) to the user through a display screen, speakers, and printers. The user can enter information (called input) by using a key- board or a pointing device such as a mouse.

Some computers are self-contained units, whereas others are interconnected through networks. Through the network cabling, the computer can read data and programs from central storage locations or send data to other computers. For the user of a networked computer it may not even be obvious which data reside on the computer itself and which are transmitted through the network.

figure 3 schematic design of a personal Computer

Printer

Mouse

Keyboard

Ports

CPU

Memory

Disk Controller

Hard disk

CD/DVD drive

Monitor

Speakers

Internet

Graphics card

Sound card

Network card

cfe2_ch01_p1_28.indd 4 10/25/10 1:03 PM

1.2 the anatomy of a Computer 5

Figure 3 gives a schematic overview of the architecture of a personal computer. Program instructions and data (such as text, numbers, audio, or video) are stored on the hard disk, on an optical disk such as a DVD, or elsewhere on the network. When a program is started, it is brought into memory, where the CPU can read it. The CPU reads the program one instruction at a time. As directed by these instructions, the CPU reads data, modifies it, and stores it. Some program instructions will cause the CPU to place dots on the display screen or printer or to vibrate the speaker. As these actions happen many times over and at great speed, the human user perceives images and sound. Some program instructions read user input from the keyboard or mouse. The program analyzes the nature of these inputs and then executes the next appropri- ate instruction.

4. Where is a program stored when it is not currently running? 5. Which part of the computer carries out arithmetic operations, such as addition

and multiplication?

Practice It Now you can try these exercises at the end of the chapter: R1.2, R1.3.

s e L f C h e C k

the enIaC (electronic numerical integrator

and computer) was the first usable electronic computer. It was designed by J. presper eckert and John Mauchly at the university of pennsylvania and was completed in 1946—two years before transistors were invented. the computer was housed in a large room and consisted of many cabinets con- taining about 18,000 vacuum tubes (see Figure 2). Vacuum tubes burned out at the rate of several tubes per day. an attendant with a shopping cart full of tubes constantly made the rounds and replaced defective ones. the com- puter was programmed by connecting wires on panels. each wir ing configura- tion would set up the computer for a particular problem. to have the com- puter work on a different problem, the wires had to be replugged.

Work on the enIaC was supported by the u.s. army, which was interested in computations of ballistic tables that would give the trajectory of a projec- tile, depending on the wind resis tance, initial velocity, and atmospheric con- ditions. to compute the trajecto ries,

one must find the numerical solu- tions of certain differential equations; hence the name “numerical integra- tor”. Before machines like the enIaC were developed, humans did this kind

of work, and until the 1950s the word “computer” referred to these people. the enIaC was later used for peace- ful purposes, such as the tabulation of u.s. Census data.

figure 4 the enIaC

Random Fact 1.1 the enIaC and the dawn of Computing

cfe2_ch01_p1_28.indd 5 10/25/10 1:03 PM

6 Chapter 1 Introduction

1.3 Machine Code and programming languages On the most basic level, computer instructions are extremely primitive. The proces- sor executes machine instructions. A typical sequence of machine instructions is

1. Move the contents of memory location 40000 into the CPU. 2. If that value is > 100, continue with the instruction that is stored in memory

location 11280.

Actually, machine instructions are encoded as numbers so that they can be stored in memory. On a Pen tium processor, this sequence of instruction is encoded as the sequence of numbers

161 40000 45 100 127 11280 On a processor from a different manufacturer, the encoding would be different. When this kind of pro cessor fetches this sequence of numbers, it decodes them and executes the associated sequence of com mands.

How can we communicate the command sequence to the computer? The simplest method is to place the actual numbers into the computer memory. This is, in fact, how the very earliest computers worked. However, a long program is composed of thousands of individual commands, and it is a tedious and error-prone affair to look up the numeric codes for all commands and place the codes manually into memory. As already mentioned, computers are really good at automating tedious and error- prone activi ties. It did not take long for computer scientists to realize that the com- puters themselves could be har nessed to help in the programming process.

Computer scientists devised high level programming lan guages that allow programmers to describe tasks, using a syn tax that is more closely related to the prob- lems to be solved. In this book, we will use the C++ programming language, which was developed by Bjarne Stroustrup in the 1980s.

Over the years, C++ has grown by the addition of many features. A standardization process culminated in the publi cation of the international C++ standard in 1998. A minor update to the standard was issued in 2003, and a major revi sion is expected to come to fruition around 2011. At this time, C++ is the most commonly used language for develop ing system software such as databases and operating systems. Just as importantly, C++ is increasingly used for program ming “embedded systems”, small computers that control devices such as automobile engines or cellular telephones.

Here is a typical statement in C++: if (int_rate > 100) { cout << "Interest rate error"; }

This means, “If the interest rate is over 100, display an error message”. A special com- puter program, a compiler, translates this high-level description into machine instruc- tions for a particular processor.

High-level languages are independent of the underlying hardware. C++ instruc- tions work equally well on an Intel Pentium and a processor in a cell phone. Of course, the compiler-generated machine instruc tions are different, but the program- mer who uses the compiler need not worry about these differences.

Computer programs are stored as machine instructions in a code that depends on the processor type.

Bjarne Stroustrup

C++ is a general- purpose language that is in widespread use for systems and embedded programming.

high-level programming languages are independent of the processor.

6. Is the compiler a part of the computer hardware or software? 7. Does a person who uses a computer for office work ever run a compiler? 8. What are the most important uses for C++?

Practice It Now you can try these exercises at the end of the chapter: R1.5.

1.4 Becoming Familiar with Your programming environment

Many students find that the tools they need as programmers are very different from the software with which they are familiar. You should spend some time making your- self familiar with your programming environment. Because computer systems vary widely, this book can only give an outline of the steps you need to follow. It is a good idea to participate in a hands-on lab, or to ask a knowledgeable friend to give you a tour.

step 1 Start the C++ development environment.

Computer systems differ greatly in this regard. On many computers there is an inte- grated development environment in which you can write and test your programs. On other computers you first launch an editor, a program that functions like a word processor, in which you can enter your C++ instructions; then open a console win- dow and type commands to execute your program. You need to find out how to get started with your environment.

step 2 Write a simple program.

The traditional choice for the very first program in a new programming language is a program that dis plays a simple greeting: “Hello, World!”. Let us follow that tradi- tion. Here is the “Hello, World!” pro gram in C++:

s e L f C h e C k

two standards orga- nizations, the ameri-

can national standards Institute (ansI) and the International organization for standardization (Iso), have jointly developed the definitive standard for the C++ language.

Why have standards? You encoun ter the benefits of standardization every day. When you buy a light bulb, you can be assured that it fits in the socket without having to measure the socket at home and the bulb in the store. In

fact, you may have experi enced how painful the lack of stan dards can be if you have ever purchased a flashlight with nonstand ard bulbs. replacement bulbs for such a flashlight can be dif- ficult and expen sive to obtain.

the ansI and Iso standards organi- zations are associations of industry professionals who develop standards for everything from car tires and credit card shapes to programming languages. having a standard for a programming language such as C++

means that you can take a program that you developed on one system with one manufacturer’s compiler to a different system and be assured that it will continue to work.

Random Fact 1.2 standards organizations

set aside some time to become familiar with the programming environment that you will use for your class work.

cfe2_ch01_p1_28.indd 6 10/25/10 1:03 PM

1.4 Becoming Familiar with Your programming environment 7

6. Is the compiler a part of the computer hardware or software? 7. Does a person who uses a computer for office work ever run a compiler? 8. What are the most important uses for C++?

Practice It Now you can try these exercises at the end of the chapter: R1.5.

1.4 Becoming Familiar with Your programming environment

step 1 Start the C++ development environment.

step 2 Write a simple program.

s e L f C h e C k

two standards orga- nizations, the ameri-

can national standards Institute (ansI) and the International organization for standardization (Iso), have jointly developed the definitive standard for the C++ language.

means that you can take a program that you developed on one system with one manufacturer’s compiler to a different system and be assured that it will continue to work.

Random Fact 1.2 standards organizations

set aside some time to become familiar with the programming environment that you will use for your class work.

cfe2_ch01_p1_28.indd 7 10/25/10 1:03 PM

8 Chapter 1 Introduction

#include <iostream>

using namespace std;

int main() { cout << "Hello, World!" << endl; return 0; }

We will examine this program in the next section. No matter which programming environment you use, you begin your activity by

typing the pro gram statements into an editor window. Create a new file and call it hello.cpp, using the steps that are appropriate for your

environment. (If your environment requires that you supply a project name in addi- tion to the file name, use the name hello for the project.) Enter the program instruc- tions exactly as they are given above. Alternatively, locate an electronic copy in the source files for the programs in this book and paste it into your editor.

As you write this program, pay careful attention to the various symbols, and keep in mind that C++ is case sensitive. You must enter upper- and lowercase letters exactly as they appear in the program listing. You cannot type MAIN or Endl. If you are not careful, you will run into problems—see Common Error 1.2 on page 16.

step 3 Compile and run the program.

The process for building and running a C++ program depends greatly on your pro- gramming environ ment. In some integrated development environments, you simply push a button. In other environments, you may have to type commands. When you run the test program, the message

Hello, World!

will appear somewhere on the screen (see Figures 5 and 6).

an editor is a program for entering and modifying text, such as a C++ program.

C++ is case sensitive. You must be careful about distinguishing between upper- and lowercase letters.

the compiler translates C++ programs into machine code.

figure 5 running the hello program in an Integrated development environment

It is useful to know what goes on behind the scenes when your program gets built. First, the compiler translates the C++ source code (that is, the statements that you wrote) into machine instructions. The machine code contains only the translation of the code that you wrote. That is not enough to actually run the program. To display a string on a window, quite a bit of low-level activity is necessary. The implementors of your C++ development environment provided a library that includes the definition of cout and its functionality. A library is a collection of code that has been pro- grammed and translated by someone else, ready for you to use in your program. (More complicated pro grams are built from more than one machine code file and more than one library.) A program called the linker takes your machine code and the necessary parts from the C++ library and builds an execut able file. (Figure 7 gives an overview of these steps.) The executable file is usually called hello.exe or hello, depending on your computer system. You can run the executable program even after you exit the C++ development environment.

step 4 Organize your work.

As a programmer, you write programs, try them out, and improve them. You store your programs in files. Files have names, and the rules for legal names differ from one system to another. Some systems allow spaces in file names; others don’t. Some dis- tinguish between upper- and lowercase letters; others don’t. Most C++ compilers require that C++ files end in an extension .cpp, .cxx, .cc, or .C; for example, test.cpp.

Files are stored in folders or directories. A folder can contain files as well as other folders, which themselves can contain more files and folders (see Figure 8). This hier- archy can be quite large, and you need not be concerned with all of its branches.

the linker combines machine code with library code into an executable program.

figure 7 From source Code to executable program

CompilerEditor Linker

Executable ProgramSource File

Library files

Machine code

cfe2_ch01_p1_28.indd 8 10/25/10 1:03 PM

1.4 Becoming Familiar with Your programming environment 9

figure 6 Compiling and running the hello program in a Console Window

step 4 Organize your work.

the linker combines machine code with library code into an executable program.

figure 7 From source Code to executable program

CompilerEditor Linker

Executable ProgramSource File

Library files

Machine code

cfe2_ch01_p1_28.indd 9 10/25/10 1:03 PM

10 Chapter 1 Introduction

figure 8 a Folder hierarchy

However, you should create folders for organizing your work. It is a good idea to make a separate folder for your programming class. Inside that folder, make a sepa- rate folder for each assignment.

Some programming environments place your programs into a default location if you don’t specify a folder yourself. In that case, you need to find out where those files are located.

Be sure that you understand where your files are located in the folder hierarchy. This information is essential when you submit files for grading, and for making backup copies.

You will spend many hours creating and improving C++ programs. It is easy to delete a file by acci dent, and occasionally files are lost because of a computer mal- function. To avoid the frustration of recre ating lost files, get in the habit of making backup copies of your work on a memory stick or on another computer.

9. How are programming projects stored on a computer? 10. What do you expect to see when you load an executable file into your text

editor? 11. What do you do to protect yourself from data loss when you work on program-

ming projects?

Practice It Now you can try these exercises at the end of the chapter: R1.6.

develop a strategy for keeping backup copies of your work before disaster strikes.

s e L f C h e C k

Backup Copies

Backing up files on a memory stick is an easy and convenient stor- age method for many people. Another increasingly popular form of backup is Internet file storage. Here are a few pointers to keep in mind. • Back up often. Backing up a file takes only a few seconds, and

you will hate yourself if you have to spend many hours recreating work that you could have saved easily. I rec ommend that you back up your work once every thirty minutes.

• Rotate backups. Use more than one directory for backups, and rotate them. That is, first back up onto the first directory. Then back up onto the second directory. Then use the third, and then go back to the first. That way you always have three recent backups. If your recent changes made matters worse, you can then go back to the older version.

• Pay attention to the backup direction. Backing up involves copying files from one place to another. It is important that you do this right—that is, copy from your work location to the backup location. If you do it the wrong way, you will overwrite a newer file with an older version.

• Check your backups once in a while. Double-check that your backups are where you think they are. There is nothing more frustrating than to find out that the backups are not there when you need them.

• Relax, then restore. When you lose a file and need to restore it from backup, you are likely to be in an unhappy, nervous state. Take a deep breath and think through the recovery process before you start. It is not uncommon for an agitated computer user to wipe out the last backup when trying to restore a damaged file.

1.5 analyzing Your First program In this section, we will analyze the first C++ program in detail. Here again is the source code:

ch01/hello.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 int main() 6 { 7 cout << "Hello, World!" << endl; 8 return 0; 9 }

The first line, #include <iostream>

tells the compiler to include a service for “stream input/output”. You will learn in Chapter 8 what a stream is. For now, you should simply remember to add this line into all programs that perform input or output.

programming tip 1.1

cfe2_ch01_p1_28.indd 10 10/25/10 1:03 PM

1.5 analyzing Your First program 11

Backup Copies

you will hate yourself if you have to spend many hours recreating work that you could have saved easily. I rec ommend that you back up your work once every thirty minutes.

1.5 analyzing Your First program In this section, we will analyze the first C++ program in detail. Here again is the source code:

ch01/hello.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 int main() 6 { 7 cout << "Hello, World!" << endl; 8 return 0; 9 }

The first line, #include <iostream>

programming tip 1.1

cfe2_ch01_p1_28.indd 11 10/25/10 1:03 PM

12 Chapter 1 Introduction

syntax 1.1 C++ program

#include <iostream>

using namespace std;

int main() { cout << "Hello, World!" << endl; return 0; }

Every program includes one or more headers for required services such as input/output.

Every program that uses standard services requires this directive.

Every program has a main function.

Replace this statement when you

write your own programs.

The statements of a function are enclosed in braces. Each statement ends in a semicolon.

See page 14.

The next line, using namespace std;

tells the compiler to use the “standard namespace”. Namespaces are a mechanism for avoiding naming conflicts in large programs. You need not be concerned about namespaces. For the programs that you will be writing in this book, you will always use the standard namespace. Simply add using namespace std; at the top of every pro- gram that you write, just below the #include directives.

The construction int main() { ... return 0; }

defines a function called main that “returns” an “integer” (that is, a whole number without a fractional part, called int in C++) with value 0. This value indicates that the program finished successfully. A function is a collection of programming instruc- tions that carry out a particular task. Every C++ program must have a main func tion. Most C++ programs contain other functions besides main, but it will take us until Chapter 5 to dis cuss functions and return values.

For now, it is a good idea to consider all these parts as the plumbing that is neces- sary to write a simple program. Simply place the code that you want to execute inside the braces of the main function. (The basic structure of a C++ program is shown in Syntax 1.1.)

To display values on the screen, you use an entity called cout and the << operator (sometimes called the insertion operator). For example, the statement

cout << 39 + 3;

displays the number 42.

every C++ program contains a function called main.

use cout and the << operator to display values on the screen.

The statement cout << "Hello";

displays the string Hello. A string is a sequence of characters. You must enclose the contents of a string inside quotation marks so that the compiler knows you literally mean the text "Hello" and not a function with the same name.

You can send more than one item to cout. Use a << before each one of them. For example,

cout << "The answer is " << 6 * 7;

displays The answer is 42 (in C++, the * denotes multiplication). The endl symbol denotes an end of line marker. When this marker is sent to cout,

the cursor is moved to the first column in the next screen row. If you don’t use an end of line marker, then the next displayed item will simply follow the current string on the same line. In this program we only printed one item, but in general we will want to print multiple items, and it is a good habit to end all lines of output with an end of line marker.

Finally, note that each statement in C++ ends in a semicolon, just as every English sentence ends in a period.

12. How do you modify the hello.cpp program to greet you instead? 13. What is wrong with this program?

#include <iostream> using namespace std; int main() { cout << Goodbye, World! << endl; return 0; }

14. What does the following sequence of statements print?

cout << "Hello"; cout << "World";

enclose text strings in quotation marks.

use + to add two numbers and * to multiply two numbers.

send endl to cout to end a line of displayed output.

end each statement with a semicolon.

s e L f C h e C k

cfe2_ch01_p1_28.indd 12 10/25/10 1:03 PM

1.5 analyzing Your First program 13

syntax 1.2 output statement

cout << "The answer is" << 6 * 7 << endl;

Sending endl to cout starts a new line.

Data sent to cout is displayed in a console window.

You can send strings and numbers

to cout.

Add a << symbol before each item to be displayed.

Strings are enclosed in quotation marks.

* denotes multiplication.

The statement cout << "Hello";

You can send more than one item to cout. Use a << before each one of them. For example,

cout << "The answer is " << 6 * 7;

displays The answer is 42 (in C++, the * denotes multiplication). The endl symbol denotes an end of line marker. When this marker is sent to cout,

Finally, note that each statement in C++ ends in a semicolon, just as every English sentence ends in a period.

12. How do you modify the hello.cpp program to greet you instead? 13. What is wrong with this program?

#include <iostream> using namespace std; int main() { cout << Goodbye, World! << endl; return 0; }

14. What does the following sequence of statements print?

cout << "Hello"; cout << "World";

enclose text strings in quotation marks.

use + to add two numbers and * to multiply two numbers.

send endl to cout to end a line of displayed output.

end each statement with a semicolon.

s e L f C h e C k

cfe2_ch01_p1_28.indd 13 10/25/10 1:03 PM

14 Chapter 1 Introduction

15. What does the following statement print? cout << 2 * 2 << 2;

16. What does the following statement print? cout << "Hello" << endl << endl << "World";

Practice It Now you can try these exercises at the end of the chapter: R1.7, P1.1, P1.2.

omitting semicolons

In C++ every statement must end in a semicolon. Forgetting to type a semicolon is a common error. It confuses the compiler because the compiler uses the semicolon to find where one statement ends and the next one starts. The compiler does not use line ends or closing braces to recognize the ends of statements. For example, the compiler con siders

cout << "Hello, World!" << endl return 0;

a single statement, as if you had written

cout << "Hello, World!" << endl return 0;

and then it doesn’t understand that statement, because it does not expect the word return in the middle of an output command. The remedy is simple. Just scan every statement for a terminat- ing semicolon, just as you would check that every English sentence ends in a period.

escape sequences

How can you display a string containing quotation marks, such as

Hello, "World"

You can’t use

cout << "Hello, "World"";

As soon as the compiler reads "Hello, ", it thinks the string is finished, and then it gets all confused about World. Compilers have a one-track mind, and if a simple analysis of the input doesn’t make sense to them, they just refuse to go on, and they report an error. In contrast, a human would probably realize that the second and third quotation marks were supposed to be part of the string.

Well, how do we then display quotation marks on the screen? The designers of C++ pro- vided an escape hatch. Mark each quotation mark with a backslash character (\), like this:

cout << "Hello, \"World\"";

The sequence \" denotes a literal quote, not the end of a string. Such a sequence is called an escape sequence.

There are a few other escape sequences. If you actually want to show a backslash on the display, you use the escape sequence \\. The statement

cout << "Hello\\World";

prints

Hello\World

Common error 1.1

special topic 1.1

Finally, the escape sequence \n denotes a newline character that starts a new line on the screen. The command

cout << "Hello, World!\n";

has exactly the same effect as

cout << "Hello, World!" << endl;

1.6 errors Programming languages follow very strict conven- tions. When you talk to another person, and you scramble or omit a word or two, your conversa tion partner will usually still understand what you have to say. But when you make an error in a C++ program, the compiler will not try to guess what you meant. (This is actually a good thing. If the compiler were to guess wrongly, the resulting program would do the wrong thing—quite possibly with disastrous effects.) In this section, you will learn how to cope with errors in your program.

Experiment a little with the hello.cpp program. What happens if you make a typing error such as

cot << "Hello, World!" << endl; cout << "Hello, World! << endl; cout << "Hollo, World!" << endl;

In the first case, the compiler will complain that it has no clue what you mean by cot. The exact wording of the error message is dependent on the compiler, but it might be some thing like “Undefined symbol cot”. This is a compile-time error or syntax error. Something is wrong according to the language rules, and the compiler finds it. When the compiler finds one or more errors, it will not translate the program to machine code, and as a consequence there is no program to run. You must fix the error and compile again. It is common to go through several rounds of fixing compile-time errors before compilation succeeds for the first time.

If the compiler finds an error, it will not simply stop and give up. It will try to report as many errors as it can find, so you can fix them all at once. Sometimes, how- ever, one error throws it off track. This is likely to happen with the error in the second line. Since the programmer forgot the closing quote, the compiler will keep looking for the end of the string. In such cases, it is common for the compiler to emit bogus error reports for neighboring lines. You should fix only those error messages that make sense to you and then recompile.

The error in the third line is of a different kind. The program will compile and run, but its output will be wrong. It will print

Hollo, World!

This is a run-time error. The program is syntactically correct and does something, but it doesn’t do what it is supposed to do. The compiler cannot find the error, and it must be flushed out when the program runs, by testing it and carefully looking at its

Programmers spend a fair amount of time fixing compile- time and run-time errors.

a compile-time error is a violation of the programming language rules that is detected by the compiler.

a run-time error causes a program to take an action that the programmer did not intend.

cfe2_ch01_p1_28.indd 14 10/25/10 1:03 PM

1.6 errors 15

Finally, the escape sequence \n denotes a newline character that starts a new line on the screen. The command

cout << "Hello, World!\n";

has exactly the same effect as

cout << "Hello, World!" << endl;

Experiment a little with the hello.cpp program. What happens if you make a typing error such as

cot << "Hello, World!" << endl; cout << "Hello, World! << endl; cout << "Hollo, World!" << endl;

The error in the third line is of a different kind. The program will compile and run, but its output will be wrong. It will print

Hollo, World!

Programmers spend a fair amount of time fixing compile- time and run-time errors.

a compile-time error is a violation of the programming language rules that is detected by the compiler.

a run-time error causes a program to take an action that the programmer did not intend.

cfe2_ch01_p1_28.indd 15 10/25/10 1:03 PM

16 Chapter 1 Introduction

output. Because run-time errors are caused by logical flaws in the program, they are often called logic errors. Some kinds of run-time errors are so severe that they gener- ate an exception: a signal from the processor that aborts the program with an error message. For example, if your program includes the statement cout << 1 / 0; your program may terminate with a “divide by zero” exception.

During program development, errors are unavoidable. Once a program is longer than a few lines, it requires superhuman concentration to enter it correctly without slipping up once. You will find yourself omitting semicolons or quotes more often than you would like, but the compiler will track down these problems for you.

Run-time errors are more troublesome. The compiler will not find them—in fact, the compiler will cheerfully translate any program as long as its syntax is correct— but the resulting program will do some thing wrong. It is the responsibility of the program author to test the program and find any run-time errors. Program testing is an important topic that you will encounter many times in this book.

17. Suppose you omit the () characters after main from the hello.cpp program. Will you get a compile-time error or a run-time error?

18. When you used your computer, you may have experienced a program that “crashed” (quit spontane ously) or “hung” (failed to respond to your input). Is that behavior a compile-time error or a run-time error?

19. Why can’t you test a program for run-time errors when it has compiler errors?

Practice It Now you can try these exercises at the end of the chapter: R1.10, R1.11.

misspelling Words

If you accidentally misspell a word, strange things may happen, and it may not always be completely obvious from the error messages what went wrong. Here is a good example of how simple spelling errors can cause trouble:

#include <iostream>

using namespace std;

int Main() { cout << "Hello, World!" << endl; return 0; }

This code defines a function called Main. The compiler will not consider this to be the same as the main function, because Main starts with an uppercase letter and the C++ language is case- sensitive. Upper- and lowercase letters are considered to be completely different from each other, and to the compiler Main is no better match for main than rain. The compiler will compile your Main function, but when the linker is ready to build the executable file, it will com plain about the missing main function and refuse to link the program. Of course, the message “miss- ing main function” should give you a clue where to look for the error.

If you get an error message that seems to indicate that the compiler is on the wrong track, it is a good idea to check for spelling and capitalization. In C++, most names use only lowercase letters. If you misspell the name of a symbol (for example out instead of cout), the compiler will complain about an “undefined symbol”. This error mes sage is usually a good clue that you made a spelling error.

the programmer is responsible for inspecting and testing the program to guard against run-time errors.

s e L f C h e C k

Common error 1.2

cfe2_ch01_p1_28.indd 16 10/25/10 1:03 PM

1.7 problem solving: algorithm design 17

1.7 problem solving: algorithm design You will soon learn how to program calculations and decision making in C++. But before we look at the mechanics of implementing computations in the next chapter, let’s consider the planning process that pre cedes implementation.

You may have run across advertisements that encourage you to pay for a computerized service that matches you up with a love part- ner. Think how this might work. You fill out a form and send it in. Others do the same. The data are processed by a computer program. Is it rea sonable to assume that the computer can perform the task of finding the best match for you? Suppose your younger brother, not the com puter, had all the forms on his desk. What instructions could you give him? You can’t say, “Find the best-looking person of the opposite sex who likes inline skating and browsing the Internet”. There is no objective standard for good looks, and your brother’s opinion (or that of a computer program analyzing the digitized photo) will likely be different from yours. If you can’t give written instructions for some one to solve the problem, there is no way the computer can magically solve the problem. The computer can only do what you tell it to do. It just does it faster, without getting bored or exhausted.

Now consider the following investment problem:

You put $10,000 into a bank account that earns 5 percent interest per year. How many years does it take for the account balance to be double the original?

Could you solve this problem by hand? Sure. You figure out the balance as follows:

year interest balance 0 10000 1 10000.00 x 0.05 = 500.00 10000.00 + 500.00 = 10500.00 2 10500.00 x 0.05 = 525.00 10500.00 + 525.00 = 11025.00 3 11025.00 x 0.05 = 551.25 11025.00 + 551.25 = 11576.25 4 11576.25 x 0.05 = 578.81 11576.25 + 578.81 = 12155.06

You keep going until the balance is at least $20,000. Then the last number in the year column is the answer.

Of course, carrying out this computation is intensely boring to you or your younger brother. But computers are very good at carrying out repetitive calcula- tions quickly and flawlessly. What is important to the computer is a description of the steps for finding the solution. Each step must be clear and unam biguous, requiring no guesswork. Here is such a description:

Start with a year value of 0, a column for the interest, and a balance of $10,000.

year interest balance 0 10000

Finding the perfect partner is not a problem that a computer can solve.

cfe2_ch01_p1_28.indd 17 10/25/10 1:03 PM

18 Chapter 1 Introduction

Repeat the following steps while the balance is less than $20,000 Add 1 to the year value. Compute the interest as balance x 0.05 (i.e., 5 percent interest) Add the interest to the balance.

year interest balance 0 10000 1 500.00 10500.00

14 942.82 19799.32 15 989.96 20789.28

Report the final year value as the answer.

Of course, these steps are not yet in a language that a computer can understand, but you will soon learn how to formulate them in C++. This informal description is called pseudocode.

There are no strict requirements for pseudocode because it is read by human read- ers, not a computer program. Here are the kinds of pseudocode statements that we will use in this book:

• Use statements such as the following to describe how a value is set or changed:

total cost = purchase price + operating cost

or Multiply the balance value by 1.05.

or Remove the first and last character from the word.

• You can describe decisions and repetitions as follows:

If total cost 1 < total cost 2 While the balance is less than $20,000 For each picture in the sequence

Use indentation to indicate which statements should be selected or repeated:

For each car operating cost = 10 x annual fuel cost total cost = purchase price + operating cost

Here, the indentation indicates that both statements should be executed for each car.

• Indicate results with statements such as:

Choose car1. Report the final year value as the answer.

The exact wording is not important. What is important is that pseudocode describes a sequence of steps that is

• Unambiguous • Executable • Terminating

pseudocode is an informal description of a sequence of steps for solving a problem.

figure 9 the software development process

A method is unambiguous when there are precise instructions for what to do at each step and where to go next. There is no room for guesswork or cre- ativity. A method is executable when each step can be carried out in practice. Had we asked to use the actual interest rate that will be charged in years to come, and not a fixed rate of 5 percent per year, our method would not have been executable, because there is no way for anyone to know what that interest rate will be. A method is terminating if it will eventually come to an end. In our example, it requires a bit of thought to see that the method will not go on forever: With every step, the balance goes up by at least $500, so eventually it must reach $20,000.

A sequence of steps that is unambiguous, executable, and terminating is called an algorithm. We have found an algorithm to solve our investment problem, and thus we can find the solution by programming a computer. The existence of an algorithm is an essential prerequisite for programming a task. You need to first discover and describe an algorithm for the task that you want to solve before you start program- ming (see Figure 9).

20. Suppose the interest rate was 20 percent. How long would it take for the invest- ment to double?

21. Suppose your cell phone carrier charges you $29.95 for up to 300 minutes of calls, and $0.45 for each additional minute, plus 12.5 percent taxes and fees. Give an algorithm to compute the monthly charge from a given number of minutes.

22. Consider the following pseudocode for finding the most attractive photo from a sequence of photos:

Pick the first photo and call it "the best so far". For each photo in the sequence

If it is more attractive than the "best so far" Discard "the best so far". Call this photo "the best so far". The photo called "the best so far" is the most attractive photo in the sequence.

Is this an algorithm that will find the most attractive photo?

Understand the problem

Develop and describe an algorithm

Translate the algorithm

into C++

Test the algorithm with simple inputs

Compile and test your program

An algorithm is a recipe for finding a solution.

an algorithm for solving a problem is a sequence of steps that is unambiguous, executable, and terminating.

s e L f C h e C k

cfe2_ch01_p1_28.indd 18 10/25/10 1:03 PM

1.7 problem solving: algorithm design 19

figure 9 the software development process

20. Suppose the interest rate was 20 percent. How long would it take for the invest- ment to double?

22. Consider the following pseudocode for finding the most attractive photo from a sequence of photos:

Pick the first photo and call it "the best so far". For each photo in the sequence

If it is more attractive than the "best so far" Discard "the best so far". Call this photo "the best so far". The photo called "the best so far" is the most attractive photo in the sequence.

Is this an algorithm that will find the most attractive photo?

Understand the problem

Develop and describe an algorithm

Translate the algorithm

into C++

Test the algorithm with simple inputs

Compile and test your program

An algorithm is a recipe for finding a solution.

an algorithm for solving a problem is a sequence of steps that is unambiguous, executable, and terminating.

s e L f C h e C k

cfe2_ch01_p1_28.indd 19 10/25/10 1:03 PM

20 Chapter 1 Introduction

23. Suppose each photo in Self Check 22 had a price tag. Give an algorithm for find- ing the most expen sive photo.

24. Suppose you have a random sequence of black and white marbles and want to rearrange it so that the black and white marbles are grouped together. Consider this algorithm:

Repeat until sorted Locate the first black marble that is preceded by a white marble, and switch them.

What does the algorithm do with the sequence mlmll? Spell out the steps until the algorithm stops.

25. Suppose you have a random sequence of colored marbles. Consider this pseudocode:

Repeat until sorted Locate the first marble that is preceded by a marble of a different color, and switch them.

Why is this not an algorithm?

Practice It Now you can try these exercises at the end of the chapter: R1.13, R1.14.

step 1 Determine the inputs and outputs.

step 2 Break down the problem into smaller tasks.

For each car, we need to know the total cost of driving it. Let’s do this computation separately for each car. Once we have the total cost for each car, we can decide which car is the better deal.

The total cost for each car is purchase price + operating cost.

We assume a constant usage and gas price for ten years, so the operating cost depends on the cost of driving the car for one year.

The operating cost is 10 x annual fuel cost. The annual fuel cost is price per gallon x annual fuel consumed.

The annual fuel consumed is annual miles driven / fuel efficiency. For example, if you drive the car for 15,000 miles and the fuel efficiency is 15 miles/gallon, the car consumes 1,000 gallons.

h o W t o 1 . 1 describing an algorithm with Pseudocode

step 3 Describe each subtask in pseudocode.

In your description, arrange the steps so that any intermediate values are computed before they are needed in other computations. For example, list the step

total cost = purchase price + operating cost

after you have computed operating cost. Here is the algorithm for deciding which car to buy:

For each car, compute the total cost as follows: annual fuel consumed = annual miles driven / fuel efficiency annual fuel cost = price per gallon x annual fuel consumed operating cost = 10 x annual fuel cost total cost = purchase price + operating cost If total cost1 < total cost2 Choose car1. Else Choose car2.

step 4 Test your pseudocode by working a problem.

We will use these sample values:

Car 1: $25,000, 50 miles/gallon Car 2: $20,000, 30 miles/gallon

Here is the calculation for the cost of the first car:

annual fuel consumed = annual miles driven / fuel efficiency = 15000 / 50 = 300 annual fuel cost = price per gallon x annual fuel consumed = 4 x 300 = 1200 operating cost = 10 x annual fuel cost = 10 x 1200 = 12000 total cost = purchase price + operating cost = 25000 + 12000 = 37000

Similarly, the total cost for the second car is $40,000. Therefore, the output of the algorithm is to choose car 1.

define “computer program” and programming.

• Computers execute very basic instructions in rapid succession. • A computer program is a sequence of instructions and decisions. • Programming is the act of designing and implementing computer programs.

describe the components of a computer.

• The central processing unit (CPU) performs program control and data processing.

• Storage devices include memory and secondary storage.

W o r k e d e x a M p l e 1 . 1 Writing an algorithm for tiling a floor

This Worked Example shows how to develop an algorithm for laying tile in an alternating pattern of colors.

C h a p t e r s u M M a r Y

cfe2_ch01_p1_28.indd 20 10/25/10 1:03 PM

Chapter summary 21

23. Suppose each photo in Self Check 22 had a price tag. Give an algorithm for find- ing the most expen sive photo.

24. Suppose you have a random sequence of black and white marbles and want to rearrange it so that the black and white marbles are grouped together. Consider this algorithm:

Repeat until sorted Locate the first black marble that is preceded by a white marble, and switch them.

What does the algorithm do with the sequence mlmll? Spell out the steps until the algorithm stops.

25. Suppose you have a random sequence of colored marbles. Consider this pseudocode:

Repeat until sorted Locate the first marble that is preceded by a marble of a different color, and switch them.

Why is this not an algorithm?

Practice It Now you can try these exercises at the end of the chapter: R1.13, R1.14.

step 1 Determine the inputs and outputs.

step 2 Break down the problem into smaller tasks.

For each car, we need to know the total cost of driving it. Let’s do this computation separately for each car. Once we have the total cost for each car, we can decide which car is the better deal.

The total cost for each car is purchase price + operating cost.

We assume a constant usage and gas price for ten years, so the operating cost depends on the cost of driving the car for one year.

The operating cost is 10 x annual fuel cost. The annual fuel cost is price per gallon x annual fuel consumed.

The annual fuel consumed is annual miles driven / fuel efficiency. For example, if you drive the car for 15,000 miles and the fuel efficiency is 15 miles/gallon, the car consumes 1,000 gallons.

h o W t o 1 . 1 describing an algorithm with Pseudocode

step 3 Describe each subtask in pseudocode.

In your description, arrange the steps so that any intermediate values are computed before they are needed in other computations. For example, list the step

total cost = purchase price + operating cost

after you have computed operating cost. Here is the algorithm for deciding which car to buy:

step 4 Test your pseudocode by working a problem.

We will use these sample values:

Car 1: $25,000, 50 miles/gallon Car 2: $20,000, 30 miles/gallon

Here is the calculation for the cost of the first car:

Similarly, the total cost for the second car is $40,000. Therefore, the output of the algorithm is to choose car 1.

define “computer program” and programming.

describe the components of a computer.

• The central processing unit (CPU) performs program control and data processing.

• Storage devices include memory and secondary storage.

W o r k e d e x a M p l e 1 . 1 Writing an algorithm for tiling a floor

This Worked Example shows how to develop an algorithm for laying tile in an alternating pattern of colors.

C h a p t e r s u M M a r Y

Available online at www.wiley.com/college/horstmann.

cfe2_ch01_p1_28.indd 21 10/25/10 1:03 PM

www.wiley.com/college/horstmann

22 Chapter 1 Introduction

describe the process of translating high-level languages to machine code.

• Computer programs are stored as machine instructions in a code that depends on the processor type.

• C++ is a general-purpose language that is in widespread use for systems and embedded programming.

• High-level programming languages are independent of the processor.

Become familiar with your C++ programming environment.

• Set aside some time to become familiar with the programming environment that you will use for your class work.

• An editor is a program for entering and modifying text, such as a C++ program. • C++ is case sensitive. You must be careful about distinguishing between upper-

and lowercase letters. • Develop a strategy for keeping backup copies of your work

before disaster strikes. • The compiler translates C++ programs into machine code. • The linker combines machine code with library code into

an executable program.

describe the building blocks of a simple program.

• Every C++ program contains a function called main. • Use cout and the << operator to display values on the screen. • Enclose text strings in quotation marks. • Use + to add two numbers and * to multiply two numbers. • Send endl to cout to end a line of displayed output. • End each statement with a semicolon.

Classify program errors as compile-time and run-time errors.

• A compile-time error is a violation of the programming language rules that is detected by the compiler.

• A run-time error causes a program to take an action that the programmer did not intend.

• The programmer is responsible for inspecting and testing the program to guard against run-time errors.

Write pseudocode for simple algorithms.

• Pseudocode is an informal description of a sequence of steps for solving a problem.

• An algorithm for solving a problem is a sequence of steps that is unambiguous, executable, and terminating.

r1.1 Explain the difference between using a computer program and programming a computer.

r1.2 Which parts of a computer can store program code? Which can store user data?

r1.3 Which parts of a computer serve to give information to the user? Which parts take user input?

r1.4 A toaster is a single-function device, but a computer can be programmed to carry out different tasks. Is your cell phone a single-function device, or is it a programma ble computer? (Your answer will depend on your cell phone model.)

r1.5 Explain two benefits of using C++ over machine code.

r1.6 On your own computer or on your lab computer, find the exact location (folder or directory name) of

a. The sample file hello.cpp (after you saved it in your development environment). b. The standard header file <iostream>.

r1.7 What does this program print? #include <iostream> using namespace std; int main() { cout << "6 * 7 = " << 6 * 7 << endl; return 0; }

r1.8 What does this program print? #include <iostream> using namespace std; int main() { cout << "Hello" << "World" << endl; return 0; }

Pay close attention to spaces.

r1.9 What does this program print? #include <iostream> using namespace std; int main() { cout << "Hello" << endl << "World" << endl; return 0; }

r1.10 Write three versions of the hello.cpp program that have different compile-time errors. Write a version that has a run-time error.

r1.11 How do you discover compile-time errors? How do you discover run-time errors?

r e V I e W e x e r C I s e s

cfe2_ch01_p1_28.indd 22 10/25/10 1:03 PM

review exercises 23

r1.1 Explain the difference between using a computer program and programming a computer.

r1.2 Which parts of a computer can store program code? Which can store user data?

r1.3 Which parts of a computer serve to give information to the user? Which parts take user input?

r1.5 Explain two benefits of using C++ over machine code.

r1.6 On your own computer or on your lab computer, find the exact location (folder or directory name) of

a. The sample file hello.cpp (after you saved it in your development environment). b. The standard header file <iostream>.

r1.7 What does this program print? #include <iostream> using namespace std; int main() { cout << "6 * 7 = " << 6 * 7 << endl; return 0; }

r1.8 What does this program print? #include <iostream> using namespace std; int main() { cout << "Hello" << "World" << endl; return 0; }

Pay close attention to spaces.

r1.9 What does this program print? #include <iostream> using namespace std; int main() { cout << "Hello" << endl << "World" << endl; return 0; }

r1.10 Write three versions of the hello.cpp program that have different compile-time errors. Write a version that has a run-time error.

r1.11 How do you discover compile-time errors? How do you discover run-time errors?

r e V I e W e x e r C I s e s

cfe2_ch01_p1_28.indd 23 10/25/10 1:03 PM

24 Chapter 1 Introduction

r1.12 Write an algorithm to settle the following question: A bank account starts out with $10,000. Interest is compounded monthly at 6 percent per year (0.5 percent per month). Every month, $500 is withdrawn to meet college expenses. After how many years is the account depleted?

r1.13 Consider the question in Exercise R1.12. Suppose the numbers ($10,000, 6 percent, $500) were user selectable. Are there values for which the algorithm you developed would not terminate? If so, change the algorithm to make sure it always terminates.

r1.14 In order to estimate the cost of painting a house, a painter needs to know the surface area of the exterior. Develop an algorithm for computing that value. Your inputs are the width, length, and height of the house, the number of windows and doors, and their dimensions. (Assume the windows and doors have a uniform size.)

r1.15 You want to decide whether you should drive your car to work or take the train. You know the one-way distance from your home to your place of work, and the fuel efficiency of your car (in miles per gallon). You also know the one-way price of a train ticket. You assume the cost of gas at $4 per gallon, and car maintenance at 5 cents per mile. Write an algorithm to decide which commute is cheaper.

r1.16 You want to find out which fraction of your car use is for commuting to work, and which is for personal use. You know the one-way distance from your home to your place of work. For a particular period, you recorded the beginning and ending mile age on the odometer and the number of work days. Write an algorithm to settle this question.

r1.17 In the problem described in How To 1.1 on page 20, you made assumptions about the price of gas and the annual usage. Ideally, you would like to know which car is the better deal without making these assumptions. Why can’t a computer program solve that problem?

r1.18 The value of p can be computed according to the following formula:

π 4

1 1 3

1 5

1 7

1 9

= − + − + − �

Write an algorithm to compute p. Because the formula is an infinite series and an algorithm must stop after a finite number of steps, you should stop when you have the result determined to six significant dig its.

r1.19 Suppose you put your younger brother in charge of backing up your work. Write a set of detailed instructions for carrying out his task. Explain how often he should do it, and what files he needs to copy from which folder to which location. Explain how he should verify that the backup was carried out correctly.

engineering r1.20 The San Francisco taxi commission set the following rates for 2010: • First 1̸5th of a mile: $3.10 • Each additional 1̸5th of a mile or fraction thereof: $0.45 • Each minute of waiting or traffic delay: $0.45

The charge for “waiting or traffic delay” applies instead of the mileage charge for each minute in which the speed is slower than the break-even point. The break-even point is the speed at which 1̸5th of a mile is traversed in one minute. Develop an algorithm that yields the fare for traveling a given distance in a given amount of time, assuming that the taxi moves at a constant speed.

engineering r1.21 Suppose you know how long it takes a car to accelerate from 0 to 60 miles per hour. Develop an algorithm for computing the time required to travel a given distance (for example 5 miles), assuming that the car is initially at rest, accelerates to a given speed (for example 25 miles per hour), and drives at that speed until the distance is covered. Hint: An object that starts at rest and accelerates at a constant rate a for t seconds

travels a distance of .

P1.1 Write a program that prints a greeting of your choice, perhaps in another language.

P1.2 Write a program that prints the message, “Hello, my name is Hal!” Then, on a new line, the program should print the message “What would you like me to do?” Then it’s the user’s turn to type in an input. You haven’t yet learned how to do it—just use the following lines of code:

string user_input; getline(cin, user_input);

Finally, the program should ignore the user input and print the message “I am sorry, I cannot do that.” This program uses the string data type. To access this feature, you must place the line

#include <string>

before the main function. Here is a typical program run. The user input is printed in color.

Hello, my name is Hal! What would you like me to do? Clean up my room I am sorry, I cannot do that.

When running the program, remember to press the Enter key after typing the last word of the input line.

P1.3 Write a program that prints out a message “Hello, my name is Hal!” Then, on a new line, the program should print the message “What is your name?” As in Exercise P1.2, just use the following lines of code:

string user_name; getline(cin, user_name);

Finally, the program should print the message “Hello, user name. I am glad to meet you!” To print the user name, simply use

cout << user_name;

As in Exercise P1.2, you must place the line #include <string>

before the main function. Here is a typical program run. The user input is printed in color.

Hello, my name is Hal! What is your name? Dave Hello, Dave. I am glad to meet you!

p r o G r a M M I n G e x e r C I s e s

cfe2_ch01_p1_28.indd 24 10/25/10 1:03 PM

programming exercises 25

travels a distance of s at= 1 2

P1.1 Write a program that prints a greeting of your choice, perhaps in another language.

string user_input; getline(cin, user_input);

Finally, the program should ignore the user input and print the message “I am sorry, I cannot do that.” This program uses the string data type. To access this feature, you must place the line

#include <string>

before the main function. Here is a typical program run. The user input is printed in color.

Hello, my name is Hal! What would you like me to do? Clean up my room I am sorry, I cannot do that.

When running the program, remember to press the Enter key after typing the last word of the input line.

string user_name; getline(cin, user_name);

Finally, the program should print the message “Hello, user name. I am glad to meet you!” To print the user name, simply use

cout << user_name;

As in Exercise P1.2, you must place the line #include <string>

before the main function. Here is a typical program run. The user input is printed in color.

Hello, my name is Hal! What is your name? Dave Hello, Dave. I am glad to meet you!

p r o G r a M M I n G e x e r C I s e s

cfe2_ch01_p1_28.indd 25 10/25/10 1:03 PM

26 Chapter 1 Introduction

P1.4 Write a program that prints the sum of the first ten positive integers, 1 + 2 + … + 10.

P1.5 Write a program that prints the product of the first ten positive integers, 1 × 2 × … × 10. (Use * for multiplication in C++.)

P1.6 Write a program that prints the balance of an account that earns 5 percent interest per year after the first, second, and third year.

P1.7 Write a program that displays your name inside a box on the terminal screen, like this:

Dave

Do your best to approximate lines with characters such as | - +.

P1.8 Write a program that prints your name in large letters, such as * * ** **** **** * * * * * * * * * * * * ***** * * **** **** * * * * ****** * * * * * * * * * * * * * *

P1.9 Write a program that prints a face similar to (but different from) the following: ///// +-----+ (| o o |) | ^ | | '-' | +-----+

P1.10 Write a program that prints a house that looks exactly like the following: /\ / \ +----+ | .-.| | | || +-+-++

P1.11 Write a program that prints an animal speaking a greeting, similar to (but different from) the following:

P1.12 Write a program that prints three items, such as the names of your three best friends or favorite movies, on three separate lines.

P1.13 Write a program that prints a poem of your choice. If you don’t have a favorite poem, search the Internet for “Emily Dickinson” or “e e cummings”.

P1.14 Write a program that prints an imitation of a Piet Mondrian painting. (Search the Internet if you are not familiar with his paintings.) Use character sequences such as @@@ or ::: to indicate different colors, and use - and | to form lines.

P1.15 Write a program that prints the United States flag, using * and = characters.

engineering P1.16 The atmospheres of the gas giant planets (Jupiter, Saturn, Uranus, and Neptune) are mostly comprised of hydrogen (H2) followed by helium (He). The atmospheres of the terrestrial planets are mostly comprised of carbon dioxide (CO2) followed by nitrogen (N2) for Venus and Mars, and for Earth, mostly Nitrogen (N2) followed by Oxygen (O2). Write a program that outputs this information in a chart with four columns for the type of planet, the name of the planet, its primary atmospheric gas, and secondary atmospheric gas.

engineering P1.17 Write a program that displays the following image, using characters such as / \ - | + for the lines. Write Ω as “Ohm”.

1. A program that reads the data on the CD and sends output to the speakers and the screen.

2. A CD player can do one thing—play music CDs. It cannot execute programs. 3. Nothing. 4. In secondary storage, typically a hard disk. 5. The central processing unit. 6. Software. 7. No—a compiler is intended for programmers, to translate high-level programming

instructions into machine code. 8. System software and embedded systems 9. Programs are stored in files, and files are stored in folders or directories.

10. You will see a seemingly random sequence of characters and symbols. 11. You back up your files and folders. 12. Replace "World" with your name, for example:

cout << "Hello, Harry!" << endl;

13. There are no quotes around Goodbye, World!. 14. It prints HelloWorld, without a space or comma. 15. 42, without a space. 16. Hello

World

with a blank line between the two words. 17. A compile-time error. 18. It is a run-time error. After all, the program had been compiled in order for you to

run it. 19. When a program has compiler errors, no executable file is produced, and there is

nothing to run.

a n s W e r s t o s e l F - C h e C k Q u e s t I o n s

cfe2_ch01_p1_28.indd 26 10/25/10 1:03 PM

answers to self-Check Questions 27

engineering P1.17 Write a program that displays the following image, using characters such as / \ - | + for the lines. Write Ω as “Ohm”.

+ –12 V

5 kΩ

10 kΩ

6 kΩ

4 kΩ

1. A program that reads the data on the CD and sends output to the speakers and the screen.

instructions into machine code. 8. System software and embedded systems 9. Programs are stored in files, and files are stored in folders or directories.

10. You will see a seemingly random sequence of characters and symbols. 11. You back up your files and folders. 12. Replace "World" with your name, for example:

cout << "Hello, Harry!" << endl;

13. There are no quotes around Goodbye, World!. 14. It prints HelloWorld, without a space or comma. 15. 42, without a space. 16. Hello

World

with a blank line between the two words. 17. A compile-time error. 18. It is a run-time error. After all, the program had been compiled in order for you to

run it. 19. When a program has compiler errors, no executable file is produced, and there is

nothing to run.

a n s W e r s t o s e l F - C h e C k Q u e s t I o n s

cfe2_ch01_p1_28.indd 27 10/25/10 1:03 PM

28 Chapter 1 Introduction

20. 4 years: 0 10,000 1 12,000 2 14,400 3 17,280 4 20,736

21. Is the number of minutes at most 300? a. If so, the answer is $29.95 × 1.125 = $33.70. b. If not, 1. Compute the difference: (number of minutes) – 300. 2. Multiply that difference by 0.45. 3. Add $29.95. 4. Multiply the total by 1.125. That is the answer.

22. No. The step If it is more attractive than the "best so far" is not executable because there is no objective way of deciding which of two photos is more attractive.

23. Pick the first photo and call it "the most expensive so far". For each photo in the sequence

If it is more expensive than "the most expensive so far" Discard "the most expensive so far". Call this photo "the most expensive so far". The photo called "the most expensive so far" is the most expensive photo in the sequence.

24. The first black marble that is preceded by a white one is marked in blue: mlmll

Switching the two yields lmmll

The next black marble to be switched is lmmll

yielding lmlml

The next steps are llmml

llmlm

lllmm

Now the sequence is sorted. 25. The sequence doesn’t terminate. Consider the input mlmlm. The first two mar-

bles keep getting switched.

step 1 Determine the inputs and outputs.

The inputs are the floor dimensions (length × width), measured in inches. The output is a tiled floor.

step 2 Break down the problem into smaller tasks.

A natural subtask is to lay one row of tiles. If you can solve that task, then you can solve the problem by lay- ing one row next to the other, starting from a wall, until you reach the opposite wall.

How do you lay a row? Start with a tile at one wall. If it is white, put a black one next to it. If it is black, put a white one next to it. Keep going until you reach the opposite wall. The row will contain width / 4 tiles.

step 3 Describe each subtask in pseudocode.

In the pseudocode, you want to be more precise about exactly where the tiles are placed.

Place a black tile in the northwest corner. While the floor is not yet filled, repeat the following steps: Repeat this step width / 4 – 1 times: Place a tile east of the previously placed tile. If the previously placed tile was white,

pick a black one; otherwise, a white one. Locate the tile at the beginning of the row that you just placed. If there is space to the south, place a tile of

the opposite color below it.

step 4 Test your pseudocode by working a problem.

Suppose you want to tile an area measuring 20 × 12 inches. The first step is to place a black tile in the northwest corner.

Next, alternate four tiles until reaching the east wall. (width / 4 – 1 = 20 / 4 – 1 = 4)

There is room to the south. Locate the tile at the beginning of the completed row. It is black. Place a white tile south of it.

W o r k e d e x a M p l e 1 . 1 Writing an algorithm for tiling a floor

Your task is to tile a rectangular bathroom floor with alternating black and white tiles measur- ing 4 × 4 inches. The floor dimensions, measured in inches, are multiples of 4.

cfe2_ch01_p1_28.indd 28 10/25/10 1:03 PM

2C h a p t e r

F u n d a m e n ta l d ata t y p e s

to be able to define and initialize variables and constants

to understand the properties and limitations of integer and floating-point numbers

to write arithmetic expressions and assignment statements in C++

to appreciate the importance of comments and good code layout

to create programs that read and process input, and display the results

to process strings, using the standard C++ string type

C h a p t e r G o a l s

C h a p t e r C o n t e n t s

2.1 Variables 30

Syntax 2.1: Variable definition 31 Syntax 2.2: assignment 34 Common Error 2.1: using undefined Variables 37 Common Error 2.2: using uninitialized

Variables 37 Programming Tip 2.1: Choose descriptive

Variable names 38 Special Topic 2.1: numeric types in C++ 38 Special Topic 2.2: numeric ranges and

precisions 39 Programming Tip 2.2: do not use magic

numbers 39

2.2 arithmetic 40

Common Error 2.3: unintended Integer division 43

Common Error 2.4: unbalanced parentheses 44 Common Error 2.5: Forgetting header Files 45 Common Error 2.6: roundoff errors 45 Programming Tip 2.3: spaces in expressions 46

Special Topic 2.3: Casts 46 Special Topic 2.4: Combining assignment and

arithmetic 47 Random Fact 2.1: the pentium Floating-

point Bug 47

2.3 input and Output 48

Syntax 2.3: Input statement 48

2.4 prOblem sOlVing: First dO it by hand 52

Worked Example 2.1: Computing travel time How To 2.1: Carrying out Computations 54 Worked Example 2.2: Computing the Cost

of stamps

2.5 strings 56

Random Fact 2.2: International alphabets and unicode 61

cfe2_ch02_p29_74.indd 29 10/27/10 2:29 PM

numbers and character strings (such as the ones on this display board) are important data types in any C++ program. In this chapter, you will learn how to work with numbers and text, and how to write simple programs that perform useful tasks with them.

2.1 Variables When your program carries out computations, you will want to store values so that you can use them later. In a C++ program, you use variables to store values. In this section, you will learn how to define and use variables.

To illustrate the use of variables, we will develop a pro gram that solves the following problem. Soft drinks are sold in cans and bottles. A store offers a six- pack of 12-ounce cans for the same price as a two-liter bottle. Which should you buy? (12 fluid ounces equal approxi- mately 0.355 liters.)

In our program, we will define vari- ables for the number of cans per pack and for the volume of each can. Then we will compute the volume of a six-pack in liters and print out the answer.

2.1.1 Variable definitions

The following statement defines a variable named cans_per_pack: int cans_per_pack = 6;

A variable is a storage location in a computer program. Each variable has a name and holds a value.

A variable is similar to a parking space in a parking garage. The parking space has an identifier (such as “J 053”), and it can hold a vehicle. A variable has a name (such as cans_per_pack), and it can hold a value (such as 6).

What contains more soda? A six-pack of 12-ounce cans or a two-liter bottle?

a variable is a storage location with a name.

Like a variable in a computer program, a parking space has an identifier and a contents.

When defining a variable, you usually want to initialize it. That is, you specify the value that should be stored in the variable. Consider again this variable definition:

int cans_per_pack = 6;

The variable cans_per_pack is initialized with the value 6. Like a parking space that is restricted to a certain type of vehicle (such as a compact

car, motorcycle, or electric vehicle), a variable in C++ stores data of a specific type. C++ supports quite a few data types: numbers, text strings, files, dates, and many others. You must specify the type whenever you define a variable (see Syntax 2.1).

The cans_per_pack variable is an integer, a whole number without a fractional part. In C++, this type is called int. (See the next section for more information about num- ber types in C++.)

Note that the type comes before the variable name: int cans_per_pack = 6;

Table 1 shows variations of variable definitions.

When defining a variable, you usually specify an initial value.

When defining a variable, you also specify the type of its values.

Each parking space is suitable for a particular type of vehicle, just as each variable holds a value of a particular type.

cfe2_ch02_p29_74.indd 30 10/27/10 2:29 PM

2.1 Variables 31

syntax 2.1 Variable definition

int cans_per_pack = 6; A variable definition ends with a semicolon.

Types introduced in this chapter are the number types int and double (page 32) and the string type (page 57).

Supplying an initial value is optional, but it is usually a good idea. See page 37.

See page 33 for rules and examples of valid names.

Use a descriptive variable name.

See page 38.

When defining a variable, you usually want to initialize it. That is, you specify the value that should be stored in the variable. Consider again this variable definition:

int cans_per_pack = 6;

The variable cans_per_pack is initialized with the value 6. Like a parking space that is restricted to a certain type of vehicle (such as a compact

The cans_per_pack variable is an integer, a whole number without a fractional part. In C++, this type is called int. (See the next section for more information about num- ber types in C++.)

Note that the type comes before the variable name: int cans_per_pack = 6;

Table 1 shows variations of variable definitions.

When defining a variable, you usually specify an initial value.

When defining a variable, you also specify the type of its values.

Each parking space is suitable for a particular type of vehicle, just as each variable holds a value of a particular type.

cfe2_ch02_p29_74.indd 31 10/27/10 2:29 PM

32 Chapter 2 Fundamental data types

When a fractional part is required (such as in the number 0.355), we use floating- point numbers. The most commonly used type for floating-point numbers in C++ is called double. (If you want to know the reason, read Special Topic 2.1 on page 38.) Here is the definition of a floating-point variable:

double can_volume = 0.355;

When a value such as 6 or 0.355 occurs in a C++ program, it is called a number literal. Table 2 shows how to write integer and floating-point literals in C++.

2.1.3 Variable names

When you define a variable, you should pick a name that explains its purpose. For example, it is better to use a descriptive name, such as can_volume, than a terse name, such as cv.

In C++, there are a few simple rules for variable names:

1. Variable names must start with a letter or the underscore (_) character, and the remaining characters must be letters, numbers, or underscores.

2. You cannot use other symbols such as $ or %. Spaces are not permitted inside names either. You can use an underscore instead, as in can_volume.

3. Variable names are case-sensitive, that is, Can_volume and can_volume are different names. For that rea son, it is a good idea to use only lowercase letters in variable names.

4. You cannot use reserved words such as double or return as names; these words are reserved exclu sively for their special C++ meanings. (See Appendix B.)

Table 3 shows examples of legal and illegal variable names in C++.

use the double type for floating-point numbers.

table 3 Variable names in C++

Variable name Comment

can_volume1 Variable names consist of letters, numbers, and the underscore character.

x In mathematics, you use short variable names such as x or y. This is legal in C++, but not very common, because it can make programs harder to understand (see Programming Tip 2.1 on page 38).

! Can_volume caution: Variable names are case-sensitive. This variable name is different from can_volume.

6pack error: Variable names cannot start with a number.

can volume error: Variable names cannot contain spaces.

double error: You cannot use a reserved word as a variable name.

ltr/fl.oz error: You cannot use symbols such as / or.

2.1.2

table 1 Variable definitions in C++

Variable name Comment

int cans = 6; Defines an integer variable and initializes it with 6.

int total = cans + bottles; The initial value need not be a constant. (Of course, cans and bottles must have been previously defined.)

int bottles = "10"; error: You cannot initialize a number with a string.

int bottles; Defines an integer variable without initializing it. This can be a cause for errors—see Common Error 2.2 on page 37.

int cans, bottles; Defines two integer variables in a single statement. In this book, we will define each variable in a separate statement.

! bottles = 1; caution: The type is missing. This statement is not a definition but an assignment of a new value to an existing variable—see Section 2.1.4 on page 34.

number types

In C++, there are several different types of numbers. You use the integer number type, called int in C++, to denote a whole number without a fractional part. For example, there must be an integer number of cans in any pack of cans—you cannot have a fraction of a can.

use the int type for numbers that cannot have a fractional part.

table 2 number literals in C++

number type Comment

6 int An integer has no fractional part.

–6 int Integers can be negative.

0 int Zero is an integer.

0.5 double A number with a fractional part has type double.

1.0 double An integer with a fractional part .0 has type double.

1E6 double A number in exponential notation: 1 × 106 or 1000000. Numbers in exponential notation always have type double.

2.96E-2 double Negative exponent: 2.96 × 10–2 = 2.96 / 100 = 0.0296

100,000 error: Do not use a comma as a decimal separator.

3 1/2 error: Do not use fractions; use decimal notation: 3.5.

cfe2_ch02_p29_74.indd 32 10/27/10 2:29 PM

2.1 Variables 33

double can_volume = 0.355;

When a value such as 6 or 0.355 occurs in a C++ program, it is called a number literal. Table 2 shows how to write integer and floating-point literals in C++.

2.1.3 Variable names

When you define a variable, you should pick a name that explains its purpose. For example, it is better to use a descriptive name, such as can_volume, than a terse name, such as cv.

In C++, there are a few simple rules for variable names:

1. Variable names must start with a letter or the underscore (_) character, and the remaining characters must be letters, numbers, or underscores.

2. You cannot use other symbols such as $ or %. Spaces are not permitted inside names either. You can use an underscore instead, as in can_volume.

3. Variable names are case-sensitive, that is, Can_volume and can_volume are different names. For that rea son, it is a good idea to use only lowercase letters in variable names.

4. You cannot use reserved words such as double or return as names; these words are reserved exclu sively for their special C++ meanings. (See Appendix B.)

Table 3 shows examples of legal and illegal variable names in C++.

use the double type for floating-point numbers.

table 3 Variable names in C++

Variable name Comment

can_volume1 Variable names consist of letters, numbers, and the underscore character.

x In mathematics, you use short variable names such as x or y. This is legal in C++, but not very common, because it can make programs harder to understand (see Programming Tip 2.1 on page 38).

! Can_volume caution: Variable names are case-sensitive. This variable name is different from can_volume.

6pack error: Variable names cannot start with a number.

can volume error: Variable names cannot contain spaces.

double error: You cannot use a reserved word as a variable name.

ltr/fl.oz error: You cannot use symbols such as / or.

cfe2_ch02_p29_74.indd 33 10/27/10 2:29 PM

34 Chapter 2 Fundamental data types

2.1.4 the assignment statement

You use the assignment statement to place a new value into a variable. Here is an example:

cans_per_pack = 8;

The left-hand side of an assignment statement consists of a variable. The right-hand side is an expression that has a value. That value is stored in the variable, overwriting its previous contents.

There is an important difference between a variable definition and an assignment statement:

int cans_per_pack = 6; // Variable definition ... cans_per_pack = 8; // Assignment statement

The first statement is the definition of cans_per_pack. It is an instruction to create a new variable of type int, to give it the name cans_per_pack, and to initialize it with 6. The second statement is an assignment statement: an instruction to replace the contents of the existing variable cans_per_pack with another value.

The = sign doesn’t mean that the left-hand side is equal to the right-hand side. The expression on the right is evaluated, and its value is placed into the variable on the left.

Do not confuse this assignment operation with the = used in algebra to denote equality. The assign ment operator is an instruction to do something, namely place a value into a variable. The mathematical equality states the fact that two values are equal.

For example, in C++, it is perfectly legal to write total_volume = total_volume + 2;

It means to look up the value stored in the variable total_volume, add 2 to it, and place the result back into total_volume. (See Figure 1.) The net effect of executing this state- ment is to increment total_volume by 2. For example, if total_volume was 2.13 before execution of the statement, it is set to 4.13 afterwards. Of course, in mathematics it would make no sense to write that x = x + 2. No value can equal itself plus 2.

an assignment statement stores a new value in a variable, replacing the previously stored value.

the assignment operator = does not denote mathematical equality.

syntax 2.2 assignment

double total = 0; . . total = bottles * BOTTLE_VOLUME; . . . total = total + cans * CAN_VOLUME;

The name of a previously defined variable

The same name can occur on both sides.

See Figure 1.

The expression that replaces the previous value

This is an initialization of a new variable, NOT an assignment.

This is an assignment.

2.1.5 Constants

When a variable is defined with the reserved word const, its value can never change. Constants are com monly written using capital letters to distinguish them visually from regular variables:

const double BOTTLE_VOLUME = 2;

It is good programming style to use named constants in your program to explain the meanings of numeric values. For example, compare the statements

double total_volume = bottles * 2;

and double total_volume = bottles * BOTTLE_VOLUME;

A programmer reading the first statement may not understand the significance of the number 2. The sec ond statement, with a named constant, makes the computation much clearer.

2.1.6 Comments

As your programs get more complex, you should add comments, explanations for human readers of your code. Here is an example:

const double CAN_VOLUME = 0.355; // Liters in a 12-ounce can

This comment explains the significance of the value 0.355 to a human reader. The compiler does not pro cess comments at all. It ignores everything from a // delimiter to the end of the line.

you cannot change the value of a variable that is defined as const.

use comments to add explanations for humans who read your code. the compiler ignores comments.

Just as a television commentator explains the news, you use comments in your program to explain its behavior.

cfe2_ch02_p29_74.indd 34 10/27/10 2:29 PM

2.1 Variables 35

2.1.5

Figure 1 executing the assignment total_volume = total_volume + 2

total_volume =

total_volume + 2

2.13

total_volume =

4.13

total_volume + 2

Constants

When a variable is defined with the reserved word const, its value can never change. Constants are com monly written using capital letters to distinguish them visually from regular variables:

const double BOTTLE_VOLUME = 2;

It is good programming style to use named constants in your program to explain the meanings of numeric values. For example, compare the statements

double total_volume = bottles * 2;

and double total_volume = bottles * BOTTLE_VOLUME;

A programmer reading the first statement may not understand the significance of the number 2. The sec ond statement, with a named constant, makes the computation much clearer.

2.1.6 Comments

As your programs get more complex, you should add comments, explanations for human readers of your code. Here is an example:

const double CAN_VOLUME = 0.355; // Liters in a 12-ounce can

This comment explains the significance of the value 0.355 to a human reader. The compiler does not pro cess comments at all. It ignores everything from a // delimiter to the end of the line.

you cannot change the value of a variable that is defined as const.

use comments to add explanations for humans who read your code. the compiler ignores comments.

Just as a television commentator explains the news, you use comments in your program to explain its behavior.

cfe2_ch02_p29_74.indd 35 10/27/10 2:29 PM

36 Chapter 2 Fundamental data types

You use the // syntax for single-line comments. If you have a comment that spans multiple lines, enclose it between /* and */ delimiters. The compiler ignores these delimiters and everything in between.

Here is a typical example, a long comment at the beginning of a program, to explain the program’s pur pose:

/* This program computes the volume (in liters) of a six-pack of soda cans and the total volume of a six-pack and a two-liter bottle. */

We are now ready to finish our program. The following program shows the use of variables, constants, and the assignment statement. The program displays the volume of a six-pack of cans and the total volume of the six-pack and a two-liter bottle. We use constants for the can and bottle volumes. The total_volume variable is initialized with the volume of the cans. Using an assignment statement, we add the bottle volume.

ch02/volume1.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 /* 6 This program computes the volume (in liters) of a six-pack of soda 7 cans and the total volume of a six-pack and a two-liter bottle. 8 */ 9 int main()

10 { 11 int cans_per_pack = 6; 12 const double CAN_VOLUME = 0.355; // Liters in a 12-ounce can 13 double total_volume = cans_per_pack * CAN_VOLUME; 14 15 cout << "A six-pack of 12-ounce cans contains " 16 << total_volume << " liters." << endl; 17 18 const double BOTTLE_VOLUME = 2; // Two-liter bottle 19 20 total_volume = total_volume + BOTTLE_VOLUME; 21 22 cout << "A six-pack and a two-liter bottle contain " 23 << total_volume << " liters." << endl; 24 25 return 0; 26 }

program run

A six-pack of 12-ounce cans contains 2.13 liters. A six-pack and a two-liter bottle contain 4.13 liters.

1. Define a variable suitable for holding the number of bottles in a case. 2. What is wrong with the following variable definition?

int ounces per liter = 28.35

s e l F c h e c k

3. Define and initialize two variables, unit_price and quantity, to contain the unit price of a single bottle and the number of bottles purchased. Use reasonable initial values.

4. Use the variables defined in Self Check 3 to display the total purchase price. 5. Some drinks are sold in four-packs instead of six-packs. How would you change

the volume1.cpp pro gram to compute the total volume? 6. What is wrong with this comment?

double can_volume = 0.355; /* Liters in a 12-ounce can //

7. Suppose the type of the cans_per_pack variable in the volume1.cpp program was changed from int to dou ble. What would be the effect on the program?

8. Why can’t the variable total_volume in the volume1.cpp program be declared as const?

9. How would you explain assignment using the parking space analogy?

practice it Now you can try these exercises at the end of the chapter: R2.1, R2.2, P2.1.

using undefined Variables

You must define a variable before you use it for the first time. For example, the following sequence of statements would not be legal:

double can_volume = 12 * liter_per_ounce; double liter_per_ounce = 0.0296;

In your program, the statements are compiled in order. When the compiler reaches the first statement, it does not know that liter_per_ounce will be defined in the next line, and it reports an error.

using uninitialized Variables

If you define a variable but leave it uninitialized, then your program can act unpredictably. To understand why, con sider what happens when you define a variable. Just enough space is set aside in memory to hold values of the type you specify. For example, with the definition

int bottles;

a block of memory big enough to hold integers is reserved. There is already some value in that memory. After all, you don’t get freshly minted transistors—just an area of memory that has previously been used, filled with flotsam left over from prior computations. (In this regard, a variable differs from a parking space. A parking space can be empty, containing no vehicle. But a variable always holds some value.)

If you use the variable without initializing it, then that prior value will be used, yielding unpredictable results. For example, consider the program segment

int bottles; // Forgot to initialize int bottle_volume = bottles * 2; // Result is unpredictable

There is no way of knowing what value will be computed. If you are unlucky, a plausible value will happen to appear when you run the program at home, and an entirely different result will occur when the program is graded.

Common error 2.1

Common error 2.2

cfe2_ch02_p29_74.indd 36 10/27/10 2:29 PM

2.1 Variables 37

3. Define and initialize two variables, unit_price and quantity, to contain the unit price of a single bottle and the number of bottles purchased. Use reasonable initial values.

4. Use the variables defined in Self Check 3 to display the total purchase price. 5. Some drinks are sold in four-packs instead of six-packs. How would you change

the volume1.cpp pro gram to compute the total volume? 6. What is wrong with this comment?

double can_volume = 0.355; /* Liters in a 12-ounce can //

7. Suppose the type of the cans_per_pack variable in the volume1.cpp program was changed from int to dou ble. What would be the effect on the program?

8. Why can’t the variable total_volume in the volume1.cpp program be declared as const?

9. How would you explain assignment using the parking space analogy?

practice it Now you can try these exercises at the end of the chapter: R2.1, R2.2, P2.1.

using undefined Variables

You must define a variable before you use it for the first time. For example, the following sequence of statements would not be legal:

double can_volume = 12 * liter_per_ounce; double liter_per_ounce = 0.0296;

In your program, the statements are compiled in order. When the compiler reaches the first statement, it does not know that liter_per_ounce will be defined in the next line, and it reports an error.

using uninitialized Variables

int bottles;

If you use the variable without initializing it, then that prior value will be used, yielding unpredictable results. For example, consider the program segment

int bottles; // Forgot to initialize int bottle_volume = bottles * 2; // Result is unpredictable

Common error 2.1

Common error 2.2

cfe2_ch02_p29_74.indd 37 10/27/10 2:29 PM

38 Chapter 2 Fundamental data types

choose descriptive Variable names

We could have saved ourselves a lot of typing by using shorter variable names, as in

double cv = 0.355;

Compare this definition with the one that we actually used, though. Which one is easier to read? There is no compar ison. Just reading can_volume is a lot less trouble than reading cv and then figuring out it must mean “can volume”.

In practical programming, this is particularly important when programs are written by more than one person. It may be obvious to you that cv stands for can volume and not cur- rent velocity, but will it be obvious to the person who needs to update your code years later? For that matter, will you remember yourself what cv means when you look at the code three months from now?

numeric types in c++

In addition to the int and double types, C++ has several other numeric types. C++ has two floating-point types. The float type uses half the storage of the double type

that we use in this book, but it can only store 6–7 digits. Many years ago, when computers had far less memory than they have today, float was the standard type for floating-point computa- tions, and programmers would indulge in the luxury of “double precision” only when they needed the additional digits. Today, the float type is rarely used.

By the way, these numbers are called “floating-point” because of their internal representa- tion in the computer. Consider numbers 29600, 2.96, and 0.0296. They can be represented in a very similar way: namely, as a sequence of the significant digits—296—and an indication of the position of the decimal point. When the values are multiplied or divided by 10, only the position of the decimal point changes; it “floats”. Computers use base 2, not base 10, but the principle is the same.

table 4 number types

type typical range typical size

int –2,147,483,648 … 2,147,483,647 (about 2 billion) 4 bytes

unsigned 0 … 4,294,967,295 4 bytes

short –32,768 … 32,767 2 bytes

unsigned short 0 … 65,535 2 bytes

long long –9,223,372,036,854,775,808 … 9,223,372,036,854,775,807 8 bytes

double The double-precision floating-point type, with a range of about ±10308 and about 15 significant decimal digits

8 bytes

float The single-precision floating-point type, with a range of about ±1038 and about 7 significant decimal digits

4 bytes

programming tip 2.1

special topic 2.1

In addition to the int type, C++ has integer types short, long, and long long. For each integer type, there is an unsigned equivalent. For example, the short type typically has a range from –32,768 to 32,767, whereas unsigned short has a range from 0 to 65,535. These strange-looking limits are the result of the use of binary numbers in computers. A short value uses 16 binary digits, which can encode 216 = 65,536 values. Keep in mind that the ranges for integer types are not standardized, and they differ among compilers. Table 4 contains typical values.

numeric ranges and precisions

Because numbers are represented in the computer with a limited number of digits, they cannot represent arbitrary integer or floating-point numbers.

The int type has a limited range: On most platforms, it can represent numbers up to a little more than two billion. For many applications, this is not a problem, but you cannot use an int to represent the world population.

If a computation yields a value that is outside the int range, the result overflows. No error is displayed. Instead, the result is truncated to fit into an int, yielding a useless value. For example,

int one_billion = 1000000000; cout << 3 * one_billion << endl;

displays –1294967296. In situations such as this, you can switch to double values. However, read Common Error

2.6 on page 45 for more information about a related issue: roundoff errors.

do not use magic numbers

A magic number is a numeric constant that appears in your code without explanation. For example,

total_volume = bottles * 2;

Why 2? Are bottles twice as voluminous as cans? No, the reason is that every bottle con tains 2 liters. Use a named constant to make the code self-documenting:

const double BOTTLE_VOLUME = 2; total_volume = bottles * BOTTLE_VOLUME;

There is another reason for using named constants. Suppose circumstances change, and the bottle volume is now 1.5 liters. If you used a named constant, you make a single change, and you are done. Other wise, you have to look at every value of 2 in your program and ponder whether it means a bottle volume, or some thing else. In a program that is more than a few pages long, that is incredibly tedious and error-prone.

Even the most reasonable cosmic constant is going to change one day. You think there are seven days per week? Your customers on Mars are going to be pretty unhappy about your silly prejudice. Make a constant

const int DAYS_PER_WEEK = 7;

special topic 2.2

programming tip 2.2

cfe2_ch02_p29_74.indd 38 10/27/10 2:29 PM

2.1 Variables 39

numeric ranges and precisions

Because numbers are represented in the computer with a limited number of digits, they cannot represent arbitrary integer or floating-point numbers.

If a computation yields a value that is outside the int range, the result overflows. No error is displayed. Instead, the result is truncated to fit into an int, yielding a useless value. For example,

int one_billion = 1000000000; cout << 3 * one_billion << endl;

displays –1294967296. In situations such as this, you can switch to double values. However, read Common Error

2.6 on page 45 for more information about a related issue: roundoff errors.

do not use magic numbers

A magic number is a numeric constant that appears in your code without explanation. For example,

total_volume = bottles * 2;

Why 2? Are bottles twice as voluminous as cans? No, the reason is that every bottle con tains 2 liters. Use a named constant to make the code self-documenting:

const double BOTTLE_VOLUME = 2; total_volume = bottles * BOTTLE_VOLUME;

const int DAYS_PER_WEEK = 7;

special topic 2.2

programming tip 2.2

cfe2_ch02_p29_74.indd 39 10/27/10 2:29 PM

40 Chapter 2 Fundamental data types

2.2 arithmetic In the following sections, you will learn how to carry out arithmetic and mathemati- cal calculations in C++.

2.2.1 arithmetic operators

C++ supports the same four basic arithmetic operations as a calculator—addition, subtraction, multi plication, and division—but it uses different symbols for multipli- cation and division.

You must write a * b to denote multiplication. Unlike in mathematics, you can not write a b, a . b or a × b. Similarly, division is always indicated with a /, never a ÷ or a fraction bar.

For example, a b+

2 becomes (a + b) / 2.

Parentheses are used just as in algebra: to indicate in which order the subexpres- sions should be com puted. For example, in the expression (a + b) / 2, the sum a + b is computed first, and then the sum is divided by 2. In contrast, in the expression

a + b / 2

only b is divided by 2, and then the sum of a and b / 2 is formed. Just as in regular alge- braic notation, mul tiplication and division have a higher precedence than addition and subtraction. For example, in the expression a + b / 2, the / is carried out first, even though the + operation occurs further to the left. If both arguments of an arithmetic operation are integers, the result is an integer. If one or both arguments are floating- point numbers, the result is a floating-point number. For example, 4 * 0.5 is 2.0.

2.2.2 Increment and decrement

Changing a variable by adding or subtracting 1 is so common that there is a special shorthand for it, namely

counter++; counter--;

The ++ increment operator gave the C++ programming language its name. C++ is the incremental improvement of the C language.

2.2.3 Integer division and remainder

Division works as you would expect, as long as at least one of the numbers involved is a floating-point number. That is, 7.0 / 4.0, 7 / 4.0, and 7.0 / 4 all yield 1.75. However, if both numbers are integers, then the result of the division is always an integer, with the remainder discarded. That is,

7 / 4

evaluates to 1 because 7 divided by 4 is 1 with a remainder of 3 (which is discarded). This can be a source of subtle programming errors—see Common Error 2.3 on page 43.

use * for multiplication and / for division.

the ++ operator adds 1 to a variable; the -- operator subtracts 1.

If both arguments of / are integers, the remainder is discarded.

If you are interested in the remainder only, use the % operator: 7 % 4

is 3, the remainder of the integer division of 7 by 4. The % symbol has no analog in algebra. It was chosen because it looks similar to /, and the remainder operation is related to division. The operator is called modulus. (Some people call it modulo or mod.) It has no relationship with the percent operation that you find on some calculators.

Here is a typical use for the integer / and % operations. Suppose you have an amount of pennies in a piggybank:

int pennies = 1729;

You want to determine the value in dollars and cents. You obtain the dollars through an integer division by 100.

int dollars = pennies / 100; // Sets dollars to 17

The integer division discards the remainder. To obtain the remainder, use the % operator:

int cents = pennies % 100; // Sets cents to 29

Another common use of the % operator is to check whether a number is even or odd. If a number n is even, then n % 2 is zero.

2.2.4 Converting Floating-point numbers to Integers

When a floating-point value is assigned to an integer variable, the fractional part is discarded:

double price = 2.55; int dollars = price; // Sets dollars to 2

Discarding the fractional part is not always what you want. Often, you want to round to the nearest inte ger. To round a positive floating-point value to the nearest integer, add 0.5 and then convert to an integer:

int dollars = price + 0.5; // Rounds to the nearest integer

In our example, adding 0.5 turns all values above 2.5 into values above 3. In particular, 2.55 is turned into 3.05, which is then truncated to 3. (For a negative floating-point value, you subtract 0.5.)

Because truncation is a potential cause for errors, your compiler may issue a warn- ing that assigning a floating-point value to an integer variable is unsafe. See Special Topic 2.3 on page 46 on how to avoid this warning.

2.2.5 powers and roots

In C++, there are no symbols for powers and roots. To compute them, you must call functions. To take the square root of a number, you use the sqrt function. For exam- ple, is written as sqrt(x). To com pute xn, you write pow(x, n).

the % operator computes the remainder of an integer division.

Integer division and the % operator yield the dollar and cent values of a piggybank full of pennies.

assigning a floating- point variable to an integer drops the fractional part.

cfe2_ch02_p29_74.indd 40 10/27/10 2:29 PM

2.2 arithmetic 41

If you are interested in the remainder only, use the % operator: 7 % 4

Here is a typical use for the integer / and % operations. Suppose you have an amount of pennies in a piggybank:

int pennies = 1729;

You want to determine the value in dollars and cents. You obtain the dollars through an integer division by 100.

int dollars = pennies / 100; // Sets dollars to 17

The integer division discards the remainder. To obtain the remainder, use the % operator:

int cents = pennies % 100; // Sets cents to 29

Another common use of the % operator is to check whether a number is even or odd. If a number n is even, then n % 2 is zero.

2.2.4 Converting Floating-point numbers to Integers

When a floating-point value is assigned to an integer variable, the fractional part is discarded:

double price = 2.55; int dollars = price; // Sets dollars to 2

int dollars = price + 0.5; // Rounds to the nearest integer

2.2.5 powers and roots

In C++, there are no symbols for powers and roots. To compute them, you must call functions. To take the square root of a number, you use the sqrt function. For exam- ple, x is written as sqrt(x). To com pute xn, you write pow(x, n).

the % operator computes the remainder of an integer division.

Integer division and the % operator yield the dollar and cent values of a piggybank full of pennies.

assigning a floating- point variable to an integer drops the fractional part.

cfe2_ch02_p29_74.indd 41 10/27/10 2:29 PM

42 Chapter 2 Fundamental data types

Figure 2 analyzing an expression

b * pow(1 + r / 100, n)

r 100

r 1 +

100

r n

 

 

1 + 100

b r

× +  

 

1 100

To use the sqrt and pow functions, you must place the line #include <cmath> at the top of your program file. The header file <cmath> is a standard C++ header that is available with all C++ systems, as is <iostream>.

As you can see, the effect of the /, sqrt, and pow operations is to flatten out math- ematical terms. In alge bra, you use fractions, exponents, and roots to arrange expres- sions in a compact two-dimensional form. In C++, you have to write all expressions in a linear arrangement. For example, the mathematical expres sion

b r

× +  

 

1 100

becomes b * pow(1 + r / 100, n)

Figure 2 shows how to analyze such an expression.

the C++ library defines many mathematical functions such as sqrt (square root) and pow (raising to a power).

table 5 arithmetic expressions

mathematical expression

C++ expression

Comments

x y+ 2 (x + y) / 2

The parentheses are required; x + y / 2 computes x

y +

2 .

xy 2 x * y / 2

Parentheses are not required; operators with the same precedence are evaluated left to right.

1 100

+  

 

r n

pow(1 + r / 100, n) Remember to add #include <cmath> to the top of your program.

a b2 2+ sqrt(a * a + b * b) a * a is simpler than pow(a, 2).

i j k+ + 3 (i + j + k) / 3.0

If i, j, and k are integers, using a denominator of 3.0 forces floating-point division.

Table 6 shows additional functions that are declared in the <cmath> header. Inputs and outputs are float ing-point numbers.

10. A bank account earns interest of p percent per year. In C++, how do you com- pute the interest earned in one year? Assume variables p and balance of type double have already been defined.

11. In C++, how do you compute the side length of a square whose area is stored in the variable area?

12. The volume of a sphere is given by .

If the radius is given by a variable radius of type double, write a C++ expression for the volume. You may assume that p is defined by a constant PI.

13. What is the value of 1729 / 10 and 1729 % 10? 14. Suppose a punch recipe calls for a given amount of

orange soda, measured in ounces. int amount = 32;

We can compute the number of 12-ounce cans needed, assuming that the amount does not evenly divide into 12: int cans_needed = amount / 12 + 1;

Use the % operator to determine how many ounces will be left over. For example, if 32 ounces are required, we need 3 cans and have 4 ounces left over.

practice it Now you can try these exercises at the end of the chapter: R2.3, R2.5, P2.2.

unintended integer division

It is unfortunate that C++ uses the same symbol, namely /, for both integer and floating-point division. These are really quite different operations. It is a common error to use integer divi- sion by accident. Consider this segment that computes the average of three integers:

cout << "Please enter your last three test scores: "; int s1; int s2;

s e l F c h e c k

Common error 2.3

cfe2_ch02_p29_74.indd 42 10/27/10 2:29 PM

2.2 arithmetic 43

table 6 other mathematical Functions

Function description

sin(x) sine of x (x in radians)

cos(x) cosine of x

tan(x) tangent of x

log10(x) decimal log( ) ( ) >log ,10 0x x abs(x) absolute value x

Table 6 shows additional functions that are declared in the <cmath> header. Inputs and outputs are float ing-point numbers.

10. A bank account earns interest of p percent per year. In C++, how do you com- pute the interest earned in one year? Assume variables p and balance of type double have already been defined.

11. In C++, how do you compute the side length of a square whose area is stored in the variable area?

12. The volume of a sphere is given by V r= 4 3

3π . If the radius is given by a variable radius of type double, write a C++ expression for the volume. You may assume that p is defined by a constant PI.

13. What is the value of 1729 / 10 and 1729 % 10? 14. Suppose a punch recipe calls for a given amount of

orange soda, measured in ounces. int amount = 32;

We can compute the number of 12-ounce cans needed, assuming that the amount does not evenly divide into 12: int cans_needed = amount / 12 + 1;

Use the % operator to determine how many ounces will be left over. For example, if 32 ounces are required, we need 3 cans and have 4 ounces left over.

practice it Now you can try these exercises at the end of the chapter: R2.3, R2.5, P2.2.

unintended integer division

cout << "Please enter your last three test scores: "; int s1; int s2;

s e l F c h e c k

Common error 2.3

cfe2_ch02_p29_74.indd 43 10/27/10 2:29 PM

44 Chapter 2 Fundamental data types

int s3; cin >> s1 >> s2 >> s3; double average = (s1 + s2 + s3) / 3; // Error cout << "Your average score is " << average << endl;

What could be wrong with that? Of course, the average of s1, s2, and s3 is

s1 s2 s3+ +

Here, however, the / does not mean division in the mathematical sense. It denotes integer division because both s1 + s2 + s3 and 3 are integers. For example, if the scores add up to 14, the average is computed to be 4, the result of the integer division of 14 by 3. That integer 4 is then moved into the floating-point variable average. The remedy is to make the numerator or denominator into a floating-point number:

double total = s1 + s2 + s3; double average = total / 3;

double average = (s1 + s2 + s3) / 3.0;

unbalanced parentheses

Consider the expression

(-(b * b - 4 * a * c) / (2 * a)

What is wrong with it? Count the parentheses. There are three ( and two ). The parenthe- ses are unbalanced. This kind of typing error is very common with complicated expressions. Now consider this expression.

-(b * b - (4 * a * c))) / (2 * a

This expression has three ( and three ), but it still is not correct. In the middle of the expres- sion,

-(b * b - (4 * a * c))) / (2 * a ↑

there are only two ( but three ), which is an error. In the middle of an expression, the count of ( must be greater than or equal to the count of ), and at the end of the expression the two counts must be the same.

Here is a simple trick to make the counting easier without using pencil and paper. It is diffi- cult for the brain to keep two counts simultaneously. Keep only one count when scanning the expression. Start with 1 at the first opening parenthesis, add 1 whenever you see an opening parenthesis, and subtract one whenever you see a closing parenthe sis. Say the numbers aloud as you scan the expression. If the count ever drops below zero, or is not zero at the end, the parentheses are unbalanced. For example, when scanning the previous expression, you would mutter

-(b * b - (4 * a * c ) ) ) / (2 * a 1 2 1 0 –1

and you would find the error.

Common error 2.4

Forgetting header Files

Every program that carries out input or output needs the <iostream> header. If you use mathemat- ical functions such as sqrt, you need to include <cmath>. If you forget to include the appropriate header file, the compiler will not know sym bols such as cout or sqrt. If the compiler complains about an undefined function or symbol, check your header files.

Sometimes you may not know which header file to include. Suppose you want to compute the absolute value of an integer using the abs function. As it happens, this version of abs is not defined in the <cmath> header but in <cstdlib>. How can you find the cor rect header file? You need to locate the documentation of the abs function, preferably using the online help of your development environment or a reference site on the Internet such as http://www.cplusplus.com (see Figure 3). The documentation includes a short description of the function and the name of the header file that you must include.

roundoff errors

Roundoff errors are a fact of life when calculating with floating-point numbers. You probably have encountered that phenomenon yourself with manual calculations. If you calculate to two decimal places, you get 0.33. Multiply ing again by 3, you obtain 0.99, not 1.00.

In the processor hardware, numbers are represented in the binary number system, not in decimal. You still get roundoff errors when binary digits are lost. They just may crop up at dif- ferent places than you might expect. Here is an example.

#include <iostream>

using namespace std;

Common error 2.5

Figure 3 online documentation

Common error 2.6

cfe2_ch02_p29_74.indd 44 10/27/10 2:29 PM

2.2 arithmetic 45

Forgetting header Files

roundoff errors

Roundoff errors are a fact of life when calculating with floating-point numbers. You probably have encountered that phenomenon yourself with manual calculations. If you calculate 1 3 to two decimal places, you get 0.33. Multiply ing again by 3, you obtain 0.99, not 1.00.

#include <iostream>

using namespace std;

Common error 2.5

Figure 3 online documentation

Common error 2.6

cfe2_ch02_p29_74.indd 45 10/27/10 2:29 PM

http://www.cplusplus.com

46 Chapter 2 Fundamental data types

int main() { double price = 4.35; int cents = 100 * price; // Should be 100 * 4.35 = 435 cout << cents << endl; // Prints 434! return 0; }

Of course, one hundred times 4.35 is 435, but the program prints 434. Most computers represent numbers in the binary system. In the binary system, there is

no exact representation for 4.35, just as there is no exact representation for 1/3 in the decimal system. The representation used by the com puter is just a little less than 4.35, so 100 times that value is just a little less than 435. When a floating-point value is converted to an integer, the entire fractional part, which is almost 1, is thrown away, and the integer 434 is stored in cents. The remedy is to add 0.5 in order to round to the nearest integer:

int cents = 100 * price + 0.5;

spaces in expressions

It is easier to read

x1 = (-b + sqrt(b * b - 4 * a * c)) / (2 * a);

than

x1=(-b+sqrt(b*b-4*a*c))/(2*a);

Simply put spaces around all operators + - * / % =. However, don’t put a space after a unary minus: a – used to negate a single quantity, such as -b. That way, it can be easily distinguished from a binary minus, as in a - b.

It is customary not to put a space after a function name. That is, write sqrt(x) and not sqrt (x).

casts

Occasionally, you need to store a value into a variable of a different type. Whenever there is the risk of information loss, the compiler issues a warning. For example, if you store a double value into an int variable, you can lose informa tion in two ways: • The fractional part is lost. • The magnitude may be too large. For example,

int n = 1.0E100; // NO

is not likely to work, because 10100 is larger than the largest representable integer. Nevertheless, sometimes you do want to convert a floating-point value into an integer

value. If you are prepared to lose the fractional part and you know that this particular floating- point number is not larger than the largest pos sible integer, then you can turn off the warning by using a cast. A cast is a conversion from one type (such as double) to another type (such as int) that is not safe in general, but that you know to be safe in a particular circumstance. You express a cast in C++ as follows:

int cents = static_cast<int>(100 * price + 0.5);

programming tip 2.3

special topic 2.3

combining assignment and arithmetic

In C++, you can combine arithmetic and assignment. For example, the instruction

total += cans * CAN_VOLUME;

is a shortcut for

total = total + cans * CAN_VOLUME;

Similarly,

total *= 2;

is another way of writing

total = total * 2;

Many programmers find this a convenient shortcut. If you like it, go ahead and use it in your own code. For simplic ity, we won’t use it in this book, though.

special topic 2.4

In 1994, Intel Corporation released what was then its most powerful processor, the

pentium. unlike previous generations of its processors, it had a very fast floating-point unit. Intel’s goal was to com- pete aggressively with the makers of higher-end proces sors for engineering workstations. the pentium was a huge suc- cess immediately.

In the summer of 1994, dr. thomas nicely of lynchburg College, Virginia, ran an extensive set of computations to analyze the sums of reciprocals of certain sequences of prime numbers. the results were not always what his the- ory predicted, even after he took into account the inevita ble roundoff errors. then dr. nicely noted that the same pro- gram did produce the correct results when running on the slower 486 processor that preceded the pentium in Intel’s lineup. this should not have happened. the optimal round- off behavior of floating-point calculations were standard- ized by the Institute for electrical and electronic engineers (Ieee) and Intel claimed to adhere to the Ieee standard in both the 486 and the pentium processors. upon further checking, dr. nicely discovered that there was a very small set of numbers for which the prod uct of two numbers was computed differently on the two processors. For example,

4 195 835 4 195 835 3 145 727 3 145 727, , , , , , , ,− ( ) ×( ) is mathematically equal to 0, and it did compute as 0 on a 486 processor. on his pentium processor the result was 256.

as it turned out, Intel had independently discovered the bug in its testing and had started to produce chips that fixed it. the bug was caused by an error in a table that was used to speed up the processor’s floating-point multipli- cation algo rithm. Intel determined that the problem was exceedingly rare. they claimed that under normal use, a typical consumer would only notice the problem once every 27,000 years. unfortunately for Intel, dr. nicely had not been a normal user.

now Intel had a real problem on its hands. It figured that the cost of replacing all pentium processors that it had sold so far would cost a great deal of money. Intel already had more orders for the chip than it could produce, and it would be particularly galling to have to give out the scarce chips as free replacements instead of selling them. Intel’s management decided to punt and initially offered to replace the processors only for those customers who could prove that their work required absolute precision in mathematical calculations. naturally, that did not go over well with the hundreds of thousands of customers who had paid retail prices of $700 and more for a pentium chip and did not want to live with the nagging feeling that perhaps, one day, their income tax program would produce a faulty return. ultimately, Intel caved in to public demand and replaced all defective chips, at a cost of about 475 million dollars.

1 .4

1 .2

1 .0

0 .8

0 .6

0 .4

0 .2

0 .0

-0 .2

-0 .4

-0 .6

-0 .8

-1 .0

-1 .2

-1 .4

-1 .6

-1 .8

-2 .0

1.40

1.10

0.80

0.50

0.20

-0.10

-0.40

-0.70 -1.00

-1.30

1.333680000

1.333700000

1.333720000

1.333740000

1.333760000

1.333780000

1.333800000

1.333820000

1.333840000

x /y

4195835+

3145727+

Pentium FDIV error

This graph shows a set of numbers for which the original Pentium processor obtained the wrong quotient.

Random Fact 2.1 the pentium Floating-point Bug

cfe2_ch02_p29_74.indd 46 10/27/10 2:29 PM

2.2 arithmetic 47

combining assignment and arithmetic

In C++, you can combine arithmetic and assignment. For example, the instruction

total += cans * CAN_VOLUME;

is a shortcut for

total = total + cans * CAN_VOLUME;

Similarly,

total *= 2;

is another way of writing

total = total * 2;

Many programmers find this a convenient shortcut. If you like it, go ahead and use it in your own code. For simplic ity, we won’t use it in this book, though.

special topic 2.4

In 1994, Intel Corporation released what was then its most powerful processor, the

4 195 835 4 195 835 3 145 727 3 145 727, , , , , , , ,− ( ) ×( ) is mathematically equal to 0, and it did compute as 0 on a 486 processor. on his pentium processor the result was 256.

1 .4

1 .2

1 .0

0 .8

0 .6

0 .4

0 .2

0 .0

-0 .2

-0 .4

-0 .6

-0 .8

-1 .0

-1 .2

-1 .4

-1 .6

-1 .8

-2 .0

1.40

1.10

0.80

0.50

0.20

-0.10

-0.40

-0.70 -1.00

-1.30

1.333680000

1.333700000

1.333720000

1.333740000

1.333760000

1.333780000

1.333800000

1.333820000

1.333840000

x /y

4195835+

3145727+

Pentium FDIV error

This graph shows a set of numbers for which the original Pentium processor obtained the wrong quotient.

Random Fact 2.1 the pentium Floating-point Bug

cfe2_ch02_p29_74.indd 47 10/27/10 2:30 PM

48 Chapter 2 Fundamental data types

2.3 Input and output

2.3.1 Input

In this section, you will see how to place user input into a variable. Consider for example the volume1.cpp program on page 36. Rather than assuming that the price for the two-liter bottle and the six-pack of cans are identical, we can ask the program user for the prices.

When a program asks for user input, it should first print a message that tells the user which input is expected. Such a message is called a prompt.

cout << "Please enter the number of bottles: "; // Display prompt

Do not add an endl after the prompt. You want the input to appear after the colon, not on the following line.

Next, the program issues a command to read the input. The cin object reads input from the console window. You use the >> operator (sometimes called the extraction operator) to place an input value into a variable, like this:

int bottles; cin >> bottles;

When the program executes the input statement, it waits for the user to provide input. The user also needs to hit the Enter key so that the program accepts the input. After the user supplies the input, the number is placed into the bottles variable, and the pro- gram continues.

Note that in this code segment, there was no need to initialize the bottles variable because it is being filled by the very next statement. As a rule of thumb, you should initialize a variable when you declare it unless it is filled in an input statement that fol- lows immediately.

You can read more than one value in a single input statement: cout << "Please enter the number of bottles and cans: "; cin >> bottles >> cans;

The user can supply both inputs on the same line: Please enter the number of bottles and cans: 2 6

Alternatively, the user can press the Enter key after each input: Please enter the number of bottles and cans: 2 6

use the >> operator to read a value and place it in a variable.

syntax 2.3 Input statement

cout << "Enter the number of bottles: "; int bottles; cin >> bottles;

Display a prompt in the console window.

The program waits for user input, then places the input into the variable.

Define a variable to hold the input value.

Don't use endl here.

2.3.2 Formatted output

When you print the result of a computation, you often want some control over its appearance. For exam ple, when you print an amount in dollars and cents, you usually want it to be rounded to two significant digits. That is, you want the output to look like

Price per ounce: 0.04

instead of Price per ounce: 0.0409722

The following command instructs cout to use two digits after the decimal point for all floating-point numbers:

cout << fixed << setprecision(2);

This command does not produce any output; it just manipulates cout so that it will change the output for mat. The values fixed and setprecision are called manipulators. We will discuss manipulators in detail in Chapter 8. For now, just remember to include the statement given above whenever you want currency values displayed neatly.

To use manipulators, you must include the <iomanip> header in your program: #include <iomanip>

You can combine the manipulators and the values to be displayed into a single statement.

cout << fixed << setprecision(2) << "Price per ounce: " << price_per_ounce << endl;

There is another manipulator that is sometimes handy. When you display several rows of data, you usu ally want the columns to line up.

You use the setw manipulator to set the width of the next output field. The width is the total number of characters used for showing the value, including digits, the deci- mal point, and spaces. Controlling the width is important when you want columns of numbers to line up.

For example, if you want a number to be printed in a column that is eight charac- ters wide, you use

cout << setw(8) << price_per_ounce;

you use manipulators to specify how values should be formatted.

You use manipulators to line up your output in neat columns.

cfe2_ch02_p29_74.indd 48 10/27/10 2:30 PM

2.3 Input and output 49

2.3.2 Formatted output

Price per ounce: 0.04

instead of Price per ounce: 0.0409722

The following command instructs cout to use two digits after the decimal point for all floating-point numbers:

cout << fixed << setprecision(2);

To use manipulators, you must include the <iomanip> header in your program: #include <iomanip>

You can combine the manipulators and the values to be displayed into a single statement.

cout << fixed << setprecision(2) << "Price per ounce: " << price_per_ounce << endl;

There is another manipulator that is sometimes handy. When you display several rows of data, you usu ally want the columns to line up.

For example, if you want a number to be printed in a column that is eight charac- ters wide, you use

cout << setw(8) << price_per_ounce;

you use manipulators to specify how values should be formatted.

You use manipulators to line up your output in neat columns.

cfe2_ch02_p29_74.indd 49 10/27/10 2:30 PM

50 Chapter 2 Fundamental data types

This command prints the value price_per_ounce in a field of width 8, for example

0 . 0 4

(where each represents a space). There is a notable difference between the setprecision and setw manipulators. Once

you set the preci sion, that value is used for all floating-point numbers. But the width affects only the next value. Subse quent values are formatted without added spaces.

Our next example program will prompt for the price of a six-pack and the volume of each can, then print out the price per ounce. The program puts to work what you just learned about reading input and formatting output.

ch02/volume2.cpp

1 #include <iostream> 2 #include <iomanip> 3 4 using namespace std; 5 6 int main() 7 { 8 // Read price per pack 9

10 cout << "Please enter the price for a six-pack: "; 11 double pack_price; 12 cin >> pack_price; 13 14 // Read can volume 15 16 cout << "Please enter the volume for each can (in ounces): "; 17 double can_volume; 18 cin >> can_volume; 19 20 // Compute pack volume 21 22 const double CANS_PER_PACK = 6; 23 double pack_volume = can_volume * CANS_PER_PACK; 24 25 // Compute and print price per ounce 26 27 double price_per_ounce = pack_price / pack_volume; 28 29 cout << fixed << setprecision(2); 30 cout << "Price per ounce: " << price_per_ounce << endl; 31 32 return 0; 33 }

program run

Please enter the price for a six-pack: 2.95 Please enter the volume for each can (in ounces): 12 Price per ounce: 0.04

cfe2_ch02_p29_74.indd 50 10/27/10 2:30 PM

2.3 Input and output 51

15.

table 7 Formatting output

output statement output Comment

cout << 12.345678; 12.3457 By default, a number is printed with 6 significant digits.

cout << fixed << setprecision(2) << 12.3;

12.30 Use the fixed and setprecision manipulators to control the number of digits after the decimal point.

cout << ":" << setw(6) << 12;

: 12 Four spaces are printed before the number, for a total width of 6 characters.

cout << ":" << setw(2) << 123;

:123 If the width not sufficient, it is ignored.

cout << setw(6) << ":" << 12;

:12.3 The width only refers to the next item. Here, the : is preceded by five spaces.

What is wrong with the following statement sequence? cout << "Please enter the unit price: "; double unit_price; cin >> unit_price; int quantity; cin >> quantity;

16. What is problematic about the following statement sequence? cout << "Please enter the unit price: "; int unit_price; cin >> unit_price;

17. What is the output of the following statement sequence? double bottles = 10; cout << "The total volume is" << 2 * bottles;

18. How do you print the floating-point variable total_price in dollars and cents, like this: $1.22?

19. Using the setw manipulator, improve the output statement cout << "Bottles: " << bottles << endl << "Cans: " << cans << endl;

so that the output looks like this: Bottles: 8 Cans: 24

The numbers to the right should line up. (You may assume that the numbers have at most 8 digits.)

practice it Now you can try these exercises at the end of the chapter: R2.7, R2.8, P2.6, P2.7.

s e l F c h e c k

cfe2_ch02_p29_74.indd 51 10/27/10 2:30 PM

52 Chapter 2 Fundamental data types

2.4 problem solving: First do It By hand A very important step for developing an algorithm is to first carry out the computa- tions by hand. If you can’t compute a solution yourself, it’s unlikely that you’ll be able to write a program that automates the computation.

To illustrate the use of hand calculations, consider the following problem. A row of black and white tiles needs to be placed along a wall. For aesthetic rea-

sons, the architect has specified that the first and last tile shall be black. Your task is to compute the number of tiles needed and the gap at each end, given

the space available and the width of each tile.

Total width

Gap

To make the problem more concrete, let’s assume the following dimensions:

• Total width: 100 inches • Tile width: 5 inches

The obvious solution would be to fill the space with 20 tiles, but that would not work—the last tile would be white.

Instead, look at the problem this way: The first tile must always be black, and then we add some num ber of white/black pairs:

The first tile takes up 5 inches, leaving 95 inches to be covered by pairs. Each pair is 10 inches wide. Therefore the number of pairs is 95 / 10 = 9.5. However, we need to dis- card the fractional part since we can’t have fractions of tile pairs.

Therefore, we will use 9 tile pairs or 18 tiles, together with the initial black tile. Altogether, we require 19 tiles.

The tiles span 19 × 5 = 95 inches, leaving a total gap of 100 – 19 × 5 = 5 inches. The gap should be evenly distributed at both ends. At each end, the gap is (100 – 19 × 5) / 2 = 2.5 inches.

This computation gives us enough information to devise an algorithm with arbi- trary values for the total width and tile width.

number of pairs = integer part of (total width - tile width) / (2 x tile width) number of tiles = 1 + 2 x number of pairs gap at each end = (total width - number of tiles x tile width) / 2

As you can see, doing a hand calculation gives enough insight into the problem that it becomes easy to develop an algorithm.

pick concrete values for a typical situation to use in a hand calculation.

20. Translate the pseudocode for computing the number of tiles and the gap width into C++.

21. Suppose the architect specifies a pattern with black, gray, and white tiles, like this:

Again, the first and last tile should be black. How do you need to modify the algorithm?

22. A robot needs to tile a floor with alternating black and white tiles. Develop an algorithm that yields the color (0 for black, 1 for white), given the row and column number. Start with specific values for the row and column, and then generalize.

23. For a particular car, repair and maintenance costs in year 1 are estimated at $100; in year 10, at $1,500. Assuming that the repair cost increases by the same amount every year, develop pseudocode to com pute the repair cost in year 3 and then generalize to year n.

24. The shape of a bottle is approximated by two cylinders of radius r1 and r2 and heights h1 and h2, joined by a cone section of height h3. Using the formulas for the volume of a cylinder, , and a cone section,

develop pseudocode to compute the volume of the bottle. Using an actual bottle with known volume as a sample, make a hand calculation of your pseudocode.

practice it Now you can try these exercises at the end of the chapter: R2.13, R2.15, R2.16.

s e l F c h e c k

W o r k e d e x a m p l e 2 . 1 computing travel time

In this Worked Example, we develop a hand calculation to compute the time that a robot requires to retrieve an item from rocky terrain.

cfe2_ch02_p29_74.indd 52 10/27/10 2:30 PM

2.4 problem solving: First do It By hand 53

20. Translate the pseudocode for computing the number of tiles and the gap width into C++.

21. Suppose the architect specifies a pattern with black, gray, and white tiles, like this:

Again, the first and last tile should be black. How do you need to modify the algorithm?

1 2 3 4

V r r r r h

= + +( )

π 1 2

1 2 2 2

3 ,

develop pseudocode to compute the volume of the bottle. Using an actual bottle with known volume as a sample, make a hand calculation of your pseudocode.

practice it Now you can try these exercises at the end of the chapter: R2.13, R2.15, R2.16.

s e l F c h e c k

W o r k e d e x a m p l e 2 . 1 computing travel time

In this Worked Example, we develop a hand calculation to compute the time that a robot requires to retrieve an item from rocky terrain.

Available online at www.wiley.com/college/horstmann.

cfe2_ch02_p29_74.indd 53 10/27/10 2:30 PM

www.wiley.com/college/horstmann

54 Chapter 2 Fundamental data types

step 1 Understand the problem: What are the inputs? What are the desired outputs?

In this problem, there are two inputs: • The denomination of the bill that the customer inserts • The price of the purchased item There are two desired outputs: • The number of dollar coins that the machine returns • The number of quarters that the machine returns

step 2 Work out examples by hand.

Let’s assume that a customer purchased an item that cost $2.25 and inserted a $5 bill. The cus- tomer is due $2.75, or two dollar coins and three quarters.

That is easy for you to see, but how can a C++ program come to the same conclusion? The computation is sim pler if you work in pennies, not dollars. The amount due the customer is 275 pennies. Dividing by 100 yields 2, the number of dollars. Dividing the remainder (75) by 25 yields 3, the number of quarters.

step 3 Write pseudocode for computing the answers.

In the previous step, you worked out a specific instance of the problem. You now need to come up with a method that works in general.

Given an arbitrary item price and payment, how can you compute the coins due? First, compute the amount due in pennies:

amount due = 100 x bill value - item price in pennies

To get the dollars, divide by 100 and discard the remainder:

dollar coins = amount due / 100 (without remainder)

h o W t o 2 . 1 carrying out computations

Many programming problems require that you carry out arithmetic computations. This How To shows you how to turn a problem statement into pseudocode and, ultimately, a C++ program.

For example, suppose you are asked to write a program that simulates a vending machine. A customer selects an item for purchase and inserts a bill into the vending machine. The vend- ing machine dispenses the purchased item and gives change. We will assume that all item prices are multiples of 25 cents, and the machine gives all change in dollar coins and quarters. Your task is to compute how many coins of each type to return.

A vending machine takes bills and gives change in coins.

cfe2_ch02_p29_74.indd 54 10/27/10 2:30 PM

2.4 problem solving: First do It By hand 55

step 1 Understand the problem: What are the inputs? What are the desired outputs?

step 2 Work out examples by hand.

Let’s assume that a customer purchased an item that cost $2.25 and inserted a $5 bill. The cus- tomer is due $2.75, or two dollar coins and three quarters.

step 3 Write pseudocode for computing the answers.

In the previous step, you worked out a specific instance of the problem. You now need to come up with a method that works in general.

Given an arbitrary item price and payment, how can you compute the coins due? First, compute the amount due in pennies:

amount due = 100 x bill value - item price in pennies

To get the dollars, divide by 100 and discard the remainder:

dollar coins = amount due / 100 (without remainder)

h o W t o 2 . 1 carrying out computations

Many programming problems require that you carry out arithmetic computations. This How To shows you how to turn a problem statement into pseudocode and, ultimately, a C++ program.

A vending machine takes bills and gives change in coins.

The remaining amount due can be computed in two ways. If you are familiar with the modu- lus operator, you can simply compute

amount due = amount due % 100

Alternatively, subtract the penny value of the dollar coins from the amount due:

amount due = amount due - 100 x dollar coins

To get the quarters due, divide by 25:

quarters = amount due / 25

step 4 Define the variables and constants that you need, and specify their types.

Here, we have five variables: • bill_value • item_price • amount_due • dollar_coins • quarters Should we introduce constants to explain 100 and 25 as PENNIES_PER_DOLLAR and PENNIES_PER_ QUARTER? Doing so will make it easier to convert the program to international markets, so we will take this step.

It is very important that amount_due and PENNIES_PER_DOLLAR are of type int because the com- putation of dollar_coins uses integer division. Similarly, the other variables are integers.

step 5 Turn the pseudocode into C++ statements.

If you did a thorough job with the pseudocode, this step should be easy. Of course, you have to know how to express mathematical operations (such as powers or integer division) in C++.

amount_due = PENNIES_PER_DOLLAR * bill_value - item_price; dollar_coins = amount_due / PENNIES_PER_DOLLAR; amount_due = amount_due % PENNIES_PER_DOLLAR; quarters = amount_due / PENNIES_PER_QUARTER;

step 6 Provide input and output.

Before starting the computation, we prompt the user for the bill value and item price:

cout << "Enter bill value (1 = $1 bill, 5 = $5 bill, etc.): "; cin >> bill_value; cout << "Enter item price in pennies: "; cin >> item_price;

When the computation is finished, we display the result. For extra credit, we use the setw manipulator to make sure that the output lines up neatly.

cout << "Dollar coins: " << setw(6) << dollar_coins << endl << "Quarters: " << setw(6) << quarters << endl;

step 7 Include the required headers and provide a main function.

We need the <iostream> header for all input and output. Because we use the setw manipula- tor, we also require <iomanip>. This program does not use any special mathematical functions. Therefore, we do not include the <cmath> header.

In the main function, you need to define constants and variables (Step 4), carry out com- putations (Step 5), and pro vide input and output (Step 6). Clearly, you will want to first get the input, then do the computations, and finally show the output. Define the constants at the beginning of the function, and define each variable just before it is needed.

cfe2_ch02_p29_74.indd 55 10/27/10 2:30 PM

56 Chapter 2 Fundamental data types

Here is the complete program, ch02/vending.cpp:

#include <iostream> #include <iomanip>

using namespace std;

int main() { const int PENNIES_PER_DOLLAR = 100; const int PENNIES_PER_QUARTER = 25;

cout << "Enter bill value (1 = $1 bill, 5 = $5 bill, etc.): "; int bill_value; cin >> bill_value; cout << "Enter item price in pennies: "; int item_price; cin >> item_price;

int amount_due = PENNIES_PER_DOLLAR * bill_value - item_price; int dollar_coins = amount_due / PENNIES_PER_DOLLAR; amount_due = amount_due % PENNIES_PER_DOLLAR; int quarters = amount_due / PENNIES_PER_QUARTER;

cout << "Dollar coins: " << setw(6) << dollar_coins << endl << "Quarters: " << setw(6) << quarters << endl; }

program run

Enter bill value (1 = $1 bill, 5 = $5 bill, etc.): 5 Enter item price in pennies: 225 Dollar coins: 2 Quarters: 3

2.5 strings Many programs process text, not numbers. Text consists of characters: letters, numbers, punc- tuation, spaces, and so on. A string is a sequence of characters. For example, the string "Harry" is a sequence of five char acters.

W o r k e d e x a m p l e 2 . 2 computing the cost of stamps

This Worked Example uses arithmetic functions to simulate a stamp vending machine.

strings are sequences of characters.

2.5.1 the string type

You can define variables that hold strings. string name = "Harry";

The string type is a part of the C++ standard. To use it, simply include the header file, <string>:

#include <string>

We distinguish between string variables (such as the variable name defined above) and string literals (char acter sequences enclosed in quotes, such as "Harry"). The string stored in a string variable can change. A string literal denotes a particular string, just as a number literal (such as 2) denotes a particular number.

Unlike number variables, string variables are guaranteed to be initialized even if you do not supply an initial value. By default, a string variable is set to an empty string: a string containing no characters. An empty string literal is written as "". The definition

string response;

has the same effect as string response = "";

2.5.2 Concatenation

Given two strings, such as "Harry" and "Morgan", you can concatenate them to one long string. The result consists of all characters in the first string, followed by all characters in the second string. In C++, you use the + operator to concatenate two strings. For example,

string fname = "Harry"; string lname = "Morgan"; string name = fname + lname;

results in the string "HarryMorgan"

What if you’d like the first and last name separated by a space? No problem: string name = fname + " " + lname;

This statement concatenates three strings: fname, the string literal " ", and lname. The result is

"Harry Morgan"

2.5.3 string Input

You can read a string from the console: cout << "Please enter your name: "; string name; cin >> name;

use the + operator to concatenate strings; that is, to put them together to yield a longer string.

Available online at www.wiley.com/college/horstmann.

cfe2_ch02_p29_74.indd 56 10/27/10 2:30 PM

www.wiley.com/college/horstmann

2.5 strings 57

Here is the complete program, ch02/vending.cpp:

#include <iostream> #include <iomanip>

using namespace std;

int main() { const int PENNIES_PER_DOLLAR = 100; const int PENNIES_PER_QUARTER = 25;

cout << "Enter bill value (1 = $1 bill, 5 = $5 bill, etc.): "; int bill_value; cin >> bill_value; cout << "Enter item price in pennies: "; int item_price; cin >> item_price;

cout << "Dollar coins: " << setw(6) << dollar_coins << endl << "Quarters: " << setw(6) << quarters << endl; }

program run

Enter bill value (1 = $1 bill, 5 = $5 bill, etc.): 5 Enter item price in pennies: 225 Dollar coins: 2 Quarters: 3

W o r k e d e x a m p l e 2 . 2 computing the cost of stamps

This Worked Example uses arithmetic functions to simulate a stamp vending machine.

strings are sequences of characters.

2.5.1 the string type

You can define variables that hold strings. string name = "Harry";

The string type is a part of the C++ standard. To use it, simply include the header file, <string>:

#include <string>

string response;

has the same effect as string response = "";

2.5.2 Concatenation

string fname = "Harry"; string lname = "Morgan"; string name = fname + lname;

results in the string "HarryMorgan"

What if you’d like the first and last name separated by a space? No problem: string name = fname + " " + lname;

This statement concatenates three strings: fname, the string literal " ", and lname. The result is

"Harry Morgan"

2.5.3 string Input

You can read a string from the console: cout << "Please enter your name: "; string name; cin >> name;

use the + operator to concatenate strings; that is, to put them together to yield a longer string.

cfe2_ch02_p29_74.indd 57 10/27/10 2:30 PM

58 Chapter 2 Fundamental data types

When a string is read with the >> operator, only one word is placed into the string variable. For example, suppose the user types

Harry Morgan

as the response to the prompt. This input consists of two words. After the call cin >> name, the string "Harry" is placed into the variable name. Use another input statement to read the second word.

2.5.4 string Functions

The number of characters in a string is called the length of the string. For example, the length of "Harry" is 5. You can compute the length of a string with the length function. Unlike the sqrt or pow function, the length function is invoked with the dot notation. That is, you write the string whose length you want, then a period, then the name of the function, followed by parentheses:

int n = name.length();

Many C++ functions require you to use this dot notation, and you must memorize (or look up) which do and which don’t. These functions are called member func- tions. We say that the member function length is invoked on the variable name.

Once you have a string, you can extract substrings by using the substr member function. The member function call

s.substr(start, length)

returns a string that is made from the characters in the string s, starting at character start, and containing length characters. Here is an example:

string greeting = "Hello, World!"; string sub = greeting.substr(0, 5); // sub is "Hello"

The substr operation makes a string that consists of five characters taken from the string greeting. Indeed, "Hello" is a string of length 5 that occurs inside greeting. A curious aspect of the substr operation is the starting position. Starting position 0 means “start at the beginning of the string”. The first position in a string is labeled 0, the second one 1, and so on. For example, here are the position numbers in the greet- ing string:

0 1 2 3 4 5 6 7 8 9 10 11 12

H e l l o , W o r l d !

The position number of the last character (12) is always one less than the length of the string.

Let’s figure out how to extract the substring "World". Count characters starting at 0, not 1. You find that W, the 8th character, has position number 7. The string you want is 5 characters long. Therefore, the appro priate substring command is

string w = greeting.substr(7, 5);

0 1 2 3 4 5 6 7 8 9 10 11 12

H e l l o , W o r l d !

the length member function yields the number of characters in a string.

a member function is invoked using the dot notation.

use the substr member function to extract a substring of a string.

cfe2_ch02_p29_74.indd 58 10/27/10 2:30 PM

2.5 strings 59

If you omit the length, you get all characters from the given position to the end of the string. For exam ple,

greeting.substr(7)

is the string "World!" (including the exclamation mark). Here is a simple program that puts these concepts to work. The program asks for

your name and that of your significant other. It then prints out your initials. The operation first.substr(0, 1) makes a string

consisting of one char acter, taken from the start of first. The program does the same for the second. Then it concatenates the resulting one-character strings with the string literal "&" to get a string of length 3, the initials string. (See Figure 4.)

ch02/initials.cpp

1 #include <iostream> 2 #include <string> 3 4 using namespace std; 5 6 int main() 7 { 8 cout << "Enter your first name: "; 9 string first;

10 cin >> first; 11 cout << "Enter your significant other's first name: "; 12 string second; 13 cin >> second; 14 string initials = first.substr(0, 1) 15 + "&" + second.substr(0, 1); 16 cout << initials << endl; 17 18 return 0; 19 }

program run

Enter your first name: Rodolfo Enter your significant other's first name: Sally R&S

Initials are formed from the first letter of each name.Figure 4 Building the initials string

0 1 2 R & Sinitials =

0 1 2 3 4 S a l l ysecond =

0 1 2 3 4 5 R o d o l f

6 ofirst =

cfe2_ch02_p29_74.indd 59 10/27/10 2:30 PM

60 Chapter 2 Fundamental data types

25.

table 8 string operations

statement result Comment

string str = "C"; str = str + "++";

str is set to "C++" When applied to strings, + denotes concatenation.

string str = "C" + "++"; error error: You cannot concatenate two string literals.

cout << "Enter name: "; cin >> name;

(User input: Harry Morgan)

name contains "Harry" The >> operator places the next word into the string variable.

cout << "Enter name: "; cin >> name >> last_name;

(User input: Harry Morgan)

name contains "Harry", last_name contains "Morgan"

Use multiple >> operators to read more than one word.

string greeting = "H & S"; int n = greeting.length();

n is set to 5 Each space counts as one character.

string str = "Sally"; string str2 = str.substr(1, 3);

str2 is set to "all" Extracts the substring of length 3 starting at position 1. (The initial position is 0.)

string str = "Sally"; string str2 = str.substr(1);

str2 is set to "ally" If you omit the length, all characters from the position until the end are included.

string a = str.substr(0, 1); a is set to the initial letter in str

Extracts the substring of length 1 starting at position 0.

string b = str.substr(str.length() - 1); b is set to the last letter in str

The last letter has position str.length() - 1. We need not specify the length.

What is the length of the string "C++ Program"? 26. Consider this string variable.

string str = "C++ Program";

Give a call to the substr member function that returns the substring "gram". 27. Use string concatenation to turn the string variable str from Self Check 26 to

"C++ Programming". 28. What does the following statement sequence print?

string str = "Harry"; cout << str.substr(0, 1) + str.substr(str.length() - 1);

29. Give an input statement to read a name of the form “John Q. Public”.

practice it Now you can try these exercises at the end of the chapter: R2.6, R2.9, P2.12, P2.19.

s e l F c h e c k

cfe2_ch02_p29_74.indd 60 10/27/10 2:30 PM

2.5 strings 61

Hebrew, Arabic, and English

the situation is much more dra matic in languages that use the Chi nese script: the Chinese dialects, Japanese, and korean. the Chinese script is not alphabetic but ideo- graphic. a character represents an idea or thing. most words are made up of one, two, or three of these ideo graphic characters. (over 50,000 ideo graphs are known, of which about 20,000 are in active use.) therefore, two bytes are needed to encode them. China, taiwan, Japan, and korea have incompatible encoding standards for them. (Japanese and korean writing uses a mixture of native syllabic and Chinese ideographic characters.)

the inconsistencies among charac ter encodings have been a major nui sance for international electronic commu- nication and for software man ufacturers vying for a global market. starting in 1988, a consortium of hardware and software manufacturers developed a uniform 21-bit encod- ing scheme called unicode that is capable of encoding text in essentially all writ ten languages of the world. about 100,000 characters have been given codes, including more than 70,000 Chinese, Japanese, and korean ideo graphs. there are even plans to add codes for extinct languages, such as egyptian hieroglyphs.

The Chinese Script

Random Fact 2.2 International alphabets and unicode the english alphabet is pretty simple: upper- and lowercase a to z. other euro-

pean languages have accent marks and special characters. For example, German has three so-called umlaut charac- ters, ä, ö, ü, and a double-s char acter ß. these are not optional frills; you couldn’t write a page of German text without using these characters a few times. German key- boards have keys for these characters.

The German Keyboard Layout

this poses a problem for computer users and designers. the american standard character encoding (called asCII, for american standard Code for Information Interchange) specifies 128 codes: 52 upper- and lowercase char acters, 10 digits, 32 typographical symbols, and 34 control charac- ters (such as space, newline, and 32 others for controlling printers and other devices). the umlaut and double-s are not among them. some German data processing systems replace seldom-used asCII characters with German letters: [ \ ] { | } ~ are replaced with Ä Ö Ü ä ö ü ß. While most people can live without these characters, C++ pro grammers defi- nitely cannot. other encoding schemes take advantage of the fact that one byte can encode 256 different characters, of which only 128 are standardized by asCII. unfor tunately, there are multiple incompati ble standards for such encod- ings, resulting in a certain amount of aggra vation among european computer users.

many countries don’t use the roman script at all. rus- sian, Greek, hebrew, arabic, and thai letters, to name just a few, have completely diff erent shapes. to complicate mat- ters, hebrew and arabic are typed from right to left. each of these alphabets has between 30 and 100 letters, and the countries using them have estab lished encoding standards for them.

cfe2_ch02_p29_74.indd 61 10/27/10 2:30 PM

62 Chapter 2 Fundamental data types

Write variable definitions in c++.

• A variable is a storage location with a name. • When defining a variable, you usually specify

an initial value. • When defining a variable, you also specify the

type of its values. • Use the int type for numbers that cannot have

a fractional part. • Use the double type for floating-point numbers. • An assignment statement stores a new value in a variable, replac ing the previously

stored value. • The assignment operator = does not denote mathematical equality. • You cannot change the value of a variable that is defined as const. • Use comments to add explanations for humans who read your code. The com-

piler ignores comments.

use the arithmetic operations in c++.

• Use * for multiplication and / for division. • The ++ operator adds 1 to a variable; the -- operator subtracts 1. • If both arguments of / are integers, the remain der is discarded. • The % operator computes the remainder of an integer division. • Assigning a floating-point variable to an inte ger drops the

fractional part. • The C++ library defines many mathematical functions such as sqrt (square root)

and pow (raising to a power).

Write programs that read user input and write formatted output.

• Use the >> operator to read a value and place it in a variable.

• You use manipulators to specify how val ues should be formatted.

carry out hand calculations when developing an algorithm.

• Pick concrete values for a typical situation to use in a hand calculation.

Write programs that process strings.

• Strings are sequences of characters. • Use the + operator to concatenate strings; that is, put them together to yield a

longer string. • The length member function yields the number of characters in a string.

C h a p t e r s u m m a r y • A member function is invoked using the dot notation. • Use the substr member function to extract a substring of a string

r2.1 What is the value of mystery after this sequence of statements? int mystery = 1; mystery = 1 - 2 * mystery; mystery = mystery + 1;

r2.2 What is wrong with the following sequence of statements? int mystery = 1; mystery = mystery + 1; int mystery = 1 - 2 * mystery;

r2.3 Write the following mathematical expressions in C++.

r2.4 Write the following C++ expressions in mathematical notation. a. dm = m * (sqrt(1 + v / c) / sqrt(1 - v / c) - 1); b. volume = PI * r * r * h; c. volume = 4 * PI * pow(r, 3) / 3; d. z = sqrt(x * x + y * y);

r2.5 What are the values of the following expressions? In each line, assume that double x = 2.5; double y = -1.5; int m = 18; int n = 4;

a. x + n * y - (x + n) * y b. m / n + m % n c. 5 * x - n / 5 d. 1 - (1 - (1 - (1 - (1 - n)))) e. sqrt(sqrt(n))

r2.6 What are the values of the following expressions? In each line, assume that string s = "Hello"; string t = "World";

r e V I e W e x e r C I s e s

cfe2_ch02_p29_74.indd 62 10/27/10 2:30 PM

review exercises 63

• A member function is invoked using the dot notation. • Use the substr member function to extract a substring of a string

r2.1 What is the value of mystery after this sequence of statements? int mystery = 1; mystery = 1 - 2 * mystery; mystery = mystery + 1;

r2.2 What is wrong with the following sequence of statements? int mystery = 1; mystery = mystery + 1; int mystery = 1 - 2 * mystery;

r2.3 Write the following mathematical expressions in C++.

s s v t gt

G a

p m m

= + +

= +

= ⋅ +

0 0 2

2 3

2 1 2

1 2

π ( )

FV PV INT 1000

YRS  

 

= + −c a b ab2 2 2 cosγ

r2.5 What are the values of the following expressions? In each line, assume that double x = 2.5; double y = -1.5; int m = 18; int n = 4;

a. x + n * y - (x + n) * y b. m / n + m % n c. 5 * x - n / 5 d. 1 - (1 - (1 - (1 - (1 - n)))) e. sqrt(sqrt(n))

r2.6 What are the values of the following expressions? In each line, assume that string s = "Hello"; string t = "World";

r e V I e W e x e r C I s e s

cfe2_ch02_p29_74.indd 63 10/27/10 2:30 PM

64 Chapter 2 Fundamental data types

a. s.length() + t.length() b. s.substr(1, 2) c. s.substr(s.length() / 2, 1) d. s + t e. t + s

r2.7 Find at least five compile-time errors in the following program. #include iostream

int main(); { cout << "Please enter two numbers:" cin << x, y; cout << "The sum of << x << "and" << y << "is: " x + y << endl; return; }

r2.8 Find at least four run-time errors in the following program. #include <iostream>

using namespace std;

int main() { int total; int x1; cout << "Please enter a number:"; cin >> x1; total = total + x1; cout << "Please enter another number:"; int x2; cin >> x2; total = total + x1; double average = total / 2; cout << "The average of the two numbers is " << average << "endl"; return 0; }

r2.9 Explain the differences between 2, 2.0, "2", and "2.0".

r2.10 Explain what each of the following program segments computes. a. int x = 2;

int y = x + x;

b. string s = "2"; string t = s + s;

r2.11 Write pseudocode for a program that reads a word and then prints the first charac ter, the last character, and the characters in the middle. For example, if the input is Harry, the program prints H y arr.

r2.12 Write pseudocode for a program that reads a name (such as Harold James Morgan) and then prints a monogram consisting of the initial letters of the first, middle, and last names (such as HJM).

cfe2_ch02_p29_74.indd 64 10/27/10 2:30 PM

review exercises 65

r2.13 Write pseudocode for a program that computes the first and last digit of a number. For example, if the input is 23456, the program should print out 2 and 6. Hint: %, log10.

r2.14 Modify the pseudocode for the program in How To 2.1 so that the pro gram gives change in quarters, dimes, and nickels. You can assume that the price is a multiple of 5 cents. To develop your pseudocode, first work with a couple of spe cific values.

r2.15 A cocktail shaker is composed of three cone sections. Using realistic values for the radii and heights, compute the total volume, using the formula given in Self Check 24 for a cone section. Then develop an algorithm that works for arbitrary dimensions.

r2.16 You are cutting off a piece of pie like this, where c is the length of the straight part (called the chord length) and h is the height of the piece.

There is an approximate formula for the area: A ch h

c ≈ +2

2 However, h is not so easy to measure, whereas the diameter d of a pie is usually well-known. Calculate the area where the diameter of the pie is 12 inches and the chord length of the segment is 10 inches. Gen eralize to an algorithm that yields the area for any diameter and chord length.

r2.17 The following pseudocode describes how to obtain the name of a day, given the day number (0 = Sunday, 1 = Monday, and so on.)

Define a string called names containing "SunMonTueWedThuFriSat". Compute the starting position as 3 x the day number. Extract the substring of names at the starting position with length 3.

Check this pseudocode, using the day number 4. Draw a diagram of the string that is being computed, similar to Figure 4 on page 59.

r2.18 The following pseudocode describes how to swap two letters in a word.

We are given a string str and two positions i and j. (i comes before j) Set first to the substring from the start of the string to the last position before i. Set middle to the substring from positions i + 1 to j - 1. Set last to the substring from position j + 1 to the end of the string. Concatenate the following five strings: first, the string containing just the character at position j, middle,

the string containing just the character at position i, and last.

Check this pseudocode, using the string "Gateway" and positions 2 and 4. Draw a diagram of the string that is being computed, similar to Figure 4 on page 59.

cfe2_ch02_p29_74.indd 65 10/27/10 2:30 PM

66 Chapter 2 Fundamental data types

r2.19 Run the following program, and explain the output you get. #include <iostream>

using namespace std;

int main() { int total; cout << "Please enter a number: "; double x1; cin >> x1; total = total + x1; cout << "total: " << total << endl; cout << "Please enter a number: "; double x2; cin >> x2; total = total + x2; cout << "total: " << total << endl; total = total / 2; cout << "total: " << total << endl; cout << "The average is " << total << endl; return 0; }

Note the trace messages (in blue) that are inserted to show the current contents of the total variable. How do you fix the program? (The program has two separate errors.)

r2.20 Write a program that prints the values 3 * 1000 * 1000 * 1000 3.0 * 1000 * 1000 * 1000

Explain the results.

r2.21 This chapter contains a number of recommendations regarding variables and con- stants that make programs easier to read and maintain. Briefly summarize these rec ommendations.

p2.1 Write a program that displays the dimensions of a letter-size (8.5 × 11 inches) sheet of paper in millimeters. There are 25.4 millimeters per inch. Use con stants and com- ments in your program.

p2.2 Write a program that computes and displays the circumference of a letter-size (8.5 × 11 inches) sheet of paper and the length of its diagonal.

p2.3 Write a program that reads a number and displays the square, cube, and fourth power. Use the pow function only for the fourth power.

p2.4 Write a program that prompts the user for two integers and then prints • The sum • The difference

p r o G r a m m I n G e x e r C I s e s

cfe2_ch02_p29_74.indd 66 10/27/10 2:30 PM

programming exercises 67

• The product • The average

p2.5 Write a program that prompts the user for two integers and then prints • The distance (absolute value of the difference) • The maximum (the larger of the two) • The minimum (the smaller of the two)

Hint: The max and min functions are defined in the <algorithm> header.

p2.6 Write a program that prompts the user for a measurement in meters and then con verts it to miles, feet, and inches.

p2.7 Write a program that prompts the user for a radius and then prints • The area and circumference of a circle with that radius • The volume and surface area of a sphere with that radius

p2.8 Write a program that asks the user for the lengths of the sides of a rectangle and then prints

• The area and perimeter of the rectangle • The length of the diagonal (use the Pythagorean theorem)

p2.9 Improve the program discussed in the How To 2.1 to allow input of quarters in addition to bills.

p2.10 Write a program that helps a person decide whether to buy a hybrid car. Your pro gram’s inputs should be:

• The cost of a new car • The estimated miles driven per year • The estimated gas price • The estimated resale value after 5 years

Compute the total cost of owning the car for 5 years. (For simplic ity, we will not take the cost of financing into account.) Obtain realistic prices for a new and used hybrid and a comparable car from the Web. Run your program twice, using today’s gas price and 15,000 miles per year. Include pseudo- code and the program runs with your assignment.

p2.11 The following pseudocode describes how a bookstore computes the price of an order from the total price and the number of the books that were ordered.

Read the total book price and the number of books. Compute the tax (7.5% of the total book price). Compute the shipping charge ($2 per book). The price of the order is the sum of the total book price, the tax, and the shipping charge. Print the price of the order.

Translate this pseudocode into a C++ program.

cfe2_ch02_p29_74.indd 67 10/27/10 2:30 PM

68 Chapter 2 Fundamental data types

p2.12 The following pseudocode describes how to turn a string containing a ten-digit phone number (such as "4155551212") into a more readable string with parentheses and dashes, like this: "(415) 555-1212".

Take the substring consisting of the first three characters and surround it with "(" and ")". This is the area code.

Concatenate the area code, the substring consisting of the next three characters, a hyphen, and the substring consisting of the last four characters. This is the formatted number.

Translate this pseudocode into a C++ program that reads a telephone number into a string variable, com putes the formatted number, and prints it.

p2.13 The following pseudocode describes how to extract the dollars and cents from a price given as a floating-point value. For example, a price 2.95 yields values 2 and 95 for the dollars and cents.

Assign the price to an integer variable dollars. Multiply the difference price - dollars by 100 and add 0.5. Assign the result to an integer variable cents.

Translate this pseudocode into a C++ program. Read a price and print the dollars and cents. Test your program with inputs 2.95 and 4.35.

p2.14 Giving change. Implement a program that directs a cashier how to give change. The program has two inputs: the amount due and the amount received from the customer. Display the dollars, quarters, dimes, nickels, and pennies that the customer should receive in return.

p2.15 Write a program that asks the user to input • The number of gallons of gas in the tank • The fuel efficiency in miles per gallon • The price of gas per gallon

Then print the cost per 100 miles and how far the car can go with the gas in the tank.

p2.16 File names and extensions. Write a program that prompts the user for the drive letter (C), the path (\Windows\System), the file name (Readme), and the extension (txt). Then print the complete file name C:\Windows\System\Readme.txt. (If you use UNIX or a Macintosh, skip the drive name and use / instead of \ to separate directories.)

p2.17 Write a program that reads a number between 1,000 and 999,999 from the user and prints it with a comma separating the thousands. Here is a sample dialog; the user input is in color:

Please enter an integer between 1000 and 999999: 23456 23,456

p2.18 Write a program that reads a number between 1,000 and 999,999 from the user, where the user enters a comma in the input. Then print the number without a comma. Here is a sample dialog; the user input is in color:

Please enter an integer between 1,000 and 999,999: 23,456 23456

Hint: Read the input as a string. Measure the length of the string. Suppose it contains n characters. Then extract substrings consisting of the first n – 4 characters and the last three characters.

cfe2_ch02_p29_74.indd 68 10/27/10 2:30 PM

programming exercises 69

p2.19 Printing a grid. Write a program that prints the following grid to play tic-tac-toe. +--+--+--+ | | | | +--+--+--+ | | | | +--+--+--+ | | | | +--+--+--+

Of course, you could simply write seven statements of the form

cout << "+--+--+--+";

You should do it the smart way, though. Define string variables to hold two kinds of patterns: a comb-shaped pattern

+--+--+--+ | | | |

and the bottom line. Print the comb three times and the bottom line once.

p2.20 Write a program that reads an integer and breaks it into a sequence of individual digits. For example, the input 16384 is displayed as

1 6 3 8 4

You may assume that the input has no more than five digits and is not negative.

p2.21 Write a program that reads two times in military format (0900, 1730) and prints the number of hours and minutes between the two times. Here is a sample run. User input is in color.

Please enter the first time: 0900 Please enter the second time: 1730 8 hours 30 minutes

Extra credit if you can deal with the case where the first time is later than the second: Please enter the first time: 1730 Please enter the second time: 0900 15 hours 30 minutes

p2.22 Writing large letters. A large letter H can be produced like this: * * * * ***** * * * *

It can be defined as a string constant like this: const string LETTER_H = "* *\n* *\n*****\n* *\n* *\n";

(The \n character is explained in Special Topic 1.1.) Do the same for the letters E, L, and O. Then write the message

H E L L O

in large letters.

cfe2_ch02_p29_74.indd 69 10/27/10 2:30 PM

70 Chapter 2 Fundamental data types

p2.23 Write a program that transforms numbers 1, 2, 3, …, 12 into the corresponding month names January, February, March, …, December. Hint: Make a very long string "January February March ...", in which you add spaces such that each month name has the same length. Then use substr to extract the month you want.

engineering p2.24 Consider the following circuit.

R2 R3

Write a program that reads the resistances of the three resistors and computes the total resistance, using Ohm’s law.

engineering p2.25 The dew point temperature Td can be calculated (approximately) from the relative humidity RH and the actual temperature T by

T b f T RH

a f T RH

f T RH a T b T

d = ⋅ ( ) − ( )

( ) = ⋅ +

+ ( )

, ln

where a = 17.27 and b = 237.7° C. Write a program that reads the relative humidity (between 0 and 1) and the tem- perature (in degrees C) and prints the dew point value. Use the C++ function log to compute the natural logarithm.

engineering p2.26 The pipe clip temperature sensors shown here are robust sensors that can be clipped directly onto copper pipes to measure the temperature of the liquids in the pipes.

Each sensor contains a device called a thermistor. Thermistors are semiconductor devices that exhibit a temperature-dependent resistance described by:

R R e T T

= −



 



 

1 1

cfe2_ch02_p29_74.indd 70 10/27/10 2:30 PM

programming exercises 71

where R is the resistance (in Ω) at the temperature T (in °K), and R0 is the resistance (in Ω) at the temperature T0 (in °K). β is a constant that depends on the material used to make the thermistor. Thermistors are specified by providing values for R0, T0, and β. The thermistors used to make the pipe clip temperature sensors have R0 = 1075 Ω at T0 = 85 °C, and β = 3969 °K. (Notice that β has units of °K. Recall that the tempera- ture in °K is obtained by adding 273 to the temperature in °C.) The liquid tempera- ture, in °C, is determined from the resistance R, in Ω, using

T T

T R

= 

 



  +

− β

0 0

273

Write a C++ program that prompts the user for the thermistor resistance R and prints a message giving the liquid temperature in °C.

engineering p2.27 The circuit shown below illustrates some important aspects of the connection between a power company and one of its customers. The customer is represented by three parameters, Vt, P, and pf. Vt is the voltage accessed by plugging into a wall outlet. Customers depend on having a dependable value of Vt in order for their appliances to work properly. Accordingly, the power company regulates the value of Vt carefully. P describes the amount of power used by the customer and is the primary factor in determining the customer’s electric bill. The power factor, pf, is less familiar. (The power factor is calculated as the cosine of an angle so that its value will always be between zero and one.) In this problem you will be asked to write a C++ program to investigate the significance of the power factor.

Customer

+ –

R = 10 Ω

Power Lines

Power Company

R = 10 Ω

P = 260 W p f = 0.6

Vt = 120 Vrms

–

In the figure, the power lines are represented, somewhat simplistically, as resistances in Ohms. The power company is represented as an AC voltage source. The source voltage, Vs, required to provide the customer with power P at voltage Vt can be determined using the formula

V V RP V

RP pf V

pfs t t t

= + 

 

 +



 

 −( )2 2 1

2 2 2

(Vs has units of Vrms.) This formula indicates that the value of Vs depends on the value of pf. Write a C++ program that prompts the user for a power factor value and

cfe2_ch02_p29_74.indd 71 10/27/10 2:30 PM

72 Chapter 2 Fundamental data types

then prints a message giving the corresponding value of Vs, using the values for P, R, and Vt shown in the figure above.

engineering p2.28 Consider the following tuning circuit connected to an antenna, where C is a variable capacitor whose capacitance ranges from Cmin to Cmax.

L C

Antenna

The tuning circuit selects the frequency f LC

= 2π

. To design this circuit for a given

frequency, take C C C= min max and calculate the required inductance L from f and

C. Now the circuit can be tuned to any frequency in the range f LC

min max

= 2π

f LC

max min

= 2π

Write a C++ program to design a tuning circuit for a given frequency, using a vari- able capacitor with given values for Cmin and Cmax. (A typical input is f = 16.7 MHz, Cmin = 14 pF, and Cmax = 365 pF.) The program should read in f (in Hz), Cmin and Cmax (in F), and print the required inductance value and the range of frequencies to which the circuit can be tuned by varying the capacitance.

engineering p2.29 According to the Coulomb force law, the electric force between two charged par- ticles of charge Q1 and Q2 Coulombs, that are a distance r meters apart, is

F Q Q

r = 1 2

24 π ε Newtons, where ε = × −8 854 10 12. Farads/meter. Write a program

that calculates the force on a pair of charged particles, based on the user input of Q1 Coulombs, Q2 Coulombs, and r meters, and then computes and displays the electric force.

1. One possible answer is int bottles_per_case = 8;

You may choose a different variable name or a different initialization value, but your variable should have type int.

2. There are three errors: • You cannot have spaces in variable names. • The variable type should be double because it holds a fractional value. • There is a semicolon missing at the end of the statement.

3. double unit_price = 1.95; int quantity = 2;

4. cout << "Total price: " << unit_price * quantity << endl; 5. Change the definition of cans_per_pack to

int cans_per_pack = 4;

6. You need to use a */ delimiter to close a comment that begins with a /*: double can_volume = 0.355; /* Liters in a 12-ounce can */

7. The program would compile, and it would display the same result. However, a per son reading the program might find it confusing that fractional cans are being con sidered.

8. Its value is modified by the assignment statement. 9. Assignment would occur when one car is replaced by another in the parking space.

10. double interest = balance * p / 100; 11. double side_length = sqrt(area); 12. 4 * PI * pow(radius, 3) / 3

or (4.0 / 3) * PI * pow(radius, 3), but not (4 / 3) * PI * pow(radius, 3)

13. 172 and 9 14. int leftover = 12 - amount % 12; 15. There is no prompt that alerts the program user to enter the quantity. 16. The unit_price variable is defined as an int. If the user were to enter a price such as

1.95, only the 1 would be placed into the variable. 17. The output is

The total volume is20

Note that there is no space between the is and 20. 18. cout << "$" << fixed << setprecision(2) << total_price;

19. cout << "Bottles: " << setw(8) << bottles << endl << "Cans: " << setw(8) << cans << endl;

Note that the setw manipulator appears twice. Also note the added spaces in the string "Cans: ".

a n s W e r s t o s e l F - C h e C k Q u e s t I o n s

cfe2_ch02_p29_74.indd 72 10/27/10 2:30 PM

answers to self-Check Questions 73

1. One possible answer is int bottles_per_case = 8;

You may choose a different variable name or a different initialization value, but your variable should have type int.

3. double unit_price = 1.95; int quantity = 2;

4. cout << "Total price: " << unit_price * quantity << endl; 5. Change the definition of cans_per_pack to

int cans_per_pack = 4;

6. You need to use a */ delimiter to close a comment that begins with a /*: double can_volume = 0.355; /* Liters in a 12-ounce can */

7. The program would compile, and it would display the same result. However, a per son reading the program might find it confusing that fractional cans are being con sidered.

8. Its value is modified by the assignment statement. 9. Assignment would occur when one car is replaced by another in the parking space.

10. double interest = balance * p / 100; 11. double side_length = sqrt(area); 12. 4 * PI * pow(radius, 3) / 3

or (4.0 / 3) * PI * pow(radius, 3), but not (4 / 3) * PI * pow(radius, 3)

1.95, only the 1 would be placed into the variable. 17. The output is

The total volume is20

Note that there is no space between the is and 20. 18. cout << "$" << fixed << setprecision(2) << total_price;

19. cout << "Bottles: " << setw(8) << bottles << endl << "Cans: " << setw(8) << cans << endl;

Note that the setw manipulator appears twice. Also note the added spaces in the string "Cans: ".

a n s W e r s t o s e l F - C h e C k Q u e s t I o n s

cfe2_ch02_p29_74.indd 73 10/27/10 2:30 PM

74 Chapter 2 Fundamental data types

20. int pairs = (total_width - tile_width) / (2 * tile_width); int tiles = 1 + 2 * pairs; double gap = (total_width - tiles * tile_width) / 2;

Be sure that pairs is declared as an int. 21. Now there are groups of four tiles (gray/white/gray/black) following the initial

black tile. Therefore, the algorithm is now number of groups = integer part of (total width - tile width) / (4 x tile width) number of tiles = 1 + 4 x number of groups

The formula for the gap is not changed. 22. Clearly, the answer depends only on whether the row and column numbers are even

or odd, so let’s first take the remainder after dividing by 2. Then we can enumerate all expected answers: Row % 2 Column % 2 Color 0 0 0 0 1 1 1 0 1 1 1 0

In the first three entries of the table, the color is simply the sum of the remainders. In the fourth entry, the sum would be 2, but we want a zero. We can achieve that by taking another remainder operation: color = ((row % 2) + (column % 2)) % 2

23. In nine years, the repair costs increased by $1,400. Therefore, the increase per year is $1,400 / 9 ≈ $156. The repair cost in year 3 would be $100 + 2 × $156 = $412. The repair cost in year n is $100 + n × $156. To avoid accumulation of roundoff errors, it is actually a good idea to use the original expression that yielded $156, that is, Repair cost in year n = 100 + n x 1400 / 9

24. The pseudocode follows easily from the equations. bottom volume = p x r1

2 x h1 top volume = p x r2

2 x h2 middle volume = p x (r1

2 + r1 x r2 + r2 2) x h3 / 3

total volume = bottom volume + top volume + middle volume

Measuring a typical wine bottle yields r1 = 3.6, r2 = 1.2, h1 = 15, h2 = 7, h3 = 6 (all in centimeters). Therefore, bottom volume = 610.73 top volume = 31.67 middle volume = 135.72 total volume = 778.12 The actual volume is 750 ml, which is close enough to our computation to give confi- dence that it is cor rect.

25. The length is 11. The space counts as a character. 26. str.substr(7, 4) 27. str = str + "ming"; 28. Hy 29. cin >> first_name >> middle_initial >> last_name;

A robot needs to retrieve an item that is located in rocky terrain adjacent to a road. The robot can travel at a faster speed on the road than on the rocky terrain, so it will want to do so for a certain distance before moving on a straight line to the item.

Your task is to compute the total time taken by the robot to reach its goal, given the following inputs: • The distance between the robot and the item in

the x- and y-direction (dx and dy) • The speed of the robot on the road and the

rocky terrain (s1 and s2) • The length l1 of the first segment (on the road)

To make the problem more concrete, let’s assume the following dimen sions: The total time is the time for traversing both segments. The time to traverse the first seg-

ment is simply the length of the segment divided by the speed: 6 km divided by 5 km/h, or 1.2 hours.

W o r k e d e x a m p l e 2 . 1 computing travel time

In this example, we develop a hand calculation to compute the time that a robot requires to retrieve an item from rocky terrain.

dx Item

Robot

Speed = s1

Speed = s2 l2

10 km

3 km Item

Robot

6 km

Speed = 5 km/h

Speed = 2 km/h

cfe2_ch02_p29_74.indd 74 10/27/10 2:30 PM

3C h a p t e r

D e C i s i o n s

to be able to implement decisions using if statements

to learn how to compare integers, floating-point numbers, and strings

to understand the Boolean data type

to develop strategies for validating user input

C h a p t e r G o a l s

C h a p t e r C o n t e n t s

3.1 The if STaTemenT 76

Syntax 3.1: if statement 78 Programming Tip 3.1: Brace layout 79 Programming Tip 3.2: always Use Braces 80 Common Error 3.1: a semicolon after the

if Condition 80 Programming Tip 3.3: tabs 81 Special Topic 3.1: the selection operator 81 Programming Tip 3.4: avoid Duplication in

Branches 82

3.2 Comparing numberS and STringS 82

Syntax 3.2: Comparisons 83 Common Error 3.2: Confusing = and == 85 Programming Tip 3.5: Compile with Zero

Warnings 85 Common Error 3.3: exact Comparison of

Floating-point numbers 86 Special Topic 3.2: lexicographic ordering

of strings 86 How To 3.1: implementing an if statement 87 Worked Example 3.1: extracting the Middle Random Fact 3.1: the Denver airport luggage

handling system 89

3.3 mulTiple alTernaTiveS 90

Special Topic 3.3: the switch statement 93

3.4 neSTed branCheS 94

Programming Tip 3.6: hand-tracing 97 Common Error 3.4: the Dangling else problem 98

3.5 problem Solving: flowCharTS 99

3.6 problem Solving: TeST CaSeS 102

Programming Tip 3.7: Make a schedule and Make time for Unexpected problems 103

3.7 boolean variableS and operaTorS 103

Common Error 3.5: Combining Multiple relational operators 107

Common Error 3.6: Confusing && and || Conditions 107

Special Topic 3.4: short-Circuit evaluation of Boolean operators 108

Special Topic 3.5: De Morgan’s law 108

3.8 appliCaTion: inpuT validaTion 109

Random Fact 3.2: artificial intelligence 112

cfe2_ch03_p75_130.indd 75 10/28/10 7:51 PM

one of the essential features of computer programs is their ability to make decisions. like a train that changes tracks depending on how the switches are set, a program can take different actions, depending on inputs and other circumstances.

in this chapter, you will learn how to program simple and complex decisions. You will apply what you learn to the task of checking user input.

3.1 the if statement The if statement is used to implement a decision. When a condition is fulfilled, one set of statements is executed. Otherwise, another set of statements is executed (see Syntax 3.1).

Here is an example using the if statement. In many countries, the number 13 is considered unlucky. Rather than offending supersti tious ten- ants, building owners sometimes skip the thirteenth floor; floor 12 is immediately followed by floor 14. Of course, floor 13 is not usually left empty or, as some conspiracy theorists believe, filled with secret offices and research labs. It is simply called floor 14. The computer that controls the building eleva- tors needs to compensate for this foible and adjust all floor numbers above 13.

Let’s simulate this process in C++. We will ask the user to type in the desired floor number and then compute the actual floor. When the input is above 13, then we need to decrement the input to obtain the actual floor. For example, if the user provides an input of 20, the program determines the actual floor as 19. Otherwise, we simply use the supplied floor number.

int actual_floor;

if (floor > 13) { actual_floor = floor - 1; } else { actual_floor = floor; }

The flowchart in Figure 1 shows the branching behavior. In our example, each branch of the if statement contains a single statement. You

can include as many statements in each branch as you like. Sometimes, it happens that

the if statement allows a program to carry out different actions depending on the nature of the data to be processed.

This elevator panel “skips” the thirteenth floor. The floor is not actually missing—the computer that controls the elevator adjusts the floor numbers above 13.

cfe2_ch03_p75_130.indd 76 10/28/10 7:51 PM

3.1 the if statement 77

figure 1 Flowchart for if statement

floor > 13? True False

actual_floor = floor - 1

actual_floor = floor

Condition

figure 2 Flowchart for if statement with no else Branch

floor > 13? True False

actual_floor--

No else branch

there is nothing to do in the else branch of the statement. In that case, you can omit it entirely, such as in this example:

int actual_floor = floor;

if (floor > 13) { actual_floor--; } // No else needed

See Figure 2 for the flowchart. The following program puts the if statement to work. This program asks for the

desired floor and then prints out the actual floor.

An if statement is like a fork in the road. Depending upon a decision, different parts of the program are executed.

cfe2_ch03_p75_130.indd 77 10/28/10 7:51 PM

78 Chapter 3 Decisions

1. In some Asian countries, the number 14 is considered unlucky. Some building owners play it safe and skip both the thirteenth and the fourteenth floor. How would you modify the sample program to handle such a building?

2. Consider the following if statement to compute a discounted price: if (original_price > 100) { discounted_price = original_price - 20; } else { discounted_price = original_price - 10; }

What is the discounted price if the original price is 95? 100? 105? 3. Compare this if statement with the one in Self Check 2:

if (original_price < 100) { discounted_price = original_price - 10; } else { discounted_price = original_price - 20; }

Do the two statements always compute the same value? If not, when do the values differ?

4. Consider the following statements to compute a discounted price: discounted_price = original_price; if (original_price > 100) { discounted_price = original_price - 10; }

What is the discounted price if the original price is 95? 100? 105? 5. The variables fuel_amount and fuel_capacity hold the actual amount of fuel and the

size of the fuel tank of a vehicle. If less than 10 percent is remaining in the tank, a status light should show a red color; otherwise it shows a green color. Simulate this process by printing out either "red" or "green".

practice it Now you can try these exercises at the end of the chapter: R3.3, R3.4, P3.16.

brace layout

Programmers vary in how they align braces in their code. In this book, we follow the simple rule of making { and } line up.

if (floor > 13) { floor--; }

This style makes it easy to spot matching braces.

S e l f C h e C k

programming tip 3.1

Properly lining up your code makes your programs easier to read.

ch03/elevator1.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 int main() 6 { 7 int floor; 8 cout << "Floor: "; 9 cin >> floor;

10 int actual_floor; 11 if (floor > 13) 12 { 13 actual_floor = floor - 1; 14 } 15 else 16 { 17 actual_floor = floor; 18 } 19 20 cout << "The elevator will travel to the actual floor " 21 << actual_floor << endl; 22 23 return 0; 24 }

program run

Floor: 20 The elevator will travel to the actual floor 19

syntax 3.1 if statement

if (floor > 13) { actual_floor = floor - 1; } else { actual_floor = floor; }

A condition that is true or false. Often uses relational operators: == != < <= > >= (See page 83.)

If the condition is true, the statement(s) in this branch are executed in sequence; if the condition is false, they are skipped.

Braces are not required if the branch contains a single statement, but it's good to always use them. See page 80.

If the condition is false, the statement(s) in this branch are executed in sequence; if the condition is true, they are skipped.

Lining up braces is a good idea.

See page 79.

Omit the else branch if there is nothing to do.

Don’t put a semicolon here! See page 80.

cfe2_ch03_p75_130.indd 78 10/28/10 7:51 PM

3.1 the if statement 79

2. Consider the following if statement to compute a discounted price: if (original_price > 100) { discounted_price = original_price - 20; } else { discounted_price = original_price - 10; }

What is the discounted price if the original price is 95? 100? 105? 3. Compare this if statement with the one in Self Check 2:

if (original_price < 100) { discounted_price = original_price - 10; } else { discounted_price = original_price - 20; }

Do the two statements always compute the same value? If not, when do the values differ?

4. Consider the following statements to compute a discounted price: discounted_price = original_price; if (original_price > 100) { discounted_price = original_price - 10; }

What is the discounted price if the original price is 95? 100? 105? 5. The variables fuel_amount and fuel_capacity hold the actual amount of fuel and the

practice it Now you can try these exercises at the end of the chapter: R3.3, R3.4, P3.16.

brace layout

Programmers vary in how they align braces in their code. In this book, we follow the simple rule of making { and } line up.

if (floor > 13) { floor--; }

This style makes it easy to spot matching braces.

S e l f C h e C k

programming tip 3.1

Properly lining up your code makes your programs easier to read.

cfe2_ch03_p75_130.indd 79 10/28/10 7:51 PM

80 Chapter 3 Decisions

Tabs

Block-structured code has the property that nested statements are indented by one or more levels:

int main() { | int floor; | ... | if (floor > 13) | { | | floor--; | } | | ... | return 0; } | | 0 1 2 Indentation level

How do you move the cursor from the leftmost column to the appropriate indentation level? A perfectly reasonable strategy is to hit the space bar a suf ficient number of times. However, many pro- grammers use the Tab key instead. A tab moves the cursor to the next indentation level.

While the Tab key is nice, some editors use tab characters for alignment, which is not so nice. Tab characters can lead to problems when you send your file to another person or a printer. There is no universal agreement on the width of a tab character, and some soft ware will ignore tabs altogether. It is therefore best to save your files with spaces instead of tabs. Most editors have a setting to auto matically convert all tabs to spaces. Look at the documentation of your development environment to find out how to activate this useful setting.

The Selection operator

C++ has a selection operator of the form

condition ? value1 : value2 The value of that expression is either value1 if the test passes or value2 if it fails. For example, we can compute the actual floor number as

actual_floor = floor > 13 ? floor - 1 : floor;

which is equivalent to

if (floor > 13) { actual_floor = floor - 1; } else { actual_floor = floor; }

You can use the selection operator anywhere that a value is expected, for example:

cout << "Actual floor: " << (floor > 13 ? floor - 1 : floor);

We don’t use the selection operator in this book, but it is a convenient construct that you will find in many C++ pro grams.

programming tip 3.3

You use the Tab key to move the cursor to the next indentation level.

special topic 3.1

Some programmers put the opening brace on the same line as the if:

if (floor > 13) { floor--; }

This style makes it harder to match the braces, but it saves a line of code, allowing you to view more code on the screen without scroll ing. There are passionate advocates of both styles.

It is important that you pick a layout style and stick with it con sistently within a given programming project. Which style you choose may depend on your personal preference or a coding style guide that you need to follow.

always use braces

When the body of an if statement consists of a single statement, you need not use braces. For example, the following is legal:

if (floor > 13) floor--;

However, it is a good idea to always include the braces:

if (floor > 13) { floor--; }

The braces makes your code easier to read, and you are less likely to make errors such as the one described in Common Error 3.1.

a Semicolon after the if Condition

The following code fragment has an unfortunate error:

if (floor > 13) ; // ERROR { floor--; }

There should be no semicolon after the if condition. The compiler interprets this statement as follows: If floor is greater than 13, execute the statement that is denoted by a single semicolon, that is, the do-nothing statement. The statement enclosed in braces is no longer a part of the if statement. It is always executed. Even if the value of floor is not above 13, it is decremented.

Placing a semicolon after the else reserved word is also wrong:

if (floor > 13) { actual_floor = floor - 1; } else ; { actual_floor = floor; }

In this case, the do-nothing statement is executed if floor > 13 is not fulfilled. This is the end of the if statement. The next statement, enclosed in braces, is executed in both cases; that is, actual_floor is always set to floor.

programming tip 3.2

Common error 3.1

cfe2_ch03_p75_130.indd 80 10/28/10 7:51 PM

3.1 the if statement 81

Tabs

Block-structured code has the property that nested statements are indented by one or more levels:

int main() { | int floor; | ... | if (floor > 13) | { | | floor--; | } | | ... | return 0; } | | 0 1 2 Indentation level

The Selection operator

C++ has a selection operator of the form

condition ? value1 : value2 The value of that expression is either value1 if the test passes or value2 if it fails. For example, we can compute the actual floor number as

actual_floor = floor > 13 ? floor - 1 : floor;

which is equivalent to

if (floor > 13) { actual_floor = floor - 1; } else { actual_floor = floor; }

You can use the selection operator anywhere that a value is expected, for example:

cout << "Actual floor: " << (floor > 13 ? floor - 1 : floor);

We don’t use the selection operator in this book, but it is a convenient construct that you will find in many C++ pro grams.

programming tip 3.3

You use the Tab key to move the cursor to the next indentation level.

special topic 3.1

cfe2_ch03_p75_130.indd 81 10/28/10 7:51 PM

82 Chapter 3 Decisions

avoid duplication in branches

Look to see whether you duplicate code in each branch. If so, move it out of the if statement. Here is an example of such duplication:

if (floor > 13) { actual_floor = floor - 1; cout << "Actual floor: " << actual_floor << endl; } else { actual_floor = floor; cout << "Actual floor: " << actual_floor << endl; }

The output statement is exactly the same in both branches. This is not an error—the program will run correctly. However, you can simplify the program by moving the duplicated state- ment, like this:

if (floor > 13) { actual_floor = floor - 1; } else { actual_floor = floor; } cout << "Actual floor: " << actual_floor << endl;

Removing duplication is particularly important when programs are maintained for a long time. When there are two sets of statements with the same effect, it can easily happen that a programmer modifies one set but not the other.

3.2 Comparing numbers and strings Every if statement contains a condi- tion. In many cases, the condition involves comparing two values. For example, in the previous examples we tested floor > 13. The comparison > is called a relational operator. C++ has six relational operators (see Table 1).

As you can see, only two C++ rela- tional operators (> and <) look as you would expect from the mathe matical notation. Computer keyboards do not have keys for ≥, ≤, or ≠, but the >=, <=, and != operators are easy to remem- ber because they look similar. The == operator is initially confusing to most newcomers to C++. In C++, = already has a meaning, namely assignment.

programming tip 3.4

In C++, you use a relational operator to check whether one value is greater than another.

relational operators (< <= > >= == !=) are used to compare numbers and strings.

cfe2_ch03_p75_130.indd 82 10/28/10 7:51 PM

3.2 Comparing numbers and strings 83

table 1 relational operators

C++ Math notation Description

> > Greater than

>= ≥ Greater than or equal

< < Less than

<= ≤ Less than or equal

== = Equal

!= ≠ Not equal

The == operator denotes equality testing: floor = 13; // Assign 13 to floor if (floor == 13) // Test whether floor equals 13

You must remember to use == inside tests and to use = outside tests. (See Common Error 3.2 on page 85 for more information.)

You can compare strings as well: if (input == "Quit") ...

Use != to check whether two strings are different. In C++, letter case matters. For example, "Quit" and "quit" are not the same string.

syntax 3.2 Comparisons

floor > 13

floor == 13

string input; if (input == "Y")

double x; double y; const double EPSILON = 1E-14; if (fabs(x - y) < EPSILON)

These quantities are compared.

Checks for equality.

Check that you have the right direction: > (greater) or < (less)

Use ==, not =. See page 85.

One of: == != < <= > >= (See page 83.)

Ok to compare strings. (See page 86.)

Checks that these floating-point numbers are very close. See page 86.

Check the boundary condition: Do you want to include (>=) or exclude (>)?

cfe2_ch03_p75_130.indd 83 10/28/10 7:51 PM

84 Chapter 3 Decisions

10. How do you test that a string str is not the empty string?

practice it Now you can try these exercises at the end of the chapter: R3.2, R3.5, P3.14.

Confusing = and ==

The rule for the correct usage of = and == is very simple: In tests, always use == and never use =. If it is so simple, why can’t the compiler be helpful and flag any errors?

Actually, the C++ language allows the use of = inside tests. To understand this, we have to go back in time. The creators of C, the predecessor to C++, were very frugal. They did not want to have special values true and false. Instead, they allowed any numeric value inside a condition, with the convention that 0 denotes false and any non-0 value denotes true. Fur- thermore, in C and C++ assignments have values. For example, the value of the assignment expression floor = 13 is 13.

These two features—namely that numbers can be used as truth values and that assignments are expressions with values—conspire to make a horrible pitfall. The test

if (floor = 13) // ERROR

is legal C++, but it does not test whether floor and 13 are equal. Instead, the code sets floor to 13, and since that value is not zero, the condition of the if statement is always fulfilled.

Fortunately, most compilers issue a warning when they encounter such a statement. You should take such warn ings seriously. (See Programming Tip 3.5 for more advice about com- piler warnings.)

Some shell-shocked programmers are so nervous about using = that they use == even when they want to make an assignment:

floor == floor - 1; // ERROR

This statement tests whether floor equals floor - 1. It doesn’t do anything with the outcome of the test, but that is not an error. Some compilers will warn that “the code has no effect”, but others will quietly accept the code.

Compile with Zero warnings

There are two kinds of messages that the compiler gives you: errors and warnings. Error mes- sages are fatal; the com piler will not translate a program with one or more errors. Warning messages are advisory; the compiler will translate the program, but there is a good chance that the program will not do what you expect it to do.

It is a good idea to learn how to activate warnings with your compiler, and to write code that emits no warnings at all. For example, consider the test

if (floor = 13)

One C++ compiler emits a curious warning message: “Suggest parentheses around assignment used as truth value”. Sadly, the message is misleading because it was not written for students. Nevertheless, such a warning gives you another chance to look at the offending statement and fix it, in this case, by replacing the = with an ==.

In order to make warnings more visible, many compilers require you to take some special action. This might involve clicking a checkbox in an integrated environment or supplying a special option on the command line. Ask your instructor or lab assistant how to turn on warn- ings for your compiler.

Common error 3.2

programming tip 3.5

table 2 relational operator examples

expression Value Comment

3 <= 4 true 3 is less than 4; <= tests for “less than or equal”.

3 =< 4 error The “less than or equal” operator is <=, not =<. The “less than” symbol comes first.

3 > 4 false > is the opposite of <=.

4 < 4 false The left-hand side must be strictly smaller than the right-hand side.

4 <= 4 true Both sides are equal; <= tests for “less than or equal”.

3 == 5 - 2 true == tests for equality.

3 != 5 - 1 true != tests for inequality. It is true that 3 is not 5 – 1.

3 = 6 / 2 error Use == to test for equality.

1.0 / 3.0 == 0.333333333 false Although the values are very close to one another, they are not exactly equal. See Common Error 3.3 on page 86.

"10" > 5 error You cannot compare a string to a number.

Table 2 summarizes how to use relational operators in C++.

6. Which of the following conditions are true, provided a is 3 and b is 4? a. a + 1 <= b

b. a + 1 >= b

c. a + 1 != b

7. Give the opposite of the condition floor > 13

8. What is the error in this statement? if (score_a = score_b) { cout << "Tie" << endl; }

9. Supply a condition in this if statement to test whether the user entered a Y: string input; cout << "Enter Y to quit." << endl; cin >> input; if (...) { cout << "Goodbye." << endl; return 0; }

S e l f C h e C k

cfe2_ch03_p75_130.indd 84 10/28/10 7:51 PM

3.2 Comparing numbers and strings 85

10. How do you test that a string str is not the empty string?

practice it Now you can try these exercises at the end of the chapter: R3.2, R3.5, P3.14.

Confusing = and ==

The rule for the correct usage of = and == is very simple: In tests, always use == and never use =. If it is so simple, why can’t the compiler be helpful and flag any errors?

These two features—namely that numbers can be used as truth values and that assignments are expressions with values—conspire to make a horrible pitfall. The test

if (floor = 13) // ERROR

is legal C++, but it does not test whether floor and 13 are equal. Instead, the code sets floor to 13, and since that value is not zero, the condition of the if statement is always fulfilled.

Fortunately, most compilers issue a warning when they encounter such a statement. You should take such warn ings seriously. (See Programming Tip 3.5 for more advice about com- piler warnings.)

Some shell-shocked programmers are so nervous about using = that they use == even when they want to make an assignment:

floor == floor - 1; // ERROR

Compile with Zero warnings

It is a good idea to learn how to activate warnings with your compiler, and to write code that emits no warnings at all. For example, consider the test

if (floor = 13)

Common error 3.2

programming tip 3.5

cfe2_ch03_p75_130.indd 85 10/28/10 7:51 PM

86 Chapter 3 Decisions

• The space character comes before all printable characters. • Numbers come before letters. • For the ordering of punctuation marks, see Appendix D. When comparing two strings, you compare the first letters of each word, then the sec ond letters, and so on, until one of the strings ends or you find the first letter pair that doesn’t match.

If one of the strings ends, the longer string is considered the “larger” one. For example, compare "car" with "cart". The first three letters match, and we reach the end of the first string. Therefore "car" comes before "cart" in lexicographic ordering.

When you reach a mismatch, the string containing the “larger” character is considered “larger”. For example, let’s compare "cat" with "cart". The first two letters match. Since t comes after r, the string "cat" comes after "cart" in the lexico- graphic ordering.

Step 1 Decide upon the branching condition.

In our sample problem, the obvious choice for the condition is:

original price < 128?

That is just fine, and we will use that condition in our solution.

But you could equally well come up with a cor- rect solution if you choose the opposite condition: Is the original price at least (≥) $128? You might choose this condition if you put yourself into the position of a shopper who wants to know when the bigger discount applies.

Step 2 Give pseudocode for the work that needs to be done when the condition is true.

In this step, you list the action or actions that are taken in the “positive” branch. The details depend on your problem. You may want to print a message, compute values, or even exit the program.

In our example, we need to apply an 8 percent discount:

discounted price = 0.92 x original price

lexicographic order is used to compare strings.

c a r t

c a r

c a t

Letters match

r comes before t

Lexicographic Ordering

h o W t o 3 . 1 implementing an if Statement

This How To walks you through the process of implementing an if statement. We will illus- trate the steps with the following example problem:

The university bookstore has a Kilobyte Day sale every October 24, giving an 8 percent discount on all computer accessory purchases if the price is less than $128, and a 16 percent discount if the price is at least $128. Write a program that asks the cashier for the original price and then prints the discounted price.

Sales discounts are often higher for expensive products. Use the if state ment to implement such a decision.

exact Comparison of floating-point numbers

Floating-point numbers have only a limited precision, and calculations can introduce roundoff errors. You must take these inevitable roundoffs into account when comparing floating-point numbers. For example, the following code multiplies the square root of 2 by itself. Ideally, we expect to get the answer 2:

double r = sqrt(2.0); if (r * r == 2) { cout << "sqrt(2) squared is 2" << endl; } else { cout << "sqrt(2) squared is not 2 but " << setprecision(18) << r * r << endl; }

This program displays

sqrt(2) squared is not 2 but 2.00000000000000044

It does not make sense in most circumstances to compare floating-point numbers exactly. Instead, we should test whether they are close enough. That is, the magnitude of their differ- ence should be less than some threshold. Mathe matically, we would write that x and y are close enough if

x y− < ε

for a very small number, e. e is the Greek letter epsilon, a letter used to denote a very small quantity. It is common to set e to 10–14 when comparing double numbers:

const double EPSILON = 1E-14; double r = sqrt(2.0); if (fabs(r * r - 2) < EPSILON) { cout << "sqrt(2) squared is approximately 2"; }

Include the <cmath> header to use the fabs function.

lexicographic ordering of Strings

If you compare strings using < <= > >=, they are compared in “lexicographic” order. This ordering is very similar to the way in which words are sorted in a dictionary.

For example, consider this code fragment.

string name = "Tom"; if (name < "Dick") ...

The condition is not fulfilled, because in the diction- ary Dick comes before Tom. There are a few differences between the ordering in a dictionary and in C++. In C++: • All uppercase letters come before the lowercase

letters. For example, "Z" comes before "a".

Common error 3.3

Take limited precision into account when comparing floatingpoint numbers.

special topic 3.2

To see which of two terms comes first in the dictionary, consider the first letter in which they differ.

cfe2_ch03_p75_130.indd 86 10/28/10 7:51 PM

3.2 Comparing numbers and strings 87

Step 1 Decide upon the branching condition.

In our sample problem, the obvious choice for the condition is:

original price < 128?

That is just fine, and we will use that condition in our solution.

Step 2 Give pseudocode for the work that needs to be done when the condition is true.

In our example, we need to apply an 8 percent discount:

discounted price = 0.92 x original price

lexicographic order is used to compare strings.

c a r t

c a r

c a t

Letters match

r comes before t

Lexicographic Ordering

h o W t o 3 . 1 implementing an if Statement

This How To walks you through the process of implementing an if statement. We will illus- trate the steps with the following example problem:

Sales discounts are often higher for expensive products. Use the if state ment to implement such a decision.

cfe2_ch03_p75_130.indd 87 10/28/10 7:51 PM

88 Chapter 3 Decisions

and fill it in, as shown in Syntax 3.1 on page 78. Omit the else branch if it is not needed. In our example, the completed statement is

if (original_price < 128) { discount_rate = 0.92; } else { discount_rate = 0.84; }

discounted_price = discount_rate * original_price;

W o r k e D e x a M p l e 3 . 1 extracting the middle

This Worked Example shows how to extract the middle character from a string, or the two middle characters if the length of the string is even. 0 1 2 3 4

c r a t e

Making decisions is an essential part of

any computer program. nowhere is this more obvious than in a computer system that helps sort luggage at an airport. after scanning the luggage identification codes, the system sorts the items and routes them to different conveyor belts. human operators then place the items onto trucks. When the city of Denver built a huge airport to replace an outdated and congested facility, the luggage system contractor went a step further. the new system was designed to replace the human operators with robotic carts. Unfortu- nately, the system plainly did not work. it was plagued by mechanical prob- lems, such as luggage falling onto the tracks and jamming carts. equally frus- trating were the software glitches. Carts would uselessly accu mulate at some locations when they were needed elsewhere.

the airport had been scheduled to open in 1993, but without a func- tioning luggage system, the opening was delayed for over a year while the contractor tried to fix the problems. the contractor never succeeded, and ultimately a manual system was installed. the delay cost the city and airlines close to a billion dollars, and the contractor, once the leading lug- gage systems vendor in the United states, went bankrupt.

Clearly, it is very risky to build a large system based on a technology that has never been tried on a smaller scale. as robots and the software that controls them get better over time, they will take on a larger share of lug- gage handling in the future. But it is likely that this will happen in an incre- mental fashion.

The Denver airport originally had a fully automatic system for moving lug gage, replacing human operators with robotic carts. Unfortunately, the sys tem never worked and was dismantled before the airport was opened.

Random Fact 3.1 the Denver airport luggage handling system

Step 3 Give pseudocode for the work (if any) that needs to be done when the condition is not true.

What do you want to do in the case that the condition of Step 1 is not fulfilled? Sometimes, you want to do nothing at all. In that case, use an if statement without an else branch.

In our example, the condition tested whether the price was less than $128. If that condition is not true, the price is at least $128, so the higher discount of 16 percent applies to the sale:

discounted price = 0.84 x original price

Step 4 Double-check relational operators.

First, be sure that the test goes in the right direction. It is a common error to confuse > and <. Next, consider whether you should use the < operator or its close cousin, the <= operator.

What should happen if the original price is exactly $128? Reading the problem carefully, we find that the lower discount applies if the original price is less than $128, and the higher dis- count applies when it is at least $128. A price of $128 should therefore not fulfill our condition, and we must use <, not <=.

Step 5 Remove duplication.

Check which actions are common to both branches, and move them outside. (See Program- ming Tip 3.4 on page 82.)

In our example, we have two statements of the form

discounted price = ___ x original price

They only differ in the discount rate. It is best to just set the rate in the branches, and to do the computation after wards:

If original price < 128 discount rate = 0.92 Else discount rate = 0.84 discounted price = discount rate x original price

Step 6 Test both branches.

Formulate two test cases, one that fulfills the condition of the if statement, and one that does not. Ask yourself what should happen in each case. Then follow the pseudocode and act each of them out.

In our example, let us consider two scenarios for the original price: $100 and $200. We expect that the first price is discounted by $8, the second by $32.

When the original price is 100, then the condition 100 < 128 is true, and we get

discount rate = 0.92 discounted price = 0.92 x 100 = 92

When the original price is 200, then the condition 200 < 128 is false, and

discount rate = 0.84 discounted price = 0.84 x 200 = 168

In both cases, we get the expected answer.

Step 7 Assemble the if statement in C++.

Type the skeleton

if () { } else { }

cfe2_ch03_p75_130.indd 88 10/28/10 7:51 PM

3.2 Comparing numbers and strings 89

and fill it in, as shown in Syntax 3.1 on page 78. Omit the else branch if it is not needed. In our example, the completed statement is

if (original_price < 128) { discount_rate = 0.92; } else { discount_rate = 0.84; }

discounted_price = discount_rate * original_price;

W o r k e D e x a M p l e 3 . 1 extracting the middle

This Worked Example shows how to extract the middle character from a string, or the two middle characters if the length of the string is even. 0 1 2 3 4

c r a t e

Making decisions is an essential part of

Random Fact 3.1 the Denver airport luggage handling system

Available online at www.wiley.com/college/horstmann.

cfe2_ch03_p75_130.indd 89 10/28/10 7:51 PM

www.wiley.com/college/horstmann

90 Chapter 3 Decisions

3.3 Multiple alternatives In Section 3.1, you saw how to program a two-way branch with an if statement. In many situations, there are more than two cases. In this section, you will see how to implement a decision with multiple alterna tives. For example, consider a program that displays the effect of an earthquake, as measured by the Rich ter scale (see Table 3).

The 1989 Loma Prieta earth quake that damaged the Bay Bridge in San Fran cisco and destroyed many buildings measured 7.1 on the Richter scale.

table 3 richter scale

Value effect

8 Most structures fall

7 Many buildings destroyed

6 Many buildings considerably damaged, some collapse

4.5 Damage to poorly constructed buildings

The Richter scale is a measurement of the strength of an earthquake. Every step in the scale, for example from 6.0 to 7.0, signifies a tenfold increase in the strength of the quake.

In this case, there are five branches: one each for the four descriptions of damage, and one for no destruction. Figure 3 shows the flowchart for this multiple-branch statement.

You use multiple if statements to implement multiple alternatives, like this:

if (richter >= 8.0) { cout << "Most structures fall"; } else if (richter >= 7.0) { cout << "Many buildings destroyed"; } else if (richter >= 6.0) { cout << "Many buildings considerably damaged, some collapse"; } else if (richter >= 4.5) { cout << "Damage to poorly constructed buildings"; } else { cout << "No destruction of buildings"; }

As soon as one of the four tests succeeds, the effect is displayed, and no further tests are attempted. If none of the four cases applies, the final else clause applies, and a default message is printed. (See the ch03/rich ter.cpp file for the full program.)

Multiple alternatives are required for decisions that have more than two cases.

cfe2_ch03_p75_130.indd 90 10/28/10 7:51 PM

3.3 Multiple alternatives 91

figure 3 Multiple alternatives

richter ≥ 8.0?

richter ≥ 7.0?

richter ≥ 6.0?

richter ≥ 4.5?

No destruction of buildings

False

True

Most structures

fall

Many buildings destroyed

Many buildings considerably

damaged, some collapse

Damage to poorly constructed

buildings

Here you must sort the conditions and test against the largest cutoff first. Suppose we reverse the order of tests:

if (richter >= 4.5) // Tests in wrong order { cout << "Damage to poorly constructed buildings"; } else if (richter >= 6.0) { cout << "Many buildings considerably damaged, some collapse"; } else if (richter >= 7.0) { cout << "Many buildings destroyed"; } else if (richter >= 8.0) {

cfe2_ch03_p75_130.indd 91 10/28/10 7:51 PM

92 Chapter 3 Decisions

The switch Statement

A sequence of if statements that compares a single integer value against several constant alter- natives can be imple mented as a switch statement. For example,

int digit; ... switch (digit) { case 1: digit_name = "one"; break; case 2: digit_name = "two"; break; case 3: digit_name = "three"; break; case 4: digit_name = "four"; break; case 5: digit_name = "five"; break; case 6: digit_name = "six"; break; case 7: digit_name = "seven"; break; case 8: digit_name = "eight"; break; case 9: digit_name = "nine"; break; default: digit_name = ""; break; }

This is a shortcut for

int digit; if (digit == 1) { digit_name = "one"; } else if (digit == 2) { digit_name = "two"; } else if (digit == 3) { digit_name = "three"; } else if (digit == 4) { digit_name = "four"; } else if (digit == 5) { digit_name = "five"; } else if (digit == 6) { digit_name = "six"; } else if (digit == 7) { digit_name = "seven"; } else if (digit == 8) { digit_name = "eight"; } else if (digit == 9) { digit_name = "nine"; } else { digit_name = ""; }

Well, it isn’t much of a shortcut, but it has one advan- tage—it is obvious that all branches test the same value, namely digit.

It is possible to have multiple case clauses for a branch, such as

case 1: case 3: case 5: case 7: case 9: odd = true; break;

The default branch is chosen if none of the case clauses match.

Every branch of the switch must be terminated by a break instruction. If the break is missing, execution falls through to the next branch, and so on, until finally a break or the end of the switch is reached. In practice, this fall-through behavior is rarely useful, but it is a com- mon cause of errors. If you accidentally forget the break statement, your program compiles but exe cutes unwanted code. Many programmers consider the switch statement somewhat dan- gerous and prefer the if statement.

We leave it to you to use the switch statement for your own code or not. At any rate, you need to have a reading knowledge of switch in case you find it in other programmers’ code.

special topic 3.3

The switch statement lets you choose from a fixed set of alternatives.

cout << "Most structures fall"; }

This does not work. Suppose the value of richter is 7.1. That value is at least 4.5, matching the first case. The other tests will never be attempted.

In this example, it is also important that we use a sequence of else if clauses, not just multiple indepen dent if statements. Consider this sequence of independent tests:

if (richter >= 8.0) // Didn’t use else { cout << "Most structures fall"; } if (richter >= 7.0) { cout << "Many buildings destroyed"; } if (richter >= 6.0) { cout << "Many buildings considerably damaged, some collapse"; } if (richter >= 4.5) { cout << "Damage to poorly constructed buildings";

}

Now the alternatives are no longer exclusive. If richter is 7.1, then the last three tests all match, and three messages are printed.

11. In a game program, the scores of players A and B are stored in variables score_a and score_b. Assum ing that the player with the larger score wins, write a sequence of conditional statements that prints out "A won", "B won", or "Game tied".

12. Write a conditional statement with three branches that sets s to 1 if x is positive, to –1 if x is negative, and to 0 if x is zero.

13. How could you achieve the task of Self Check 12 with only two branches? 14. Beginners sometimes write statements such as the following:

if (price > 100) { discounted_price = price - 20; } else if (price <= 100) { discounted_price = price - 10; }

Explain how this code can be improved. 15. Suppose the user enters -1 into the richter.cpp program. What is printed? 16. Suppose we want to have the richter.cpp program check whether the user

entered a negative number. What branch would you add to the if statement, and where?

practice it Now you can try these exercises at the end of the chapter: R3.20, P3.1, P3.9, P3.10.

When using multiple if statements, pay attention to the order of the conditions.

S e l f C h e C k

cfe2_ch03_p75_130.indd 92 10/28/10 7:51 PM

3.3 Multiple alternatives 93

The switch Statement

A sequence of if statements that compares a single integer value against several constant alter- natives can be imple mented as a switch statement. For example,

This is a shortcut for

Well, it isn’t much of a shortcut, but it has one advan- tage—it is obvious that all branches test the same value, namely digit.

It is possible to have multiple case clauses for a branch, such as

case 1: case 3: case 5: case 7: case 9: odd = true; break;

The default branch is chosen if none of the case clauses match.

We leave it to you to use the switch statement for your own code or not. At any rate, you need to have a reading knowledge of switch in case you find it in other programmers’ code.

special topic 3.3

The switch statement lets you choose from a fixed set of alternatives.

cfe2_ch03_p75_130.indd 93 10/28/10 7:51 PM

94 Chapter 3 Decisions

3.4 nested Branches It is often necessary to include an if statement inside another. Such an arrangement is called a nested set of statements. Here is a typical example.

In the United States, different tax rates are used depending on the taxpayer’s mari- tal status. There are different tax sched ules for single and for married taxpayers. Mar- ried taxpayers add their income together and pay taxes on the total. Table 4 gives the tax rate computations, using a simplification of the schedules in effect for the 2008 tax year. A different tax rate applies to each “bracket”. In this schedule, the income at the first bracket is taxed at 10 percent, and the income at the sec ond bracket is taxed at 25 percent. The income limits for each bracket depend on the marital status.

Now compute the taxes due, given a filing status and an income figure. The key point is that there are two levels of decision making. First, you must branch on the marital status. Then, for each filing status, you must have another branch on income level.

table 4 Federal tax rate schedule

if your status is single and if the taxable income is the tax is of the amount over

at most $32,000 10% $0

over $32,000 $3,200 + 25% $32,000

if your status is Married and if the taxable income is the tax is of the amount over

at most $64,000 10% $0

over $64,000 $6,400 + 25% $64,000

The two-level decision process is reflected in two levels of if statements in the pro- gram at the end of this section. (See Figure 4 for a flowchart.)

When a decision statement is contained inside the branch of another decision statement, the statements are nested.

nested decisions are required for problems that have two levels of decision making.

Computing income taxes requires multiple levels of decisions.

cfe2_ch03_p75_130.indd 94 10/28/10 7:51 PM

3.4 nested Branches 95

figure 4 income tax Computation

10% bracket

25% bracket

Single income ≤ 32,000

10% bracket

25% bracket

income ≤ 64,000

False

True

False

True

False

In theory, nesting can go deeper than two levels. A three-level decision process (first by state, then by filing status, then by income level) requires three nesting levels.

ch03/tax.cpp

1 #include <iostream> 2 #include <string> 3 4 using namespace std; 5 6 int main() 7 { 8 const double RATE1 = 0.10; 9 const double RATE2 = 0.25;

10 const double RATE1_SINGLE_LIMIT = 32000; 11 const double RATE1_MARRIED_LIMIT = 64000; 12 13 double tax1 = 0; 14 double tax2 = 0; 15 16 double income; 17 cout << "Please enter your income: "; 18 cin >> income; 19 20 cout << "Please enter s for single, m for married: "; 21 string marital_status; 22 cin >> marital_status; 23

cfe2_ch03_p75_130.indd 95 10/28/10 7:51 PM

96 Chapter 3 Decisions

hand-Tracing

For example, let’s trace the tax program with the data from the program run on page 95. In lines 13 and 14, tax1 and tax2 are initial- ized to 0.

6 int main() 7 { 8 const double RATE1 = 0.10; 9 const double RATE2 = 0.25;

10 const double RATE1_SINGLE_LIMIT = 32000; 11 const double RATE1_MARRIED_LIMIT = 64000; 12 13 double tax1 = 0; 14 double tax2 = 0; 15

In lines 18 and 22, income and marital_status are initialized by input statements.

16 double income; 17 cout << "Please enter your income: "; 18 cin >> income; 19 20 cout << "Please enter s for single, m for married: "; 21 string marital_status; 22 cin >> marital_status; 23

Because marital_status is not "s", we move to the else branch of the outer if statement (line 36).

Since income is not <= 64000, we move to the else branch of the inner if statement (line 42).

38 if (income <= RATE1_MARRIED_LIMIT)

39 { 40 tax1 = RATE1 * income; 41 } 42 else 43 { 44 tax1 = RATE1 * RATE1_MARRIED_LIMIT; 45 tax2 = RATE2 * (income - RATE1_MARRIED_LIMIT); 46 }

programming tip 3.6

Handtracing helps you understand whether a program works correctly.

marital tax1 tax2 income status

0 0

marital tax1 tax2 income status

0 0 80000 m

24 if (marital_status == "s") 25 { 26 if (income <= RATE1_SINGLE_LIMIT) 27 { 28 tax1 = RATE1 * income; 29 } 30 else 31 { 32 tax1 = RATE1 * RATE1_SINGLE_LIMIT; 33 tax2 = RATE2 * (income - RATE1_SINGLE_LIMIT); 34 } 35 } 36 else 37 { 38 if (income <= RATE1_MARRIED_LIMIT) 39 { 40 tax1 = RATE1 * income; 41 } 42 else 43 { 44 tax1 = RATE1 * RATE1_MARRIED_LIMIT; 45 tax2 = RATE2 * (income - RATE1_MARRIED_LIMIT); 46 } 47 } 48 49 double total_tax = tax1 + tax2; 50 51 cout << "The tax is $" << total_tax << endl; 52 return 0; 53 }

program run

Please enter your income: 80000 Please enter s for single, m for married: m The tax is $10400

17. What is the amount of tax that a single taxpayer pays on an income of $32,000? 18. Would that amount change if the first nested if statement changed from

if (income <= RATE1_SINGLE_LIMIT)

to if (income < RATE1_SINGLE_LIMIT)

19. Suppose Harry and Sally each make $40,000 per year. Would they save taxes if they married?

20. How would you modify the tax.cpp program in order to check that the user entered a correct value for the marital status (i.e., s or m)?

21. Some people object to higher tax rates for higher incomes, claiming that you might end up with less money after taxes when you get a raise for working hard. What is the flaw in this argument?

practice it Now you can try these exercises at the end of the chapter: R3.7, R3.19, P3.13, P3.19.

S e l f C h e C k

cfe2_ch03_p75_130.indd 96 10/28/10 7:51 PM

3.4 nested Branches 97

hand-Tracing

For example, let’s trace the tax program with the data from the program run on page 95. In lines 13 and 14, tax1 and tax2 are initial- ized to 0.

6 int main() 7 { 8 const double RATE1 = 0.10; 9 const double RATE2 = 0.25;

10 const double RATE1_SINGLE_LIMIT = 32000; 11 const double RATE1_MARRIED_LIMIT = 64000; 12 13 double tax1 = 0; 14 double tax2 = 0; 15

In lines 18 and 22, income and marital_status are initialized by input statements.

16 double income; 17 cout << "Please enter your income: "; 18 cin >> income; 19 20 cout << "Please enter s for single, m for married: "; 21 string marital_status; 22 cin >> marital_status; 23

Because marital_status is not "s", we move to the else branch of the outer if statement (line 36).

Since income is not <= 64000, we move to the else branch of the inner if statement (line 42).

38 if (income <= RATE1_MARRIED_LIMIT)

39 { 40 tax1 = RATE1 * income; 41 } 42 else 43 { 44 tax1 = RATE1 * RATE1_MARRIED_LIMIT; 45 tax2 = RATE2 * (income - RATE1_MARRIED_LIMIT); 46 }

programming tip 3.6

Handtracing helps you understand whether a program works correctly.

marital tax1 tax2 income status

0 0

marital tax1 tax2 income status

0 0 80000 m

cfe2_ch03_p75_130.indd 97 10/28/10 7:51 PM

98 Chapter 3 Decisions

3.5 problem solving: Flowcharts You have seen examples of flowcharts earlier in this chapter. A flowchart shows the structure of decisions and tasks that are required to solve a problem. When you have to solve a complex problem, it is a good idea to draw a flowchart to visualize the flow of control.

The basic flowchart elements are shown in Figure 5.

The basic idea is simple enough. Link tasks and input/output boxes in the sequence in which they should be executed. Whenever you need to make a decision, draw a dia- mond with two outcomes (see Figure 6).

Each branch can contain a sequence of tasks and even additional decisions. If there are multiple choices for a value, lay them out as in Figure 7.

Flow charts are made up of elements for tasks, input/outputs, and decisions.

figure 5 Flowchart elements

True

False

ConditionSimple task Input/output

each branch of a decision can contain tasks and further decisions.

figure 6 Flowchart with two outcomes

True

False

False branch True branch

Condition

figure 7 Flowchart with Multiple Choices

True

False

Choice 1 “Choice 1”

branch

True

False

Choice 2 “Choice 2”

branch

True

False

Choice 3 “Choice 3”

branch

“Other” branch

The values of tax1 and tax2 are updated.

43 { 44 tax1 = RATE1 * RATE1_MARRIED_LIMIT; 45 tax2 = RATE2 * (income - RATE1_MARRIED_LIMIT); 46 } 47 }

Their sum total_tax is computed and printed. Then the program ends.

48 49 double total_tax = tax1 + tax2; 50 51 cout << "The tax is $" << total_tax << endl; 52 return 0; 53 }

Because the program trace shows the expected output ($10,400), it suc cessfully demonstrated that this test case works correctly.

The dangling else problem

When an if statement is nested inside another if statement, the following error may occur.

double shipping_charge = 5.00; // $5 inside continental U.S. if (country == "USA") if (state == "HI") shipping_charge = 10.00; // Hawaii is more expensive else // Pitfall! shipping_charge = 20.00; // As are foreign shipments

The indentation level seems to suggest that the else is grouped with the test country == "USA". Unfortunately, that is not the case. The compiler ignores all indentation and matches the else with the preceding if. That is, the code is actually

That isn’t what you want. You want to group the else with the first if. The ambiguous else is called a dangling else. You can avoid this pitfall if you always use

braces, as recommended in Programming Tip 3.2 on page 80:

double shipping_charge = 5.00; // $5 inside continental U.S. if (country == "USA") { if (state == "HI") { shipping_charge = 10.00; // Hawaii is more expensive } } else { shipping_charge = 20.00; // As are foreign shipments }

marital tax1 tax2 income status

0 0 80000 m

6400 4000

marital total tax1 tax2 income status tax

0 0 80000 m

6400 4000 10400

Common error 3.4

cfe2_ch03_p75_130.indd 98 10/28/10 7:51 PM

3.5 problem solving: Flowcharts 99

The basic flowchart elements are shown in Figure 5.

Each branch can contain a sequence of tasks and even additional decisions. If there are multiple choices for a value, lay them out as in Figure 7.

Flow charts are made up of elements for tasks, input/outputs, and decisions.

figure 5 Flowchart elements

True

False

ConditionSimple task Input/output

each branch of a decision can contain tasks and further decisions.

figure 6 Flowchart with two outcomes

True

False

False branch True branch

Condition

figure 7 Flowchart with Multiple Choices

True

False

Choice 1 “Choice 1”

branch

True

False

Choice 2 “Choice 2”

branch

True

False

Choice 3 “Choice 3”

branch

“Other” branch

cfe2_ch03_p75_130.indd 99 10/28/10 7:51 PM

100 Chapter 3 Decisions

There is one issue that you need to be aware of when drawing flow charts. Unconstrained branching and merging can lead to “spaghetti code”, a messy net- work of possible pathways through a program.

There is a simple rule for avoiding spaghetti code: Never point an arrow inside another branch.

To understand the rule, consider this example: Shipping costs are $5 inside the United States, except that to Hawaii and Alaska they are $10. Inter national shipping costs are also $10. You might start out with a flowchart like the following:

False

True

Shipping cost = $10

Inside US?

True

False

Continental US?

Shipping cost = $5

Now you may be tempted to reuse the “shipping cost = $10” task:

False

True

Shipping cost = $10

Inside US?

True

False

Continental US?

Shipping cost = $5

Spaghetti code has so many pathways that it becomes impossible to understand.

never point an arrow inside another branch.

cfe2_ch03_p75_130.indd 100 10/28/10 7:51 PM

3.5 problem solving: Flowcharts 101

Don’t do that! The red arrow points inside a different branch. Instead, add another task that sets the ship ping cost to $10, like this:

False

True

Shipping cost = $10

Inside US?

True

False

Continental US?

Shipping cost = $10

Shipping cost = $5

Not only do you avoid spaghetti code, but it is also a better design. In the future it may well happen that the cost for international shipments is different from that to Alaska and Hawaii.

Flowcharts can be very useful for getting an intuitive understanding of the flow of an algorithm. However, they get large rather quickly when you add more details. At that point, it makes sense to switch from flowcharts to pseudocode.

22. Draw a flowchart for a program that reads a value temp and prints “Frozen” if it is less than zero.

23. What is wrong with the flowchart at right? 24. How do you fix the flowchart of

Self Check 23? 25. Draw a flowchart for a program that reads a

value x. If it is less than zero, print “Error”. Otherwise, print its square root.

26. Draw a flowchart for a program that reads a value temp. If it is less than zero, print “Ice”. If it is greater than 100, print “Steam”. Otherwise, print “Liquid”.

practice it Now you can try these exercises at the end of the chapter: R3.10, R3.11, R3.12.

S e l f C h e C k

True

False

Input < 0?

True

False

Input > 100?

Status = “OK” Status = “Error”

cfe2_ch03_p75_130.indd 101 10/28/10 7:51 PM

102 Chapter 3 Decisions

make a Schedule and make Time for unexpected problems

Commercial software is notorious for being delivered later than promised. For example, Microsoft originally prom ised that its Windows Vista operating system would be available late in 2003, then in 2005, then in March 2006; it finally was released in January 2007. Some of the early promises might not have been realistic. It was in Microsoft’s interest to let prospective customers expect the imminent availability of the product. Had customers known the actual delivery date, they might have switched to a different product in the meantime. Undeniably, though, Microsoft had not anticipated the full complexity of the tasks it had set itself to solve.

Microsoft can delay the delivery of its product, but it is likely that you cannot. As a student or a programmer, you are expected to manage your time wisely and to finish your assignments on time. You can probably do simple pro gramming exercises the night before the due date, but an assignment that looks twice as hard may well take four times as long, because more things can go wrong. You should therefore make a schedule whenever you start a pro gramming project.

First, estimate realistically how much time it will take you to: • Design the program logic. • Develop test cases. • Type in the program and fix syntax errors. • Test and debug the program. For example, for the income tax program I might estimate an hour for the design; 30 minutes for developing test cases; an hour for data entry and fixing syntax errors; and an hour for testing and debugging. That is a total of 3.5 hours. If I work two hours a day on this project, it will take me almost two days.

Then think of things that can go wrong. Your computer might break down. You might be stumped by a problem with the computer sys- tem. (That is a particularly important concern for beginners. It is very common to lose a day over a trivial problem just because it takes time to track down a person who knows the magic command to over come it.) As a rule of thumb, double the time of your estimate. That is, you should start four days, not two days, before the due date. If nothing went wrong, great; you have the program done two days early. When the inevitable problem occurs, you have a cushion of time that protects you from embar rassment and failure.

3.7 Boolean Variables and operators Sometimes, you need to evaluate a logical condition in one part of a program and use it elsewhere. To store a condition that can be true or false, you use a Boolean variable. Boolean variables are named after the mathematician George Boole (1815–1864), a pioneer in the study of logic.

In C++, the bool data type represents the Boolean type. Variables of type bool can hold exactly two val ues, denoted false and true. These values are not strings or inte- gers; they are special values, just for Bool ean variables.

programming tip 3.7

Make a schedule for your programming work and build in time for problems.

the Boolean type bool has two values, false and true.

3.6 problem solving: test Cases Consider how to test the tax computation program from Section 3.4. Of course, you cannot try out all possible inputs of filing status and income level. Even if you could, there would be no point in trying them all. If the program correctly computes one or two tax amounts in a given bracket, then we have a good reason to believe that all amounts will be correct.

You want to aim for complete coverage of all decision points. Here is a plan for obtaining a compre hensive set of test cases:

• There are two possibilities for the filing status and two tax brackets for each status, yielding four test cases.

• Test a handful of boundary conditions, such as an income that is at the boundary between two brack ets, and a zero income.

• If you are responsible for error checking (which is discussed in Section 3.8), also test an invalid input, such as a negative income.

Make a list of the test cases and the expected outputs:

Test Case Expected Output Comment 30,000 s 3,000 10% bracket 72,000 s 13,200 3,200 + 25% of 40,000 50,000 m 5,000 10% bracket

104,000 m 16,400 6,400 + 25% of 40,000 32,000 s 3,200 boundary case

0 0 boundary case

When you develop a set of test cases, it is helpful to have a flowchart of your program (see Section 3.5). Check off each branch that has a test case. Include test cases for the boundary cases of each decision. For example, if a decision checks whether an input is less than 100, test with an input of 100.

It is always a good idea to design test cases before starting to code. Working through the test cases gives you a better understanding of the algorithm that you are about to implement.

27. Using Figure 1 on page 77 as a guide, follow the process described in Section 3.6 to design a set of test cases for the elevator.cpp program in Section 3.1.

28. What is a boundary test case for the algorithm in How To 3.1 on page 87? What is the expected out put?

29. Using Figure 3 on page 91 as a guide, follow the process described in Section 3.6 to design a set of test cases for the richter.cpp program in Section 3.3.

30. Suppose you are designing a part of a program for a medical robot that has a sensor returning an x and y location (measured in cm). You need to check whether the sensor location is inside the circle, outside the circle, on the boundary (specifically, having a distance of less than 1 mm from the boundary). Assume the circle has center (0, 0) and radius 2 cm. Give a set of test cases.

practice it Now you can try these exercises at the end of the chapter: R3.13, R3.14.

each branch of your program should be covered by a test case.

it is a good idea to design test cases before implementing a program.

S e l f C h e C k

cfe2_ch03_p75_130.indd 102 10/28/10 7:51 PM

3.7 Boolean Variables and operators 103

make a Schedule and make Time for unexpected problems

programming tip 3.7

Make a schedule for your programming work and build in time for problems.

the Boolean type bool has two values, false and true.

cfe2_ch03_p75_130.indd 103 10/28/10 7:51 PM

104 Chapter 3 Decisions

Conversely, let’s test whether water is not liquid at a given temperature. That is the case when the tem perature is at most 0 or at least 100. Use the || (or) operator to combine the expressions:

if (temp <= 0 || temp >= 100) { cout << "Not liquid"; }

Figure 9 shows flowcharts for these examples. Sometimes you need to invert a condition with the not logical operator. The !

operator takes a single condition and evaluates to true if that condition is false and to false if the condition is true. In this exam ple, output occurs if the value of the Boolean variable frozen is false:

if (!frozen) { cout << "Not frozen"; }

to invert a condition, use the ! (not) operator.

figure 9 Flowcharts for and and or Combinations

True True True

True

False

False False Temperature

> 0?

Temperature < 100?

Water is liquid

Water is not liquid

Temperature ≤ 0?

Temperature ≥ 100?

Both conditions must be true

At least one condition must be true

and or

Here is a definition of a Boolean variable: bool failed = true;

You can use the value later in your program to make a decision: if (failed) // Only executed if failed has been set to true { ... }

When you make complex decisions, you often need to combine Boolean values. An operator that com bines Boolean conditions is called a Boolean operator. In C++, the && operator (called and) yields true only when both conditions are true. The || opera- tor (called or) yields the result true if at least one of the conditions is true.

Suppose you write a program that processes temperature values, and you want to test whether a given temperature corresponds to liquid water. (At sea level, water freezes at 0 degrees Celsius and boils at 100 degrees.) Water is liquid if the tempera- ture is greater than zero and less than 100:

if (temp > 0 && temp < 100) { cout << "Liquid"; }

The condition of the test has two parts, joined by the && operator. (As shown in Table 5 and Appendix C, the > and < operators have higher precedence than the && operator.)

Each part is a Boolean value that can be true or false. The combined expression is true if both individ ual expressions are true. If either one of the expressions is false, then the result is also false (see Figure 8).

A Boolean variable is also called a flag because it can be either up (true) or down (false).

C++ has two Boolean operators that combine conditions: && (and) and || (or).

a B a && B

true true true

true false false

false true false

false false false

a B a || B

true true true

true false true

false true true

false false false

a !a

true false

false true

figure 8 Boolean truth tables

At this geyser in Iceland, you can see ice, liquid water, and steam.

cfe2_ch03_p75_130.indd 104 10/28/10 7:51 PM

3.7 Boolean Variables and operators 105

table 5 selected operators and their precedence

operator Description

++ -- + (unary) – (unary) !

Increment, decrement, positive, negative, Boolean not

* / % Multiplication, division, remainder

+ - Addition, subtraction

< <= > >= Comparisons

== != Equal, not equal

&& Boolean and

|| Boolean or

Conversely, let’s test whether water is not liquid at a given temperature. That is the case when the tem perature is at most 0 or at least 100. Use the || (or) operator to combine the expressions:

if (temp <= 0 || temp >= 100) { cout << "Not liquid"; }

Figure 9 shows flowcharts for these examples. Sometimes you need to invert a condition with the not logical operator. The !

if (!frozen) { cout << "Not frozen"; }

to invert a condition, use the ! (not) operator.

figure 9 Flowcharts for and and or Combinations

True True True

True

False

False False Temperature

> 0?

Temperature < 100?

Water is liquid

Water is not liquid

Temperature ≤ 0?

Temperature ≥ 100?

Both conditions must be true

At least one condition must be true

and or

cfe2_ch03_p75_130.indd 105 10/28/10 7:51 PM

106 Chapter 3 Decisions

Combining multiple relational operators

Consider the expression

if (0 <= temp <= 100) // Error

This looks just like the mathematical test 0 ≤ temp ≤ 100. Unfortunately, it is not. Let us dissect the expression 0 <= temp <= 100. The first half, 0 <= temp, is a test with out-

come true or false, depending on the value of temp. The outcome of that test (true or false) is then compared against 100. Can one com pare truth values and floating-point numbers? Is true larger than 100 or not? Unfortunately, to stay compatible with the C language, C++ converts false to 0 and true to 1. Therefore, the expression will always evaluate to true.

You must be careful not to mix logical and arithmetic expressions in your programs. Instead, use and to combine two separate tests:

if (0 <= temp && temp <= 100) ...

Another common error, along the same lines, is to write

if (x && y > 0) ... // Error

instead of

if (x > 0 && y > 0) ...

Unfortunately, the compiler will not issue an error message. Instead, it converts x to true or false. Zero is converted to false, and any nonzero value is converted to true. If x is not zero, then it tests whether y is greater than 0, and finally it computes the and of these two truth val- ues. Naturally, that computation makes no sense.

Confusing && and || Conditions

It is a surprisingly common error to confuse and and or conditions. A value lies between 0 and 100 if it is at least 0 and at most 100. It lies outside that range if it is less than 0 or greater than 100. There is no golden rule; you just have to think carefully.

Often the and or or is clearly stated, and then it isn’t too hard to implement it. But some- times the wording isn’t as explicit. It is quite common that the individual conditions are nicely set apart in a bulleted list, but with little indica tion of how they should be combined. Consider these instructions for filing a tax return. You can claim single filing status if any one of the fol- lowing is true: • You were never married. • You were legally separated or divorced on the last day of the tax year. • You were widowed, and did not remarry. Since the test passes if any one of the conditions is true, you must combine the conditions with or. Elsewhere, the same instructions state that you may use the more advantageous status of married filing jointly if all five of the fol lowing conditions are true: • Your spouse died less than two years ago and you did not remarry. • You have a child whom you can claim as dependent. • That child lived in your home for all of the tax year. • You paid over half the cost of keeping up your home for this child. • You filed a joint return with your spouse the year he or she died. Because all of the conditions must be true for the test to pass, you must combine them with an and.

Common error 3.5

Common error 3.6

table 6 Boolean operators

expression Value Comment

0 < 200 && 200 < 100 false Only the first condition is true. Note that the < operator has a higher precedence than the && operator.

0 < 200 || 200 < 100 true The first condition is true.

0 < 200 || 100 < 200 true The || is not a test for “either-or”. If both conditions are true, the result is true.

0 < 200 < 100 true error: The expression 0 < 200 is true, which is converted to 1. The expression 1 < 100 is true. You never want to write such an expression; see Common Error 3.5 on page 107.

-10 && 10 > 0 true error: –10 is not zero. It is converted to true. You never want to write such an expression; see Common Error 3.5 on page 107.

0 < x && x < 100 || x == -1 (0 < x && x < 100) || x == -1

The && operator has a higher precedence than the || operator.

!(0 < 200) false 0 < 200 is true, therefore its negation is false.

frozen == true frozen There is no need to compare a Boolean variable with true.

frozen == false !frozen It is clearer to use ! than to compare with false.

Table 6 illustrates additional examples of evaluating Boolean operators.

31. Suppose x and y are two integers. How do you test whether both of them are zero?

32. How do you test whether at least one of them is zero? 33. How do you test whether exactly one of them is zero? 34. What is the value of !!frozen? 35. What is the advantage of using the type bool rather than strings "false"/"true" or

integers 0/1?

practice it Now you can try these exercises at the end of the chapter: R3.27, P3.22, P3.24.

S e l f C h e C k

cfe2_ch03_p75_130.indd 106 10/28/10 7:51 PM

3.7 Boolean Variables and operators 107

Combining multiple relational operators

Consider the expression

if (0 <= temp <= 100) // Error

This looks just like the mathematical test 0 ≤ temp ≤ 100. Unfortunately, it is not. Let us dissect the expression 0 <= temp <= 100. The first half, 0 <= temp, is a test with out-

You must be careful not to mix logical and arithmetic expressions in your programs. Instead, use and to combine two separate tests:

if (0 <= temp && temp <= 100) ...

Another common error, along the same lines, is to write

if (x && y > 0) ... // Error

instead of

if (x > 0 && y > 0) ...

Confusing && and || Conditions

Common error 3.5

Common error 3.6

cfe2_ch03_p75_130.indd 107 10/28/10 7:51 PM

108 Chapter 3 Decisions

Short-Circuit evaluation of boolean operators

When the && and || operators are computed, evaluation stops as soon as the truth value is determined. When an && is evaluated and the first condition is false, the second condition is not evaluated, because it does not matter what the outcome of the second test is.

For example, consider the expression

quantity > 0 && price / quantity < 10

Suppose the value of quantity is zero. Then the test quantity > 0 fails, and the second test is not attempted. That is just as well, because it is illegal to divide by zero.

Similarly, when the first condition of an || expression is true, then the remainder is not evaluated since the result must be true.

This process is called short-circuit evaluation.

In a short circuit, electricity travels along the path of least resistance. Similarly, shortcircuit evaluation takes the fastest path for

computing the result of a Boolean expression.

de morgan’s law

Humans generally have a hard time comprehending logical conditions with not operators applied to and/or expres sions. De Morgan’s Law, named after the logician Augustus De Mor- gan (1806–1871), can be used to simplify these Boolean expressions.

Suppose we want to charge a higher shipping rate if we don’t ship within the continental United States.

if (!(country == "USA" && state != "AK" && state != "HI")) shipping_charge = 20.00;

This test is a little bit complicated, and you have to think carefully through the logic. When it is not true that the country is USA and the state is not Alaska and the state is not Hawaii, then charge $20.00. Huh? It is not true that some people won’t be confused by this code.

The computer doesn’t care, but it takes human programmers to write and maintain the code. Therefore, it is use ful to know how to simplify such a condition.

De Morgan’s Law has two forms: one for the negation of an and expression and one for the negation of an or expression:

!(A && B) is the same as !A || !B !(A || B) is the same as !A && !B

Pay particular attention to the fact that the and and or operators are reversed by moving the not inward. For exam ple, the negation of “the state is Alaska or it is Hawaii”,

!(state == "AK" || state == "HI")

is “the state is not Alaska and it is not Hawaii”:

!(state == "AK") && !(state == "HI")

special topic 3.4

the && and || operators are computed using shortcircuit evaluation: as soon as the truth value is determined, no further conditions are evaluated.

special topic 3.5

De Morgan’s law tells you how to negate && and || conditions.

cfe2_ch03_p75_130.indd 108 10/28/10 7:52 PM

3.8 application: input Validation 109

That is, of course, the same as

state != "AK" && state != "HI"

Now apply the law to our shipping charge computation:

!(country == "USA" && state != "AK" && state != "HI")

is equivalent to

!(country == "USA") || !(state != "AK") || !(state != "HI")

That yields the simpler test

country != "USA" || state == "AK" || state == "HI"

To simplify conditions with negations of and or or expressions, it is usually a good idea to apply De Morgan’s Law to move the negations to the innermost level.

3.8 application: input Validation An important application for the if statement is input validation. Whenever your program accepts user input, you need to make sure that the user-supplied values are valid before you use them in your computations.

Consider our elevator program. Assume that the elevator panel has buttons labeled 1 through 20 (but not 13). The following are illegal inputs:

• The number 13 • Zero or a negative number • A number larger than 20 • An input that is not a sequence of digits, such as five In each of these cases, we will want to give an error message and exit the program.

It is simple to guard against an input of 13: if (floor == 13) { cout << "Error: There is no thirteenth floor." << endl; return 1; }

The statement return 1;

immediately exits the main function and therefore terminates the program. It is a con- vention to return with the value 0 if the program completed normally, and with a non-zero value when an error was encountered.

Like a quality control worker, you want to make sure that user input is correct before processing it.

cfe2_ch03_p75_130.indd 109 10/28/10 7:52 PM

110 Chapter 3 Decisions

Here is how you ensure that the user doesn’t enter a number outside the valid range:

if (floor <= 0 || floor > 20) { cout << "Error: The floor must be between 1 and 20." << endl; return 1; }

However, dealing with an input that is not a valid integer is a more serious problem. When the statement

cin >> floor;

is executed, and the user types in an input that is not an integer (such as five), then the integer variable floor is not set. Instead, the input stream cin is set to a failed state. You call the fail member function to test for that failed state.

if (cin.fail()) { cout << "Error: Not an integer." << endl; return 1; }

The order of the if statements is important. You must first test for cin.fail(). After all, if the input failed, no value has been assigned to floor, and it makes no sense to compare it against other values.

Input failure is quite serious in C++. Once input has failed, all subsequent attempts at input will fail as well. You will learn in Chapter 8 how to write programs that are more tolerant of bad input. For now, our goal is simply to detect bad input and to exit the program when it occurs.

Here is the complete elevator program with input validation.

ch03/elevator2.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 int main() 6 { 7 int floor; 8 cout << "Floor: "; 9 cin >> floor;

10 11 // The following statements check various input errors 12 if (cin.fail()) 13 { 14 cout << "Error: Not an integer." << endl; 15 return 1; 16 } 17 if (floor == 13) 18 { 19 cout << "Error: There is no thirteenth floor." << endl; 20 return 1; 21 } 22 if (floor <= 0 || floor > 20) 23 { 24 cout << "Error: The floor must be between 1 and 20." << endl; 25 return 1;

When reading a value, check that it is within the required range.

Use the fail function to test whether the input stream has failed.

cfe2_ch03_p75_130.indd 110 10/28/10 7:52 PM

3.8 application: input Validation 111

26 } 27 28 // Now we know that the input is valid 29 int actual_floor; 30 if (floor > 13) 31 { 32 actual_floor = floor - 1; 33 } 34 else 35 { 36 actual_floor = floor; 37 } 38 39 cout << "The elevator will travel to the actual floor " 40 << actual_floor << endl; 41 42 return 0; 43 }

program run

Floor: 13 Error: There is no thirteenth floor.

36. Consider the elevator2.cpp program. What output do you get when the input is a. 100? b. –1? c. 20? d. thirteen?

37. Your task is to rewrite the elevator2.cpp program so that there is a single if state- ment with a complex condition: if (...) { cout << "Error: Bad input" << endl; return 1; }

What is the condition? 38. In the Sherlock Holmes story “The Adventure of the Sussex Vampire”, the

inimitable detective uttered these words: “Matilda Briggs was not the name of a young woman, Watson, … It was a ship which is associated with the giant rat of Sumatra, a story for which the world is not yet prepared.” Over a hundred years later, researchers found giant rats in Western New Guinea, another part of Indonesia. Suppose you are charged with writing a program that processes rat weights. It contains the state ments double weight; cout << "Enter weight in kg: "; cin >> weight;

What input checks should you supply?

When processing inputs, you want to reject values that are too large. But how large is too large? These giant rats, found in Western New Guinea, are about five times the size of a city rat.

S e l f C h e C k

cfe2_ch03_p75_130.indd 111 10/28/10 7:52 PM

112 Chapter 3 Decisions

use the if statement to implement a decision.

• The if statement allows a program to carry out dif ferent actions depending on the nature of the data to be processed.

implement comparisons of numbers and objects.

• Relational operators (< <= > >= == !=) are used to compare numbers and strings. • Lexicographic order is used to compare strings.

implement complex decisions that require multiple if statements.

• Multiple alternatives are required for decisions that have more than two cases. • When using multiple if statements, pay attention to the order of the conditions.

C h a p t e r s U M M a r Y

are necessary to actually understand the sentences. For exam ple, consider the sentence “last fall she enrolled in Michigan state”. the reader automati- cally realizes that “fall” is not related to falling down in this context, but refers to the season. While there is a state of Michigan, here Michigan state denotes the university. a priori, a com- puter program has none of this knowl- edge. the goal of the CYC project is to extract and store the requisite facts— that is, (1) people enroll in universities; (2) Michigan is a state; (3) many states have universi ties named x state Uni- versity, often abbreviated as x state; (4) most peo ple enroll in a university in the fall. By 1995, the project had codi- fied about 100,000 common-sense concepts and about a million facts of knowledge relating them. even this massive amount of data has not proven suffi cient for useful applications.

in recent years, artificial intelli- gence technology has seen substantial advances. one of the most astound-

ing examples is the out- come of a series of “grand challenges” for autono- mous vehicles posed by the Defense advanced research projects agency (Darpa). Competitors were invited to submit a com- puter-controlled vehicle that had to complete an obstacle course without a human driver or remote control. the first event, in 2004, was a disap pointment, with none of the entrants finish- ing the route. in 2005, five vehicles completed a gru- eling 212 km course in the Mojave desert. stan ford’s stanley came in first, with an average speed of 30 km/h. in 2007, Darpa moved the com- petition to an “urban” environment, an abandoned air force base. Vehicles had to be able to interact with each other, following California traffic laws. as stanford’s sebastian thrun explained:

“in the last Grand Challenge, it didn’t really mat ter whether an obstacle was a rock or a bush, because either way you’d just drive around it. the current challenge is to move from just sensing the envi ronment to understanding the envi ronment.”

Winner of the 2007 DARPA Urban Challenge

39. Consider the following test program: int main() { int m = 1; cout << "Enter an integer: "; cin >> m; int n = 2; cout << "Enter another integer: "; cin >> n; cout << m << " " << n << endl; return 0; }

Run this program and enter three at the first prompt. What happens? Why?

practice it Now you can try these exercises at the end of the chapter: R3.1, R3.30, P3.26.

When one uses a sophisticated com-

puter program such as a tax prepara- tion package, one is bound to attribute some intelligence to the computer. the computer asks sensible questions and makes computations that we find a mental challenge. after all, if doing one’s taxes were easy, we wouldn’t need a computer to do it for us.

as programmers, however, we know that all this apparent intelli gence is an illusion. human program mers have carefully “coached” the software in all possible scenarios, and it simply replays the actions and deci sions that were programmed into it.

Would it be possible to write com- puter programs that are genuinely intelligent in some sense? From the earliest days of computing, there was a sense that the human brain might be nothing but an immense computer, and that it might well be feasible to program computers to imitate some processes of human thought. seri-

ous research into artificial intelligence began in the mid-1950s, and the first twenty years brought some impres- sive successes. programs that play chess—surely an activity that appears to require remarkable intellectual pow- ers—have become so good that they now routinely beat all but the best human players. as far back as 1975, an expertsystem program called Mycin gained fame for being better in diag- nosing meningitis in patients than the average physician.

however, there were serious set- backs as well. From 1982 to 1992, the Japanese government embarked on a massive research project, funded at over 40 billion Japanese yen. it was known as the FifthGeneration Project. its goal was to develop new hardware and software to greatly improve the performance of expert system soft- ware. at its outset, the project created fear in other countries that the Japa- nese computer industry was about to become the undisputed leader in the

field. however, the end results were disappointing and did little to bring artificial intelligence applications to market.

From the very outset, one of the stated goals of the ai community was to produce software that could trans- late text from one language to another, for example from english to russian. that undertaking proved to be enor- mously complicated. human language appears to be much more subtle and interwoven with the human experience than had originally been thought. even the grammar-checking tools that come with word-processing programs today are more of a gim mick than a useful tool, and analyzing grammar is just the first step in trans lating sentences.

the CYC (from encyclopedia) proj- ect, started by Douglas lenat in 1984, tries to codify the implicit assump- tions that underlie human speech and writing. the team members started out analyzing news articles and asked themselves what unmen tioned facts

Random Fact 3.2 artificial intelligence

cfe2_ch03_p75_130.indd 112 10/28/10 7:52 PM

Chapter summary 113

use the if statement to implement a decision.

• The if statement allows a program to carry out dif ferent actions depending on the nature of the data to be processed.

implement comparisons of numbers and objects.

• Relational operators (< <= > >= == !=) are used to compare numbers and strings. • Lexicographic order is used to compare strings.

implement complex decisions that require multiple if statements.

• Multiple alternatives are required for decisions that have more than two cases. • When using multiple if statements, pay attention to the order of the conditions.

C h a p t e r s U M M a r Y

in recent years, artificial intelli- gence technology has seen substantial advances. one of the most astound-

Winner of the 2007 DARPA Urban Challenge

Run this program and enter three at the first prompt. What happens? Why?

practice it Now you can try these exercises at the end of the chapter: R3.1, R3.30, P3.26.

When one uses a sophisticated com-

field. however, the end results were disappointing and did little to bring artificial intelligence applications to market.

Random Fact 3.2 artificial intelligence

cfe2_ch03_p75_130.indd 113 10/28/10 7:52 PM

114 Chapter 3 Decisions

implement decisions whose branches require further decisions.

• When a decision statement is contained inside the branch of another decision statement, the statements are nested.

• Nested decisions are required for problems that have two levels of decision mak ing.

draw flowcharts for visualizing the control flow of a program.

• Flow charts are made up of elements for tasks, input/ outputs, and decisions.

• Each branch of a decision can contain tasks and further decisions.

• Never point an arrow inside another branch.

design test cases for your programs.

• Each branch of your program should be covered by a test case. • It is a good idea to design test cases before implementing a program.

use the boolean data type to store and combine conditions that can be true or false.

• The Boolean type bool has two values, false and true. • C++ has two Boolean operators that combine conditions: && (and) and || (or). • To invert a condition, use the ! (not) operator. • The && and || operators are computed using short-circuit evaluation: As soon as

the truth value is determined, no further conditions are evaluated. • De Morgan’s law tells you how to negate && and || conditions.

apply if statements to detect whether user input is valid.

• When reading a value, check that it is within the required range. • Use the fail function to test whether the input stream has failed.

r3.1 Find the errors in the following if statements. a. if x > 0 then cout << x; b. if (x > 0) ; { y = 1; } else ; { y = -1; } c. if (1 + x > pow(x, sqrt(2)) { y = y + x; } d. if (x = 1) { y++; } e. cin >> x; if (cin.fail()) { y = y + x; }

r3.2 What do these code fragments print? a. int n = 1; int m = -1;

if (n < -m) { cout << n; } else { cout << m; }

b. int n = 1; int m = -1; if (-n >= m) { cout << n; } else { cout << m; }

True

False

Condition

r e V i e W e x e r C i s e s

cfe2_ch03_p75_130.indd 114 10/28/10 7:52 PM

review exercises 115

c. double x = 0; double y = 1; if (fabs(x - y) < 1) { cout << x; } else { cout << y; }

d. double x = sqrt(2); double y = 2; if (x * x == y) { cout << x; } else { cout << y; }

r3.3 Suppose x and y are variables of type double. Write a code fragment that sets y to x if x is positive and to 0 otherwise.

r3.4 Suppose x and y are variables of type double. Write a code fragment that sets y to the absolute value of x without calling the fabs function. Use an if statement.

r3.5 Explain why it is more difficult to compare floating-point numbers than integers. Write C++ code to test whether an integer n equals 10 and whether a floating-point number x equals 10.

r3.6 Common Error 3.2 on page 85 explains that a C++ compiler will not report an error when you use an assignment operator instead of a test for equality, but it may issue a warning. Write a test program containing a statement

if (floor = 13)

What does your compiler do when you compile the program?

r3.7 Each square on a chess board can be described by a letter and number, such as g5 in this example:

1 2

The following pseudocode describes an algorithm that determines whether a square with a given letter and number is dark (black) or light (white).

If the letter is an a, c, e, or g If the number is odd

color = "black" Else

color = "white" Else

If the number is even color = "black"

Else color = "white"

Using the procedure in Programming Tip 3.6 on page 97, trace this pseudocode with input g5.

r3.8 Give a set of four test cases for the algorithm of Exercise R3.7 that covers all branches.

cfe2_ch03_p75_130.indd 115 10/28/10 7:52 PM

116 Chapter 3 Decisions

r3.9 In a scheduling program, we want to check whether two appointments overlap. For simplicity, appointments start at a full hour, and we use military time (with hours 0–23). The following pseudocode describes an algorithm that determines whether the appointment with start time start1 and end time end1 overlaps with the appoint- ment with start time start2 and end time end2.

If start1 > start2 s = start1

Else s = start2

If end1 < end2 e = end1

Else e = end2

If s < e The appointments overlap.

Else The appointments don’t overlap.

Trace this algorithm with an appointment from 10–12 and one from 11–13, then with an appointment from 10–11 and one from 12–13.

r3.10 Draw a flow chart for the algorithm in Exercise R3.9.

r3.11 Draw a flow chart for the algorithm in Exercise P3.12.

r3.12 Draw a flow chart for the algorithm in Exercise P3.13.

r3.13 Develop a set of test cases for the algorithm in Exercise R3.9.

r3.14 Develop a set of test cases for the algorithm in Exercise P3.13.

r3.15 Write pseudocode for a program that prompts the user for a month and day and prints out whether it is one of the following four holidays:

• New Year’s Day (January 1) • Independence Day (July 4) • Veterans Day (November 11) • Christmas Day (December 25)

r3.16 Write pseudocode for a program that assigns letter grades for a quiz, according to the following table:

Score Grade 90-100 A 80-89 B 70-79 C 60-69 D < 60 F

r3.17 Explain how the lexicographic ordering of strings in C++ differs from the ordering of words in a dictionary or telephone book. Hint: Consider strings such as IBM, wiley.com, Century 21, and While-U-Wait.

r3.18 Of the following pairs of strings, which comes first in lexicographic order? a. "Tom", "Dick" b. "Tom", "Tomato" c. "church", "Churchill"

cfe2_ch03_p75_130.indd 116 10/28/10 7:52 PM

review exercises 117

d. "car manufacturer", "carburetor" e. "Harry", "hairy" f. "C++", " Car" g. "Tom", "Tom" h. "Car", "Carl" i. "car", "bar"

r3.19 Explain the difference between a sequence of else if clauses and nested if state- ments. Give an example for each.

r3.20 Give an example of a sequence of else if clauses where the order of the tests does not matter. Give an example where the order of the tests matters.

r3.21 Rewrite the condition in Section 3.3 to use < operators instead of >= operators. What is the impact on the order of the comparisons?

r3.22 Give a set of test cases for the tax program in Exercise P3.18. Manually compute the expected results.

r3.23 Make up another C++ code example that shows the dangling else problem, using the following statement. A student with a GPA of at least 1.5, but less than 2, is on probation. With less than 1.5, the student is failing.

r3.24 Complete the following truth table by finding the truth values of the Boolean expressions for all combinations of the Boolean inputs p, q, and r.

p q r (p && q) || !r !(p && (q || !r))

false false false

false false true

false true false

. . .

5 more combinations

. . .

r3.25 True or false? A && B is the same as B && A for any Boolean conditions A and B.

r3.26 The “advanced search” feature of many search engines allows you to use Boolean operators for complex queries, such as “(cats OR dogs) AND NOT pets”. Contrast these search operators with the Boolean operators in C++.

r3.27 Suppose the value of b is false and the value of x is 0. What is the value of each of the fol lowing expressions?

a. b && x == 0 b. b || x == 0 c. !b && x == 0 d. !b || x == 0

e. b && x != 0 f. b || x != 0 g. !b && x != 0 h. !b || x != 0

cfe2_ch03_p75_130.indd 117 10/28/10 7:52 PM

118 Chapter 3 Decisions

r3.28 Simplify the following expressions. Here, b is a variable of type bool. a. b == true b. b == false c. b != true d. b != false

r3.29 Simplify the following statements. Here, b is a variable of type bool and n is a vari able of type int.

a. if (n == 0) { b = true; } else { b = false; } (Hint: What is the value of n == 0?)

b. if (n == 0) { b = false; } else { b = true; } c. b = false; if (n > 1) { if (n < 2) { b = true; } } d. if (n < 1) { b = true; } else { b = n > 2; }

r3.30 What is wrong with the following program? cout << "Enter the number of quarters: "; cin >> quarters; total = total + quarters * 0.25; cout << "Total: " << total << endl; if (cin.fail()) { cout << "Input error."; }

r3.31 Reading numbers is surprisingly difficult because a C++ input stream looks at the input one character at a time. First, white space is skipped. Then the stream con- sumes those input characters that can be a part of a number. Once the stream has recognized a number, it stops reading if it finds a character that cannot be a part of a number. However, if the first non-white space character is not a digit or a sign, or if the first character is a sign and the second one is not a digit, then the stream fails. Consider a program reading an integer:

cout << "Enter the number of quarters: "; int quarters; cin >> quarters;

For each of the following user inputs, circle how many characters have been read and whether the stream is in the failed state or not.

a. 15.9 b. 15 9 c. +159 d. -15A9 e. Fifteen f. -Fifteen g. + 15 h. 1.5E3 i. +1+5

p3.1 Write a program that reads a temperature value and the letter C for Celsius or F for Fahrenheit. Print whether water is liquid, solid, or gaseous at the given temperature at sea level.

p r o G r a M M i n G e x e r C i s e s

cfe2_ch03_p75_130.indd 118 10/28/10 7:52 PM

programming exercises 119

p3.2 The boiling point of water drops by about one degree centigrade for every 300 meters (or 1,000 feet) of altitude. Improve the program of Exercise P3.1 to allow the user to supply the altitude in meters or feet.

p3.3 Write a program that reads in three floating-point numbers and prints the largest of the three inputs. For example:

Please enter three numbers: 4 9 2.5 The largest number is 9.

p3.4 Write a program that reads in three strings and sorts them lexicographically. Enter three strings: Charlie Able Baker Able Baker Charlie

p3.5 Write a program that reads an integer and prints how many digits the number has, by checking whether the number is ≥ 10, ≥ 100, and so on. (Assume that all integers are less than ten billion.) If the number is negative, first multiply it with –1.

p3.6 Write a program that reads three numbers and prints “all the same” if they are all the same, “all different” if they are all different, and “neither” otherwise.

p3.7 Write a program that reads three numbers and prints “increasing” if they are in increasing order, “decreasing” if they are in decreasing order, and “neither” other- wise. Here, “increasing” means “strictly increasing”, with each value larger than its pre decessor. The sequence 3 4 4 would not be considered increasing.

p3.8 Repeat Exercise P3.7, but before reading the numbers, ask the user whether increas- ing/decreasing should be “strict” or “lenient”. In lenient mode, the sequence 3 4 4 is increasing and the sequence 4 4 4 is both increasing and decreasing.

p3.9 Write a program that translates a letter grade into a number grade. Letter grades are A, B, C, D, and F, possibly followed by + or –. Their numeric values are 4, 3, 2, 1, and 0. There is no F+ or F–. A + increases the numeric value by 0.3, a – decreases it by 0.3. However, an A+ has value 4.0.

Enter a letter grade: B- The numeric value is 2.7.

p3.10 Write a program that translates a number between 0 and 4 into the closest letter grade. For example, the number 2.8 (which might have been the average of several grades) would be converted to B–. Break ties in favor of the better grade; for exam ple 2.85 should be a B.

p3.11 Write a program that takes user input describing a playing card in the following shorthand notation:

A Ace 2 ... 10 Card values J Jack Q Queen K King D Diamonds H Hearts S Spades C Clubs

cfe2_ch03_p75_130.indd 119 10/28/10 7:52 PM

120 Chapter 3 Decisions

Your program should print the full description of the card. For example, Enter the card notation: QS Queen of Spades

p3.12 When two points in time are compared, each given as hours (in military time, rang ing from 0 and 23) and minutes, the following pseudocode determines which comes first.

If hour1 < hour2 time1 comes first.

Else if hour1 and hour2 are the same If minute1 < minute2

time1 comes first. Else if minute1 and minute2 are the same

time1 and time2 are the same. Else

time2 comes first. Else

time2 comes first.

Write a program that prompts the user for two points in time and prints the time that comes first, then the other time.

p3.13 The following algorithm yields the season (Spring, Summer, Fall, or Winter) for a given month and day.

If month is 1, 2, or 3, season = "Winter" Else if month is 4, 5, or 6, season = "Spring" Else if month is 7, 8, or 9, season = "Summer" Else if month is 10, 11, or 12, season = "Fall" If month is divisible by 3 and day >= 21

If season is "Winter", season = "Spring" Else if season is "Spring", season = "Summer" Else if season is "Summer", season = "Fall" Else season = "Winter"

Write a program that prompts the user for a month and day and then prints the season, as determined by this algorithm.

p3.14 Write a program that reads in two floating-point numbers and tests whether they are the same up to two decimal places. Here are two sample runs.

Enter two floating-point numbers: 2.0 1.99998 They are the same up to two decimal places. Enter two floating-point numbers: 2.0 1.98999 They are different.

p3.15 Write a program to simulate a bank transaction. There are two bank accounts: check- ing and savings. First, ask for the initial balances of the bank accounts; reject negative balances. Then ask for the transactions; options are deposit, withdrawal, and trans- fer. Then ask for the account; options are checking and savings. Then ask for the amount; reject transactions that overdraw an account. At the end, print the balances of both accounts.

cfe2_ch03_p75_130.indd 120 10/28/10 7:52 PM

programming exercises 121

p3.16 Write a program that reads in the name and salary of an employee. Here the salary will denote an hourly wage, such as $9.25. Then ask how many hours the employee worked in the past week. Be sure to accept fractional hours. Any overtime work (over 40 hours per week) is paid at 150 percent of the regular wage. Compute the pay. Print a paycheck for the employee.

p3.17 Write a program that prompts for the day and month of the user’s birthday and then prints a horoscope. Make up fortunes for programmers, like this:

Please enter your birthday (month and day): 6 16 Gemini are experts at figuring out the behavior of complicated programs. You feel where bugs are coming from and then stay one step ahead. Tonight, your style wins approval from a tough critic.

Each fortune should contain the name of the astrological sign. (You will find the names and date ranges of the signs at a distressingly large number of sites on the Internet.)

p3.18 Write a program that computes taxes for the following schedule:

if your status is single and if the taxable income is over but not over the tax is of the amount over

$0 $8,000 10% $0

$8,000 $32,000 $800 + 15% $8,000

$32,000 $4,400 + 25% $32,000

if your status is Married and if the taxable income is over but not over the tax is of the amount over

$0 $16,000 10% $0

$16,000 $64,000 $1,600 + 15% $16,000

$64,000 $8,800 + 25% $64,000

p3.19 The original U.S. income tax of 1913 was quite simple. The tax was • 1 percent on the first $50,000. • 2 percent on the amount over $50,000 up to $75,000. • 3 percent on the amount over $75,000 up to $100,000. • 4 percent on the amount over $100,000 up to $250,000. • 5 percent on the amount over $250,000 up to $500,000. • 6 percent on the amount over $500,000.

There was no separate schedule for single or married taxpayers. Write a program that computes the income tax according to this schedule.

p3.20 The tax.cpp program uses a simplified version of the 2008 U.S. income tax schedule. Look up the tax brackets and rates for the current year, for both single and married filers, and implement a program that computes the actual income tax.

cfe2_ch03_p75_130.indd 121 10/28/10 7:52 PM

122 Chapter 3 Decisions

p3.21 Unit conversion. Write a unit conversion program that asks the users from which unit they want to convert (fl. oz, gal, oz, lb, in, ft, mi) and to which unit they want to convert (ml, l, g, kg, mm, cm, m, km). Reject incompatible conversions (such as gal → km). Ask for the value to be converted, then display the result:

Convert from? gal Convert to? ml Value? 2.5 2.5 gal = 9462.5 ml

p3.22 Write a program that prompts the user to provide a single character from the alpha- bet. Print Vowel or Consonant, depending on the user input. If the user input is not a letter (between a and z or A and Z), or is a string of length > 1, print an error message.

p3.23 Roman numbers. Write a program that converts a positive integer into the Roman number system. The Roman number system has digits

I 1 V 5 X 10 L 50 C 100 D 500 M 1,000

Numbers are formed according to the following rules. (1) Only numbers up to 3,999 are represented. (2) As in the decimal system, the thousands, hundreds, tens, and ones are expressed separately. (3) The num bers 1 to 9 are expressed as

I 1 II 2 III 3 IV 4 V 5 VI 6 VII 7 VIII 8 IX 9

As you can see, an I preceding a V or X is subtracted from the value, and you can never have more than three I’s in a row. (4) Tens and hundreds are done the same way, except that the let ters X, L, C and C, D, M are used instead of I, V, X, respec tively. Your program should take an input, such as 1978, and convert it to Roman numerals, MCMLXXVIII.

cfe2_ch03_p75_130.indd 122 10/28/10 7:52 PM

programming exercises 123

p3.24 Write a program that asks the user to enter a month (1 for January, 2 for February, and so on) and then prints the number of days in the month. For February, print “28 or 29 days”.

Enter a month: 5 30 days

Do not use a separate if/else branch for each month. Use Boolean operators.

p3.25 A year with 366 days is called a leap year. A year is a leap year if it is divisible by four (for example, 1980), except that it is not a leap year if it is divisible by 100 (for example, 1900); however, it is a leap year if it is divisible by 400 (for example, 2000). There were no exceptions before the introduction of the Gregorian calendar on October 15, 1582 (1500 was a leap year). Write a program that asks the user for a year and computes whether that year is a leap year.

p3.26 Add error handling to Exercise P3.2. If the user does not enter a number when expected, or provides an invalid unit for the altitude, print an error message and end the program.

engineering p3.27 Write a program that prompts the user for a wavelength value and prints a descrip- tion of the corresponding part of the electromagnetic spectrum, as given in Table 7.

table 7 electromagnetic spectrum

type Wavelength (m) Frequency (hz)

Radio Waves > 10–1 < 3 × 109

Microwaves 10–3 to 10–1 3 × 109 to 3 × 1011

Infrared 7 × 10–7 to 10–3 3 × 1011 to 4 × 1014

Visible light 4 × 10–7 to 7 × 10–7 4 × 1014 to 7.5 × 1014

Ultraviolet 10–8 to 4 × 10–7 7.5 × 1014 to 3 × 1016

X-rays 10–11 to 10–8 3 × 1016 to 3 × 1019

Gamma rays < 10–11 > 3 × 1019

engineering p3.28 Repeat Exercise P3.27, modifying the program so that it prompts for the frequency instead.

engineering p3.29 Repeat Exercise P3.27, modifying the program so that it first asks the user whether the input will be a wavelength or a frequency.

engineering p3.30 A minivan has two sliding doors. Each door can be opened by either a dashboard switch, its inside handle, or its outside handle. However, the inside handles do not work if a child lock switch is activated. In order for the sliding doors to open, the gear shift must be in park, and the master unlock switch must be activated. (This book’s author is the long-suffering owner of just such a vehicle.)

cfe2_ch03_p75_130.indd 123 10/28/10 7:52 PM

124 Chapter 3 Decisions

Your task is to simulate a portion of the control software for the vehicle. The input is a sequence of values for the switches and the gear shift, in the following order:

• Dashboard switches for left and right sliding door, child lock, and master unlock (0 for off or 1 for activated)

• Inside and outside handles on the left and right sliding doors (0 or 1) • The gear shift setting (one of P N D 1 2 3 R).

A typical input would be 0 0 0 1 0 1 0 0 P. Print “left door opens” and/or “right door opens” as appropriate. If neither door opens, print “both doors stay closed”.

engineering p3.31 Sound level L in units of decibel (dB) is determined by

L = 20 log10(p/p0)

where p is the sound pressure of the sound (in Pascals, abbreviated Pa), and p0 is a reference sound pres sure equal to 20 × 10–6 Pa (where L is 0 dB). The following table gives descriptions for certain sound lev els.

Threshold of pain 130 dB Possible hearing damage 120 dB Jack hammer at 1 m 100 dB Traffic on a busy roadway at 10 m 90 dB Normal conversation 60 dB Calm library 30 dB Light leaf rustling 0 dB

Write a program that reads a value and a unit, either dB or Pa, and then prints the closest description from the list above.

engineering p3.32 The electric circuit shown below is designed to measure the temperature of the gas in a chamber.

+ –Vs = 20 V

Rs = 75 Ω

R Vm

–

Voltmeter

11.43 V

The resistor R represents a temperature sensor enclosed in the chamber. The resis- tance R, in Ω, is related to the temperature T, in °C, by the equation

R R kT= +0 In this device, assume R0 = 100 Ω and k = 0.5. The voltmeter displays the value of the voltage, Vm , across the sensor. This voltage Vm indicates the temperature, T, of the gas according to the equation

T R k

R k

V V V

R k

s m

s m = − =

− −0 0

cfe2_ch03_p75_130.indd 124 10/28/10 7:52 PM

programming exercises 125

Suppose the voltmeter voltage is constrained to the range Vmin = 12 volts ≤ Vm ≤ Vmax = 18 volts. Write a program that accepts a value of Vm and checks that it’s between 12 and 18. The program should return the gas temperature in degrees Celsius when Vm is between 12 and 18 and an error message when it isn’t.

engineering p3.33 Crop damage due to frost is one of the many risks confronting farmers. The figure below shows a simple alarm circuit designed to warn of frost. The alarm circuit uses a device called a thermistor to sound a buzzer when the temperature drops below freezing. Thermistors are semiconductor devices that exhibit a temperature depen- dent resistance described by the equation

R R e T T= −

 

 

1 1

where R is the resistance, in Ω, at the temperature T, in °K, and R0 is the resistance, in Ω, at the temperature T0, in°K. β is a constant that depends on the material used to make the thermistor.

–

9 V

R 3

R 4R 2

RThermistor

9 V

Comparator

Buzzer

The circuit is designed so that the alarm will sound when

R R

R R 2

3 4+ <

The thermistor used in the alarm circuit has R0 = 33,192 Ω at T0 = 40 °C, and β = 3,310 °K. (Notice that β has units of °K. Recall that the temperature in °K is obtained by adding 273° to the temperature in °C.) The resistors R2, R3, and R4 have a resis- tance of 156.3 kΩ = 156,300 Ω. Write a C++ program that prompts the user for a temperature in °F and prints a message indicating whether or not the alarm will sound at that temperature.

engineering p3.34 A mass m = 2 kilograms is attached to the end of a rope of length r = 3 meters. The mass is whirled around at high speed. The rope can withstand a maximum tension of T = 60 Newtons. Write a program that accepts a rotation speed v and determines if such a speed will cause the rope to break. Hint: T m v r= 2 .

engineering p3.35 A mass m is attached to the end of a rope of length r = 3 meters. The rope can only be whirled around at speeds of 1, 10, 20, or 40 meters per second. The rope can with- stand a maximum tension of T = 60 Newtons. Write a program where the user enters the value of the mass m, and the program determines the greatest speed at which it can be whirled without breaking the rope. Hint: T m v r= 2 .

cfe2_ch03_p75_130.indd 125 10/28/10 7:52 PM

126 Chapter 3 Decisions

engineering p3.36 The average person can jump off the ground with a velocity of 7 mph without fear of leaving the planet. However, if an astronaut jumps with this velocity while standing on Halley’s Comet, will the astronaut ever come back down? Create a program that allows the user to input a launch velocity (in mph) from the surface of Halley’s Comet and determine whether a jumper will return to the surface. If not, the program should calculate how much more massive the comet must be in order to return the jumper to the surface.

Hint: Escape velocity is v G M

Rescape = 2 , where G N m kg= × −6 67 10 11 2 2. is

the gravitational constant, M kg= ×1 3 1022. is the mass of Halley’s comet, and

R m= ×1 153 106. is its radius.

1. Change the if statement to if (floor > 14) { actual_floor = floor - 2; }

2. 85. 90. 85. 3. The only difference is if original_price is 100. The statement in Self Check 2 sets

discounted_price to 90; this one sets it to 80. 4. 95. 100. 95. 5. if (fuel_amount < 0.10 * fuel_capacity)

{ cout << "red" << endl; } else { cout << "green" << endl; }

6. (a) and (b) are both true, (c) is false. 7. floor <= 13 8. The values should be compared with ==, not =. 9. input == "Y"

10. str != "" or str.length() > 0 11. if (score_a > score_b)

{ cout << "A won"; } else if (score_a < score_b) { cout << "B won";

a n s W e r s t o s e l F - C h e C k Q U e s t i o n s

cfe2_ch03_p75_130.indd 126 10/28/10 7:52 PM

answers to self-Check Questions 127

} else { cout << "Game tied"; }

12. if (x > 0) { s = 1; } else if (x < 0) { s = -1; } else { s = 0; }

13. You could first set s to one of the three values: s = 0; if (x > 0) { s = 1; } else if (x < 0) { s = -1; }

14. The if (price <= 100) can be omitted, making it clear that the else branch is the sole alternative.

15. No destruction of buildings 16. Add a branch before the final else:

else if (richter < 0) { cout << "Error: Negative input" << endl; }

17. $3,200 18. No. Then the computation is 0.10 × 32000 + 0.25 (32000 – 32000). 19. No. Their individual tax is $5,200 each, and if they married, they would pay $10,400.

Actually, taxpayers in higher tax brackets (which our program does not model) may pay higher taxes when they marry, a phenomenon known as the mar riage penalty.

20. Change else in line 36 to else if (marital_status == "m"), and add another branch after line 47: else { cout << "Error: marital status should be s or m." << endl; }

21. The higher tax rate is only applied on the income in the higher bracket. Suppose you are single and make $31,900. Should you try to get a $200 raise? Absolutely: you get to keep 90 percent of the first $100 and 75 percent of the next $100.

22.

True

False

temp < 0? Print “Frozen”

Read temp

cfe2_ch03_p75_130.indd 127 10/28/10 7:52 PM

128 Chapter 3 Decisions

23. The “True” arrow from the first decision points into the “True” branch of the sec- ond decision, creating spaghetti code.

24. Here is one solution. In Section 3.7, you will see how you can combine the condi- tions for a more elegant solution.

True

False

Input < 0? Status = “Error”

True

False

Input > 100?

Status = “OK”

Status = “Error”

25.

True

False

Print Print “Error”

x < 0?

Read x

cfe2_ch03_p75_130.indd 128 10/28/10 7:52 PM

answers to self-Check Questions 129

26.

27. Test Case Expected Output Comment 12 12 Below 13th floor 14 13 Above 13th floor 13 ? The specification is not clear— See Section 3.8 for a

version of this program with error handling

28. A boundary test case is a price of $128. A 16 percent discount should apply because the problem statement states that the larger discount applies if the price is at least $128. Thus, the expected output is $107.52.

29. Test Case Expected Output Comment 9 Most structures fall

7.5 Many buildings destroyed 6.5 Many buildings considerably... 5 Damage to poorly... 3 No destruction...

8.0 Most structures fall Boundary case. In this program, boundary cases are not as significant since the behavior of an earthquake changes gradually.

-1 The specification is not clear—see Self Check 16 for a version of this program with error handling.

True

False

temp < 0? Print “Ice”

True

False

temp > 100? Print “Steam”

Print “Liquid”

Read temp

cfe2_ch03_p75_130.indd 129 10/28/10 7:52 PM

130 Chapter 3 Decisions

Step 1 Decide on the branching condition.

We need to take different actions for strings of odd and even length. Therefore, the condition is

Is the length of the string odd?

In C++, you use the remainder of division by 2 to find out whether a value is even or odd. Then the test becomes

str.length() % 2 == 1?

Step 2 Give pseudocode for the work that needs to be done when the condition is true.

We need to find the position of the middle character. If the length is 5, the position is 2.

In general,

position = str.length() / 2 (with the remainder discarded) result = str.substr(position, 1)

Step 3 Give pseudocode for the work (if any) that needs to be done when the condition is not true.

Again, we need to find the position of the middle character. If the length is 6, the starting posi- tion is 2, and the ending position is 3.

In general,

position = str.length() / 2 - 1 result = str.substr(position, 2)

Step 4 Double-check relational operators.

Do we really want str.length() % 2 == 1? For example, when the length is 5, 5 % 2 is the remainder of the division 5 / 2, which is 1. In general, dividing an odd number by 2 leaves a remainder of 1. (Actually, dividing a negative odd num ber by 2 leaves a remainder of –1, but the string length is never negative.) Therefore, our condition is correct.

Step 5 Remove duplication.

Here is the statement that we have developed:

If str.length() % 2 == 1 position = str.length() / 2 (with remainder discarded) result = str.substr(position, 1) Else position = str.length() / 2 - 1 result = str.substr(position, 2)

W o r k e D e x a M p l e 3 . 1 extracting the middle

Your task is to extract a string containing the middle character from a given string str. For example, if the string is “crate”, the result is the string “a”. However, if the string has an even number of letters, extract the middle two characters. If the string is “crates”, the result is “at”.

30. Test Case Expected Output Comment (0.5, 0.5) inside

(4, 2) outside (0, 2) on the boundary Exactly on the boundary

(1.414, 1.414) on the boundary Close to the boundary (0, 1.9) inside Not less than 1 mm from the boundary (0, 2.1) outside Not less than 1 mm from the boundary

31. x == 0 && y == 0 32. x == 0 || y == 0 33. (x == 0 && y != 0) || (y == 0 && x != 0) 34. The same as the value of frozen. 35. You are guaranteed that there are no other values. With strings or integers, you

would need to check that no values such as "maybe" or –1 enter your calculations. 36. (a) Error: The floor must be between 1 and 20. (b) Error: The floor must be between 1 and

20. (c) The elevator will travel to the actual floor 19 (d) Error: Not an integer. 37. cin.fail() || floor == 13 || floor <= 0 || floor > 20 38. Check for cin.fail(), to make sure a researcher didn’t supply an input such as oh my.

Check for weight <= 0, since any rat must surely have a positive weight. We don’t know how giant a rat could be, but the New Guinea rats weighed no more than 2 kg. A regular house rat (rattus rattus) weighs up to 0.2 kg, so we’ll say that any weight > 10 kg was surely an input error, perhaps confusing grams and kilograms. Thus, the checks are if (cin.fail()) { cout << "Error: Not a number" << endl; return 1; }

if (weight < 0) { cout << "Error: Weight cannot be negative." << endl; return 1; }

if (weight > 10) { cout << "Error: Weight > 10 kg." << endl; return 1; }

39. The first input fails. The value of m is unchanged. Because a previous input failed, the next input doesn’t even try to get additional keystrokes. It also fails, and n is un- changed. The program prints 1 2.

cfe2_ch03_p75_130.indd 130 10/28/10 7:52 PM

4C h a p t e r

131

L o o p s

to implement while, for, and do loops

to avoid infinite loops and off-by-one errors

to understand nested loops

to implement programs that read and process data sets

to use a computer for simulations

C h a p t e r G o a L s

C h a p t e r C o n t e n t s

4.1 The while loop 132

Syntax 4.1: while statement 133 Common Error 4.1: Infinite Loops 136 Common Error 4.2: Don’t think “are We

there Yet?” 137 Common Error 4.3: off-by-one errors 137 Random Fact 4.1: the First Bug 138

4.2 problem Solving: hand-Tracing 139

4.3 The for loop 142

Syntax 4.2: for statement 144 Programming Tip 4.1: Use for Loops for their

Intended purpose only 147 Programming Tip 4.2: Choose Loop Bounds that

Match Your task 147 Programming Tip 4.3: Count Iterations 147

4.4 The do loop 148

Programming Tip 4.4: Flowcharts for Loops 149

4.5 proceSSing inpuT 150

Special Topic 4.1: Clearing the Failure state 153 Special Topic 4.2: the Loop-and-a-half problem

and the break statement 153 Special Topic 4.3: redirection of Input and

output 154

4.6 problem Solving: SToryboardS 154

4.7 common loop algoriThmS 157

How To 4.1: Writing a Loop 162 Worked Example 4.1: Credit Card processing

4.8 neSTed loopS 165

4.9 random numberS and SimulaTionS 168

Random Fact 4.2: software piracy 172

cfe2_ch04_p131_192.indd 131 10/28/10 8:12 PM

132

In a loop, a part of a program is repeated over and over, until a specific goal is reached. Loops are important for calculations that require repeated steps and for processing input consisting of many data items. In this chapter you will learn about loop statements in C++, as well as techniques for writing programs that process input and simulate activities in the real world.

4.1 the while Loop In this section, you will learn how to repeatedly execute statements until a goal has been reached.

Recall the investment problem from Chapter 1. You put $10,000 into a bank account that earns 5 percent interest per year. How many years does it take for the account balance to be double the origi- nal investment?

In Chapter 1 we developed the following algo- rithm for this problem:

Start with a year value of 0, a column for the interest, and a balance of $10,000.

year interest balance 0 $10,000

Repeat the following steps while the balance is less than $20,000 Add 1 to the year value. Compute the interest as balance x 0.05 (i.e., 5 percent interest). Add the interest to the balance.

Report the final year value as the answer.

You now know how to define and update the variables in C++. What you don’t yet know is how to carry out “Repeat steps while the balance is less than $20,000”.

Because the interest earned also earns interest, a bank balance grows exponentially.

In a particle accelerator, subatomic particles traverse a loop-shaped tunnel multiple times, gaining the speed required for physical experiments. Similarly, in computer science, statements in a loop are executed while a condition is true.

In C++, the while statement implements such a repetition (see Syntax 4.1). The code

while (condition) { statements }

keeps executing the statements while the condition is true. In our case, we want to increment the year counter and add interest while the balance is less than the target balance of $20,000:

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

A while statement is an example of a loop. If you draw a flowchart, the flow of execu- tion loops again to the point where the condition is tested (see Figure 1).

Loops execute a block of code repeatedly while a condition remains true.

syntax 4.1 while statement

double balance = 0; . . . while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

If the condition never becomes false, an infinite loop occurs. See page 136.

These statements are executed while the condition is true.

Braces are not required if the body contains a single statement, but it’s good to always use them. See page 80.

Don’t put a semicolon here! See page 80.

Beware of “off-by-one” errors in the loop condition.

See page 137.

Lining up braces is a good idea.

See page 79.

This variable is defined outside the loop and updated in the loop.

This variable is created in each loop iteration.

cfe2_ch04_p131_192.indd 132 10/28/10 8:12 PM

4.1 the while Loop 133

figure 1 Flowchart of a while Loop

False

True

Add interest to balance

Increment year

balance < TARGET?

In C++, the while statement implements such a repetition (see Syntax 4.1). The code

while (condition) { statements }

keeps executing the statements while the condition is true. In our case, we want to increment the year counter and add interest while the balance is less than the target balance of $20,000:

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

A while statement is an example of a loop. If you draw a flowchart, the flow of execu- tion loops again to the point where the condition is tested (see Figure 1).

Loops execute a block of code repeatedly while a condition remains true.

syntax 4.1 while statement

double balance = 0; . . . while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

If the condition never becomes false, an infinite loop occurs. See page 136.

These statements are executed while the condition is true.

Braces are not required if the body contains a single statement, but it’s good to always use them. See page 80.

Don’t put a semicolon here! See page 80.

Beware of “off-by-one” errors in the loop condition.

See page 137.

Lining up braces is a good idea.

See page 79.

This variable is defined outside the loop and updated in the loop.

This variable is created in each loop iteration.

cfe2_ch04_p131_192.indd 133 10/28/10 8:12 PM

134 Chapter 4 Loops

When you define a variable inside the loop body, the variable is created for each iteration of the loop and removed after the end of each iteration. For example, con- sider the interest variable in this loop:

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; } // interest no longer defined here

In contrast, the balance and years variables were defined outside the loop body. That way, the same vari able is used for all iterations of the loop.

A new interest variable is created in each iteration.

figure 2 execution of the doublinv Loop

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; } cout << year << endl;

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

Check the loop condition1 The condition is true

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

Execute the statements in the loop2

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

Check the loop condition again3 The condition is still true

while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; }

After 15 iterations4 The condition is no longer true

Execute the statement following the loop5

year = 0

balance = 10000

year = 1

interest = 500

balance = 10500

year = 1

balance = 10500

year = 15

balance = 20789.28

year = 15

balance = 20789.28

cfe2_ch04_p131_192.indd 134 10/28/10 8:12 PM

4.1 the while Loop 135

Here is the program that solves the investment problem. Figure 2 illustrates the program’s execution.

ch04/doublinv.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 int main() 6 { 7 const double RATE = 5; 8 const double INITIAL_BALANCE = 10000; 9 const double TARGET = 2 * INITIAL_BALANCE;

10 11 double balance = INITIAL_BALANCE; 12 int year = 0; 13 14 while (balance < TARGET) 15 { 16 year++; 17 double interest = balance * RATE / 100; 18 balance = balance + interest; 19 } 20 21 cout << "The investment doubled after " 22 << year << " years." << endl; 23 24 return 0; 25 }

program run

The investment doubled after 15 years.

1. How many years does it take for the investment to triple? Modify the program and run it.

2. If the interest rate is 10 percent per year, how many years does it take for the investment to double? Modify the program and run it.

3. Modify the program so that the balance after each year is printed. How did you do that?

4. Suppose we change the program so that the condition of the while loop is while (balance <= TARGET)

What is the effect on the program? Why? 5. What does the following loop print?

int n = 1; while (n < 100) { n = 2 * n;

cout << n << " "; }

practice it Now you can try these exercises at the end of the chapter: R4.3, P4.11, P4.16.

S e l f c h e c k

cfe2_ch04_p131_192.indd 135 10/28/10 8:12 PM

136 Chapter 4 Loops

table 1 while Loop examples

Loop output explanation

i = 5; while (i > 0) { cout << i << " "; i--; }

5 4 3 2 1 When i is 0, the loop condition is false, and the loop ends.

i = 5; while (i > 0) { cout << i << " "; i++; }

5 6 7 8 9 10 11 ... The i++ statement is an error causing an “infinite loop” (see Common Error 4.1 on page 136).

i = 5; while (i > 5) { cout << i << " "; i--; }

(No output) The statement i > 5 is false, and the loop is never executed.

i = 5; while (i < 0) { cout << i << " "; i--; }

(No output) The programmer probably thought, “Stop when i is less than 0”. However, the loop condition controls when the loop is executed, not when it ends (see Common Error 4.2 on page 137).

i = 5; while (i > 0) ; { cout << i << " "; i--; }

(No output, program does not terminate)

Note the semicolon before the {. This loop has an empty body. It runs forever, checking whether i > 0 and doing nothing in the body.

infinite loops

A very annoying loop error is an infinite loop: a loop that runs forever and can be stopped only by killing the pro gram or restarting the computer. If there are output statements in the program, then line after line of output flashes by on the screen. Otherwise, the program just sits there and hangs, seeming to do nothing. On some systems, you can terminate a hanging program by hitting Ctrl + C. On others, you can close the window in which the program runs.

A common reason for infinite loops is forgetting to update the variable that controls the loop:

year = 1; while (year <= 20) {

Common error 4.1

balance = balance * (1 + RATE / 100); }

Here the programmer forgot to add a year++ command in the loop. As a result, the year always stays at 1, and the loop never comes to an end.

Another common reason for an infinite loop is accidentally incrementing a counter that should be decremented (or vice versa). Consider this example:

year = 20; while (year > 0) { balance = balance * (1 + RATE / 100); year++; }

The year variable really should have been decremented, not incremented. This is a common error because increment ing counters is so much more common than decrementing that your fingers may type the ++ on autopilot. As a con sequence, year is always larger than 0, and the loop never ends. (Actually, year may eventually exceed the largest representable positive integer and wrap around to a negative number. Then the loop ends—of course, with a com pletely wrong result.)

don’t Think “are we There yet?”

When doing something repetitive, most of us want to know when we are done. For exam ple, you may think, “I want to get at least $20,000,” and set the loop condition to

balance >= TARGET

But the while loop thinks the opposite: How long am I allowed to keep going? The correct loop condition is

while (balance < TARGET)

In other words: “Keep at it while the balance is less than the target.”

When writing a loop condition, don’t ask, “Are we there yet?” The condition determines how long the loop will keep going.

off-by-one errors

Consider our computation of the number of years that are required to double an investment:

int year = 0; while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; } cout << "The investment doubled after " << year << " years." << endl;

Like this hamster who can’t stop running in the tread mill, an infinite loop never ends.

Common error 4.2

Common error 4.3

cfe2_ch04_p131_192.indd 136 10/28/10 8:12 PM

4.1 the while Loop 137

balance = balance * (1 + RATE / 100); }

Here the programmer forgot to add a year++ command in the loop. As a result, the year always stays at 1, and the loop never comes to an end.

Another common reason for an infinite loop is accidentally incrementing a counter that should be decremented (or vice versa). Consider this example:

year = 20; while (year > 0) { balance = balance * (1 + RATE / 100); year++; }

don’t Think “are we There yet?”

When doing something repetitive, most of us want to know when we are done. For exam ple, you may think, “I want to get at least $20,000,” and set the loop condition to

balance >= TARGET

But the while loop thinks the opposite: How long am I allowed to keep going? The correct loop condition is

while (balance < TARGET)

In other words: “Keep at it while the balance is less than the target.”

When writing a loop condition, don’t ask, “Are we there yet?” The condition determines how long the loop will keep going.

off-by-one errors

Consider our computation of the number of years that are required to double an investment:

int year = 0; while (balance < TARGET) { year++; double interest = balance * RATE / 100; balance = balance + interest; } cout << "The investment doubled after " << year << " years." << endl;

Like this hamster who can’t stop running in the tread mill, an infinite loop never ends.

Common error 4.2

Common error 4.3

cfe2_ch04_p131_192.indd 137 10/28/10 8:12 PM

138 Chapter 4 Loops

Should year start at 0 or at 1? Should you test for balance < TARGET or for balance <= TARGET? It is easy to be off by one in these expressions.

Some people try to solve off-by-one errors by randomly inserting +1 or -1 until the pro- gram seems to work—a terrible strategy. It can take a long time to compile and test all the vari- ous possibilities. Expending a small amount of mental effort is a real time saver.

Fortunately, off-by-one errors are easy to avoid, simply by working through a couple of test cases and using the information from the test cases to come up with a rationale for your decisions.

Should year start at 0 or at 1? Look at a scenario with simple val- ues: an initial balance of $100 and an interest rate of 50 percent. After year 1, the balance is $150, and after year 2 it is $225, or over $200. So the investment doubled after 2 years. The loop executed two times, incrementing year each time. Hence year must start at 0, not at 1.

year balance 0 $100 1 $150 2 $225

In other words, the balance variable denotes the balance after the end of the year. At the outset, the balance variable contains the balance after year 0 and not after year 1.

Next, should you use a < or <= comparison in the test? If you want to settle this question with an example, you need to find a scenario in which the final balance is exactly twice the initial balance. This happens when the interest is 100 percent. The loop executes once. Now year is 1, and balance is exactly equal to 2 * INITIAL_BALANCE. Has the investment doubled after one year? It has. Therefore, the loop should not execute again. If the test condition is balance < TARGET, the loop stops, as it should. If the test condition had been balance <= TARGET, the loop would have executed once more.

In other words, you keep adding interest while the balance has not yet doubled.

an off-by-one error is a common error when programming loops. think through simple test cases to avoid this type of error.

according to legend, the first bug was

found in the Mark II, a huge electrome- chanical computer at harvard Univer- sity. It really was caused by a bug—a moth was trapped in a relay switch.

actually, from the note that the operator left in the log book next to the moth (see the photo), it appears as if the term “bug” had already been in active use at the time.

The First Bug

the pioneering computer scientist Maurice Wilkes wrote, “somehow, at the Moore school and afterwards, one had always assumed there would be no particular difficulty in getting pro-

grams right. I can remember the exact instant in time at which it dawned on me that a great part of my future life would be spent finding mistakes in my own programs.”

Random Fact 4.1 the First Bug

4.2 problem solving: hand-tracing In Programming Tip 3.6, you learned about the method of hand-tracing. When you hand-trace code or pseudocode, you write the names of the variables on a sheet of paper, mentally execute each step of the code and update the variables.

It is best to have the code written or printed on a sheet of paper. Use a marker, such as a paper clip, to mark the current line. Whenever a variable changes, cross out the old value and write the new value below. When a program produces output, also write down the output in another column.

Consider this example. What value is displayed? int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

There are three variables: n, sum, and digit.

The first two variables are initialized with 1729 and 0 before the loop is entered. int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

Because n is greater than zero, enter the loop. The variable digit is set to 9 (the remain- der of dividing 1729 by 10). The variable sum is set to 0 + 9 = 9.

int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

hand-tracing is a simulation of code execution in which you step through instructions and track the values of the variables.

n sum digit 1729 0

n sum digit 1729 0 9 9

cfe2_ch04_p131_192.indd 138 10/28/10 8:13 PM

4.2 problem solving: hand-tracing 139

Consider this example. What value is displayed? int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

There are three variables: n, sum, and digit.

n sum digit

Because n is greater than zero, enter the loop. The variable digit is set to 9 (the remain- der of dividing 1729 by 10). The variable sum is set to 0 + 9 = 9.

int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

hand-tracing is a simulation of code execution in which you step through instructions and track the values of the variables.

n sum digit 1729 0

n sum digit 1729 0 9 9

cfe2_ch04_p131_192.indd 139 10/28/10 8:13 PM

140 Chapter 4 Loops

Finally, n becomes 172. (Recall that the remainder in the division 1729 / 10 is dis- carded because both argu ments are integers.)

Cross out the old values and write the new ones under the old ones. int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

Now check the loop condition again. int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

Because n is still greater than zero, repeat the loop. Now digit becomes 2, sum is set to 9 + 2 = 11, and n is set to 17.

Repeat the loop once again, setting digit to 7, sum to 11 + 7 = 18, and n to 1.

Enter the loop for one last time. Now digit is set to 1, sum to 19, and n becomes zero.

n sum digit 1729 0 172 9 9

n sum digit 1729 0 172 9 9 17 11 2

n sum digit 1729 0 172 9 9 17 11 2 1 18 7

n sum digit 1729 0 172 9 9 17 11 2 1 18 7 0 19 1

int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

The condition n > 0 is now false. Continue with the statement after the loop. int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

This statement is an output statement. The value that is output is the value of sum, which is 19.

Of course, you can get the same answer by just running the code. However, hand- tracing can give you an insight that you would not get if you simply ran the code. Consider again what happens in each itera tion:

• We extract the last digit of n. • We add that digit to sum. • We strip the digit off n.

In other words, the loop forms the sum of the digits in n. You now know what the loop does for any value of n, not just the one in the example. (Why would anyone want to form the sum of the digits? Operations of this kind are useful for checking the validity of credit card numbers and other forms of ID numbers—see Exercise P4.5.)

Hand-tracing does not just help you understand code that works correctly. It is a powerful technique for finding errors in your code. When a program behaves in a way that you don’t expect, get out a sheet of paper and track the values of the vari- ables as you mentally step through the code.

You don’t need a working program to do hand-tracing. You can hand-trace pseudocode. In fact, it is an excellent idea to hand-trace your pseudocode before you go to the trouble of translating it into actual code, to confirm that it works correctly.

6. Hand-trace the following code, showing the value of n and the output. int n = 5; while (n >= 0) { n--; cout << n << endl; }

n sum digit output 1729 0 172 9 9 17 11 2 1 18 7 0 19 1 19

hand-tracing can help you understand how an unfamiliar algorithm works.

hand-tracing can show errors in code or pseudocode.

S e l f c h e c k

cfe2_ch04_p131_192.indd 140 10/28/10 8:13 PM

4.2 problem solving: hand-tracing 141

int n = 1729; int sum = 0; while (n > 0)

Because n equals zero, this condition is not true.

{ int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

The condition n > 0 is now false. Continue with the statement after the loop. int n = 1729; int sum = 0; while (n > 0) { int digit = n % 10; sum = sum + digit; n = n / 10; } cout << sum << endl;

This statement is an output statement. The value that is output is the value of sum, which is 19.

• We extract the last digit of n. • We add that digit to sum. • We strip the digit off n.

6. Hand-trace the following code, showing the value of n and the output. int n = 5; while (n >= 0) { n--; cout << n << endl; }

n sum digit output 1729 0 172 9 9 17 11 2 1 18 7 0 19 1 19

hand-tracing can help you understand how an unfamiliar algorithm works.

hand-tracing can show errors in code or pseudocode.

S e l f c h e c k

cfe2_ch04_p131_192.indd 141 10/28/10 8:13 PM

142 Chapter 4 Loops

7. Hand-trace the following code, showing the value of n and the output. What potential error do you notice? int n = 1; while (n <= 3) { cout << n << ", "; n++; }

8. Hand-trace the following code, assuming that a is 2 and n is 4. Then explain what the code does for arbitrary values of a and n. int r = 1; int i = 1; while (i <= n) { r = r * a; i++; }

9. Trace the following code. What error do you observe? int n = 1; while (n != 50) { cout << n << endl; n = n + 10; }

10. The following pseudocode is intended to count the number of digits in the number n:

count = 1 temp = n while (temp > 10)

Increment count. Divide temp by 10.

Trace the pseudocode for n = 123 and n = 100. What error do you find?

practice it Now you can try these exercises at the end of the chapter: R4.1, R4.5.

4.3 the for Loop It often happens that you want to execute a sequence of statements a given number of times. You can use a while loop that is controlled by a counter, as in the following example:

counter = 1; // Initialize the counter while (counter <= 10) // Check the counter { cout << counter << endl; counter++; // Update the counter }

Because this loop type is so common, there is a special form for it, called the for loop (see Syntax 4.2).

the for loop is used when a value runs from a starting point to an ending point with a constant increment or decrement.

cfe2_ch04_p131_192.indd 142 10/28/10 8:13 PM

4.3 the for Loop 143

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

The for loop neatly groups the initialization, condi- tion, and update expressions together. However, it is important to realize that these expressions are not exe- cuted together (see Figure 3).

• The initialization is executed once, before the loop is entered. 1 • The condition is checked before each iteration. 2 5 • The update is executed after each iteration. 4

You can visualize the for loop as an orderly sequence of steps.

figure 3 execution of a for Loop

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Initialize counter1

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Check condition2

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Execute loop body3

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Update counter4

for (counter = 1; counter <= 10; counter++) { cout << counter << endl; }

Check condition again5

counter = 1

counter = 2

cfe2_ch04_p131_192.indd 143 10/28/10 8:13 PM

144 Chapter 4 Loops

syntax 4.2 for statement

for (int i = 5; i <= 10; i++) { sum = sum + i; }

This loop executes 6 times. See page 147.

These three expressions should be related.

See page 147.

This initialization happens once before the loop starts.

The loop is executed while this condition is true.

This update is executed after each iteration.

The variable i is defined only in this for loop.

See page 144.

A for loop can count down instead of up: for (counter = 10; counter >= 0; counter--) ...

The increment or decrement need not be in steps of 1: for (counter = 0; counter <= 10; counter = counter + 2) ...

See Table 2 on page 146 for additional variations. So far, we assumed that the counter variable had already been defined before the for

loop. Alternatively, you can define a variable in the loop initialization. Such a variable is defined only in the loop:

for (int counter = 1; counter <= 10; counter++) { ... } // counter no longer defined here

Here is a typical use of the for loop. We want to print the balance of our savings account over a period of years, as shown in this table:

The for loop pattern applies because the variable year starts at 1 and then moves in constant increments until it reaches the target:

Year Balance

1 10500.00

2 11025.00

3 11576.25

4 12155.06

5 12762.82

cfe2_ch04_p131_192.indd 144 10/28/10 8:13 PM

4.3 the for Loop 145

for (int year = 1; year <= nyears; year++) {

Update balance. Print year and balance.

}

Here is the complete program. Figure 4 shows the corresponding flowchart.

figure 4 Flowchart of a for Loop

ch04/invtable.cpp

1 #include <iostream> 2 #include <iomanip> 3 4 using namespace std; 5 6 int main() 7 { 8 const double RATE = 5; 9 const double INITIAL_BALANCE = 10000;

10 double balance = INITIAL_BALANCE; 11 int nyears; 12 cout << "Enter number of years: "; 13 cin >> nyears; 14 15 cout << fixed << setprecision(2); 16 for (int year = 1; year <= nyears; year++) 17 { 18 balance = balance * (1 + RATE / 100); 19 cout << setw(4) << year << setw(10) << balance << endl; 20 } 21 22 return 0; 23 }

True

False

year++

year ≤ nyears ?

year = 1

Update balance; Print year and

balance

cfe2_ch04_p131_192.indd 145 10/28/10 8:13 PM

146 Chapter 4 Loops

program run

Enter number of years: 10 1 10500.00 2 11025.00 3 11576.25 4 12155.06 5 12762.82 6 13400.96 7 14071.00 8 14774.55 9 15513.28 10 16288.95

11. Write the for loop of the invtable.cpp program as a while loop.

table 2 for Loop examples

Loop Values of i Comment

for (i = 0; i <= 5; i++) 0 1 2 3 4 5 Note that the loop is executed 6 times. (See Programming Tip 4.3 on page 147.)

for (i = 5; i >= 0; i--) 5 4 3 2 1 0 Use i-- for decreasing values.

for (i = 0; i < 9; i = i + 2) 0 2 4 6 8 Use i = i + 2 for a step size of 2.

for (i = 0; i != 9; i = i + 2) 0 2 4 6 8 10 12 14 ... (infinite loop)

You can use < or <= instead of != to avoid this problem.

for (i = 1; i <= 20; i = i * 2) 1 2 4 8 16 You can specify any rule for modifying i, such as doubling it in every step.

for (i = 0; i < str.length(); i++) 0 1 2 … until the last valid index of the string str

In the loop body, use the expression str.substr(i, 1) to get a string containing the ith character.

12. How many numbers does this loop print? for (int n = 10; n >= 0; n--) { cout << n << endl; }

ances until the invest ment has doubled?

practice it Now you can try these exercises at the end of the chapter: R4.2, R4.7, P4.12.

S e l f c h e c k

use for loops for Their intended purpose only

A for loop is an idiom for a loop of a particular form. A value runs from the start to the end, with a constant incre ment or decrement.

The compiler won’t check whether the initialization, condition, and update expressions are related. For example, the following loop is legal:

// Confusing—unrelated expressions for (cout << "Inputs: "; cin >> x; sum = sum + x) { count++; }

However, programmers reading such a for loop will be confused because it does not match their expectations. Use a while loop for iterations that do not follow the for idiom.

choose loop bounds That match your Task

Suppose you want to print line numbers that go from 1 to 10. Of course, you will want to use a loop

for (int i = 1; i <= 10; i++)

The values for i are bounded by the relation 1 ≤ i ≤ 10. Because there are ≤ on both bounds, the bounds are called symmetric.

When traversing the characters in a string, it is more natural to use the bounds

for (int i = 0; i < str.length(); i++)

In this loop, i traverses all valid positions in the string. You can access the ith character as str. substr(i, 1). The val ues for i are bounded by 0 ≤ i < str.length(), with a ≤ to the left and a < to the right. That is appropriate, because str.length() is not a valid position. Such bounds are called asymmetric.

In this case, it is not a good idea to use symmetric bounds:

for (int i = 0; i <= str.length() - 1; i++) // Use < instead

The asymmetric form is easier to understand.

count iterations

Finding the correct lower and upper bounds for an iteration can be confusing. Should you start at 0 or at 1? Should you use <= or < in the termination condition?

Counting the number of iterations is a very useful device for better understanding a loop. Counting is easier for loops with asymmetric bounds. The loop

for (int i = a; i < b; i++)

is executed b - a times. For example, the loop

for (int i = 0; i < 10; i++)

runs ten times, with values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The loop with symmetric bounds,

for (int i = a; i <= b; i++)

is executed b - a + 1 times. That “+1” is the source of many programming errors.

programming tip 4.1

programming tip 4.2

programming tip 4.3

cfe2_ch04_p131_192.indd 146 10/28/10 8:13 PM

4.3 the for Loop 147

use for loops for Their intended purpose only

A for loop is an idiom for a loop of a particular form. A value runs from the start to the end, with a constant incre ment or decrement.

The compiler won’t check whether the initialization, condition, and update expressions are related. For example, the following loop is legal:

// Confusing—unrelated expressions for (cout << "Inputs: "; cin >> x; sum = sum + x) { count++; }

However, programmers reading such a for loop will be confused because it does not match their expectations. Use a while loop for iterations that do not follow the for idiom.

choose loop bounds That match your Task

Suppose you want to print line numbers that go from 1 to 10. Of course, you will want to use a loop

for (int i = 1; i <= 10; i++)

The values for i are bounded by the relation 1 ≤ i ≤ 10. Because there are ≤ on both bounds, the bounds are called symmetric.

When traversing the characters in a string, it is more natural to use the bounds

for (int i = 0; i < str.length(); i++)

In this case, it is not a good idea to use symmetric bounds:

for (int i = 0; i <= str.length() - 1; i++) // Use < instead

The asymmetric form is easier to understand.

count iterations

Finding the correct lower and upper bounds for an iteration can be confusing. Should you start at 0 or at 1? Should you use <= or < in the termination condition?

Counting the number of iterations is a very useful device for better understanding a loop. Counting is easier for loops with asymmetric bounds. The loop

for (int i = a; i < b; i++)

is executed b - a times. For example, the loop

for (int i = 0; i < 10; i++)

runs ten times, with values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The loop with symmetric bounds,

for (int i = a; i <= b; i++)

is executed b - a + 1 times. That “+1” is the source of many programming errors.

programming tip 4.1

programming tip 4.2

programming tip 4.3

cfe2_ch04_p131_192.indd 147 10/28/10 8:13 PM

148 Chapter 4 Loops

For example,

for (int i = 0; i <= 10; i++)

runs 11 times. Maybe that is what you want; if not, start at 1 or use < 10. One way to visualize this “+1” error is by looking at a fence. Each section has one fence

post to the left, and there is a final post on the right of the last section. Forgetting to count the last value is often called a “fence post error”.

4.4 the do Loop Sometimes you want to execute the body of a loop at least once and perform the loop test after the body is executed. The do loop serves that purpose:

do { statements } while (condition);

The body of the do loop is executed first, then the condition is tested. Some people call such a loop a post-test loop because the condition is tested after

completing the loop body. In contrast, while and for loops are pre-test loops. In those loop types, the condition is tested before entering the loop body.

A typical example for such a loop is input validation. Suppose you ask a user to enter a value < 100. If the user didn’t pay attention and entered a larger value, you ask again, until the value is correct. Of course, you cannot test the value until the user has entered it. This is a perfect fit for the do loop (see Figure 5):

int value; do { cout << "Enter a value < 100: "; cin >> value; } while (value >= 100);

How many posts do you need for a fence with four sections? It is easy to be “off by one” with problems such as this one.

the do loop is appropriate when the loop body must be executed at least once.

figure 5 Flowchart of a do Loop

16. Suppose that we want to check for inputs that are at least 0 and at most 100. Modify the do loop for this check.

17. Rewrite the input check, using a while loop. What is the disadvantage of your solution?

18. Suppose C++ didn’t have a do loop. Could you rewrite any do loop as a while loop?

19. Write a do loop that reads integers and computes their sum. Stop when reading the value 0.

20. Write a do loop that reads positive integers and computes their sum. Stop when reading the same value twice in a row. For example, if the input is 1 2 3 4 4, then the sum is 14 and the loop stops.

practice it Now you can try these exercises at the end of the chapter: R4.8, R4.12, R4.13.

flowcharts for loops

In Section 3.5, you learned how to use flowcharts to visualize the flow of control in a program. There are two types of loops that you can include in a flowchart; they correspond to a while loop and a do loop in C++. They differ in the placement of the condition—either before or after the loop body.

As described in Section 3.5, you want to avoid “spaghetti code” in your flowcharts. For loops, that means that you never want to have an arrow that points inside a loop body.

True

False

value ≥ 100?

Prompt user to enter

a value < 100

Copy the input to value

S e l f c h e c k

programming tip 4.4

cfe2_ch04_p131_192.indd 148 10/28/10 8:13 PM

4.4 the do Loop 149

figure 5 Flowchart of a do Loop

16. Suppose that we want to check for inputs that are at least 0 and at most 100. Modify the do loop for this check.

17. Rewrite the input check, using a while loop. What is the disadvantage of your solution?

18. Suppose C++ didn’t have a do loop. Could you rewrite any do loop as a while loop?

19. Write a do loop that reads integers and computes their sum. Stop when reading the value 0.

practice it Now you can try these exercises at the end of the chapter: R4.8, R4.12, R4.13.

flowcharts for loops

False

True

Loop body

Condition?

True

False

Loop body

Condition?

As described in Section 3.5, you want to avoid “spaghetti code” in your flowcharts. For loops, that means that you never want to have an arrow that points inside a loop body.

True

False

value ≥ 100?

Prompt user to enter

a value < 100

Copy the input to value

S e l f c h e c k

programming tip 4.4

cfe2_ch04_p131_192.indd 149 10/28/10 8:13 PM

150 Chapter 4 Loops

4.5 processing Input In this section, you will learn how to read and pro- cess a sequence of input values.

Whenever you read a sequence of inputs, you need to have some method of indicating the end of the sequence. Sometimes you are lucky and no input value can be zero. Then you can prompt the user to keep entering numbers, or 0 to finish the sequence. If zero is allowed but negative numbers are not, you can use –1 to indicate termination. A value that serves as a signal for termination is called a sentinel.

Let’s put this technique to work in a program that computes the average of a set of salary values. In our sample program, we will use –1 as a sentinel. An employee would surely not work for a negative salary, but there may be volunteers who work for free.

Inside the loop, we read an input. If the input is not –1, we process it. In order to compute the aver- age, we need the total sum of all salaries, and the number of inputs.

while (...) {

cin >> salary; if (salary != -1) { sum = sum + salary; count++; } }

We stay in the loop while the sentinel value is not detected.

while (salary != -1) { ... }

There is just one problem: When the loop is entered for the first time, no data value has been read. Be sure to initialize salary with some value other than the sentinel:

double salary = 0; // Any value other than –1 will do

Alternatively, use a do loop

do { ... } while (salary != -1)

In the military, a sentinel guards a border or passage. In computer science, a sentinel value denotes the end of an input sequence or the border between input sequences.

a sentinel value denotes the end of a data set, but it is not part of the data.

cfe2_ch04_p131_192.indd 150 10/28/10 8:13 PM

4.5 processing Input 151

The following program reads inputs until the user enters the sentinel, and then com- putes and prints the average.

ch04/sentinel.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 int main() 6 { 7 double sum = 0; 8 int count = 0; 9 double salary = 0;

10 cout << "Enter salaries, -1 to finish: "; 11 while (salary != -1) 12 { 13 cin >> salary; 14 if (salary != -1) 15 { 16 sum = sum + salary; 17 count++; 18 } 19 } 20 if (count > 0) 21 { 22 double average = sum / count; 23 cout << "Average salary: " << average << endl; 24 } 25 else 26 { 27 cout << "No data" << endl; 28 } 29 return 0; 30 }

program run

Enter salaries, -1 to finish: 10 10 40 -1 Average salary: 20

Numeric sentinels only work if there is some restriction on the input. In many cases, though, there isn’t. Suppose you want to compute the average of a data set that may contain 0 or negative values. Then you cannot use 0 or –1 to indicate the end of the input.

In such a situation, you can read input data until input fails. As you have seen in Section 3.8, the condi tion

cin.fail()

is true if the preceding input has failed. For example, suppose that the input was read with these state ments:

double value; cin >> value;

If the user enters a value that is not a number (such as Q), then the input fails.

cfe2_ch04_p131_192.indd 151 10/28/10 8:13 PM

152 Chapter 4 Loops

We now encounter an additional complexity. You only know that input failed after you have entered the loop and attempted to read it. To remember the failure, use a Boolean variable:

cout << "Enter values, Q to quit: "; bool more = true; while (more) { cin >> value; if (cin.fail()) { more = false; } else { Process value. } }

Some programmers dislike the introduction of a Boolean variable to control a loop. Special Topic 4.2 on page 153 shows an alternative mechanism for leaving a loop. How- ever, when reading input, there is an easier way. The expression

cin >> value

can be used in a condition. It evaluates to true if cin has not failed after reading value. Therefore, you can read and process a set of inputs with the following loop:

cout << "Enter values, Q to quit: "; while (cin >> value) { Process value. }

This loop is suitable for processing a single sequence of inputs. You will learn more about reading inputs in Chapter 8.

21. What does the sentinel.cpp program print when the user immediately types –1 when prompted for a value?

22. Why does the sentinel.cpp program have two checks of the form salary != -1

23. What would happen if the definition of the salary variable in sentinel.cpp was changed to double salary = -1;

24. We prompt the user “Enter values, Q to quit.” What happens when the user enters a different letter?

25. What is wrong with the following loop for reading a sequence of values? cout << "Enter values, Q to quit: "; while (!cin.fail()) { double value; cin >> value; sum = sum + value; count++; }

You can use a Boolean variable to control a loop. set the variable to true before entering the loop, then set it to false to leave the loop.

S e l f c h e c k

practice it Now you can try these exercises at the end of the chapter: R4.10, P4.6, P4.7.

clearing the failure State

When an input operation has failed, all further input operations also fail. If you want to read two number sequences and use a letter as a sentinel, you need to clear the failure state after reading the first sentinel. Call the clear function:

cout << "Enter values, Q to quit.\n"; while (cin >> values) { Process input. } cin.clear();

Suppose the user has entered 30 10 5 Q. The input of Q has caused the failure. Because only suc- cessfully processed characters are removed from the input, the Q character is still present. Read it into a dummy variable:

string sentinel; cin >> sentinel;

Now you can go on and read more inputs.

The loop-and-a-half problem and the break Statement

Some programmers dislike loops that are controlled by a Boolean variable, such as:

bool more = true; while (more) { cin >> value; if (cin.fail()) { more = false; } else { Process value. } }

The actual test for loop termination is in the middle of the loop, not at the top. This is called a loop and a half because one must go halfway into the loop before knowing whether one needs to terminate.

As an alternative, you can use the break reserved word.

while (true) { cin >> value; if (cin.fail()) { break; } Process value. }

The break statement breaks out of the enclosing loop, independent of the loop condition. In the loop-and-a-half case, break statements can be beneficial. But it is difficult to lay down

clear rules as to when they are safe and when they should be avoided. We do not use the break statement in this book.

special topic 4.1

special topic 4.2

cfe2_ch04_p131_192.indd 152 10/28/10 8:13 PM

4.5 processing Input 153

practice it Now you can try these exercises at the end of the chapter: R4.10, P4.6, P4.7.

clearing the failure State

cout << "Enter values, Q to quit.\n"; while (cin >> values) { Process input. } cin.clear();

string sentinel; cin >> sentinel;

Now you can go on and read more inputs.

The loop-and-a-half problem and the break Statement

Some programmers dislike loops that are controlled by a Boolean variable, such as:

bool more = true; while (more) { cin >> value; if (cin.fail()) { more = false; } else { Process value. } }

As an alternative, you can use the break reserved word.

while (true) { cin >> value; if (cin.fail()) { break; } Process value. }

The break statement breaks out of the enclosing loop, independent of the loop condition. In the loop-and-a-half case, break statements can be beneficial. But it is difficult to lay down

clear rules as to when they are safe and when they should be avoided. We do not use the break statement in this book.

special topic 4.1

special topic 4.2

cfe2_ch04_p131_192.indd 153 10/28/10 8:13 PM

154 Chapter 4 Loops

redirection of input and output

Consider the sentinel program that computes the average value of an input sequence. If you use such a program, then it is quite likely that you already have the values in a file, and it seems a shame that you have to type them all in again. The command line interface of your operating system provides a way to link a file to the input of a pro gram, as if all the characters in the file had actually been typed by a user. If you type

sentinel < numbers.txt

the program is executed. Its input instructions no longer expect input from the keyboard. All input commands get their input from the file numbers.txt. This process is called input redirection.

Input redirection is an excellent tool for testing programs. When you develop a program and fix its bugs, it is bor ing to keep entering the same input every time you run the program. Spend a few minutes putting the inputs into a file, and use redirection.

You can also redirect output. In this program, that is not terribly useful. If you run

sentinel < numbers.txt > output.txt

the file output.txt contains the input prompts and the output, such as

Enter a value, -1 to finish: Enter a value, -1 to finish: Enter a value, -1 to finish: Enter a value, -1 to finish: Average: 15

However, redirecting output is obviously useful for programs that produce lots of output. You can print the file con taining the output or edit it before you turn it in for grading.

4.6 problem solving: storyboards When you design a program that interacts with a user, you need to make a plan for that interaction. What information does the user provide, and in which order? What information will your program display, and in which format? What should happen when there is an error? When does the program quit?

This planning is similar to the development of a movie or a computer game, where storyboards are used to plan action sequences. A storyboard is made up of panels that show a sketch of each step. Annota tions explain what is happening and note any spe- cial situations. Storyboards are also used to develop software—see Figure 6.

Making a storyboard is very helpful when you begin designing a program. You need to ask yourself which information you need in order to compute the answers that the program user wants. You need to decide how to present those answers. These are important considerations that you want to settle before you design an algorithm for computing the answers.

Let’s look at a simple example. We want to write a program that helps users with questions such as “How many tablespoons are in a pint?” or “How many inches are 30 centimeters?”

What information does the user provide?

• The quantity and unit to convert from • The unit to convert to

special topic 4.3

Use input redirection to read input from a file. Use output redirection to capture program output in a file.

a storyboard consists of annotated sketches for each step in an action sequence.

Developing a storyboard helps you understand the inputs and outputs that are required for a program.

cfe2_ch04_p131_192.indd 154 10/28/10 8:13 PM

4.6 problem solving: storyboards 155

figure 6 storyboard for the Design of a Web application

What if there is more than one quantity? A user may have a whole table of centimeter values that should be converted into inches.

What if the user enters units that our program doesn’t know how to handle, such as angstrom?

What if the user asks for impossible conversions, such as inches to gallons? Let’s get started with a storyboard panel. It is a good idea to write the user inputs in

a different color. (Underline them if you don’t have a color pen handy.)

What unit do you want to convert from? cm What unit do you want to convert to? in Enter values, terminated by zero 30 30 cm = 11.81 in 100 100 cm = 39.37 in 0 What unit do you want to convert from?

Format makes clear what got converted

Allows conversion of multiple values

Converting a Sequence of Values

The storyboard shows how we deal with a potential confusion. A user who wants to know how many inches are 30 centimeters may not read the first prompt carefully and specify inches. But then the output is “30 in = 76.2 cm”, alerting the user to the problem.

The storyboard also raises an issue. How is the user supposed to know that “cm” and “in” are valid units? Would “centimeter” and “inches” also work? What happens

cfe2_ch04_p131_192.indd 155 10/28/10 8:13 PM

156 Chapter 4 Loops

when the user enters a wrong unit? Let’s make another storyboard to demonstrate error handling.

What unit do you want to convert from? cm What unit do you want to convert to? inches Sorry, unknown unit. What unit do you want to convert to? inch Sorry, unknown unit. What unit do you want to convert to? grrr

Handling Unknown Units (needs improvement)

To eliminate frustration, it is better to list the units that the user can supply.

From unit (in, ft, mi, mm, cm, m, km, oz, lb, g, kg, tsp, tbsp, pint, gal): cm To unit: in

No need to list the units again

We switched to a shorter prompt to make room for all the unit names. Exercise R4.17 explores a different alternative.

There is another issue that we haven’t addressed yet. How does the user quit the program? The first storyboard gives the impression that the program will go on forever.

We can ask the user after seeing the sentinel that terminates an input sequence.

From unit (in, ft, mi, mm, cm, m, km, oz, lb, g, kg, tsp, tbsp, pint, gal): cm To unit: in Enter values, terminated by zero 30 30 cm = 11.81 in 0 More conversions (y, n)? n (Program exits)

Sentinel triggers the prompt to exit

Exiting the Program

As you can see from this case study, a storyboard is essential for developing a work- ing program. You need to know the flow of the user interaction in order to structure your program.

26. Provide a storyboard panel for a program that reads a number of test scores and prints the average score. The program only needs to process one set of scores. Don’t worry about error handling.

S e l f c h e c k

cfe2_ch04_p131_192.indd 156 10/28/10 8:13 PM

4.7 Common Loop algorithms 157

27. Google has a simple interface for converting units. You just type the question, and you get the answer.

Make storyboards for an equivalent interface in a C++ program. Show the “happy day” scenario in which all goes well, and show the handling of two kinds of errors.

28. Consider a modification of the program in Self Check 26. Drop the lowest score before computing the average. Provide a storyboard for the situation in which a user only provides one score.

29. What is the problem with implementing the following storyboard in C++?

Enter scores: 90 80 90 100 80 The average is 88 Enter scores: 100 70 70 100 80 The average is 88 Enter scores: -1 (Program exits)

-1 is used as a sentinel to exit the program

Computing Multiple Averages

30. Produce a storyboard for a program that compares the growth of a $10,000 investment for a given number of years under two interest rates.

practice it Now you can try these exercises at the end of the chapter: R4.17, R4.18, R4.19.

4.7 Common Loop algorithms In the following sections, we discuss some of the most common algorithms that are implemented as loops. You can use them as starting points for your loop designs.

4.7.1 sum and average Value

Computing the sum of a number of inputs is a very common task. Keep a running total: a variable to which you add each input value. Of course, the total should be ini- tialized with 0.

double total = 0; double input; while (cin >> input) { total = total + input; }

cfe2_ch04_p131_192.indd 157 10/28/10 8:13 PM

158 Chapter 4 Loops

To compute an average, count how many values you have, and divide by the count. Be sure to check that the count is not zero.

double total = 0; int count = 0; double input; while (cin >> input) { total = total + input; count++; } double average = 0; if (count > 0) { average = total / count; }

4.7.2 Counting Matches

You often want to know how many values fulfill a particular condition. For example, you may want to count how many spaces are in a string. Keep a counter, a variable that is initialized with 0 and incremented whenever there is a match.

int spaces = 0; for (int i = 0; i < str.length(); i++) { string ch = str.substr(i, 1); if (ch == " ") { spaces++; } }

For example, if str is the string "My Fair Lady", spaces is incremented twice (when i is 2 and 7).

Note that the spaces variable is declared outside the loop. We want the loop to update a single variable. The ch variable is declared inside the loop. A separate vari- able is created for each iteration and removed at the end of each loop iteration.

This loop can also be used for scanning inputs. The following loop reads text, a word at a time, and counts the number of words with at most three letters:

int short_words = 0; string input; while (cin >> input) { if (input.length() <= 3) { short_words++; } }

to compute an average, keep a total and a count of all values.

to count values that fulfill a condition, check all values and increment a counter for each match.

In a loop that counts matches, a counter is incremented whenever a match is found.

4.7.3 Finding the First Match

When you count the values that fulfill a con- dition, you need to look at all values. How- ever, if your task is to find a match, then you can stop as soon as the condition is fulfilled.

Here is a loop that finds the first space in a string. Because we do not visit all elements in the string, a while loop is a better choice than a for loop:

bool found = false; int position = 0; while (!found && position < str.length()) { string ch = str.substr(position, 1); if (ch == " ") { found = true; } else { position++; } }

If a match was found, then found is true and position is the index of the first match. If the loop did not find a match, then found remains false after the end of the loop.

In the preceding example, we searched a string for a character that matches a con- dition. You can apply the same process for user input. Suppose you are asking a user to enter a positive value < 100. Keep asking until the user provides a correct input:

bool valid = false; double input; while (!valid) { cout << "Please enter a positive value < 100: "; cin >> input; if (0 < input && input < 100) { valid = true; } else { cout << "Invalid input." << endl; } }

Note that the variable input is declared outside the while loop because you will want to use the input after the loop has finished. If it had been declared inside the loop body, you would not be able to use it outside the loop.

4.7.4 Maximum and Minimum

To compute the largest value in a sequence, keep a variable that stores the largest ele- ment that you have encountered, and update it when you find a larger one:

double largest; cin >> largest; double input; while (cin >> input) { if (input > largest) { largest = input; } }

This algorithm requires that there is at least one input.

When searching, you look at items until a match is found.

If your goal is to find a match, exit the loop when the match is found.

to find the largest value, update the largest value seen so far whenever you see a larger one.

cfe2_ch04_p131_192.indd 158 10/28/10 8:13 PM

4.7 Common Loop algorithms 159

4.7.3 Finding the First Match

When you count the values that fulfill a con- dition, you need to look at all values. How- ever, if your task is to find a match, then you can stop as soon as the condition is fulfilled.

Here is a loop that finds the first space in a string. Because we do not visit all elements in the string, a while loop is a better choice than a for loop:

bool found = false; int position = 0; while (!found && position < str.length()) { string ch = str.substr(position, 1); if (ch == " ") { found = true; } else { position++; } }

If a match was found, then found is true and position is the index of the first match. If the loop did not find a match, then found remains false after the end of the loop.

4.7.4 Maximum and Minimum

To compute the largest value in a sequence, keep a variable that stores the largest ele- ment that you have encountered, and update it when you find a larger one:

double largest; cin >> largest; double input; while (cin >> input) { if (input > largest) { largest = input; } }

This algorithm requires that there is at least one input.

When searching, you look at items until a match is found.

If your goal is to find a match, exit the loop when the match is found.

to find the largest value, update the largest value seen so far whenever you see a larger one.

cfe2_ch04_p131_192.indd 159 10/28/10 8:13 PM

160 Chapter 4 Loops

To find the height of the tallest bus rider, remember the largest value so far, and update it whenever you see a taller one.

To compute the smallest value, simply reverse the comparison: double smallest; cin >> smallest; double input; while (cin >> input) { if (input < smallest) { smallest = input; } }

4.7.5 Comparing adjacent Values

When processing a sequence of values in a loop, you sometimes need to compare a value with the value that just preceded it. For example, suppose you want to check whether a sequence of inputs contains adjacent duplicates such as 1 7 2 9 9 4 9.

Now you face a challenge. Consider the typical loop for reading a value: double input; while (cin >> input) { // Now input contains the current input ... }

How can you compare the current input with the preceding one? At any time, input contains the current input, overwriting the previous one.

The answer is to store the previous input, like this: double input; double previous; while (cin >> input) { if (input == previous) { cout << "Duplicate input" << endl; } previous = input; }

to compare adjacent inputs, store the preceding input in a variable.

cfe2_ch04_p131_192.indd 160 10/28/10 8:13 PM

4.7 Common Loop algorithms 161

When comparing adjacent values, store the previous value in a variable.

One problem remains. When the loop is entered for the first time, previous has not yet been set. You can solve this problem with an initial input operation outside the loop:

double input; double previous; cin >> previous; while (cin >> input) { if (input == previous) { cout << "Duplicate input" << endl; } previous = input; }

31. What total is computed when no user input is provided in the algorithm in Section 4.7.1?

32. How do you compute the total of all positive inputs? 33. What is the value of position when no match is found in the algorithm in

Section 4.7.3? 34. What is wrong with the following loop for finding the position of the first space

in a string? bool found = false; for (int position = 0; !found && position < str.length(); position++) { string ch = str.substr(position, 1); if (ch == " ") { found = true; } }

35. How do you find the last space in a string? 36. What is wrong with the following loop for finding the smallest input value?

double smallest = 0; double input; while (cin >> input) { if (input < smallest) { smallest = input; } }

37. What happens with the algorithm in Section 4.7.5 when no input is provided at all?

practice it Now you can try these exercises at the end of the chapter: P4.8, P4.13, P4.14.

S e l f c h e c k

cfe2_ch04_p131_192.indd 161 10/28/10 8:13 PM

162 Chapter 4 Loops

Step 1 Decide what work must be done inside the loop.

Every loop needs to do some kind of repetitive work, such as • Reading another item. • Updating a value (such as a bank balance or total). • Incrementing a counter. If you can’t figure out what needs to go inside the loop, start by writing down the steps that you would take if you solved the problem by hand. For example, with the temperature reading problem, you might write

Read first value. Read second value. If second value is higher than the first, set highest temperature to that value, highest month to 2. Read next value. If value is higher than the first and second, set highest temperature to that value, highest month to 3. Read next value. If value is higher than the highest temperature seen so far, set highest temperature to that value,

highest month to 4. . . .

Now look at these steps and reduce them to a set of uniform actions that can be placed into the loop body. The first action is easy:

Read next value.

Similarly, we must find a general way of setting the highest month. We need a variable that stores the current month, running from 1 to 12. Then we can formulate the second loop action:

If value is higher than the highest temperature, set highest temperature to that value, highest month to current month.

h o W t o 4 . 1 writing a loop

This How To walks you through the process of implementing a loop statement. We will illustrate the steps with the following example problem:

18.2 22.6 26.4 31.1 36.6 42.2 45.7 44.5 40.2 33.1 24.2 17.6

In this case, the month with the highest tem- perature (45.7 degrees Celsius) is July, and the program should display 7.

Altogether our loop is

Loop Read next value. If value is higher than the highest temperature, set highest temperature to that value,

highest month to current month. Increment current month.

Step 2 Specify the loop condition.

What goal do you want to reach in your loop? Typical examples are: • Has the counter reached the final value? • Have you read the last input value? • Has a value reached a given threshold? In our example, we simply want the current month to reach 12.

Step 3 Determine the loop type.

We distinguish between two major loop types. A definite or count-controlled loop is executed a definite number of times. In an indefinite or event-controlled loop, the number of iterations is not known in advance—the loop is exe cuted until some event happens. A typical example of the latter is a loop that reads data until a sentinel is encoun tered.

If you know in advance how many times a loop is repeated, use a for statement. For other loops, consider the loop condition. Do you need to complete one iteration of the loop body before you can tell when to terminate the loop? In that case, you should choose a do loop. Oth- erwise, use a while loop.

In our example, we read 12 temperature values. Therefore, we choose a for loop.

Step 4 Set up variables for entering the loop for the first time.

List all variables that are used and updated in the loop, and determine how to initialize them. Commonly, counters are initialized with 0 or 1, totals with 0.

In our example, the variables are

current month highest value highest month

We need to be careful how we set up the highest temperature value. We can’t simply set it to 0. After all, our program needs to work with temperature values from Antarctica, all of which may be negative.

A good option is to set the highest temperature value to the first input value. Of course, then we need to remem ber to only read in another 11 values, with the current month starting at 2.

We also need to initialize the highest month with 1. After all, in an Australian city, we may never find a month that is warmer than January.

Step 5 Process the result after the loop has finished.

In many cases, the desired result is simply a variable that was updated in the loop body. For example, in our temper ature program, the result is the highest month. Sometimes, the loop computes values that contribute to the final result. For example, suppose you are asked to average the temperatures. Then the loop should compute the sum, not the average. After the loop has completed, you are ready to compute the average: divide the sum by the number of inputs.

cfe2_ch04_p131_192.indd 163 10/28/10 8:13 PM

164 Chapter 4 Loops

Here is our complete loop:

Read first value; store as highest value. highest month = 1 for (current month = 2; current month <= 12; current month++)

Read next value. If value is higher than the highest value, set highest value to that value, highest month to current month.

Step 6 Trace the loop with typical examples.

Hand-trace your loop code, as described in Section 4.2. Choose example values that are not too complex—executing the loop 3–5 times is enough to check for the most common errors. Pay special attention when entering the loop for the first and last time.

Sometimes, you want to make a slight modification to make tracing feasible. For example, when hand-tracing the investment doubling problem, use an interest rate of 20 percent rather than 5 percent. When hand-tracing the tem perature loop, use 4 data values, not 12.

Let’s say the data are 22.6 36.6 44.5 24.2. Here is the walkthrough:

current month current value highest month highest value 1 22.6 2 36.6 2 36.6 3 44.5 3 44.5 4 24.2

The trace demonstrates that highest month and highest value are properly set.

Step 7 Implement the loop in C++.

Here’s the loop for our example. Exercise P4.4 asks you to complete the program.

double highest_value; cin >> highest_value; int highest_month = 1; for (int current_month = 2; current_month <= 12; current_month++) { double next_value; cin >> next_value; if (next_value > highest_value) { highest_value = next_value; highest_month = current_month; } } cout << highest_month << endl;

W o r k e D e x a M p L e 4 . 1 credit card processing

This Worked Example uses a loop to remove spaces from a credit card number.

4.8 nested Loops In Section 3.4, you saw how to nest two if statements. Similarly, complex iterations sometimes require a nested loop: a loop inside another loop statement. When pro- cessing tables, nested loops occur naturally. An outer loop iterates over all rows of the table. An inner loop deals with the columns in the current row.

In this section you will see how to print a table. For simplicity, we will simply print powers xn, as in the table at right.

Here is the pseudocode for printing the table:

Print table header. For x from 1 to 10

Print table row. Print endl.

How do you print a table row? You need to print a value for each expo nent. This requires a second loop:

For n from 1 to 4 Print xn.

This loop must be placed inside the preceding loop. We say that the inner loop is nested inside the outer loop (see Figure 7).

When the body of a loop contains another loop, the loops are nested. a typical use of nested loops is printing a table with rows and columns.

x1 x2 x3 x4

1 1 1 1

2 4 8 16

3 9 27 81

… … … …

10 100 1000 10000

figure 7 Flowchart of a nested Loop

True

False x ≤ 10 ?

x = 1

True

False n ≤ 4 ?

n = 1

n++

Print xn

x++

Print new line

This loop is nested in the outer loop.

Available online at www.wiley.com/college/horstmann.

cfe2_ch04_p131_192.indd 164 10/28/10 8:13 PM

www.wiley.com/college/horstmann

4.8 nested Loops 165

Here is our complete loop:

Read first value; store as highest value. highest month = 1 for (current month = 2; current month <= 12; current month++)

Read next value. If value is higher than the highest value, set highest value to that value, highest month to current month.

Step 6 Trace the loop with typical examples.

Let’s say the data are 22.6 36.6 44.5 24.2. Here is the walkthrough:

The trace demonstrates that highest month and highest value are properly set.

Step 7 Implement the loop in C++.

Here’s the loop for our example. Exercise P4.4 asks you to complete the program.

W o r k e D e x a M p L e 4 . 1 credit card processing

This Worked Example uses a loop to remove spaces from a credit card number.

In this section you will see how to print a table. For simplicity, we will simply print powers xn, as in the table at right.

Here is the pseudocode for printing the table:

Print table header. For x from 1 to 10

Print table row. Print endl.

How do you print a table row? You need to print a value for each expo nent. This requires a second loop:

For n from 1 to 4 Print xn.

This loop must be placed inside the preceding loop. We say that the inner loop is nested inside the outer loop (see Figure 7).

When the body of a loop contains another loop, the loops are nested. a typical use of nested loops is printing a table with rows and columns.

x1 x2 x3 x4

1 1 1 1

2 4 8 16

3 9 27 81

… … … …

10 100 1000 10000

figure 7 Flowchart of a nested Loop

True

False x ≤ 10 ?

x = 1

True

False n ≤ 4 ?

n = 1

n++

Print xn

x++

Print new line

This loop is nested in the outer loop.

cfe2_ch04_p131_192.indd 165 10/28/10 8:13 PM

166 Chapter 4 Loops

There are 10 rows in the outer loop. For each x, the program prints four columns in the inner loop. Thus, a total of 10 × 4 = 40 values are printed.

Following is the complete program. Note that we also use loops to print the table header. However, those loops are not nested.

ch04/powtable.cpp

1 #include <iostream> 2 #include <iomanip> 3 #include <cmath> 4 5 using namespace std; 6 7 int main() 8 { 9 const int NMAX = 4;

10 const double XMAX = 10; 11 12 // Print table header 13 14 for (int n = 1; n <= NMAX; n++) 15 { 16 cout << setw(10) << n; 17 } 18 cout << endl; 19 for (int n = 1; n <= NMAX; n++) 20 { 21 cout << setw(10) << "x "; 22 } 23 cout << endl << endl; 24 25 // Print table body 26 27 for (double x = 1; x <= XMAX; x++) 28 { 29 // Print table row 30 31 for (int n = 1; n <= NMAX; n++) 32 { 33 cout << setw(10) << pow(x, n); 34 } 35 cout << endl; 36 } 37 38 return 0; 39 }

The hour and minute displays in a digital clock are an exam ple of nested loops. The hours loop 12 times, and for each hour, the minutes loop 60 times.

cfe2_ch04_p131_192.indd 166 10/28/10 8:13 PM

4.8 nested Loops 167

program run

1 2 3 4 x x x x

1 1 1 1 2 4 8 16 3 9 27 81 4 16 64 256 5 25 125 625 6 36 216 1296 7 49 343 2401 8 64 512 4096 9 81 729 6561 10 100 1000 10000

table 3 nested Loop examples

nested Loops output explanation

for (i = 1; i <= 3; i++) { for (j = 1; j <= 4; j++) { cout << "*"; } cout << endl; }

**** **** ****

Prints 3 rows of 4 asterisks each.

for (i = 1; i <= 4; i++) { for (j = 1; j <= 3; j++) { cout << "*"; } cout << endl; }

*** *** *** ***

Prints 4 rows of 3 asterisks each.

for (i = 1; i <= 4; i++) { for (j = 1; j <= i; j++) { cout << "*"; } cout << endl; }

* ** *** ****

Prints 4 rows of lengths 1, 2, 3, and 4.

for (i = 1; i <= 3; i++) { for (j = 1; j <= 5; j++) { if (j % 2 == 0) { cout << "*"; } else { cout << "-"; } } cout << endl; }

-*-*- -*-*- -*-*-

Prints asterisks in even columns, dashes in odd columns.

for (i = 1; i <= 3; i++) { for (j = 1; j <= 5; j++) { if ((i + j) % 2 == 0) { cout << "*"; } else { cout << " "; } } cout << endl; }

* * * * * * * *

Prints a checkerboard pattern.

cfe2_ch04_p131_192.indd 167 10/28/10 8:13 PM

168 Chapter 4 Loops

38. Why is there a statement cout << endl in the outer loop but not in the inner loop? 39. How would you change the program so that all powers from x0 to x5 are

displayed? 40. If you make the change in Self Check 39, how many values are displayed? 41. What do the following nested loops display?

for (int i = 0; i < 3; i++) { for (int j = 0; j < 4; j++) { cout << i + j; } cout << endl; }

42. Write nested loops that make the following pattern of brackets: [][][][] [][][][] [][][][]

practice it Now you can try these exercises at the end of the chapter: R4.23, P4.21, P4.22.

4.9 random numbers and simulations A simulation program uses the computer to simulate an activity in the real world (or an imaginary one). Simulations are commonly used for predicting climate change, analyzing traffic, picking stocks, and many other applications in science and busi- ness. In the following sections, you will learn how to imple ment simulations that model phenomena with a degree of randomness.

4.9.1 Generating random numbers

Many events in the real world are difficult to predict with absolute precision, yet we can sometimes know the average behavior quite well. For example, a store may know from experience that a customer arrives every five minutes. Of course, that is an aver- age—customers don’t arrive in five minute intervals. To accurately model customer traffic, you want to take that random fluctuation into account. Now, how can you run such a simulation in the computer?

The C++ library has a random number generator, which produces numbers that appear to be com pletely random. Calling rand() yields a random integer between 0 and RAND_MAX (which is an implementa tion-dependent constant, typically, but not always, the largest valid int value). Call rand() again, and you get a different number. The rand function is declared in the <cstdlib> header.

The following program calls the rand function ten times.

ch04/random.cpp

1 #include <iostream> 2 #include <cstdlib> 3 4 using namespace std;

S e l f c h e c k

In a simulation, you use the computer to simulate an activity. You can introduce randomness by calling the random number generator.

cfe2_ch04_p131_192.indd 168 10/28/10 8:13 PM

4.9 random numbers and simulations 169

5 6 int main() 7 { 8 for (int i = 1; i <= 10; i++) 9 {

10 int r = rand(); 11 cout << r << endl; 12 } 13 return 0; 14 }

program run

1804289383 846930886 1681692777 1714636915 1957747793 424238335 719885386 1649760492 596516649 118964142

Actually, the numbers are not completely random. They are drawn from sequences of numbers that don’t repeat for a long time. These sequences are actually computed from fairly simple formulas; they just behave like random numbers. For that reason, they are often called pseudorandom numbers.

Try running the program again. You will get the exact same output! This confirms that the random numbers are generated by formulas. However, when running simu- lations, you don’t always want to get the same results. To overcome this problem, specify a seed for the random number sequence. Every time you use a new seed, the random number generator starts generating a new sequence. The seed is set with the srand function. A simple value to use as a seed is the current time:

srand(time(0));

Simply make this call once in your program, before generating any random numbers. Then the random numbers will be different in every program run. Also include the <ctime> header that declares the time function.

4.9.2 simulating Die tosses

In actual applications, you need to transform the output from the random num ber generator into different ranges. For exam- ple, to simulate the throw of a die, you need random numbers between 1 and 6.

Here is the general recipe for computing random integers between two bounds a and b. As you know from Program- ming Tip 4.3 on page 147, there are b - a + 1 values between a and b, including the bounds themselves. First compute rand() % (b - a + 1) to obtain a random value between 0 and b - a, then add a, yielding a random value between a and b:

int r = rand() % (b - a + 1) + a;

cfe2_ch04_p131_192.indd 169 10/28/10 8:13 PM

170 Chapter 4 Loops

Here is a program that simulates the throw of a pair of dice.

ch04/dice.cpp

1 #include <iostream> 2 #include <string> 3 #include <cstdlib> 4 #include <ctime> 5 6 using namespace std; 7 8 int main() 9 {

10 srand(time(0)); 11 12 for (int i = 1; i <= 10; i++) 13 { 14 int d1 = rand() % 6 + 1; 15 int d2 = rand() % 6 + 1; 16 cout << d1 << " " << d2 << endl; 17 } 18 cout << endl; 19 return 0; 20 }

program run

5 1 2 1 1 2 5 1 1 2 6 4 4 4 6 1 6 3 5 2

4.9.3 the Monte Carlo Method

The Monte Carlo method is an inge- nious method for finding approxi- mate solutions to problems that can- not be precisely solved. (The method is named after the famous casino in Monte Carlo.) Here is a typical example: It is difficult to compute the number p, but you can approxi- mate it quite well with the following simulation.

Simulate shooting a dart into a square surrounding a circle of radius 1. That is easy: generate random x and y coordinates between –1 and 1.

cfe2_ch04_p131_192.indd 170 10/28/10 8:13 PM

4.9 random numbers and simulations 171

If the generated point lies inside the circle, we count it as a hit. That is the case when x2 + y2 ≤ 1. Because our shots are entirely random, we expect that the ratio of hits ̸ tries is approximately equal to the ratio of the areas of the circle and the square, that is, p ̸ 4. Therefore, our estimate for p is 4 × hits ̸ tries. This method yields an esti- mate for p, using nothing but simple arithmetic.

To run the Monte Carlo simulation, you have to work a little harder with random number generation. When you throw a die, it has to come up with one of six faces. When throwing a dart, however, there are many possible outcomes. You must generate a random floating-point number.

First, generate the following value: double r = rand() * 1.0 / RAND_MAX; // Between 0 and 1

The value r is a random floating-point value between 0 and 1. (You have to multiply by 1.0 to ensure that one of the operands of the / operator is a floating-point number. The division rand() / RAND_MAX would be an integer division—see Common Error 2.3.)

To generate a random value between –1 and 1, you compute: double x = -1 + 2 * r; // Between –1 and 1

As r ranges from 0 to 1, x ranges from –1 + 2 × 0 = –1 to –1 + 2 × 1 = 1. Here is the program that carries out the simulation.

ch04/montecarlo.cpp

1 #include <iostream> 2 #include <cstdlib> 3 #include <cmath> 4 #include <ctime> 5 6 using namespace std; 7 8 int main() 9 {

10 const int TRIES = 10000; 11 12 srand(time(0)); 13 14 int hits = 0; 15 for (int i = 1; i <= TRIES; i++) 16 { 17 double r = rand() * 1.0 / RAND_MAX; // Between 0 and 1 18 double x = -1 + 2 * r; // Between –1 and 1 19 r = rand() * 1.0 / RAND_MAX; 20 double y = -1 + 2 * r; 21 if (x * x + y * y <= 1) { hits++; } 22 } 23 double pi_estimate = 4.0 * hits / TRIES; 24 cout << "Estimate for pi: " << pi_estimate << endl; 25 return 0; 26 }

program run

Estimate for pi: 3.1504

1–1

–1

cfe2_ch04_p131_192.indd 171 10/28/10 8:13 PM

172 Chapter 4 Loops

43. How do you simulate a coin toss with the rand function?

44. How do you simulate the picking of a random playing card?

45. Why does the dice.cpp file include the <ctime> header?

46. In many games, you throw a pair of dice to get a value between 2 and 12. What is wrong with this simulated throw of a pair of dice? int sum = rand() % 11 + 2;

47. How do you generate a random floating-point number between 0 and 100?

practice it Now you can try these exercises at the end of the chapter: R4.24, P4.10, P4.25.

S e l f c h e c k

as you read this, you have written a

few computer programs, and you have experienced firsthand how much effort it takes to write even the hum blest of programs. Writing a real soft ware prod- uct, such as a financial application or a computer game, takes a lot of time and money. Few people, and fewer compa- nies, are going to spend that kind of time and money if they don’t have a rea- sonable chance to make more money from their effort. (actually, some com- panies give away their software in the hope that users will upgrade to more elaborate paid versions or pay for con- sulting. other companies give away the software that enables users to read and use files but sell the software needed to create those files. Finally, there are individuals who donate their time, out of enthusiasm, and produce programs that you can copy freely. see random Fact 9.2 for more information.)

When selling software, a company must rely on the honesty of its cus- tomers. It is an easy matter for an unscrupulous person to make copies of computer programs without paying for them. In most countries that is ille- gal. Most governments provide legal protection, such as copyright laws and patents, to encourage the develop-

ment of new products. Countries that tolerate widespread piracy have found that they have an ample cheap supply of foreign software, but no local man- ufacturers willing to design good soft- ware for their own citizens, such as word processors in the local script or financial programs adapted to the local tax laws.

When a mass market for software first appeared, vendors were enraged by the money they lost through piracy. they tried to fight back by var ious schemes to ensure that only the legiti- mate owner could use the soft ware, such as dongles—devices that must be attached to a printer port before the software will run. Legitimate users hated these mea sures. they paid for the software, but they had to suffer through inconve niences, such as hav- ing multiple don gles stick out from their computer. In the United states, market pressures forced most vendors to give up on these copy protection schemes, but they are still common- place in other parts of the world.

Because it is so easy and inexpen- sive to pirate software, and the chance of being found out is minimal, you have to make a moral choice for your- self. If a package that you would really like to have is too expensive for your

budget, do you steal it, or do you stay honest and get by with a more afford- able product?

of course, piracy is not limited to software. the same issues arise for other digital products as well. You may have had the opportunity to obtain copies of songs or movies with out payment. or you may have been frustrated by a copy protec- tion device on your music player that made it diffi cult for you to listen to songs that you paid for. admittedly, it can be diffi cult to have a lot of sym- pathy for a musical ensemble whose publisher charges a lot of money for what seems to have been very little effort on their part, at least when compared to the effort that goes into designing and implementing a soft- ware package. nevertheless, it seems only fair that artists and authors receive some compensation for their efforts. how to pay artists, authors, and programmers fairly, without bur dening honest customers, is an unsolved problem at the time of this writing, and many computer scientists are engaged in research in this area.

Random Fact 4.2 software piracy

explain the flow of execution in a loop.

• Loops execute a block of code repeatedly while a condition remains true.

• An off-by-one error is a common error when programming loops. Think through simple test cases to avoid this type of error.

use the technique of hand-tracing to analyze the behavior of a pro gram.

• Hand-tracing is a simulation of code execution in which you step through instructions and track the values of the variables.

• Hand-tracing can help you understand how an unfamiliar algorithm works. • Hand-tracing can show errors in code or pseudocode.

use for loops for implementing counting loops.

• The for loop is used when a value runs from a starting point to an ending point with a constant increment or decrement.

choose between the while loop and the do loop.

• The do loop is appropriate when the loop body must be executed at least once.

implement loops that read sequences of input data.

• A sentinel value denotes the end of a data set, but it is not part of the data.

• You can use a Boolean variable to control a loop. Set the variable to true before entering the loop, then set it to false to leave the loop.

• Use input redirection to read input from a file. Use output redirection to capture program output in a file.

use the technique of storyboarding for planning user interactions.

• A storyboard consists of annotated sketches for each step in an action sequence. • Developing a storyboard helps you understand the inputs and outputs that are

required for a program.

C h a p t e r s U M M a r Y

cfe2_ch04_p131_192.indd 172 10/28/10 8:13 PM

Chapter summary 173

explain the flow of execution in a loop.

• Loops execute a block of code repeatedly while a condition remains true.

• An off-by-one error is a common error when programming loops. Think through simple test cases to avoid this type of error.

use the technique of hand-tracing to analyze the behavior of a pro gram.

• Hand-tracing is a simulation of code execution in which you step through instructions and track the values of the variables.

• Hand-tracing can help you understand how an unfamiliar algorithm works. • Hand-tracing can show errors in code or pseudocode.

use for loops for implementing counting loops.

• The for loop is used when a value runs from a starting point to an ending point with a constant increment or decrement.

choose between the while loop and the do loop.

• The do loop is appropriate when the loop body must be executed at least once.

implement loops that read sequences of input data.

• A sentinel value denotes the end of a data set, but it is not part of the data.

• You can use a Boolean variable to control a loop. Set the variable to true before entering the loop, then set it to false to leave the loop.

• Use input redirection to read input from a file. Use output redirection to capture program output in a file.

use the technique of storyboarding for planning user interactions.

• A storyboard consists of annotated sketches for each step in an action sequence. • Developing a storyboard helps you understand the inputs and outputs that are

required for a program.

C h a p t e r s U M M a r Y

cfe2_ch04_p131_192.indd 173 10/28/10 8:13 PM

174 Chapter 4 Loops

know the most common loop algorithms.

• To compute an average, keep a total and a count of all values. • To count values that fulfill a condition, check all values and increment a counter

for each match. • If your goal is to find a match, exit the loop when the match is found. • To find the largest value, update the largest value seen so far whenever you see a

larger one. • To compare adjacent inputs, store the preceding input in a variable.

use nested loops to implement multiple levels of iteration.

• When the body of a loop contains another loop, the loops are nested. A typical use of nested loops is printing a table with rows and columns.

apply loops to the implementation of simulations.

• In a simulation, you use the computer to simulate an activity. You can introduce randomness by calling the random number generator.

r4.1 Provide trace tables for these loops. a. int i = 0; int j = 10; int n = 0;

while (i < j) { i++; j--; n++; }

b. int i = 0; int j = 0; int n = 0; while (i < 10) { i++; n = n + i + j; j++; }

c. int i = 10; int j = 0; int n = 0; while (i > 0) { i--; j++; n = n + i - j; }

d. int i = 0; int j = 10; int n = 0; while (i != j) { i = i + 2; j = j - 2; n++; }

r4.2 What do these loops print? a. for (int i = 1; i < 10; i++) { cout << i << " "; } b. for (int i = 1; i < 10; i += 2) { cout << i << " "; } c. for (int i = 10; i > 1; i--) { cout << i << " "; } d. for (int i = 0; i < 10; i++) { cout << i << " "; } e. for (int i = 1; i < 10; i = i * 2) { cout << i << " "; } f. for (int i = 1; i < 10; i++) { if (i % 2 == 0) { cout << i << " "; } }

r4.3 What is an infinite loop? On your computer, how can you terminate a program that executes an infinite loop?

r4.4 What is an “off-by-one” error? Give an example from your own programming experience.

r e V I e W e x e r C I s e s

cfe2_ch04_p131_192.indd 174 10/28/10 8:13 PM

review exercises 175

r4.5 Write a program trace for the pseudocode in Exercise P4.9, assuming the input val ues are 4 7 –2 –5 0.

r4.6 Is the following code legal? for (int i = 0; i < 10; i++) { for (int i = 0; i < 10; i++) { cout << i << " "; } cout << endl; }

What does it print? Is it good coding style? If not, how would you improve it?

r4.7 How often do the following loops execute? Assume that i is not changed in the loop body.

a. for (int i = 1; i <= 10; i++) ... b. for (int i = 0; i < 10; i++) ... c. for (int i = 10; i > 0; i--) ... d. for (int i = -10; i <= 10; i++) ... e. for (int i = 10; i >= 0; i++) ... f. for (int i = -10; i <= 10; i = i + 2) ... g. for (int i = -10; i <= 10; i = i + 3) ...

r4.8 Write pseudocode for a program that prints a calendar such as the following:

Su M T W Th F Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

r4.9 Write pseudocode for a program that prints a Celsius/Fahrenheit conversion table such as the following:

Celsius | Fahrenheit --------+----------- 0 | 32 10 | 50 20 | 68 ... ... 100 | 212

r4.10 Write pseudocode for a program that reads a sequence of student records and prints the total score for each student. Each record has the student’s first and last name, followed by a sequence of test scores and a sentinel of –1. The sequence is termi- nated by the word END. Here is a sample sequence:

Harry Morgan 94 71 86 95 -1 Sally Lin 99 98 100 95 90 -1 END

Provide a trace table for this sample input.

cfe2_ch04_p131_192.indd 175 10/28/10 8:13 PM

176 Chapter 4 Loops

r4.11 Rewrite the following for loop into a while loop. int s = 0; for (int i = 1; i <= 10; i++) { s = s + i; }

r4.12 Rewrite the following do/while loop into a while loop. int n; cin >> n; double x = 0; double s; do { s = 1.0 / (1 + n * n); n++; x = x + s; } while (s > 0.01);

r4.13 Provide trace tables of the following loops. a. int s = 1;

int n = 1; while (s < 10) { s = s + n; } n++;

b. int s = 1; for (int n = 1; n < 5; n++) { s = s + n; }

c. int s = 1; int n = 1; do { s = s + n; n++; } while (s < 10 * n);

r4.14 What do the following loops print? Work out the answer by tracing the code, not by using the computer.

a. int s = 1; for (int n = 1; n <= 5; n++) { s = s + n; cout << s << " "; }

b. int s = 1; for (int n = 1; s <= 10; cout << s << " ") { n = n + 2; s = s + n; }

c. int s = 1; int n; for (n = 1; n <= 5; n++) { s = s + n; n++;

cfe2_ch04_p131_192.indd 176 10/28/10 8:13 PM

review exercises 177

} cout << s << " " << n;

r4.15 What do the following program segments print? Find the answers by tracing the code, not by using the computer.

a. int n = 1; for (int i = 2; i < 5; i++) { n = n + i; } cout << n;

b. int i; double n = 1 / 2; for (i = 2; i <= 5; i++) { n = n + 1.0 / i; } cout << i;

c. double x = 1; double y = 1; int i = 0; do { y = y / 2; x = x + y; i++; } while (x < 1.8); cout << i;

d. double x = 1; double y = 1; int i = 0; while (y >= 1.5) { x = x / 2; y = x + y; i++; } cout << i;

r4.16 Give an example of a for loop where symmetric bounds are more natural. Give an example of a for loop where asymmetric bounds are more natural.

r4.17 Add a storyboard panel for the conversion program in Section 4.6 on page 154 that shows a sce nario where a user enters incompatible units.

r4.18 In Section 4.6, we decided to show users a list of all valid units in the prompt. If the program supports many more units, this approach is unworkable. Give a story board panel that illustrates an alternate approach: If the user enters an unknown unit, a list of all known units is shown.

r4.19 Change the storyboards in Section 4.6 to support a menu that asks users whether they want to convert units, see program help, or quit the program. The menu should be displayed at the beginning of the program, when a sequence of values has been converted, and when an error is displayed.

r4.20 Draw a flow chart for a program that carries out unit conversions as described in Section 4.6.

r4.21 In Section 4.7.4, the code for finding the largest and smallest input initializes the largest and smallest variables with an input value. Why can’t you initialize them with zero?

r4.22 What are nested loops? Give an example where a nested loop is typically used.

cfe2_ch04_p131_192.indd 177 10/28/10 8:13 PM

178 Chapter 4 Loops

r4.23 The nested loops for (int i = 1; i <= height; i++) { for (int j = 1; j <= width; j++) { cout << "*"; } cout << endl; }

display a rectangle of a given width and height, such as **** **** ****

Write a single for loop that displays the same rectangle.

r4.24 Suppose you design an educational game to teach children how to read a clock. How do you generate random values for the hours and minutes?

r4.25 In a travel simulation, Harry will visit one of his friends that are located in three states. He has ten friends in California, three in Nevada, and two in Utah. How do you produce a random number between 1 and 3, denoting the destination state, with a probability that is proportional to the number of friends in each state?

p4.1 Write programs with loops that compute a. The sum of all even numbers between 2 and 100 (inclusive). b. The sum of all squares between 1 and 100 (inclusive). c. All powers of 2 from 20 up to 220. d. The sum of all odd numbers between a and b (inclusive), where a and b are

inputs. e. The sum of all odd digits of an input. (For example, if the input is 32677, the

sum would be 3 + 7 + 7 = 17.)

p4.2 Write programs that read a sequence of integer inputs and print a. The smallest and largest of the inputs. b. The number of even and odd inputs. c. Cumulative totals. For example, if the input is 1 7 2 9, the program should print

1 8 10 19. d. All adjacent duplicates. For example, if the input is 1 3 3 4 5 5 6 6 2, the program

should print 3 5 6.

p4.3 Write programs that read a line of input as a string and print a. Only the uppercase letters in the string. b. Every second letter of the string. c. The string, with all vowels replaced by an underscore. d. The number of vowels in the string. e. The positions of all vowels in the string.

p r o G r a M M I n G e x e r C I s e s

cfe2_ch04_p131_192.indd 178 10/28/10 8:13 PM

programming exercises 179

p4.4 Complete the program in How To 4.1 on page 162. Your program should read twelve temperature values and print the month with the highest temperature.

p4.5 Credit Card Number Check. The last digit of a credit card number is the check digit, which protects against transcription errors such as an error in a single digit or switching two digits. The following method is used to verify actual credit card numbers but, for simplicity, we will describe it for numbers with 8 digits instead of 16:

• Starting from the rightmost digit, form the sum of every other digit. For example, if the credit card number is 43589795, then you form the sum 5 + 7 + 8 + 3 = 23.

• Double each of the digits that were not included in the preceding step. Add all digits of the resulting numbers. For example, with the number given above, doubling the digits, starting with the next-to-last one, yields 18 18 10 8. Adding all digits in these values yields 1 + 8 + 1 + 8 + 1 + 0 + 8 = 27.

• Add the sums of the two preceding steps. If the last digit of the result is 0, the number is valid. In our case, 23 + 27 = 50, so the number is valid.

Write a program that implements this algorithm. The user should supply an 8-digit number, and you should print out whether the number is valid or not. If it is not valid, you should print out the value of the check digit that would make the number valid.

p4.6 Currency conversion. Write a program that first asks the user to type today’s ex- change rate between U.S. dollars and Japanese yen, then reads U.S. dollar values and converts each to yen. Use 0 as a sentinel.

p4.7 Write a program that first asks the user to type in today’s exchange rate between U.S. dollars and Japanese yen, then reads U.S. dollar values and converts each to Japanese yen. Use 0 as the sentinel value to denote the end of dollar inputs. Then the program reads a sequence of yen amounts and converts them to dollars. The second sequence is terminated by another zero value.

p4.8 Write a program that reads a set of floating-point values. Ask the user to enter the values, then print

• the average of the values. • the smallest of the values. • the largest of the values. • the range, that is the difference between the smallest and largest.

Of course, you may only prompt for the values once.

cfe2_ch04_p131_192.indd 179 10/28/10 8:13 PM

180 Chapter 4 Loops

p4.9 Translate the following pseudocode for finding the minimum value from a set of inputs into a C++ program.

Set a Boolean variable "first" to true. While another value has been read successfully

If first is true Set the minimum to the value. Set first to false.

Else if the value is less than the minimum Set the minimum to the value. Print the minimum.

p4.10 Translate the following pseudocode for randomly permuting the characters in a string into a C++ program.

Read a word. Repeat word.length() times

Pick a random position i in the word. Pick a random position j > i in the word. Swap the letters at positions j and i.

Print the word.

To swap the letters, construct substrings as follows:

first middle lasti j

Then replace the string with

first + word.substr(j, 1) + middle + word.substr(i, 1) + last

p4.11 Write a program that reads a word and prints each character of the word on a sepa- rate line. For example, if the user provides the input "Harry", the program prints

H a r r y

p4.12 Write a program that reads a word and prints the word in reverse. For example, if the user provides the input "Harry", the program prints

yrraH

p4.13 Write a program that reads a word and prints the number of vowels in the word. For this exercise, assume that a e i o u y are vowels. For example, if the user pro vides the input "Harry", the program prints 2 vowels.

p4.14 Write a program that reads a word and prints the number of syllables in the word. For this exercise, assume that syllables are determined as follows: Each sequence of vowels a e i o u y, except for the last e in a word, is a vowel. However, if that algo- rithm yields a count of 0, change it to 1. For example,

Word Syllables Harry 2 hairy 2 hare 1 the 1

cfe2_ch04_p131_192.indd 180 10/28/10 8:13 PM

programming exercises 181

p4.15 Write a program that reads a word and prints all substrings, sorted by length. For example, if the user provides the input "rum", the program prints

r u m ru um rum

p4.16 Write a program that reads a number and prints all of its binary digits: Print the remainder number % 2, then replace the number with number / 2. Keep going until the number is 0. For example, if the user provides the input 13, the output should be

1 0 1 1

p4.17 Mean and standard deviation. Write a program that reads a set of floating-point data values. Choose an appropriate mechanism for prompting for the end of the data set. When all values have been read, print out the count of the values, the average, and the standard deviation. The average of a data set {x1, . . ., xn} is x x ni= ∑ , where ∑ = + +x x xi n1 … is the sum of the input values. The stan dard deviation is

s x x

n i=

−( ) −

∑ 2 1

However, this formula is not suitable for the task. By the time the program has computed x , the individ ual xi are long gone. Until you know how to save these values, use the numerically less stable formula

s x x

n i n i=

− ( ) −

∑∑ 2 1 2

You can compute this quantity by keeping track of the count, the sum, and the sum of squares as you process the input values.

p4.18 The Fibonacci numbers are defined by the sequence

f f fn n n

1 2

= +− −

Reformulate that as fold1 = 1; fold2 = 1; fnew = fold1 + fold2;

After that, discard fold2, which is no longer needed, and set fold2 to fold1 and fold1 to fnew. Repeat fnew an appropriate number of times. Implement a program that computes the Fibonacci numbers in that way.

Fibonacci numbers describe the growth of a rabbit population.

cfe2_ch04_p131_192.indd 181 10/28/10 8:13 PM

182 Chapter 4 Loops

p4.19 Factoring of integers. Write a program that asks the user for an integer and then prints out all its factors. For example, when the user enters 150, the program should print

2 3 5 5

p4.20 Prime numbers. Write a program that prompts the user for an integer and then prints out all prime numbers up to that integer. For example, when the user enters 20, the program should print

2 3 5 7 11 13 17 19

Recall that a number is a prime number if it is not divisible by any number except 1 and itself.

p4.21 Write a program that prints a multiplication table, like this: 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 ... 10 20 30 40 50 60 70 80 90 100

p4.22 Write a program that reads an integer and displays, using asterisks, a filled and hol low square, placed next to each other. For example if the side length is 5, the pro gram should display

***** ***** ***** * * ***** * * ***** * * ***** *****

p4.23 Write a program that reads an integer and displays, using asterisks, a filled diamond of the given side length. For example, if the side length is 4, the program should dis play

* *** ***** ******* ***** *** *

p4.24 The game of Nim. This is a well-known game with a number of variants. The fol lowing variant has an interesting winning strategy. Two players alternately take marbles from a pile. In each move, a player chooses how many marbles to take. The player must take at least one but at most half of the marbles. Then the other player takes a turn. The player who takes the last marble loses.

cfe2_ch04_p131_192.indd 182 10/28/10 8:13 PM

programming exercises 183

You will write a program in which the computer plays against a human opponent. Generate a random integer between 10 and 100 to denote the initial size of the pile. Generate a random integer between 0 and 1 to decide whether the computer or the human takes the first turn. Generate a random integer between 0 and 1 to decide whether the computer plays smart or stupid. In stupid mode the computer simply takes a random legal value (between 1 and n̸2) from the pile whenever it has a turn. In smart mode the computer takes off enough marbles to make the size of the pile a power of two minus 1—that is, 3, 7, 15, 31, or 63. That is always a legal move, except when the size of the pile is currently one less than a power of two. In that case, the computer makes a random legal move. You will note that the computer cannot be beaten in smart mode when it has the first move, unless the pile size happens to be 15, 31, or 63. Of course, a human player who has the first turn and knows the win ning strategy can win against the computer.

p4.25 The Drunkard’s Walk. A drunkard in a grid of streets randomly picks one of four directions and stumbles to the next intersection, then again randomly picks one of four directions, and so on. You might think that on average the drunkard doesn’t move very far because the choices cancel each other out, but that is actually not the case. Represent locations as integer pairs (x, y). Implement the drunkard’s walk over 100 intersections and print the beginning and ending location.

p4.26 The Monty Hall Paradox. Marilyn vos Savant described the following problem (loosely based on a game show hosted by Monty Hall) in a popular magazine: “Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advan- tage to switch your choice?” Ms. vos Savant proved that it is to your advantage, but many of her readers, includ- ing some mathematics professors, disagreed, arguing that the probability would not change because another door was opened. Your task is to simulate this game show. In each iteration, ran domly pick a door number between 1 and 3 for placing the car. Randomly have the player pick a door. Randomly have the game show host pick one of the two doors having a goat. Now incre ment a counter for strategy 1 if the player wins by switching to the third door, and increment a counter for strategy 2 if the player wins by sticking with the original choice. Run 1,000 iterations and print both counters.

p4.27 The Buffon Needle Experiment. The follow ing experiment was devised by Comte Georges-Louis Leclerc de Buffon (1707–1788), a French naturalist. A needle of length 1 inch is dropped onto paper that is ruled with lines 2 inches apart. If the needle drops onto a line, we count it as a hit. (See Figure 8.) Buffon conjectured that the quotient tries/hits approximates p. figure 8 the Buffon needle experiment

cfe2_ch04_p131_192.indd 183 10/28/10 8:13 PM

184 Chapter 4 Loops

figure 9 a hit in the Buffon needle experiment 2

yhighyy

ylowyy α

For the Buffon needle experiment, you must generate two random numbers: one to describe the starting position and one to describe the angle of the needle with the x-axis. Then you need to test whether the needle touches a grid line. Generate the lower point of the needle. Its x-coordinate is irrelevant, and you may assume its y-coordi nate ylow to be any random number between 0 and 2. The angle α between the needle and the x-axis can be any value between 0 degrees and 180 degrees (p radians). The upper end of the needle has y-coordinate

y yhigh low= + sinα

The needle is a hit if yhigh is at least 2, as shown in Figure 9. Stop after 10,000 tries and print the quotient tries/hits. (This program is not suitable for computing the value of p. You need p in the computation of the angle.)

engineering p4.28 In a predator-prey simulation, you compute the populations of predators and prey, using the following equations:

prey prey A B pred

pred pred C D n n n

n n

= × + − ×( ) = × − + ×

1 ppreyn( ) Here, A is the rate at which prey birth exceeds natural death, B is the rate of predation, C is the rate at which predator deaths exceed births without food, and D represents predator increase in the presence of food. Write a program that prompts users for these rates, the initial population sizes, and the number of peri ods. Then print the populations for the given number of periods. As inputs, try A = 0.1, B = C = 0.01, and D = 0.00002 with initial prey and predator populations of 1,000 and 20.

engineering p4.29 Projectile flight. Suppose a cannonball is propelled straight into the air with a start ing velocity v0. Any calculus book will state that the position of the ball after t sec onds is s t gt v t( ) = − +1

2 2

0 , where g = 9 81. m sec 2 is the gravi tational force of the earth.

No calculus book ever mentions why someone would want to carry out such an obviously dangerous experiment, so we will do it in the safety of the computer. In fact, we will confirm the theorem from calculus by a simulation. In our simula- tion, we will consider how the ball moves in very short time intervals Δt. In a short

cfe2_ch04_p131_192.indd 184 10/28/10 8:13 PM

programming exercises 185

time interval the velocity v is nearly con stant, and we can compute the distance the ball moves as Δs = vΔt. In our program, we will simply set

const double DELTA_T = 0.01;

and update the position by s = s + v * DELTA_T;

The velocity changes constantly—in fact, it is reduced by the gravitational force of the earth. In a short time interval, Δv = –gΔt, we must keep the velocity updated as

v = v - g * DELTA_T;

In the next iteration the new velocity is used to update the distance. Now run the simulation until the cannonball falls back to the earth. Get the initial velocity as an input (100 m̸sec is a good value). Update the position and velocity 100 times per second, but print out the posi tion only every full second. Also printout the values from the exact formula s t gt v t( ) = − +1

2 2

0 for com parison. Note: You may wonder whether there is a benefit to this simulation when an exact formula is available. Well, the formula from the calculus book is not exact. Actually, the gravitational force diminishes the farther the cannonball is away from the surface of the earth. This complicates the algebra sufficiently that it is not possible to give an exact formula for the actual motion, but the computer simulation can simply be extended to apply a variable gravitational force. For cannonballs, the calculus-book formula is actually good enough, but computers are necessary to compute accurate trajectories for higher-flying objects such as ballistic mis siles.

engineering p4.30 A simple model for the hull of a ship is given by

y B x

L z T

= −  

 



  



  

−  

 



  



  2

1 2

1 2 2

where B is the beam, L is the length, and T is the draft.

cfe2_ch04_p131_192.indd 185 10/28/10 8:13 PM

186 Chapter 4 Loops

(Note: There are two values of y for each x and z because the hull is symmetric from starboard to port.) The cross-sectional area at a point x is called the “section” in nautical parlance. To compute it, let z go from 0 to –T in n increments, each of size T n. For each value of z, compute the value for y. Then sum the areas of trapezoidal strips. At right are the strips where n = 4. Write a program that reads in values for B, L, T, x, and n and then prints out the cross-sectional area at x.

engineering p4.31 Radioactive decay of radioactive materials can be modeled by the equation A = A0e

-t (log 2̸h), where A is the amount of the material at time t, A0 is the amount at time 0, and h is the half-life. Technetium-99 is a radioisotope that is used in imaging of the brain. It has a half-life of 6 hours. Your program should display the relative amount A ̸ A0 in a patient body every hour for 24 hours after receiving a dose.

engineering p4.32 The photo at left shows an electric device called a “transformer”. Transformers are often constructed by wrapping coils of wire around a ferrite core. The figure below illustrates a situation that occurs in various audio devices such as cell phones and music players. In this circuit, a transformer is used to connect a speaker to the output of an audio amplifier.

Vs = 40 V

Speaker

+ –

R0 = 20 Ω

Rs = 8 Ω

TransformerAmplifier

1 : n

The symbol used to represent the transformer is intended to suggest two coils of wire. The parameter n of the transformer is called the “turns ratio” of the trans- former. (The number of times that a wire is wrapped around the core to form a coil is called the number of turns in the coil. The turns ratio is literally the ratio of the number of turns in the two coils of wire.) When designing the circuit, we are concerned primarily with the value of the power delivered to the speakers—that power causes the speakers to produce the sounds we want to hear. Suppose we were to connect the speakers directly to the amplifier without using the transformer. Some fraction of the power available from the amplifier would get to the speakers. The rest of the available power would be lost in the amplifier itself. The transformer is added to the circuit to increase the fraction of the amplifier power that is delivered to the speakers. The power, Ps, delivered to the speakers is calculated using the formula

P R nV

n R R s s

= +



 



 2

Write a C++ program that models the circuit shown and varies the turns ratio from 0.01 to 2 in 0.01 increments, then determines the value of the turns ratio that maxi- mizes the power delivered to the speakers.

1. 23 years. 2. 7 years. 3. Add a statement

cout << balance << endl;

as the last statement in the while loop. 4. The program prints the same output. This is because the balance after 14 years is

slightly below $20,000, and after 15 years, it is slightly above $20,000. 5. 2 4 8 16 32 64 128

Note that the value 128 is printed even though it is larger than 100. 6. n output

5 4 4 3 3 2 2 1 1 0 0 -1 -1

7. n output 1 1, 2 1, 2, 3 1, 2, 3,

There is a comma after the last value. Usually, commas are between values only. 8. a n r i

2 4 1 1 2 2 4 3 8 4 16 5

The code computes an. 9. n output

1 1 11 11 21 21 31 31 41 41 51 51 61 61 ...

This is an infinite loop. n is never equal to 50. 10. count n

1 123 2 12.3 3 1.23

a n s W e r s t o s e L F - C h e C k Q U e s t I o n s

cfe2_ch04_p131_192.indd 186 10/28/10 8:13 PM

answers to self-Check Questions 187

1. 23 years. 2. 7 years. 3. Add a statement

cout << balance << endl;

as the last statement in the while loop. 4. The program prints the same output. This is because the balance after 14 years is

slightly below $20,000, and after 15 years, it is slightly above $20,000. 5. 2 4 8 16 32 64 128

Note that the value 128 is printed even though it is larger than 100. 6. n output

5 4 4 3 3 2 2 1 1 0 0 -1 -1

7. n output 1 1,

2 1, 2, 3 1, 2, 3, 4

There is a comma after the last value. Usually, commas are between values only. 8. a n r i

2 4 1 1 2 2 4 3 8 4 16 5

The code computes an. 9. n output

1 1 11 11 21 21 31 31 41 41 51 51 61 61 ...

This is an infinite loop. n is never equal to 50. 10. count n

1 123 2 12.3 3 1.23

a n s W e r s t o s e L F - C h e C k Q U e s t I o n s

cfe2_ch04_p131_192.indd 187 10/28/10 8:13 PM

188 Chapter 4 Loops

This yields the correct answer. The number 123 has 3 digits. count n 1 100 2 10

This yields the wrong answer. The number 100 also has 3 digits. The loop condition should have been while (temp >= 10)

11. int year = 1; while (year <= nyears) { balance = balance * (1 + RATE / 100); cout << setw(4) << year << setw(10) << balance << endl; year++; }

12. 11 numbers: 10 9 8 7 6 5 4 3 2 1 0

13. for (int i = 10; i <= 20; i = i + 2) { cout << n << endl; }

14. int sum = 0; for (int i = 1; i <= n; i++) { sum = sum + i; }

15. for (int year = 1; balance <= 2 * INITIAL_BALANCE; year++) However, it is best not to use a for loop in this case because the loop condition does not relate to the year variable. A while loop would be a better choice.

16. do { cout << "Enter a value between 0 and 100: "; cin >> value; } while (value < 0 || value > 100);

17. int value = 100; while (value >= 100) { cout << "Enter a value < 100: "; cin >> value; }

Here, the variable value had to be initialized with an artificial value to ensure that the loop is entered at least once.

18. Yes. The do loop do { body } while (condition);

is equivalent to this while loop: bool first = true; while (first || condition) { body; first = false; }

19. int x; int sum = 0; do {

cfe2_ch04_p131_192.indd 188 10/28/10 8:13 PM

answers to self-Check Questions 189

cin >> x; sum = sum + x; } while (x != 0);

20. int x = 0; int previous; do { previous = x; cin >> x; sum = sum + x; } while (previous != x);

21. No data 22. The first check ends the loop after the sentinel has been read. The second check

ensures that the sentinel is not processed as an input value. 23. The while loop would never be entered. The user would never be prompted for in-

put. Since count stays 0, the program would then print "No data". 24. The stream also fails. A more accurate prompt would have been: “Enter values, a key

other than a digit to quit.” But that might be more confusing to the program user who would need now ponder which key to choose.

25. You don’t know whether the input fails until after you try reading input. 26. Computing the aver age

27. Simple conversion

Unknown unit

Program doesn’t understand question syntax

Enter scores, Q to quit: 90 80 90 100 80 Q The average is 88 (Program exits)

Your conversion question: How many in are 30 cm 30 cm = 11.81 in (Program exits) Run program again for another question

Only one value can be converted.

Your conversion question: How many inches are 30 cm? Unknown unit: inches Known units are in, ft, mi, mm, cm, m, km, oz, lb, g, kg, tsp, tbsp, pint, gal (Program exits)

Your conversion question: What is an ångström? Please formulate your question as “How many (unit) are (value) (unit)?” (Program exits)

cfe2_ch04_p131_192.indd 189 10/28/10 8:13 PM

190 Chapter 4 Loops

28. One score is not enough

29. It would not be possible to implement this interface using the C++ features we have covered up to this point. There is no way for the program to know when the first set of inputs ends. (When you read numbers with cin >> value, it is your choice whether to put them on a single line or multiple lines.)

30. Comparing two inter est rates

31. The total is zero. 32. double total = 0;

double input; while (cin >> input) { if (input > 0) { total = total + input; } }

33. position is str.length(). 34. The loop will stop when a match is found, but you cannot access the match because

position is not defined outside the loop. 35. Start the loop at the end of string:

bool found = false; int position = str.length() - 1; while (!found && position >= 0) { string ch = str.substr(position, 1); if (ch == " ") { found = true; } else { position--; } }

36. Unless the input contains zero or negative numbers, the smallest value is incorrectly computed as 0.

37. When executing cin >> previous, cin fails and previous is unchanged. The statement cin >> input also fails, and the while loop is never entered.

38. All values in the inner loop should be displayed on the same line.

Enter scores, Q to quit: 90 Q Error: At least two scores are required. (Program exits)

First interest rate in percent: 5 Second interest rate in percent: 10 Years: 5 Year 5% 10% 0 10000.00 10000.00 1 10500.00 11000.00 2 11025.00 12100.00 3 11576.25 13310.00 4 12155.06 14641.00 5 12762.82 16105.10

This row clarifies that 1 means the end of the first year

cfe2_ch04_p131_192.indd 190 10/28/10 8:13 PM

answers to self-Check Questions 191

39. Change lines 14, 19, and 31 to for (int n = 0; n <= NMAX; n++). Change NMAX to 5.

40. 60: The outer loop is executed 10 times, and the inner loop 6 times. 41. 0123

1234 2345

42. for (int i = 1; i <= 3; i++) { for (int j = 1; j <= 4; j++) { cout << "[]"; } cout << endl; }

43. Compute rand() % 2, and use 0 for heads, 1 for tails, or the other way around. 44. Compute rand() % 4 and associate the numbers 0 ... 3 with the four suits. Then com-

pute rand() % 13 and associate the numbers 0 ... 12 with Jack, Ace, 2 ... 10, Queen, and King.

45. It is required for calling the time function. 46. The call will produce a value between 2 and 12, but all values have the same proba-

bility. When throwing a pair of dice, the number 7 is six times as likely as the num ber 2. The correct formula is int sum = rand() % 6 + rand() % 6 + 2;

47. rand() * 100.0 / RAND_MAX

cfe2_ch04_p131_192.indd 191 10/28/10 8:13 PM

This page intentionally left blank

5C h a p t e r

193

F u n C t i o n s

to be able to implement functions

to become familiar with the concept of parameter passing

to appreciate the importance of function comments

to develop strategies for decomposing complex tasks into simpler ones

to be able to determine the scope of a variable

to recognize when to use value and reference parameters

C h a p t e r G o a l s

C h a p t e r C o n t e n t s

5.1 Functions as Black Boxes 194

5.2 implementing Functions 196

Syntax 5.1: Function Definition 197 Programming Tip 5.1: Function Comments 199

5.3 parameter passing 199

Programming Tip 5.2: Do not Modify parameter Variables 201

5.4 return Values 202

Common Error 5.1: Missing return Value 203 Special Topic 5.1: Function Declarations 203 How To 5.1: implementing a Function 204 Worked Example 5.1: Matching and replacing

parts of a string Worked Example 5.2: using a Debugger

5.5 Functions Without return Values 206

5.6 proBlem solVing: reusaBle Functions 208

5.7 proBlem solVing: stepWise reFinement 210

Programming Tip 5.3: Keep Functions short 216 Programming Tip 5.4: tracing Functions 216 Programming Tip 5.5: stubs 217 Worked Example 5.3: Calculating a

Course Grade

5.8 VariaBle scope and gloBal VariaBles 218

Programming Tip 5.6: avoid Global Variables 220

5.9 reFerence parameters 220

Programming Tip 5.7: prefer return Values to reference parameters 225

Special Topic 5.2: Constant references 225

5.10 recursiVe Functions (optional) 226

How To 5.2: thinking recursively 229 Random Fact 5.1: the explosive Growth of

personal Computers 230

cfe2_ch05_p193_248.indd 193 10/26/10 6:14 PM

194

Functions are a fundamental building block of C++ programs. a function packages a computation into a form that can be easily understood and reused. (the person in the image to the left is executing the function “make two cups of espresso”.) in this chapter, you will learn how to design and implement your own functions. using the process of stepwise refinement, you will be able to break up complex tasks into sets of cooperating functions.

5.1 Functions as Black Boxes A function is a sequence of instructions with a name. You have already encountered several functions. For example, the function named pow, which was introduced in Chapter 2, contains instructions to com pute a power xy. Moreover, every C++ pro- gram has a function called main.

You call a function in order to execute its instructions. For example, consider the following program:

int main() { double z = pow(2, 3); ... }

By using the expression pow(2, 3), main calls the pow function, asking it to compute the power 23. The main function is temporarily suspended. The instructions of the pow function execute and compute the result. The pow function returns its result (that is, the value 8) back to main, and the main function resumes execu tion (see Figure 1).

a function is a named sequence of instructions.

Figure 1 execution Flow During a Function Call

Wait

Pass 2 and 3 to pow

Use result

main

Pass result to caller

Compute 23

pow

When another function calls the pow function, it provides “inputs”, such as the expressions 2 and 3 in the call pow(2, 3). These expressions are called arguments. This terminology avoids confusion with other inputs, such as those pro vided by a human user. Similarly, the “output” that the pow function computes is called the return value.

Functions can have multiple arguments, but they have only one return value. Note that the return value of a function is returned to the calling function, not dis-

played on the screen. For example, suppose your program contains a statement double z = pow(2, 3);

When the pow function returns its result, the return value is stored in the variable z. If you want the value to be displayed, you need to add a statement such as cout << z.

At this point, you may wonder how the pow function performs its job. For example, how does pow(2, 3) compute that 23 is 8? By multiplying 2 × 2 × 2? With logarithms? Fortunately, as a user of the function, you don’t need to know how the function is implemented. You just need to know the specification of the function: If you provide arguments x and y, the function returns xy. Engineers use the term black box for a device with a given specification but unknown implementation. You can think of pow as a black box, as shown in Figure 2.

When you design your own functions, you will want to make them appear as black boxes to other pro grammers. Those programmers want to use your functions with- out knowing what goes on inside. Even if you are the only person working on a pro- gram, making each function into a black box pays off: there are fewer details that you need to keep in mind.

arguments are supplied when a function is called. the return value is the result that the function computes.

Although a thermostat is usually white, you can think of it as a black box. The input is the desired temperature, and the output is a signal to the heater or air conditioner.

cfe2_ch05_p193_248.indd 194 10/26/10 6:14 PM

5.1 Functions as Black Boxes 195

Figure 2 the pow Function as a Black Box

2, 3

pow

Inputs

Output

Functions can have multiple arguments, but they have only one return value. Note that the return value of a function is returned to the calling function, not dis-

played on the screen. For example, suppose your program contains a statement double z = pow(2, 3);

When the pow function returns its result, the return value is stored in the variable z. If you want the value to be displayed, you need to add a statement such as cout << z.

arguments are supplied when a function is called. the return value is the result that the function computes.

Although a thermostat is usually white, you can think of it as a black box. The input is the desired temperature, and the output is a signal to the heater or air conditioner.

cfe2_ch05_p193_248.indd 195 10/26/10 6:14 PM

196 Chapter 5 Functions

1. Consider the function call pow(3, 2). What are the arguments and return value? 2. What is the return value of the function call pow(pow(2, 2), 2)? 3. The ceil function in the C++ standard library takes a single argument x and

returns the smallest inte ger ≥ x. What is the return value of ceil(2.3)? 4. It is possible to determine the answer to Self Check 3 without knowing how the

ceil function is implemented. Use an engineering term to describe this aspect of the ceil function.

practice it Now you can try these exercises at the end of the chapter: R5.1, P5.1.

5.2 implementing Functions In this section, you will learn how to implement a function from a given specification. We will use a very simple example: a function to compute the volume of a cube with a given side length.

The cube_volume function uses a given side length to compute the volume of a cube.

When writing this function, you need to

• Pick a name for the function (cube_volume). • Declare a variable for each argument (double side_length). These variables are

called parameter vari ables. • Specify the type of the return value (double).

Put all this information together to form the first line of the function’s definition: double cube_volume(double side_length)

Next, specify the body of the function: the statements that are executed when the function is called.

The volume of a cube of side length s is s × s × s. However, for greater clarity, our parameter variable has been called side_length, not s, so we need to compute side_ length * side_length * side_length.

We will store this value in a variable called volume: double volume = side_length * side_length * side_length;

In order to return the result of the function, use the return statement: return volume;

The body of a function is enclosed in braces. Here is the complete function: double cube_volume(double side_length) { double volume = side_length * side_length * side_length; return volume; }

s e l F c h e c k

When defining a function, you provide a name for the function, a variable for each argument, and a type for the result.

cfe2_ch05_p193_248.indd 196 10/26/10 6:14 PM

5.2 implementing Functions 197

The return statement gives the function’s result to the caller.

Let’s put this function to use. We’ll supply a main function that calls the cube_volume function twice.

int main() { double result1 = cube_volume(2); double result2 = cube_volume(10); cout << "A cube with side length 2 has volume " << result1 << endl; cout << "A cube with side length 10 has volume " << result2 << endl;

return 0; }

When the function is called with different arguments, the function returns different results. Consider the call cube_volume(2). The argument 2 corresponds to the side_ length parameter variable. Therefore, in this call, side_length is 2. The function com- putes side_length * side_length * side_length, or 2 * 2 * 2. When the function is called with a different argument, say 10, then the function computes 10 * 10 * 10.

Now we combine both functions into a test program. Because main calls cube_ volume, the cube_volume function must be known before the main function is defined. This is easily achieved by placing cube_volume first and main last in the source file. (See Special Topic 5.1 on page 203 for an alternative.)

syntax 5.1 Function Definition

double cube_volume(double side_length) { double volume = side_length * side_length * side_length;

return volume; }

Type of return value

Name of function

Type of parameter variable

Name of parameter variable

return statement exits function and returns result.

See page 202.

Function body, executed when function is called.

cfe2_ch05_p193_248.indd 197 10/26/10 6:14 PM

198 Chapter 5 Functions

Here is the com plete program. Note the comment that describes the behavior of the function. (Programming Tip 5.1 on page 199 describes the format of the comment.)

ch05/cube.cpp

1 #include <iostream> 2 3 using namespace std; 4 5 /** 6 Computes the volume of a cube. 7 @param side_length the side length of the cube 8 @return the volume 9 */

program run

A cube with side length 2 has volume 8 A cube with side length 10 has volume 1000

5. What is the value of cube_volume(3)? 6. What is the value of cube_volume(cube_volume(2))? 7. Provide an alternate implementation of the body of the cube_volume function by

calling the pow func tion. 8. Define a function square_area that computes the area of a square of a given side

length. 9. Consider this function:

int mystery(int x, int y) { double result = (x + y) / (y - x); return result; }

What is the result of the call mystery(2, 3)?

practice it Now you can try these exercises at the end of the chapter: R5.2, P5.2, P5.7.

s e l F c h e c k

Function comments

Whenever you write a function, you should comment its behavior. Comments are for human readers, not compilers, and there is no universal standard for the layout of a function com- ment. In this book, we will use the following lay out:

/** Computes the volume of a cube. @param side_length the side length of the cube @return the volume */ double cube_volume(double side_length) { double volume = side_length * side_length * side_length; return volume; }

This particular documentation style is borrowed from the Java programming language. It is widely supported by C++ tools as well, for example by the Doxygen tool (www.doxygen.org).

The first line of the comment describes the purpose of the function. Each @param clause describes a parameter vari able and the @return clause describes the return value.

Note that the function comment does not document the implementation (how the function does what it does) but rather the design (what the function does, its inputs, and its results). The comment allows other programmers to use the function as a “black box”.

5.3 parameter passing In this section, we examine the mechanism of passing arguments into functions. When a function is called, its parameter variables are created (Another commonly used term for a parameter variable is for mal parameter.) In the function call, an expression is supplied for each parameter variable, called the argument. (Another commonly used term for this expression is actual parameter.) Each parameter vari- able is initialized with the value of the corresponding argument.

Consider the function call illustrated in Figure 3: double result1 = cube_volume(2);

programming tip 5.1

Function comments explain the purpose of the function, the meaning of the parameter variables and return value, as well as any special requirements.

parameter variables hold the argument values supplied in the function call.

A recipe for a fruit pie may say to use any kind of fruit. Here, “fruit” is an example of a parameter variable. Apples and cherries are examples of arguments.

pie(fruit) pie(fruit)

cfe2_ch05_p193_248.indd 198 10/26/10 6:14 PM

5.3 parameter passing 199

Function comments

This particular documentation style is borrowed from the Java programming language. It is widely supported by C++ tools as well, for example by the Doxygen tool (www.doxygen.org).

The first line of the comment describes the purpose of the function. Each @param clause describes a parameter vari able and the @return clause describes the return value.

Consider the function call illustrated in Figure 3: double result1 = cube_volume(2);

programming tip 5.1

Function comments explain the purpose of the function, the meaning of the parameter variables and return value, as well as any special requirements.

parameter variables hold the argument values supplied in the function call.

A recipe for a fruit pie may say to use any kind of fruit. Here, “fruit” is an example of a parameter variable. Apples and cherries are examples of arguments.

pie(fruit) pie(fruit)

cfe2_ch05_p193_248.indd 199 10/26/10 6:14 PM

www.doxygen.org

200 Chapter 5 Functions

•

Figure 3 parameter passing

1 Function call result1 =

side_length =

2 Initializing function parameter variable result1 =

side_length = 2

3 About to return to the caller result1 =

side_length =

volume = 8

4 After function call result1 = 8

double result1 = cube_volume(2);

double volume = side_length * side_length * side_length; return volume;

double result1 = cube_volume(2);

The parameter variable side_length of the cube_volume function is created. 1 • The parameter variable is initialized with the value of the argument that was

passed in the call. In our case, side_length is set to 2. 2 • The function computes the expression side_length * side_length * side_length,

which has the value 8. That value is stored in the variable volume. 3 • The function returns. All of its variables are removed. The return value is trans-

ferred to the caller, that is, the function calling the cube_volume function. 4 Now consider what happens in a subsequent call cube_volume(10). A new parameter variable is created. (Recall that the previous parameter variable was removed when the first call to cube_volume returned.) It is initialized with the argument 10, and the process repeats. After the second function call is complete, its variables are again removed.

Like any other variables, parameter variables can only be set to values of compat- ible types. For exam ple, the side_length parameter variable of the cube_volume function has type double. It is valid to call cube_volume(2.0) or cube_volume(2). In the latter call, the integer 2 is automatically converted to the double value 2.0. However, a call cube_ volume("two") is not legal.

10. What does this program print? Use a diagram like Figure 3 to find the answer. double mystery(int x, int y) { double z = x + y; z = z / 2.0;

s e l F c h e c k

return z; } int main() { int a = 4; int b = 7; cout << mystery(a, b) << endl; }

11. What does this program print? Use a diagram like Figure 3 to find the answer. int mystery(int x) { int y = x * x; return y; } int main() { int a = 4; cout << mystery(a + 1) << endl; }

12. What does the following program print? Use a diagram like Figure 3 to find the answer. int mystery(int n) { n++; n++; return n; } int main() { int a = 5; cout << mystery(a) << endl; }

practice it Now you can try these exercises at the end of the chapter: R5.5, P5.10.

do not modify parameter Variables

In C++, a parameter variable is just like any other variable. You can modify the values of the parameter variables in the body of a function. For example,

int total_cents(int dollars, int cents) { cents = dollars * 100 + cents; // Modifies parameter variable return cents; }

However, many programmers find this practice confusing. It mixes the concept of a parameter (input to the func tion) with that of a variable (storage for a value). To avoid the confusion, simply introduce a separate variable:

int total_cents(int dollars, int cents) { int result = dollars * 100 + cents; return result; }

programming tip 5.2

cfe2_ch05_p193_248.indd 200 10/26/10 6:14 PM

5.3 parameter passing 201

return z; } int main() { int a = 4; int b = 7; cout << mystery(a, b) << endl; }

11. What does this program print? Use a diagram like Figure 3 to find the answer. int mystery(int x) { int y = x * x; return y; } int main() { int a = 4; cout << mystery(a + 1) << endl; }

12. What does the following program print? Use a diagram like Figure 3 to find the answer. int mystery(int n) { n++; n++; return n; } int main() { int a = 5; cout << mystery(a) << endl; }

practice it Now you can try these exercises at the end of the chapter: R5.5, P5.10.

do not modify parameter Variables

In C++, a parameter variable is just like any other variable. You can modify the values of the parameter variables in the body of a function. For example,

int total_cents(int dollars, int cents) { cents = dollars * 100 + cents; // Modifies parameter variable return cents; }

int total_cents(int dollars, int cents) { int result = dollars * 100 + cents; return result; }

programming tip 5.2

cfe2_ch05_p193_248.indd 201 10/26/10 6:14 PM

202 Chapter 5 Functions

5.4 return Values You use the return statement to specify the result of a function. When the return state- ment is processed, the function exits immediately. This behavior is convenient for handling exceptional cases at the begin ning:

double cube_volume(double side_length) { if (side_length < 0) { return 0; } double volume = side_length * side_length * side_length; return volume; }

If the function is called with a negative value for side_length, then the function returns 0 and the remain der of the function is not executed. (See Figure 4.)

In the preceding example, each return statement returned a constant or a variable. Actually, the return statement can return the value of any expression. Instead of sav- ing the return value in a variable and returning the variable, it is often possible to eliminate the variable and return a more complex expression:

double cube_volume(double side_length) { return side_length * side_length * side_length; }

It is important that every branch of a function return a value. Consider the following incorrect function:

double cube_volume(double side_length) { if (side_length >= 0) { return side_length * side_length * side_length; } // Error }

Suppose you call cube_volume with a negative value for the side length. Of course, you aren’t supposed to call that, but it might happen as the result of a coding error. Because the if condition is not true, the return statement is not executed. However, the func- tion must return something. Depending on the circumstances, the compiler might

the return statement terminates a function call and yields the function result.

side_length < 0? return 0

return volume

volume = side_length × side_length × side_length

True

False

Figure 4 A return statement exits a Function immediately

flag this as an error, or the function might return a random value. Protect against this problem by returning some safe value:

double cube_volume(double side_length) { if (side_length >= 0) { return side_length * side_length * side_length; } return 0; }

The last statement of every function ought to be a return statement. This ensures that some value gets returned when the function reaches the end.

missing return Value

A function always needs to return something. If the code of the function contains several branches, make sure that each one of them returns a value:

int sign(double x) { if (x < 0) { return -1; } if (x > 0) { return 1; } // Error: missing return value if x equals 0 }

This function computes the sign of a number: –1 for negative numbers and +1 for positive numbers. If the argument is zero, however, no value is returned. Most compilers will issue a warning in this situation, but if you ignore the warning and the function is ever called with an argument of 0, a random quantity will be returned.

Function declarations

It is a compile-time error to call a function that the compiler does not know, just as it is an error to use an undefined variable. You can avoid this error if you define all functions before they are first used. First define lower-level helper functions, then the mid-level workhorse functions, and finally main in your program.

Some programmers prefer to list the main function first in their programs. If you share that preference, you need to learn how to declare the other functions at the top of the program. A declaration of a function lists the return type, function name, and parameter variables, but it contains no body:

double cube_volume(double side_length);

This is an advertisement that promises that the function is implemented elsewhere. It is easy to distinguish declara tions from definitions: Declarations end in a semicolon, whereas defini- tions are followed by a {...} block. Declara tions are also called prototypes.

In a function prototype, the names of the parameters are optional. You could also write

double cube_volume(double);

However, it is a good idea to include parameter names in order to document the purpose of each parameter.

The declarations of common functions such as pow are contained in header files. If you have a look inside <cmath>, you will find the declaration of pow and the other math functions.

Common error 5.1

special topic 5.1

cfe2_ch05_p193_248.indd 202 10/26/10 6:14 PM

5.4 return Values 203

flag this as an error, or the function might return a random value. Protect against this problem by returning some safe value:

double cube_volume(double side_length) { if (side_length >= 0) { return side_length * side_length * side_length; } return 0; }

The last statement of every function ought to be a return statement. This ensures that some value gets returned when the function reaches the end.

missing return Value

A function always needs to return something. If the code of the function contains several branches, make sure that each one of them returns a value:

int sign(double x) { if (x < 0) { return -1; } if (x > 0) { return 1; } // Error: missing return value if x equals 0 }

Function declarations

double cube_volume(double side_length);

In a function prototype, the names of the parameters are optional. You could also write

double cube_volume(double);

However, it is a good idea to include parameter names in order to document the purpose of each parameter.

The declarations of common functions such as pow are contained in header files. If you have a look inside <cmath>, you will find the declaration of pow and the other math functions.

Common error 5.1

special topic 5.1

cfe2_ch05_p193_248.indd 203 10/26/10 6:14 PM

204 Chapter 5 Functions

Here is an alternate organization of the cube.cpp file:

#include <iostream>

using namespace std;

// Declaration of cube_volume double cube_volume(double side_length);

int main() { double result1 = cube_volume(2); // Use of cube_volume double result2 = cube_volume(10); cout << "A cube with side length 2 has volume " << result1 << endl; cout << "A cube with side length 10 has volume " << result2 << endl; return 0; }

// Definition of cube_volume double cube_volume(double side_length) { return side_length * side_length * side_length; }

If you prefer this approach, go ahead and use it in your programs. You just need to be aware of one drawback. Whenever you change the name of a function or one of the parameter types, you need to fix it in both places: in the declaration and in the definition.

step 1 Describe what the function should do.

Provide a simple English description, such as “Compute the volume of a pyramid whose base is a square.”

step 2 Determine the function’s “inputs”.

Make a list of all the parameters that can vary. It is common for beginners to implement functions that are overly specific. For example, you may know that the great pyramid of Giza, the largest of the Egyptian pyramids, has a height of 146 meters and a base length of 230 meters. You should not use these numbers in your calculation, even if the original problem only asked about the great pyramid. It is just as easy—and far more useful—to write a function that com putes the volume of any pyramid.

h o W t o 5 . 1 implementing a Function

A function is a computation that can be used multiple times with different parameters, either in the same program or in different programs. Whenever a computation is needed more than once, turn it into a function.

To illustrate this process, suppose that you are helping archaeologists who research Egyp- tian pyramids. You have taken on the task of writing a function that determines the volume of a pyramid, given its height and base length.

cfe2_ch05_p193_248.indd 204 10/26/10 6:14 PM

5.4 return Values 205

Here is an alternate organization of the cube.cpp file:

#include <iostream>

using namespace std;

// Declaration of cube_volume double cube_volume(double side_length);

// Definition of cube_volume double cube_volume(double side_length) { return side_length * side_length * side_length; }

step 1 Describe what the function should do.

Provide a simple English description, such as “Compute the volume of a pyramid whose base is a square.”

step 2 Determine the function’s “inputs”.

h o W t o 5 . 1 implementing a Function

In our case, the parameters are the pyramid’s height and base length. At this point, we have enough information to document the function:

/** Computes the volume of a pyramid whose base is a square. @param height the height of the pyramid @param base_length the length of one side of the pyramid’s base @return the volume of the pyramid */

step 3 Determine the types of the parameter variables and the return value.

The height and base length can both be floating-point numbers. Therefore, we will choose the type double for both parameter variables. The computed volume is also a floating-point num- ber, yielding a return type of double. There fore, the function will be defined as

double pyramid_volume(double height, double base_length)

step 4 Write pseudocode for obtaining the desired result.

In most cases, a function needs to carry out several steps to find the desired answer. You may need to use mathemat ical formulas, branches, or loops. Express your function in pseudocode.

An Internet search yields the fact that the volume of a pyramid is computed as

volume = 1/3 x height x base area

Since the base is a square, we have

base area = base length x base length

Using these two equations, we can compute the volume from the parameter variables.

step 5 Implement the function body.

In our example, the function body is quite simple. Note the use of the return statement to return the result.

{ double base_area = base_length * base_length; return height * base_area / 3; }

step 6 Test your function.

After implementing a function, you should test it in isolation. Such a test is called a unit test. Work out test cases by hand, and make sure that the function produces the correct results. For example, for a pyramid with height 9 and base length 10, we expect the area to be 1̸ 3 × 9 × 100 = 300. If the height is 0, we expect an area of 0.

int main() { cout << "Volume: " << pyramid_volume(9, 10) << endl; cout << "Expected: 300" cout << "Volume: " << pyramid_volume(0, 10) << endl; cout << "Expected: 0" return 0; }

The output confirms that the function worked as expected:

Volume: 300 Expected: 300 Volume: 0 Expected: 0

cfe2_ch05_p193_248.indd 205 10/26/10 6:14 PM

206 Chapter 5 Functions

5.5 Functions Without return Values Sometimes, you need to carry out a sequence of instructions that does not yield a value. If that instruction sequence occurs multiple times, you will want to package it into a function. In C++, you use the return type void to indicate the absence of a return value.

Here is a typical example. Your task is to print a string in a box, like this:

------- !Hello! -------

However, different strings can be substituted for Hello. A function for this task can be defined as follows:

void box_string(string str)

Now you develop the body of the function in the usual way, by formulating a general method for solving the task.

• Print a line that contains the - character n + 2 times, where n is the length of the string. • Print a line containing the string, surrounded with a ! to the left and right. • Print another line containing the - character n + 2 times.

Here is the function implementation: /** Prints a string in a box. @param str the string to print */ void box_string(string str) {

W o r K e D e x a M p l e 5 . 1 matching and replacing parts of a string

This Worked Example creates a function to find the first occurrence of one string in a given string and replace it with a second string.

W o r K e D e x a M p l e 5 . 2 using a debugger

In this Worked Example, you will learn how to use a debugger to find errors in a program.

A void function returns no value, but it can produce output.

use a return type of void to indicate that a function does not return a value.

Available online at www.wiley.com/college/horstmann.

cfe2_ch05_p193_248.indd 206 10/26/10 6:14 PM

www.wiley.com/college/horstmann

5.5 Functions Without return Values 207

Here is a typical example. Your task is to print a string in a box, like this:

------- !Hello! -------

However, different strings can be substituted for Hello. A function for this task can be defined as follows:

void box_string(string str)

Now you develop the body of the function in the usual way, by formulating a general method for solving the task.

Here is the function implementation: /** Prints a string in a box. @param str the string to print */ void box_string(string str) {

W o r K e D e x a M p l e 5 . 1 matching and replacing parts of a string

This Worked Example creates a function to find the first occurrence of one string in a given string and replace it with a second string.

W o r K e D e x a M p l e 5 . 2 using a debugger

In this Worked Example, you will learn how to use a debugger to find errors in a program.

A void function returns no value, but it can produce output.

use a return type of void to indicate that a function does not return a value.

int n = str.length(); for (int i = 0; i < n + 2; i++) { cout << "-"; } cout << endl; cout << "!" << str << "!" << endl; for (int i = 0; i < n + 2; i++) { cout << "-"; } cout << endl; }

Note that this function doesn’t compute any value. It performs some actions and then returns to the caller. (See the sample program ch05/box.cpp.)

Because there is no return value, you cannot use box_string in an expression. You can call

box_string("Hello");

but not result = box_string("Hello"); // Error: box_string doesn’t return a result.

If you want to return from a void function before reaching the end, you use a return statement without a value. For example,

void box_string(string str) { int n = str.length(); if (n == 0) { return; // Return immediately } ... }

13. How do you generate the following printout, using the box_string function? ------- !Hello! ------- ------- !World! -------

14. What is wrong with the following statement? cout << box_string("Hello");

15. Implement a function shout that prints a line consisting of a string followed by three exclamation marks. For example, shout("Hello") should print Hello!!!. The function should not return a value.

16. How would you modify the box_string function to leave a space around the string that is being boxed, like this: --------- ! Hello ! ---------

17. The box_string function contains the code for printing a line of - characters twice. Place that code into a separate function print_line, and use that function to sim- plify box_string. What is the code of both functions?

practice it Now you can try these exercises at the end of the chapter: R5.4, P5.24.

s e l F c h e c k

cfe2_ch05_p193_248.indd 207 10/26/10 6:14 PM

208 Chapter 5 Functions

5.6 problem solving: reusable Functions You have used many functions from the C++ standard library. These functions have been provided as a part of standard C++ so that programmers need not recreate them. Of course, the C++ library doesn’t cover every conceivable need. You will often be able to save yourself time by designing your own func tions that can be used for mul- tiple problems.

When you write nearly identical code or pseudocode multiple times, either in the same program or in separate programs, consider introducing a function. Here is a typical example of code replication:

int hours; do { cout << "Enter a value between 0 and 23: "; cin >> hours; } while (hours < 0 || hours > 23);

int minutes; do { cout << "Enter a value between 0 and 59: "; cin >> minutes; } while (minutes < 0 || minutes > 59);

This program segment reads two variables, making sure that each of them is within a certain range. It is easy to extract the common behavior into a function:

/** Prompts a user to enter a value up to a given maximum until the user provides a valid input. @param high the largest allowable input @return the value provided by the user (between 0 and high, inclusive) */ int read_int_up_to(int high) { int input; do { cout << "Enter a value between 0 and " << high << ": "; cin >> input; } while (input < 0 || input > high); return input; }

Then use this function twice: int hours = read_int_up_to(23); int minutes = read_int_up_to(59);

We have now removed the replication of the loop—it only occurs once, inside the function.

Note that the function can be reused in other programs that need to read integer values. However, we should consider the possibility that the smallest value need not always be zero.

eliminate replicated code or pseudocode by defining a function.

Here is a better alterna tive: /** Prompts a user to enter a value within a given range until the user provides a valid input. @param low the smallest allowable input @param high the largest allowable input @return the value provided by the user (between low and high, inclusive) */ int read_int_between(int low, int high) { int input; do { cout << "Enter a value between " << low << " and " << high << ": "; cin >> input; } while (input < low || input > high); return input; }

In our program, we call int hours = read_int_between(0, 23);

Another program can call int month = read_int_between(1, 12);

In general, you will want to provide parameter variables for the values that vary when a function is reused.

18. Consider the following statements: int total_pennies = static_cast<int>(100 * total + 0.5); int total_tax_pennies = static_cast<int>(100 * total * tax_rate + 0.5);

Introduce a function to reduce code duplication. 19. Consider this code that prints a page number on the left or right side of a page:

if (page % 2 == 0) { cout << page << endl; } else { cout << setw(80) << page << endl; }

Introduce a function with return type bool to make the condition in the if statement easier to under stand.

Design your functions to be reusable. supply parameter variables for the values that can vary when the function is reused.

s e l F c h e c k

cfe2_ch05_p193_248.indd 208 10/26/10 6:14 PM

5.6 problem solving: reusable Functions 209

When carrying out the same task multiple times, use a function.