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Allen B. Downey C++ Version, First Edition
How to think like a computer scientist
C++ Version, First Edition Copyright (C) 1999 Allen B. Downey
This book is an Open Source Textbook (OST). Permission is granted to reproduce, store or transmit the text of this book by any means, electrical, mechanical, or biological, in accordance with the terms of the GNU General Public License as published by the Free Software Foundation (version 2). This book is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The original form of this book is LaTeX source code. Compiling this LaTeX source has the effect of generating a device-independent representation of a textbook, which can be converted to other formats and printed. All intermediate representations (including DVI and Postscript), and all printed copies of the textbook are also covered by the GNU General Public License. The LaTeX source for this book, and more information about the Open Source Textbook project, is available from http://www.cs.colby.edu/~downey/ost or by writing to Allen B. Downey, 5850 Mayflower Hill, Waterville, ME 04901. The GNU General Public License is available from www.gnu.org or by writing to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. This book was typeset by the author using LaTeX and dvips, which are both free, open-source programs.
1 The 1.1 1.2 1.3 way of the program What is a programming language? What is a program? . . . . . . . . What is debugging? . . . . . . . . 1.3.1 Compile-time errors . . . . 1.3.2 Run-time errors . . . . . . . 1.3.3 Logic errors and semantics 1.3.4 Experimental debugging . . Formal and natural languages . . . The first program . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 3 4 4 4 4 5 5 7 8 11 11 12 13 13 14 15 16 17 17 18 18 21 21 22 23 24 24 26 27 27
1.4 1.5 1.6
2 Variables and types 2.1 More output . . . . . . . 2.2 Values . . . . . . . . . . 2.3 Variables . . . . . . . . 2.4 Assignment . . . . . . . 2.5 Outputting variables . . 2.6 Keywords . . . . . . . . 2.7 Operators . . . . . . . . 2.8 Order of operations . . . 2.9 Operators for characters 2.10 Composition . . . . . . 2.11 Glossary . . . . . . . . .
3 Function 3.1 Floating-point . . . . . . . . . . . 3.2 Converting from double to int . 3.3 Math functions . . . . . . . . . . 3.4 Composition . . . . . . . . . . . 3.5 Adding new functions . . . . . . 3.6 Definitions and uses . . . . . . . 3.7 Programs with multiple functions 3.8 Parameters and arguments . . . i
. . . . . . . . . .6 The return statement . . . . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 Local variables . . . . . . . .11 Glossary . . . . . . . . . . . . . . . . . . . . . .6 Boolean variables . . . . . . . . . . . . . . . . . . . . . . . . . .3 Alternative execution . . . . . . . . . . . . . . . 4. . . . .9 Returning from main . . . . . . 6. . . . . . . . . . . . . . . . . . . . . .11 3. . . Functions with results .7 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . 6. . .1 Return values . . . Functions with multiple parameters . . . . . . . . . . . . . . . functions . . . . . . . .12 Parameters and variables are local . . . . . . . . . . . . . . . . . . .10 More generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. . . . . . . . . . . . . . . . . . . . . . . . . . .13 Glossary . . . . . . . . . . . . .ii CONTENTS 3. . . . . . . . 6 Iteration 6. . . . . . . . . . . . . . . . . . . . 5. . . . . . . . 28 29 30 30 31 31 31 32 33 33 34 34 36 36 37 39 39 41 43 44 45 45 46 46 47 48 50 51 51 53 53 54 54 56 58 58 59 60 60 61 63 4 Conditionals and recursion 4. . . . . . .3 The while statement . . . . . . . . . . . . . 5. . . . . . . . . . . . . . . . . 6. . . . 5. . . . . . . . . . . . . . . . . .12 One more example . . . . . . . . . . . .7 Recursion . . . . . . 6. . 5. . . . . . . . . . . .11 Leap of faith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Composition . . . . . . .2 Iteration . . 5. 5. . . . . . . . . . . . . . . . . . . . . . 6. . . . . . . . . . . . . 4. . 6. . . . . . . . . . . . 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . . . . . . .4 Overloading . . . . . . 6. . . . . . . . . 5 Fruitful functions 5. . . . . . . . . . . . . 5. . . . . . .1 Multiple assignment . . . . . .8 Infinite recursion . . . . . . . . . . . . . . . .1 The modulus operator . . . . . . . . . . . . . . . . . . . . . . 4. . . .7 Logical operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 3.5 Two-dimensional tables . . . Glossary . . . . . . . .6 Encapsulation and generalization 6. . . .5 Nested conditionals . . . . . . . .8 Bool functions . . . . 5. . . . . . . . . . . . . . . . . . . . . . . . . . .4 Chained conditionals . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . 5. . . . . . . . .10 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. .10 More recursion . . . . . . . . . .8 More encapsulation . . .9 Stack diagrams for recursive 4. . .2 Program development 5. . . . . . . . . . .5 Boolean values . . . . . . . . 4. . . . . . . . . . . . . .4 Tables . . . . . . . . . . .10 3. . . . . . .2 Conditional execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. .
. . . . . . . . . 7. . . . 8. . . . 7. . . . . 65 65 66 66 67 67 68 68 69 69 70 71 72 72 73 73 74 75 75 75 76 77 78 78 79 80 82 82 83 85 87 87 88 88 88 90 90 91 92 92 93 94 95 . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 apstrings are comparable . . . . . . . . . . .2 Point objects . . . . . . . . . . . . . .5 Traversal . . .12 Glossary . . . . . . . 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. . . . . . . . . . . . . 7. . . . . . 9. 9 More structures 9. . 8. . . . . . . . . .3 Accessing instance variables . . . . . .11 Algorithms . . . . . . . . . . .7 Call by reference . . . . . . . . . . . . . . . . . . .4 Operations on structures . 7. . .9 Structures as return types . . .6 Call by value . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 apstring variables . . . . . . . . . . . . . .11 Getting user input . . .2 printTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. . . . . . . . .3 Extracting characters from a string 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. . 9. 8.16 Glossary . . 8. . . .5 const parameters . . 7. . . . . . . . . .8 Which is best? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. . . . . . . . . . . . . . . . . . . . . . . . . . . 7. . . . . . . . . . 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Other apstring functions . . . . . . . . . . . . . . . . . . . .7 Fill-in functions . . . . . . . . . . . . . . . . . . . . . . . . .1 Containers for strings . . . . . . . . . . . . . . . . . .6 Modifiers . . . . .4 Pure functions . . . . . . . . . . . . . . . . . . .10 Generalization . . . . . . . . . . . . . . . .12 apstrings are mutable . . . 9. 8. . . . . . . . . . . . . . . . . . 9. . . . . . .CONTENTS iii 7 Strings and things 7. . . . . . . . .8 Our own version of find . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 Character classification . 8. . . . . . . . . . . .7 The find function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. . . . . . . . . . 8 Structures 8. . . . . . . 7. . . 9. . . . . . . . . . . . . 7. . . . . . . 9. . . . . . planning . 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Length . . 7. . . .10 Passing other types by reference 8. . . . . . . .1 Compound values . . . . . . .8 Rectangles . .10 Increment and decrement operators 7. . . . . . . . . .1 Time . . . . . . .9 Looping and counting . . . . .6 A run-time error . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Structures as parameters . . . . . . . . . . . . . . . . . . 8. . . . . . . . . . .3 Functions for objects . . .12 Glossary . . . . . . . .9 Incremental development versus 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. . . . . . . . . . . . .11 String concatenation . . . . . . . . 8. . . . . . 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .12Random seeds . . . . . . . . . . . . . . . . . . . . .3 The printCard function 12. . . . . . . . . . . . . . . . . . . . . 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Yet another example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Vector of random numbers 10.6 Vectors of cards . . .13Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. . . . . .10Header files . . . . . . . . . . . . . . 11. . . . . . . . . . . . . . . .4 Another example . . . . . . . . .6 A more complicated example 11. . . 10. . . . . . . . . . . . . . . . . . . . . . 12. . . . . . . . . . . . . . . . . . . . .4 The equals function . . . . . . . . . . . . 97 98 99 99 100 100 102 102 103 104 105 105 106 106 109 109 110 111 112 113 113 114 115 115 116 119 121 121 121 123 125 126 127 129 129 130 133 133 135 135 136 138 139 11 Member functions 11. . . . 12 Vectors of Objects 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 switch statement . . .8 Initialize or construct? . 12. . . . . . . . . . 11. . 12. . . . . . . 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Objects and functions . . .3 Decks . . . . . . . . . . . . . . . . . . . . 11. . . . . . . . . . . . 10. . . . . . . . . . . . .9 Bisection search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Random numbers . . . . . . . . .4 Another constructor . . . . . . . . 11. . . . . . . .11Glossary . . . . . . . . 12. . . . . . .3 Implicit variable access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 for loops . . . . . .7 The printDeck function 12. . . . . . . . . . . 11. . . . . . . . . . . . . . . . .iv CONTENTS 10 Vectors 10.9 One last example . 10. . . . . . . 11. . . . . . . . . . . . . . . 12. . . 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 The isGreater function 12. . . . . . . . . . . . . . . . . . . .10A histogram . . . . . . . . . . . . .1 Enumerated types . . .8 Searching . . .2 Card objects . . . . . . . . . . . . 10. . . . . . . . . . . . . 13 Objects of Vectors 13. . . . . . . . . . . . . . . .4 Vector length . . . . . . . . . . . . . . . . . . . . . 10. . . . . . . . 11. . . . . .10Decks and subdecks . . . . . . . .2 Copying vectors . . . . .9 Checking the other values 10. . . . . . . . . .11A single-pass solution . . . . . . . . . . 10. . . . . . . . . . . . . . . . . . . . . . . . 10. . . . . 13. . . . . . . . . . . . .8 Counting . . . . . . . . . . . .1 Accessing elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Constructors . . . . . . .2 print . . . . . . . .11Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. . . . . . . . . . 10. . . . . . . . 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Statistics . . 13. 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Shuffling . . . . 175 . . . . . . . . . . . . . . . . . . . . . . . . . . 173 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . classes 173 . . . . . . . . . . . . . . . . . . . . . . . . 15. . . . . . . . . . . .1 Private data and classes . . . . . . . . . . . . 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Output . . . . . . . . . . . . . . . . . . . 14. . . . . . . . 14. . . . . .2 File input . . . . . . . . . . . . . . . . . . . . . . . . . . . 15. . . . . .7 Another function on Complex numbers 14. . . . . . . . . . . .4 Parsing input . . . . . . . .2 apvector . . . . . . . . . . . . . . . . . .3 apmatrix . . . . . .11Glossary . . . . . . . . . . . . . . . . . . .5 Parsing numbers . . .CONTENTS v 13. . . . . . . . . . 174 . . . . . . . . . . . . . . . . 15. . . . . . . . . . . .1 Streams . . . . . . . . . . . . . . . . . . . . . . . . 13. . . . . . . . . 13. 15. . . . 14. . . . . . . .3 Complex numbers . . . . . . . . . . . . . . 15. . . 15 File Input/Output and apmatrixes 15. . . . . . . . . . . . . . . . . . . A Quick reference for AP A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Sorting . . A. . . . . . 14. . . . . . . . . . . . . . .6 The Set data structure . .3 File output . . . . . . . . . . . . . . .1 apstring . 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. . . . . . . . . . . . .10Glossary . . . . . .9 A proper distance matrix . . .9 Preconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 Invariants . . . . . . . . . .8 Subdecks . . . . . . . . 14. . . . . . . . . . . .10Mergesort . . . . .8 A distance matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. . . . . . . . . .10Private functions . . . . . . . . . . . . . . . . . A. . . . . .9 Shuffling and dealing . . . . . . . . . . . . . . . . . . . . . . . . . . . 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Deck member functions 13. . . . . . . . . . . . . . . . . . . . . . . . . .7 apmatrix . . . . . 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 A function on Complex numbers .11Glossary . . . . . . . . . . . . . . 15. . . . . . . . . . . . . . . .2 What is a class? . . . . . . . . . . . . . . . 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. . . . . . . .4 Accessor functions . . 13. 13. . . . 139 141 141 142 143 143 145 147 147 148 149 151 152 153 153 154 155 157 158 159 159 160 161 161 163 164 167 168 169 171 14 Classes and invariants 14. . . . . . . . . . . . . .
vi CONTENTS .
Like engineers. they observe the behavior of complex systems. As you might infer from the name "high-level language. That's why this chapter is called "The way of the program. form hypotheses. assembling components into systems and evaluating tradeoffs among alternatives. though. which is a 1 . On the other hand. the exam used Pascal. along with the details of programming in C++. Like scientists. We may not take the most direct approach to that goal. you will have all the tools you need to do well on the exam. For example. sometimes referred to as machine language or assembly language.1 What is a programming language? The programming language you will be learning is C++. As it turns out.Chapter 1 The way of the program The goal of this book is to teach you to think like a computer scientist. the process of learning to program is an excellent opportunity to practice problem-solving skills. Loosely-speaking. Before that. 1. they design things. computers can only execute programs written in low-level languages. programs written in a high-level language have to be translated before they can run." Of course. if you understand the concepts in this book. Like mathematicians. This translation takes some time. I like the way computer scientists think because they combine some of the best features of Mathematics. C and FORTRAN. Both C++ and Pascal are high-level languages. and test predictions. Engineering. and express a solution clearly and accurately. there are not many exercises in this book that are similar to the AP questions. because that is the language the AP exam is based on. think creatively about solutions." there are also low-level languages. and Natural Science. computer scientists use formal languages to denote ideas (specifically computations). the other goal of this book is to prepare you for the Computer Science AP Exam. as of 1998. other high-level languages you might have heard of are Java. Thus. By that I mean the ability to formulate problems. The single most important skill for a computer scientist is problem-solving.
and the translated program is called the object code or the executable. . and it's more likely to be correct. almost all programs are written in high-level languages.2 CHAPTER 1. You might use a text editor to write the program (a text editor is a simple word processor). and have to be rewritten to run on another. high-level languages are portable. by "easier" I mean that the program takes less time to write. When the program is finished. But the advantages are enormous. it translates the program line-by-line. it's shorter and easier to read.o to contain the object code. source code interpreter The interpreter reads the source code. THE WAY OF THE PROGRAM small disadvantage of high-level languages.exe to contain the executable. Then.cpp. The compiler would read your source code.. depending on what your programming environment is like. and create a new file named program. In this case. Often you compile the program as a separate step. before executing any of the commands. As an example. There are two ways to translate a program. A compiler is a program that reads a high-level program and translates it all at once. meaning that they can run on different kinds of computers with few or no modifications. First. In effect. where "program" is an arbitrary name you make up. . you might leave the text editor and run the compiler.cpp is a convention that indicates that the file contains C++ source code. translate it. interpreting or compiling. Due to these advantages. suppose you write a program in C++... the high-level program is called the source code. and the suffix .. An interpreter is a program that reads a high-level program and does what it says. alternately reading lines and carrying out commands. and then execute the compiled code later. you might save it in a file named program. Low-level languages are only used for a few special applications. it is much easier to program in a high-level language. or program. Low-level programs can only run on one kind of computer. and the result appears on the screen. Secondly.
complex task up into smaller and smaller subtasks until eventually the subtasks are simple enough to be performed with one of these simple functions. You execute the program (one way or another). or statements) look different in different programming languages. no matter how complicated. testing: Check for certain conditions and execute the appropriate sequence of statements. the good news is that in most programming environments (sometimes called development environments).2. math: Perform basic mathematical operations like addition and multiplication. The next step is to run the program... which requires some kind of executor. output: Display data on the screen or send data to a file or other device.. Usually you will only have to write a program and type a single command to compile and run it. Believe it or not. repetition: Perform some action repeatedly. that's pretty much all there is to it. or some other device. 1.. and the result appears on the screen. . Thus. these steps are automated for you. and generates object code. or a file.1. like solving a system of equations or finding the roots of a polynomial.. . The role of the executor is to load the program (copy it from disk into memory) and make the computer start executing the program. .2 What is a program? A program is a sequence of instructions that specifies how to perform a computation. The instructions (or commands. usually with some variation.. it is useful to know what the steps are that are happening in the background. is made up of functions that look more or less like these. so that if something goes wrong you can figure out what it is. On the other hand. Every program you've ever used. Although this process may seem complicated.. WHAT IS A PROGRAM? 3 source code compiler object code executor The compiler reads the source code.. like searching and replacing text in a document or (strangely enough) compiling a program. but there are a few basic functions that appear in just about every language: input: Get data from the keyboard. The computation might be something mathematical. one way to describe programming is the process of breaking a large. but it can also be a symbolic computation.
since it requires you to work backwards by looking at the output of the program and trying to figure out what it is doing. For example. 1. you will probably spend a lot of time tracking down syntax errors. but it will not do the right thing.3. so it might be a little while before you encounter one. run-time errors are rare. For the simple sorts of programs we will be writing for the next few weeks. THE WAY OF THE PROGRAM 1.3 What is debugging? Programming is a complex process.3 Logic errors and semantics The third type of error is the logical or semantic error. So does this one For most readers.2 Run-time errors The second type of error is a run-time error. a sentence must begin with a capital letter and end with a period.3. Identifying logical errors can be tricky. Compilers are not so forgiving. For whimsical reasons. in the sense that the computer will not generate any error messages. 1. so-called because the error does not appear until you run the program. There are a few different kinds of errors that can occur in a program. The problem is that the program you wrote is not the program you wanted to write. though. it will do what you told it to do. To make matters worse. the compilation fails and you will not be able to run your program.3. this sentence contains a syntax error. there are more syntax rules in C++ than there are in English. 1. in English. and the error messages you get from the compiler are often not very helpful. the compiler will print an error message and quit. it will compile and run successfully. During the first few weeks of your programming career. Syntax refers to the structure of your program and the rules about that structure. you will make fewer errors and find them faster. and since it is done by human beings. As you gain experience. a few syntax errors are not a significant problem. and it is useful to distinguish between them in order to track them down more quickly. Specifically. it often leads to errors. It will do something else. and you will not be able to run your program. If there is a logical error in your program. programming errors are called bugs and the process of tracking them down and correcting them is called debugging. which is why we can read the poetry of e e cummings without spewing error messages. .1 Compile-time errors The compiler can only translate a program if the program is syntactically correct.4 CHAPTER 1. If there is a single syntax error anywhere in your program. otherwise. The meaning of the program (its semantics) is wrong.
formal languages tend to have strict rules about syntax. . "One of Linus's earlier projects was a program that would switch between printing AAAA and BBBB. however improbable. If your hypothesis was wrong." (from A.3. and you take a step closer to a working program. 3+3 = 6 is a syntactically correct mathematical statement. debugging them as you go. As Sherlock Holmes pointed out. Debugging is also like an experimental science. In later chapters I will make more suggestions about debugging and other programming practices. but it started out as a simple program Linus Torvalds used to explore the Intel 80386 chip. According to Larry Greenfield. For example. so that you always have a working program. and make small modifications. Once you have an idea what is going wrong. programming is the process of gradually debugging a program until it does what you want. like English. programming and debugging are the same thing. 1. and French. must be the truth. you modify your program and try again. For example. As I mentioned before. They were not designed by people (although people try to impose some order on them). challenging. whatever remains. but 2 Zz is not.4 Experimental debugging One of the most important skills you should acquire from working with this book is debugging. Conan Doyle's The Sign of Four). Linux is an operating system that contains thousands of lines of code. Chemists use a formal language to represent the chemical structure of molecules.4. You are confronted with clues and you have to infer the processes and events that lead to the results you see.4 Formal and natural languages Natural languages are the languages that people speak. you have to come up with a new one. That is. For example. H2 O is a syntactically correct chemical name. and interesting parts of programming. And most importantly: Programming languages are formal languages that have been designed to express computations. Also. In some ways debugging is like detective work. debugging is one of the most intellectually rich. then you can predict the result of the modification.1. but 3 = +6$ is not. they evolved naturally. If your hypothesis was correct. The idea is that you should always start with a working program that does something. the notation that mathematicians use is a formal language that is particularly good at denoting relationships among numbers and symbols. Although it can be frustrating. Formal languages are languages that are designed by people for specific applications. "When you have eliminated the impossible. This later evolved to Linux" (from The Linux Users' Guide Beta Version 1). Spanish. For some people. FORMAL AND NATURAL LANGUAGES 5 1.
which means that any statement has exactly one meaning. redundancy: In order to make up for ambiguity and reduce misunderstandings." you understand that "the other shoe" is the subject and "fell" is the verb. People who grow up speaking a natural language (everyone) often have a hard time adjusting to formal languages. regardless of context. syntax and semantics—there are many differences. . 2 Zz is not legal because there is no element with the abbreviation Zz. and what it means to fall. structure. that is. Although formal and natural languages have many features in common— tokens. you have to figure out what the structure of the sentence is (although in a natural language you do this unconsciously). natural languages employ lots of redundancy. that is. Formal languages mean exactly what they say. they are often verbose. ambiguity: Natural languages are full of ambiguity. Similarly. when you hear the sentence. As a result. which people deal with by using contextual clues and other information. but more so: Poetry: Words are used for their sounds as well as for their meaning. When you read a sentence in English or a statement in a formal language. In some ways the difference between formal and natural language is like the difference between poetry and prose. The statement 3=+6$ is structurally illegal. The second type of syntax error pertains to the structure of a statement. like words and numbers and chemical elements. THE WAY OF THE PROGRAM Syntax rules come in two flavors. molecular formulas have to have subscripts after the element name. Ambiguity is not only common but often deliberate. Prose: The literal meaning of words is more important and the structure contributes more meaning. you can figure out what it means. Prose is more amenable to analysis than poetry. the way the tokens are arranged. Tokens are the basic elements of the language. Formal languages are less redundant and more concise. because you can't have a plus sign immediately after an equals sign. One of the problems with 3=+6$ is that $ is not a legal token in mathematics (at least as far as I know). Formal languages are designed to be nearly or completely unambiguous. "The other shoe fell." there is probably no shoe and nothing falling. This process is called parsing. Similarly. not before. Assuming that you know what a shoe is. "The other shoe fell. and can be understood entirely by analysis of the tokens and structure. If I say. the semantics of the sentence. literalness: Natural languages are full of idiom and metaphor. but still often ambiguous.6 CHAPTER 1. pertaining to tokens and structure. you will understand the general implication of this sentence. Programs: The meaning of a computer program is unambiguous and literal. Once you have parsed a sentence. For example. and the whole poem together creates an effect or emotional response.
. and then it quits. this simple program contains several features that are hard to explain to beginning programmers. which indicates that it is a comment.5. Little things like spelling errors and bad punctuation. can make a big difference in a formal language. usually to explain what the program does. which you can get away with in natural languages. learn to parse the program in your head. When the compiler sees a //. so it is usually not a good idea to read from top to bottom. THE FIRST PROGRAM 7 Here are some suggestions for reading programs (and other formal languages). When the program runs. the structure is very important. until it gets to the last statement. meaning that it outputs or displays a message on the screen. remember that formal languages are much more dense than natural languages. C++ does reasonably well. this program looks like this: #include <iostream. First. main is a special name that indicates the place in the program where execution begins. return 0 } Some people judge the quality of a programming language by the simplicity of the "Hello. Instead. remember that the details matter. in order." program. like the first line. but the example contains only one. It is a basic output statement. cout is a special object provided by the system to allow you to send output to the screen. so it takes longer to read them. 1. left to right. Also. it starts by executing the first statement in main and it continues." because all it does is print the words "Hello. The second line begins with //. World. World. Finally. world.5 The first program Traditionally the first program people write in a new language is called "Hello. By this standard." In C++. There is no limit to the number of statements that can be in main. The symbol << is an operator that you apply to cout and a string. it ignores everything from there until the end of the line. we will ignore some of them. you can ignore the word void for now. but notice the word main.1. In the third line.h> // main: generate some simple output void main () { cout << "Hello. and that causes the string to be displayed. Even so. identifying the tokens and interpreting the structure." << endl. World. A comment is a bit of English text that you can put in the middle of a program. For now.
high-level language: A programming language like C++ that is designed to be easy for humans to read and write. modify it in various ways and see what happens. A more friendly compiler might say something like: "On line 1 of the source code file named hello. Nevertheless. indicating that it is inside the definition of main. I didn't find anything with that name.6 Glossary problem-solving: The process of formulating a problem. The next time you output something. try to remember what the message says and what caused it. For example. Is that what you meant.h. Like all statements. which helps to show visually which lines are inside the definition.cpp). by any chance?" Unfortunately. . C++ uses squiggly-braces ({ and }) to group things together.). 1. chances are that it will not compile successfully. It will take some time to gain facility at interpreting compiler messages. the output statement is enclosed in squiggly-braces. so if you see it again in the future you will know what it means. As I mentioned. but I did find something named iostream.h. the new text appears on the next line. If you make any errors when you type in the program. but from now on in this book I will assume that you know how to do it. you tried to include a header file named oistream. Starting with a working program (like hello. you might get an error message like the following: hello. In this case. the output statement ends with a semi-colon (. THE WAY OF THE PROGRAM endl is a special symbol that represents the end of a line. few compilers are so accomodating.h: No such file or directory There is a lot of information on this line. and expressing the solution. There are a few other things you should notice about the syntax of this program. but it is presented in a dense format that is not easy to interpret. and in most cases the error message you get will be only a hint about what is wrong. the compiler can be a useful tool for learning the syntax rules of a language.8 CHAPTER 1. Also. notice that the statement is indented. it causes the cursor to move to the next line of the display.cpp:1: oistream. The details of how to do that depend on your programming environment. finding a solution. the C++ compiler is a real stickler for syntax. The compiler is not really very smart. When you send an endl to cout. If you get an error message. if you misspell iostream.cpp. First. At this point it would be a good idea to sit down in front of a computer and compile and run this program.
debugging: The process of finding and removing any of the three kinds of errors. in preparation for later execution. interpret: To execute a program in a high-level language by translating it one line at a time. semantics: The meaning of a program. Also called "machine language" or "assembly language. before being compiled. algorithm: A general process for solving a category of problems. All programming languages are formal languages. object code: The output of the compiler. bug: An error in a program. logical error: An error in a program that makes it do something other than what the programmer intended. source code: A program in a high-level language.6.1." portability: A property of a program that can run on more than one kind of computer. formal language: Any of the languages people have designed for specific purposes. GLOSSARY 9 low-level language: A programming language that is designed to be easy for a computer to execute. compile: To translate a program in a high-level language into a low-level language. run-time error: An error in a program that makes it fail at run-time. after translating the program. executable: Another name for object code that is ready to be executed. syntax error: An error in a program that makes it impossible to parse (and therefore impossible to compile). like representing mathematical ideas or computer programs. natural language: Any of the languages people speak that have evolved naturally. all at once. . parse: To examine a program and analyze the syntactic structure. syntax: The structure of a program.
Often it is useful to display the output from multiple output statements all on one line. The phrases that appear in quotation marks are called strings. it is legal to put comments at the end of a line. you can put as many statements as you want in main. cout << "cruel world!" << endl. ". to output more than one line: #include <iostream.1 More output As I mentioned in the last chapter. Actually. punctuation marks. } // output one line // output another As you can see. strings can contain any combination of letters. cruel world!. You can do this by leaving out the first endl: void main () { cout << "Goodbye. numbers." << endl. } In this case the output appears on a single line as Goodbye. as well as on a line by themselves." and the second 11 . and other special characters. For example. because they are made up of a sequence (string) of letters. Notice that there is a space between the word "Goodbye.Chapter 2 Variables and types 2.h> // main: generate some simple output void main () { cout << "Hello. cout << "How are you?" << endl. world.
making it easier to read the program and locate syntax errors.2 Values A value is one of the fundamental things—like a letter or a number—that a program manipulates. like 'a' or '5'.12 CHAPTER 2. You can output character values the same way: cout << '}' << endl. too. For example. You (and the compiler) can identify string values because they are enclosed in quotation marks. ".". An integer is a whole number like 1 or 17. '5' and 5. ". There are other kinds of values. including integers and characters. VARIABLES AND TYPES quotation mark.cout<<"cruel world!"<<endl. The reason this distinction is important should become clear soon. This space appears in the output. world. although you have probably noticed that the program is getting harder and harder to read. the second is a character and the third is an integer. } This program would compile and run just as well as the original. it should be clear that the first is a string. . This example outputs a single close squiggly-brace on a line by itself. so I could have written: void main(){cout<<"Goodbye. A character value is a letter or digit or punctuation mark enclosed in single quotes.} That would work. The only values we have manipulated so far are the string values we have been outputting. Spaces that appear outside of quotation marks generally do not affect the behavior of the program. You can output integer values the same way you output strings: cout << 17 << endl. The breaks at the ends of lines (newlines) do not affect the program's behavior either. Newlines and spaces are useful for organizing your program visually. but if you pay attention to the punctuation. like "Hello. I could have written: void main () { cout<<"Goodbye. 2. cout<<"cruel world!"<<endl. It is easy to confuse different types of values. like "5". so it affects the behavior of the program.
if you saw these variable declarations: char firstLetter. we would like to store values in them. For example. character. you have to declare what type it is. you could probably make a good guess at what values would be stored in them. there are different types of variables. the syntax is int bob. you will want to make up variable names that indicate what you plan to do with the variable. and it should come as no surprise that int variables can store integers. For example. minute. . hour = 11. etc.3 Variables One of the most powerful features of a programming language is the ability to manipulate variables. where bob is the arbitrary name you made up for the variable. // give firstLetter the value 'a' // assign the value 11 to hour // set minute to 59 This example shows three assignments.4 Assignment Now that we have created some variables. A variable is a named location that stores a value. Just as there are different types of values (integer. This kind of statement is called a declaration. but we are going to skip that for now (see Chapter 7). 2. A char variable can contain characters.3. This example also demonstrates the syntax for declaring multiple variables with the same type: hour and minute are both integers (int type). There are several types in C++ that can store string values. firstLetter = 'a'. We do that with an assignment statement.2. The following statement creates a new variable named fred that has type char. The vocabulary can be confusing here. To create an integer variable. char lastLetter. the character type in C++ is called char. VARIABLES 13 2. The type of a variable determines what kind of values it can store. but the idea is straightforward: • When you declare a variable. minute = 59. In general. you create a named storage location. and the comments show three different ways people sometimes talk about assignment statements.). int hour. When you create a new variable. char fred.
// WRONG !! This rule is sometimes a source of confusion. char colon. cout << "The current time is ". is not the same thing as the number 123. you give it a value. For example. hour = "Hello. int hour. VARIABLES AND TYPES • When you make an assignment to a variable. . and C++ sometimes converts things automatically.14 CHAPTER 2. A common way to represent variables on paper is to draw a box with the name of the variable on the outside and the value of the variable on the inside. These shapes should help remind you that one of the rules in C++ is that a variable has to have the same type as the value you assign it. you cannot store a string in an int variable. // WRONG! 2. minute. which is made up of the characters 1. For example. 2 and 3. hour = 11. int hour. This assignment is illegal: minute = "59". The following statement generates a compiler error. but they are not. colon = ':'. minute = 59. because there are many ways that you can convert values from one type to another. Another source of confusion is that some strings look like integers. This kind of figure is called a state diagram because is shows what state each of the variables is in (you can think of it as the variable's "state of mind"). This diagram shows the effect of the three assignment statements: firstLetter hour minute 'a' 11 59 I sometimes use different shapes to indicate different variable types.". But for now you should remember that as a general rule variables and values have the same type.5 Outputting variables You can output the value of a variable using the same commands we used to output simple values. the string "123". and we'll talk about special cases later.
It assigns appropriate values to each of the variables and then uses a series of output statements to generate the following: The current time is 11:59 When we talk about "outputting a variable.ansi. For example: cout << "hour". The complete list of keywords is included in the C++ Standard. I said that you can make up any name you want for your variables. which is the official language definition adopted by the the International Organization for Standardization (ISO) on September 1. These words. two integers. and a character variable named colon. KEYWORDS 15 cout cout cout cout << << << << hour. If you type a variable name and it turns blue.6 Keywords A few sections ago.org/ Rather than memorize the list. This program creates two integer variables named hour and minute. cout << "The current time is " << hour << colon << minute << endl. minute. Very impressive! 2. void. strings red. colon. minute = 59." we mean outputting the value of the variable. you have to put it in quotes.6. it will get confused. this program outputs a string. As we have seen before. On one line. colon = ':'. and other code black. As you type. but that's not quite true. There are certain words that are reserved in C++ because they are used by the compiler to parse the structure of your program. . a character. You can download a copy electronically from http://www. endl and many more. char. different parts of your program should appear in different colors. and if you use them as variable names. you can include more than one value in a single output statement.2. called keywords. and the special value endl. I would suggest that you take advantage of a feature provided in many development environments: code highlighting. which can make the previous program more concise: int hour. endl. char colon. watch out! You might get some strange behavior from the compiler. include int. For example. 1998. minute. hour = 11. To output the name of a variable. keywords might be blue.
For example. because they are common mathematical symbols. not 0. and by definition integer division always rounds down. When both of the operands are integers (operands are the things operators operate on). hour = 11. In order to get an even more accurate answer. VARIABLES AND TYPES 2. Addition. cout << "Fraction of the hour that has passed: ". called floating-point. The value of the variable minute is 59. but the second line is odd. even in cases like this where the next integer is so close. cout << minute*100/60 << endl. that is capable of storing fractional values. we could use a different type of variable. cout << "Number of minutes since midnight: ". would generate the following output: Number of minutes since midnight: 719 Fraction of the hour that has passed: 0 The first line is what we expected. In each case the name of the variable is replaced with its value before the computation is performed. The following are all legal C++ expressions whose meaning is more or less obvious: 1+1 hour-1 hour*60 + minute minute/60 Expressions can contain both variables names and integer values. the operator for adding two integers is +. cout << hour*60 + minute << endl.7 Operators Operators are special symbols that are used to represent simple computations like addition and multiplication. the result must also be an integer. The result is: Percentage of the hour that has passed: 98 Again the result is rounded down. minute = 59. . cout << minute/60 << endl. The reason for the discrepancy is that C++ is performing integer division.98333. the following program: int hour. A possible alternative in this case is to calculate a percentage rather than a fraction: cout << "Percentage of the hour that has passed: ". Most of the operators in C++ do exactly what you would expect them to do.16 CHAPTER 2. For example. subtraction and multiplication all do what you expect. but you might be surprised by division. but at least now the answer is approximately correct. and 59 divided by 60 is 0. minute. We'll get to that in the next chapter.
the result would be 59*1 which is 59. A complete explanation of precedence can get complicated.8. 2. number = 'a'. as in (minute * 100) / 60. cout << number << endl. Automatic type conversion is an example of a common problem in designing a programming language. If the operations had gone from right to left.2. but that is not completely true. . which is the number that is used internally by C++ to represent the letter 'a'. So in the expression minute*100/60. the multiplication happens first. but just to get you started: • Multiplication and division happen before addition and subtraction. • Any time you want to override the rules of precedence (or you are not sure what they are) you can use parentheses. char letter. which is that there is a conflict between formalism. You can also use parentheses to make an expression easier to read. So 2*3-1 yields 5. The result is 97. int number. yielding 5900/60. ORDER OF OPERATIONS 17 2. • If the operators have the same precedence they are evaluated from left to right.8 Order of operations When more than one operator appears in an expression the order of evaluation depends on the rules of precedence. and 2/3-1 yields -1. not 1 (remember that in integer division 2/3 is 0). which is wrong. Earlier I said that you can only assign integer values to integer variables and character values to character variables. C++ converts automatically between types. so 2 * (3-1) is 4. However. which in turn yields 98. cout << letter << endl. outputs the letter b. it is almost never useful to do it. it is generally a good idea to treat characters as characters. even though it doesn't change the result. and only convert from one to the other if there is a good reason. letter = 'a' + 1. the following is legal. For example. not 4. the same mathematical operations that work on integers also work on characters. and integers as integers. For example. Expressions in parentheses are evaluated first. Although it is syntactically legal to multiply characters. In some cases.9 Operators for characters Interestingly.
and convenience. without talking about how to combine them." since in reality the multiplication has to happen before the output. One of the most useful features of programming languages is their ability to take small building blocks and compose them. More often than not. most notably. . So the following is illegal: minute+1 = hour. which is usually good for expert programmers. and variables. Actually.11 Glossary variable: A named storage location for values. VARIABLES AND TYPES which is the requirement that formal languages should have simple rules with few exceptions. it turns out we can do both at the same time: cout << 17 * 3. For example. We've already seen one example: cout << hour*60 + minute << endl. All variables have a type. not an expression. 2. which is the requirement that programming languages be easy to use in practice. we know how to multiply integers and we know how to output values. I shouldn't say "at the same time. who are spared from rigorous but unwieldy formalism. characters. In this book I have tried to simplify things by emphasizing the rules and omitting many of the exceptions. who are often baffled by the complexity of the rules and the number of exceptions.18 CHAPTER 2. This ability may not seem so impressive now. convenience wins. can be used inside an output statement. That's because the left side indicates the storage location where the result will go. and statements—in isolation. but we will see other examples where composition makes it possible to express complex computations neatly and concisely. only values. but the point is that any expression.10 Composition So far we have looked at the elements of a programming language—variables. expressions. percentage = (minute * 100) / 60. You can also put arbitrary expressions on the right-hand side of an assignment statement: int percentage. 2. the left-hand side of an assignment statement has to be a variable name. involving numbers.. WARNING: There are limits on where you can use certain expressions. which determines which values it can store. but bad for beginning programmers. Expressions do not represent storage locations.
2. operators and values that represents a single result value. So far. and output statements. Examples we have seen include int. expression: A combination of variables. . assignment: A statement that assigns a value to a variable. or other thing that can be stored in a variable. operator: A special symbol that represents a simple computation like addition or multiplication. precedence: The order in which operations are evaluated. statement: A line of code that represents a command or action. composition: The ability to combine simple expressions and statements into compound statements and expressions in order to represent complex computations concisely. the statements we have seen are declarations. operand: One of the values on which an operator operates. Expressions also have types.11. or number. void and endl. type: A set of values. as determined by their operators and operands. GLOSSARY 19 value: A letter. assignments. The types we have seen are integers (int in C++) and characters (char in C++). declaration: A statement that creates a new variable and determines its type. keyword: A reserved word that is used by the compiler to parse programs.
even though they seem to be the same number. We worked around the problem by measuring percentages instead of fractions. Although floating-point numbers are useful. It is also legal to declare a variable and assign a value to it at the same time: int x = 1. is that an integer. if you have the value 1. For example. the following is illegal int x = 1. They belong to different types. In this book we will use doubles exclusively. this syntax is quite common. called float and double. and strictly speaking. pi = 3.1 Floating-point In the last chapter we had some problems dealing with numbers that were not integers.1. which can represent fractions as well as integers. In C++. they are often a source of confusion because there seems to be an overlap between integers and floating-point numbers. there are two floating-point types. you are not allowed to make assignments between types.14159. In fact. String empty = "". For example. a floatingpoint number.14159.0. or both? Strictly speaking. but a more general solution is to use floating-point numbers. For example: double pi. You can create floating-point variables and assign values to them using the same syntax we used for the other types. A combined declaration and assignment is sometimes called an initialization.Chapter 3 Function 3. 21 . C++ distinguishes the integer value 1 from the floatingpoint value 1. double pi = 3.
.99999999.0. int x = int (pi). This sets y to 0. On the other hand. The reason is that the expression on the right appears to be the ratio of two integers. so x gets the value 3. which yields the integer value 0. for example: double y = 1 / 3. C++ converts ints to doubles automatically if necessary. 3. should technically not be legal.22 CHAPTER 3.2 Converting from double to int As I mentioned. For example. This leniency is convenient. most processors have special hardware just for performing floating-point operations. as the programmer. not throwing). especially because there are places where C++ automatically converts from one type to another. because no information is lost in the translation. The syntax for typecasting is like the syntax for a function call. going from a double to an int requires rounding off. Converted to floating-point. For every type in C++. The simplest way to convert a floating-point value to an integer is to use a typecast.333333. as expected. which is a legal floating-point value. subtraction. so C++ does integer division.0 / 3. One way to solve this problem (once you figure out what it is) is to make the right-hand side a floating-point expression: double y = 1. But it is easy to forget this rule.333333. there is a corresponding function that typecasts its argument to the appropriate type. double y = 1.14159. For example: double pi = 3. although you might be interested to know that the underlying mechanism is completely different. are aware of the loss of the fractional part of the number. C++ doesn't perform this operation automatically. but it can cause problems. Typecasting is so called because it allows you to take a value that belongs to one type and "cast" it into another type (in the sense of molding or reforming. but in fact it will get the value 0. FUNCTION because the variable on the left is an int and the value on the right is a double. The int function returns an integer. the result is 0. in order to make sure that you. Converting to an integer always rounds down. and division—work on floating-point values. even if the fraction part is 0.0.0. In fact. but C++ allows it by converting the int to a double automatically. You might expect the variable y to be given the value 0. All the operations we have seen—addition. multiplication.
and so on. There is also a function called log10 that takes logarithms base 10. double degrees = 90. Similarly. in the "Hello. Then you can evaluate the function itself. π/2 is approximately 1.0).3. because the cosine of π is -1.h> . then evaluate the function. world!" program we included a header file named iostream. Header files contain information the compiler needs about functions that are defined outside your program.5. tan) are in radians.0.h contains information about input and output (I/O) streams. First we evaluate the argument of the innermost function. MATH FUNCTIONS 23 3.h using an include statement: #include <iostream. C++ assumes that the values you use with sin and the other trigonometric functions (cos. and 1/x is 0. For example. you evaluate the expression in parentheses.1 (if x happens to be 10).3. The first example sets log to the logarithm of 17. double angle = degrees * 2 * pi / 360. including the object named cout. which is called the argument of the function.1 is -1 (assuming that log indicates the logarithm base 10). The arccosine (or inverse cosine) of -1 is π. double height = sin (angle).h> iostream.3 Math functions In mathematics. If you don't happen to know π to 15 digits. and the log of 0. you can divide by 360 and multiply by 2π. For example. double pi = acos(-1. To convert from degrees to radians. and you have learned to evaluate expressions like sin(π/2) and log(1/x). you have probably seen functions like sin and log. First. either by looking it up in a table or by performing various computations.571 is 1. base e.571. the math header file contains information about the math functions.0). The second example finds the sine of the value of the variable angle. you have to include the math header file. The math functions are invoked using a syntax that is similar to mathematical notation: double log = log (17. C++ provides a set of built-in functions that includes most of the mathematical operations you can think of.h: #include <math. The sin of 1. double angle = 1. you can calculate it using the acos function. You can include it at the beginning of your program along with iostream. Before you can use any of the math functions. This process can be applied repeatedly to evaluate more complicated expressions like log(1/ sin(π/2)).
You can also take the result of one function and pass it as an argument to another: double x = exp (log (10. meaning that you use one expression as part of another. The first couple of functions we are going to write also have no parameters. For example. I hope you know what it is. if any. This statement finds the log base e of 10 and then raises e to that power. The list of parameters specifies what information. so the syntax looks like this: void newLine () { cout << endl.0)).24 CHAPTER 3. which outputs a newline character. we have already seen one function definition: main.4 Composition Just as with mathematical functions. but it is also possible to add new functions. you have to provide in order to use (or call) the new function. } This function is named newLine. except that you can't call it main or any other C++ keyword. The function named main is special because it indicates where the execution of the program begins. represented by the special value endl. as indicated by the empty parentheses () in it's definition. FUNCTION 3. it contains only a single statement. divides it by two and adds the result to the value of angle. This statement takes the value of pi. C++ functions can be composed.5 Adding new functions So far we have only been using the functions that are built into C++. you can use any expression as an argument to a function: double x = cos (angle + pi/2). 3. The sum is then passed as an argument to the cos function. Actually. but the syntax for main is the same as for any other function definition: void NAME ( LIST OF PARAMETERS ) { STATEMENTS } You can make up any name you want for your function. In main we can call this new function using syntax that is similar to the way we call the built-in C++ commands: . main doesn't take any parameters. The result gets assigned to x.
"Second Line. newLine ()." << endl. (). ()." << endl. • You can have one function call another function.5. What if we wanted more space between the lines? We could call the same function repeatedly: void main { cout << newLine newLine newLine cout << } () "First Line. In fact. "Second Line. } newLine (). main calls threeLine and threeLine calls newLine." << endl. ADDING NEW FUNCTIONS 25 void main { cout << newLine cout << } () "First Line. cout << "Second Line. The output of this program is First line. it is quite common and useful to do so. (). this is common and useful. threeLine ()." << endl. (). . named threeLine. Again. } You should notice a few things about this program: • You can call the same procedure repeatedly. void main () { cout << "First Line. Or we could write a new function." << endl. Notice the extra space between the two lines.3. In this case. that prints three new lines: void threeLine () { newLine (). Second line." << endl.
Creating a new function can make a program smaller by eliminating repetitive code. threeLine (). there are a lot of reasons. to make your program easy to read. Functions can simplify a program by hiding a complex computation behind a single command. it may not be clear why it is worth the trouble to create all these new functions." << endl. So far. the whole program looks like this: #include <iostream. } void threeLine () { newLine (). but this example only demonstrates two: 1. cout << "Second Line. newLine (). } newLine (). Creating a new function gives you an opportunity to give a name to a group of statements. it is usually a better idea to put each statement on a line by itself.26 CHAPTER 3." << endl. } This program contains three function definitions: newLine. Which is clearer. FUNCTION • In threeLine I wrote three statements all on the same line.6 Definitions and uses Pulling together all the code fragments from the previous section. and main.h> void newLine () { cout << endl. On the other hand. newLine or cout << endl? 2. void main () { cout << "First Line. a short way to print nine consecutive new lines is to call threeLine three times. which is syntactically legal (remember that spaces and new lines usually don't change the meaning of a program). threeLine. I sometimes break that rule in this book to save space. How would you print 27 new lines? 3. For example. Actually. and by using English words in place of arcane code. .
Notice that the definition of each function appears above the place where it is used. we might have to go off and execute the statements in threeLine. it is tempting to read it from top to bottom.8 Parameters and arguments Some of the built-in functions we have used have parameters. threeLine calls newLine three times. Thus. This is necessary in C++. execute all the statements there. For example: void printTwice (char phil) { cout << phil << phil << endl. the parameter list indicates the type of each parameter. you go to the first line of the called function. we get interrupted three times to go off and execute newLine. Function calls are like a detour in the flow of execution. So it shouldn't surprise you that when you write a class definition. That sounds simple enough. until you reach a function call. Similarly. if you want to find the sine of a number. 3. regardless of where it is in the program (often it is at the bottom).3. in order. don't read from top to bottom. Fortunately. the definition of a function must appear before (above) the first use of the function. Notice that in each of these cases we have to specify not only how many parameters there are. which takes two doubles. Instead. but that is likely to be confusing. like pow. so each time newLine completes. C++ is adept at keeping track of where it is. Instead of going to the next statement. What's the moral of this sordid tale? When you read a program. PROGRAMS WITH MULTIPLE FUNCTIONS 27 Inside the definition of main.7. and then come back and pick up again where you left off. but also what type they are. there is a statement that uses or calls threeLine. because that is not the order of execution of the program. and eventually gets back to main so the program can terminate. the base and the exponent. you have to indicate what the number is. For example. } . Statements are executed one at a time. But while we are executing threeLine. which are values that you provide to let the function do its job. except that you have to remember that one function can call another. Execution always begins at the first statement of main. while we are in the middle of main. Thus. 3. follow the flow of execution. the program picks up where it left off in threeLine. You should try compiling this program with the functions in a different order and see what error messages you get.7 Programs with multiple functions When you look at a class definition that contains several functions. Some functions take more than one parameter. sin takes a double value as a parameter.
For now you should learn the general rule. the compiler will complain. we have to provide a char. but it is important to realize that they are not the same thing. Similarly. I chose the name phil to suggest that the name you give a parameter is up to you. but in general you want to choose something more illustrative than phil. The value you provide as an argument must have the same type as the parameter of the function you call. Variables like this are said to be local. 3. there is no such thing as phil. and we say that the argument is passed to the function. Whatever that parameter is (and at this point we have no idea what it is). In this case the value 'a' is passed as an argument to printTwice where it will get printed twice. named phil. . we might have a main function like this: void main () { printTwice ('a'). They can be the same or they can be different. } Notice something very important here: the name of the variable we pass as an argument (argument) has nothing to do with the name of the parameter (phil). Like state diagrams. In order to keep track of parameters and local variables. it gets printed twice. if we had a char variable. In order to call this function. If you try to use it. FUNCTION This function takes a single parameter. followed by a newline. Within the confines of main. we could use it as an argument instead: void main () { char argument = 'b'. that has type char. printTwice (argument). it is useful to draw a stack diagram.28 CHAPTER 3. inside printTwice there is no such thing as argument. This rule is important. For example. Let me say that again: The name of the variable we pass as an argument has nothing to do with the name of the parameter. but it is sometimes confusing because C++ sometimes converts arguments from one type to another automatically. and we will deal with exceptions later. Alternatively. except that they happen to have the same value (in this case the character 'b'). } The char value you provide is called an argument.9 Parameters and variables are local Parameters and variables only exist inside their own functions.
but the variables are contained in larger boxes that indicate which function they belong to. In the example. Each instance of a function contains the parameters and local variables for that function. int minute = 59. First. main has one local variable. minute). int minute).3. // WRONG! . printTime (int hour. } It might be tempting to write (int hour. 3. For example. argument. cout << minute. int minute) { cout << hour. FUNCTIONS WITH MULTIPLE PARAMETERS 29 stack diagrams show the value of each variable. cout << ":". and no parameters. For example void printTime (int hour. printTwice has no local variables and one parameter. but that format is only legal for variable declarations.10. Another common source of confusion is that you do not have to declare the types of arguments. In the diagram an instance of a function is represented by a box with the name of the function on the outside and the variables and parameters inside. it creates a new instance of that function. the state diagram for printTwice looks like this: argument main 'b' phil printTwice 'b' Whenever a function is called. The following is wrong! int hour = 11. remember that you have to declare the type of every parameter. not for parameters. named phil.10 Functions with multiple parameters The syntax for declaring and invoking functions with multiple parameters is a common source of errors.
3. like the math functions. perform an action but don't return a value. That raises some questions: • What happens if you call a function and you don't do anything with the result (i. Any time you have a question about what is legal or illegal in C++. . It is unnecessary and illegal to include the type when you pass them as arguments. argument: A value that you provide when you call a function. the one we use in this book is double.30 CHAPTER 3. This value must have the same type as the corresponding parameter. minute).12 Glossary floating-point: A type of variable (or value) that can contain fractions as well as integers. parameter: A piece of information you provide in order to call a function. you can write functions that return values. like newLine. call: Cause a function to be executed. and may or may not produce a result. yield results." and we'll do it in a couple of chapters. 3.11 Functions with results You might have noticed by now that some of the functions we are using. you don't assign it to a variable or use it as part of a larger expression)? • What happens if you use a function without a result as part of an expression. initialization: A statement that declares a new variable and assigns a value to it at the same time. like newLine() + 7? • Can we write functions that yield results. function: A named sequence of statements that performs some useful function. Parameters are like variables in the sense that they contain values and have types. or are we stuck with things like newLine and printTwice? The answer to the third question is "yes. There are a few floating-point types in C++. FUNCTION In this case. The correct syntax is printTime (hour. a good way to find out is to ask the compiler. Functions may or may not take parameters. Other functions. the compiler can tell the type of hour and minute by looking at their declarations.e. I will leave it up to you to answer the other two questions by trying them out.
the modulus operator is a percent sign. Also. yields 2. 7 divided by 3 is 2 with 1 left over. then the statements in brackets get executed. } The expression in parentheses is called the condition. x % 10 yields the rightmost digit of x (in base 10).1 The modulus operator The modulus operator works on integers (and integer expressions) and yields the remainder when the first operand is divided by the second. The first operator.Chapter 4 Conditionals and recursion 4. Thus. you can use the modulus operator to extract the rightmost digit or digits from a number. integer division. The simplest form is the if statement: if (x > 0) { cout << "x is positive" << endl. The second operator yields 1. %. int remainder = 7 % 3. nothing happens. In C++.2 Conditional execution In order to write useful programs. The syntax is exactly the same as for other operators: int quotient = 7 / 3. For example. If the condition is not true. Similarly x % 100 yields the last two digits. Conditional statements give us this ability. For example. 31 . The modulus operator turns out to be surprisingly useful. If it is true. 4. we almost always need the ability to check certain conditions and change the behavior of the program accordingly. you can check whether one number is divisible by another: if x % y is zero. then x is divisible by y.
} } . CONDITIONALS AND RECURSION The condition can contain any of the comparison operators: x x x x x x == y != y > y < y >= y <= y // // // // // // x x x x x x equals y is not equal to is greater than is less than y is greater than is less than or y y or equal to y equal to y Although these operations are probably familiar to you. 4. } else { cout << "x is odd" << endl. You can only compare ints to ints and doubles to doubles.3 Alternative execution A second form of conditional execution is alternative execution. the second set of statements is executed. as follows: void printParity (int x) { if (x%2 == 0) { cout << "x is even" << endl. As an aside. Also. there is no such thing as =< or =>. if you think you might want to check the parity (evenness or oddness) of numbers often. in which there are two possibilities. Since the condition must be true or false. = and ≤. and this code displays a message to that effect. The syntax looks like: if (x%2 == 0) { cout << "x is even" << endl. Unfortunately.32 CHAPTER 4. } else { cout << "x is odd" << endl. exactly one of the alternatives will be executed. The two sides of a condition operator have to be the same type. at this point you can't compare Strings at all! There is a way to compare Strings. you might want to "wrap" this code up in a function. the syntax C++ uses is a little different from mathematical symbols like =. A common error is to use a single = instead of a double ==. and == is a comparison operator. If the condition is false. } If the remainder when x is divided by 2 is zero. but we won't get to it for a couple of chapters. Remember that = is the assignment operator. and the condition determines which one gets executed. then we know that x is even.
4. as demonstrated in these examples. Always remember that when you call a function. < 0) { is negative" << endl. If you keep all the statements and squiggly-braces lined up. We could have written the previous example as: if (x == 0) { cout << "x is zero" << endl. } else { if (x > 0) { cout << "x is positive" << endl. One way to make them easier to read is to use standard indentation.4 Chained conditionals Sometimes you want to check for a number of related conditions and choose one of several actions. you are less likely to make syntax errors and you can find them more quickly if you do. is zero" << endl. In main you would call this function as follows: printParity (17). C++ can figure out what type they are. although they can be difficult to read if they get out of hand. // WRONG!!! 4. 4. printParity (int number). you can also nest one conditional within another. } else { cout << "x is negative" << endl. One way to do this is by chaining a series of ifs and elses: if (x > 0) { cout << "x } else if (x cout << "x } else { cout << "x } is positive" << endl. } } .4. You should resist the temptation to write things like: int number = 17. CHAINED CONDITIONALS 33 Now you have a function named printParity that will display an appropriate message for any integer you care to provide. These chains can be as long as you want.5 Nested conditionals In addition to chaining. you do not have to declare the types of the arguments you provide.
One reason to use it is if you detect an error condition: #include <math. but nevertheless. in which case it displays an error message and then uses return to exit the function. so you better get used to it. The first thing it does is check whether x is less than or equal to zero. In general. although they could have been conditional statements as well. you have to include the header file math. . and we have seen several examples of that. 4. but the second branch contains another if statement. I neglected to mention that it is also legal for a function to call itself.0) { cout << "Positive numbers only. } This defines a function named printLogarithm that takes a double named x as a parameter. The first branch contains a simple output statement. return.h. it is a good idea to avoid them when you can.6 The return statement The return statement allows you to terminate the execution of a function before you reach the end.34 CHAPTER 4. nested conditionals get difficult to read very quickly.7 Recursion I mentioned in the last chapter that it is legal for one function to call another. It may not be obvious why that is a good thing. } double result = log (x). On the other hand. Remember that any time you want to use one a function from the math library.h> void printLogarithm (double x) { if (x <= 0. which has two branches of its own. CONDITIONALS AND RECURSION There is now an outer conditional that contains two branches. I used a floating-point value on the right side of the condition because there is a floating-point variable on the left. this kind of nested structure is common. Fortunately." << endl. those two branches are both output statements. and we will see it again. Notice again that indentation helps make the structure apparent. 4. cout << "The log of x is " << result). please. but it turns out to be one of the most magical and interesting things a program can do. The flow of execution immediately returns to the caller and the remaining lines of the function are not executed.
" Otherwise. . it outputs the value 3. } else { cout << n << endl. and since n is not zero. What happens if we call this function like this: void main () { countdown (3). it outputs the word "Blastoff.. let's look again at the functions newLine and threeLine. } } The name of the function is countdown and it takes a single integer as a parameter. The execution of countdown begins with n=1.. and since n is not zero. So the total output looks like: 3 2 1 Blastoff! As a second example.4. and then calls itself.7. it outputs the value 1. it outputs the word "Blastoff!" and then returns.. countdown (n-1). The execution of countdown begins with n=2.. And then you're back in main (what a trip). it outputs the parameter and then calls a function named countdown—itself— passing n-1 as an argument. RECURSION 35 For example. The execution of countdown begins with n=0. } The execution of countdown begins with n=3. and then calls itself. If the parameter is zero. The countdown that got n=2 returns... The countdown that got n=1 returns. and since n is not zero. and then calls itself. and since n is zero. it outputs the value 2. look at the following function: void countdown (int n) { if (n == 0) { cout << "Blastoff!" << endl. The countdown that got n=3 returns.
the total number of newlines is 1 + (n-1). In most programming environments. the argument gets smaller by one. notice that each time the functions get called recursively. Although these work. nLines (n-1). it outputs one newline. } void threeLine () { newLine (). a program with an infinite recursion will not really run forever. or 106. This is the first example we have seen of a run-time error (an error that does not appear until you run the program). You should write a small program that recurses forever and run it to see what happens. A better alternative would be void nLines (int n) { if (n > 0) { cout << endl. it will go on making recursive calls forever and the program will never terminate. and then calls itself to output n-1 additional newlines. This is known as infinite recursion. If a recursion never reaches a base case. The same kind of diagram can make it easier . The process of a function calling itself is called recursion. } } This program is similar to countdown.9 Stack diagrams for recursive functions In the previous chapter we used a stack diagram to represent the state of a program during a function call. When the argument is zero. Eventually. } newLine (). something will break and the program will report an error. 4. and it is generally not considered a good idea. which usually comes out to roughly n. This case—when the function completes without making a recursive call—is called the base case. as long as n is greater than zero.8 Infinite recursion In the examples in the previous section. CONDITIONALS AND RECURSION void newLine () { cout << endl. 4. without making any recursive calls. the function returns immediately. so eventually it gets to zero. they would not be much help if I wanted to output 2 newlines. and such functions are said to be recursive. newLine ().36 CHAPTER 4. Thus.
4. invoked with the parameter n=4. nesting: Putting a conditional statement inside one or both branches of another conditional statement. GLOSSARY 37 to interpret a recursive function. . draw a stack diagram for nLines. infinite recursion: A function that calls itself recursively without every reaching the base case. This figure shows a stack diagram for countdown. The bottom of the stack. Remember that every time a function gets called it creates a new instance that contains the function's local variables and parameters. so there are no more instances of countdown. recursion: The process of calling the same function you are currently executing. The instance of main is empty because main does not have any parameters or local variables. In C++ it is denoted with a percent sign (%). countdown with n=0 is the base case. each with a different value for the parameter n.10. As an exercise. Eventually an infinite recursion will cause a run-time error. chaining: A way of joining several conditional statements in sequence. called with n = 3: main n: n: n: n: 3 2 1 0 countdown countdown countdown countdown There is one instance of main and four instances of countdown.10 Glossary modulus: An operator that works on integers and yields the remainder when one number is divided by another.4. It does not make a recursive call. conditional: A block of statements that may or may not be executed depending on some condition.
the effect of calling the function is to generate a new value. double area = pi * radius * radius. have produced results. which we usually assign to a variable or use as part of an expression. for want of a better name. that is. Instead of void. That is. return area.1 Return values Some of the built-in functions we have used. } The first thing you should notice is that the beginning of the function definition is different. countdown (n-1). which indicates a void function. But so far all the functions we have written have been void functions.0). and returns the area of a circle with the given radius: double area (double radius) { double pi = acos (-1. functions that return no value. The first example is area. like the math functions. which indicates that the return value from this function will have type double. When you call a void function. which I will refer to as fruitful functions. double height = radius * sin (angle). which takes a double as a parameter. we are going to write functions that return things. we see double. with no assignment: nLines (3).0). it is typically on a line by itself.Chapter 5 Fruitful functions 5. 39 . For example: double e = exp (1. In this chapter.
Sometimes it is useful to have multiple return statements. you are making a promise that this function will eventually produce a double. Code that appears after a return statement. Although it is legal to have more than one return statement in a function. } else { return x. If you try to return with no expression.40 CHAPTER 5. one in each branch of a conditional: double absoluteValue (double x) { if (x < 0) { return -x. Some compilers warn you if part of your code is dead. } else if (x > 0) { return x." The expression you provide can be arbitrarily complicated. or an expression with the wrong type. or any place else where it can never be executed. temporary variables like area often make debugging easier. the type of the expression in the return statement must match the return type of the function. notice that the last line is an alternate form of the return statement that includes a return value. FRUITFUL FUNCTIONS Also. "return immediately from this function and use the following expression as a return value. } // WRONG!! } . is called dead code. If you put return statements inside a conditional. } } Since these returns statements are in an alternative conditional. only one will be executed. then you have to guarantee that every possible path through the program hits a return statement. } On the other hand. when you declare that the return type is double. In either case. This statement means. so we could have written this function more concisely: double area (double radius) { return acos(-1. the function terminates without executing any subsequent statements. For example: double absoluteValue (double x) { if (x < 0) { return -x. the compiler will take you to task.0) * radius * radius. you should keep in mind that as soon as one is executed. In other words.
If only the compiler had warned you! From now on. the two points are the parameters. By the usual definition. Rather. As an example. distance = (x2 − x1 )2 + (y2 − y1 )2 (5. At this stage the . Then you give your program to someone else and they run it in another environment. you should know that there is a function in the math library called fabs that calculates the absolute value of a double—correctly. As an aside.5. Unfortunately.0. and will probably be different in different environments. In other words. y1 ) and (x2 . even though it is not the right answer. the program may compile and run. you should thank the compiler for finding your error and sparing you days of debugging. what are the inputs (parameters) and what is the output (return value). if the compiler points out an error in your program. As a result. 5. In this case. double y1. Here's the kind of thing that's likely to happen: you test absoluteValue with several values of x and it seems to work correctly. but as you gain more experience. which will have type double. You should turn this option on all the time. By now you are probably sick of seeing compiler errors. double x2.2.1) The first step is to consider what a distance function should look like in C++. } The return statement is a placekeeper so that the function will compile and return something. and it takes days of debugging to discover that the problem is an incorrect implementation of absoluteValue. I am going to suggest one technique that I call incremental development. double y2) { return 0. you will realize that the only thing worse than getting a compiler error is not getting a compiler error when your program is wrong. Some compilers have an option that tells them to be extra strict and report all the errors they can find. PROGRAM DEVELOPMENT 41 This program is not correct because if x happens to be 0. but the return value when x==0 could be anything. and it is natural to represent them using four doubles. then neither condition will be true and the function will end without hitting a return statement. y2 ). It fails in some mysterious way. The return value is the distance. imagine you want to find the distance between two points. you should not blame the compiler. But it may not be clear yet how to go about writing them.2 Program development At this point you should be able to look at complete C++ functions and tell what they do. Already we can write an outline of the function: double distance (double x1. many C++ compilers do not catch this error. given by the coordinates (x1 .
just in case you need it later. double y2) { double dx = x2 .x1. } Again. cout << "dy is " << dy << endl.0 and 4. As I mentioned. but comment it out. but it is simpler and faster to just multiply each term by itself. double dsquared = dx*dx + dy*dy. double dy = y2 . return 0. 4. but it is not part of the final product.0. double y1. } I added output statements that will let me check the intermediate values before proceeding. That way. I will store those values in temporary variables named dx and dy.0. The next step in the computation is to find the differences x2 −x1 and y2 −y1 . double distance (double x1.y1. we recompile and run the program. we can use the sqrt function to compute and return the result.0). double x2. double dy = y2 . Code like that is called scaffolding. After each incremental change.0. The next step in the development is to square dx and dy. I chose these values so that the horizontal distance is 3 and the vertical distance is 4. Sometimes it is a good idea to keep the scaffolding around. I already know that they should be 3. double y2) { double dx = x2 . double x2. the result will be 5 (the hypotenuse of a 3-4-5 triangle). return 0. Once we have checked the syntax of the function definition. We could use the pow function. that way. double y1. In order to test the new function. When you are testing a function. at any point we know exactly where the error must be—in the last line we added. Somewhere in main I would add: double dist = distance (1.y1. When the function is finished I will remove the output statements. cout << dist << endl. cout << "dx is " << dx << endl.0. but it is worthwhile to try compiling it so we can identify any syntax errors before we make it more complicated. it is useful to know the right answer.x1. cout << "dsquared is " << dsquared. we can start adding lines of code one at a time. 2.0). we have to call it with sample values. double distance (double x1. Finally. because it is helpful for building the program. I would compile and run the program at this stage and check the intermediate value (which should be 25.0. . FRUITFUL FUNCTIONS function doesn't do anything useful.42 CHAPTER 5.0. 6.
As you gain more experience programming. double xp.3 Composition As you should expect by now. double yc. yp). and asked for the area of the circle? Let's say the center point is stored in the variables xc and yc. double radius = distance (xc. COMPOSITION 43 double distance (double x1. double y1. we have a function. and you can build new functions using existing functions. once you define a new function. if there is an error.x1. xp. which is the distance between the two points. you might want to remove some of the scaffolding or consolidate multiple statements into compound expressions. double result = area (radius). but only if it does not make the program difficult to read. double yp) { double radius = distance (xc. return result.5. return result. double dsquared = dx*dx + dy*dy. double result = sqrt (dsquared). yp). distance.y1. The first step is to find the radius of the circle. incremental changes. double result = area (radius). you will know exactly where it is. yc. that does that. and return it. Nevertheless. The key aspects of the process are: • Start with a working program and make small. the center of the circle and a point on the perimeter. } Then in main. double x2. return result. 5. and the perimeter point is in xp and yp. this incremental development process can save you a lot of debugging time. yc. At any point.3. } . you might find yourself writing and debugging more than one line at a time. double dy = y2 . Wrapping that all up in a function. what if someone gave you two points. double y2) { double dx = x2 . you can use it as part of an expression. we get: double fred (double xc. xp. • Use temporary variables to hold intermediate values so you can output and check them. The second step is to find the area of a circle with that radius. we should output and check the value of the result. For example. • Once the program is working. Fortunately.
xp. You might get yourself nicely confused if you are trying to debug one version of a function while accidently calling a different one. for fred we provide two points. is legal in C++ as long as each version takes different parameters. } 5.0. double yp) { return area (distance (xc. Actually. C++ goes looking for a function named area that takes a double as an argument. it should be used with caution. but once the program is working we can make it more concise by composing the function calls: double fred (double xc. which is called overloading. that reminds me of one of the cardinal rules of debugging: make sure that the version of the program you are looking at is the version of the program that is running! Some time you may find yourself making one change after another in your program.4 Overloading In the previous section you might have noticed that fred and area perform similar functions—finding the area of a circle—but take different parameters. C++ uses the second version of area.44 CHAPTER 5. double yc. FRUITFUL FUNCTIONS The name of this function is fred. If you write double x = area (1. So we can go ahead and rename fred: double area (double xc. If you write: double x = area (3.0. and so it uses the first version. } This looks like a recursive function. yc. In other words. 2. When you call an overloaded function. 4. The temporary variables radius and area are useful for development and debugging.0). double xp. double yp) { return area (distance (xc. we have to provide the radius. C++ knows which version you want by looking at the arguments that you provide. yp)). I will explain why in the next section. and seeing the same thing every time . For area. meaning that there are different versions that accept different numbers or types of parameters. it is natural to give them the same name. but it is not. double xp. this version of area is calling the other version. it would make more sense if fred were called area. Although overloading is a useful feature. 6. yc. double yc. xp. Having more than one function with the same name. If two functions do the same thing. Many of the built-in C++ commands are overloaded. Actually. which may seem odd.0. yp)).0).
so you can store it in a bool variable . Also. Well. 5. The values true and false are keywords in C++. while (true) { // loop forever } is a standard idiom for a loop that should run forever (or until it reaches a return or break statement). and the third line is a combination of a declaration and as assignment. bool testResult = false. stick in an output statement (it doesn't matter what it says) and make sure the behavior of the program changes accordingly. 5. Boolean variables work just like the other types: bool fred. and the only values in it are true and false. and even more floating-point numbers. As I mentioned. In C++ the boolean type is called bool.5 Boolean values The types we have seen so far are pretty big. BOOLEAN VALUES 45 you run it. the second line is an assignment.5. The condition inside an if statement or a while statement is a boolean expression. we have been using boolean values for the last couple of chapters. For example. and can be used anywhere a boolean expression is called for. fred = true. there is a corresponding type of variable. the result of a comparison operator is a boolean. there is another type in C++ that is even smaller.6 Boolean variables As usual. It is called boolean. The first line is a simple variable declaration. called an initialization. the result of a comparison operator is a boolean value. the set of characters is pretty small. To check. for every type of value. This is a warning sign that for one reason or another you are not running the version of the program you think you are. For example: if (x == 5) { // do something } The operator == compares two integers and produces a boolean value. Without thinking about it. By comparison. There are a lot of integers in the world.5.
FRUITFUL FUNCTIONS bool evenFlag = (n%2 == 0). which are denoted by the symbols &&. that is.8 Bool functions Functions can return bool values just like any other type. if evenFlag is true OR the number is divisible by 3. which is often convenient for hiding complicated tests inside functions. 5. since it flags the presence or absence of some condition. For example: bool isSingleDigit (int x) { if (x >= 0 && x < 10) { return true. } A variable used in this way is called a flag. evenFlag || n%3 == 0 is true if either of the conditions is true. } } . that is. For example x > 0 && x < 10 is true only if x is greater than zero AND less than 10. so !evenFlag is true if evenFlag is false. Finally. bool positiveFlag = (x > 0). // true if n is even // true if x is positive and then use it as part of a conditional statement later if (evenFlag) { cout << "n was even when I checked it" << endl.7 Logical operators There are three logical operators in C++: AND. } else { return false. The semantics (meaning) of these operators is similar to their meaning in English. the NOT operator has the effect of negating or inverting a bool expression. how would you write the following code using a single conditional? if (x > 0) { if (x < 10) { cout << "x is a positive single digit." << endl.46 CHAPTER 5. } } 5. OR and NOT. Logical operators often provide a way to simplify nested conditional statements. For example. || and !. if the number is odd.
The most common use of bool functions is inside conditional statements if (isSingleDigit (x)) { cout << "x is little" << endl. } 5. main is not really supposed to be a void function.9 Returning from main Now that we have functions that return values. The first line outputs the value true because 2 is a single-digit number. bool bigFlag = !isSingleDigit (17). but rather the integers 1 and 0. which indicates that the program succeeded at whatever it was supposed to to. The return type is bool. . it does not display the words true and false. although it is a bit longer than it needs to be. It is common to give boolean functions names that sound like yes/no questions. and avoiding the if statement altogether: bool isSingleDigit (int x) { return (x >= 0 && x < 10). which means that every return statement has to provide a bool expression. I can let you in on a secret. 1 There is a way to fix that using the boolalpha flag. or some other value that indicates what kind of error occurred.5. so there is nothing wrong with returning it directly. } The usual return value from main is 0. but it is too hideous to mention. It's supposed to return an integer: int main () { return 0. when C++ outputs bools. If something goes wrong. RETURNING FROM MAIN 47 The name of this function is isSingleDigit. Unfortunately. } In main you can call this function in the usual ways: cout << isSingleDigit (2) << endl. The code itself is straightforward.1 The second line assigns the value true to bigFlag only if 17 is not a singledigit number. Remember that the expression x >= 0 && x < 10 has type bool. it is common to return -1.9. } else { cout << "x is big" << endl.
but a lot of the early computer scientists started as mathematicians). If you can write a recursive definition of something. in the sense that the definition contains a reference to the thing being defined. disks. mouse.) This definition says that the factorial of 0 is 1. we get 3! equal to 3 times 2 times 1 times 1. If you take a course on the Theory of Computation. you might get something like: 0! = 1 n! = n · (n − 1)! (Factorial is usually denoted with the symbol !. but that's all). which is 2 times 1!. you can usually write a C++ program to evaluate it. we'll evaluate a few recursively-defined mathematical functions. To give you an idea of what you can do with the tools we have learned so far.48 CHAPTER 5. With a little thought. you might wonder who this value gets returned to. we would need a few commands to control devices like the keyboard. Putting it all together. Proving that claim is a non-trivial exercise first accomplished by Alan Turing. and the factorial of any other value. by which I mean that anything that can be computed can be expressed in this language. if you looked up the definition of the mathematical function factorial. The first step is to decide what the parameters are for this function.10 More recursion So far we have only learned a small subset of C++. it is known as the Turing thesis. but we are not going to deal with them for a little while. but you might be interested to know that this subset is now a complete programming language. you will have a chance to see the proof. is n multiplied by the factorial of n − 1. 5. FRUITFUL FUNCTIONS Of course. There are even some parameters that are passed to main by the system. On the other hand. which is 1 times 0!. and what the return type is. So 3! is 3 times 2!. which is not to be confused with the C++ logical operator ! which means NOT. n. A recursive definition is similar to a circular definition. one of the first computer scientists (well. It turns out that when the system executes a program. you should conclude that factorial takes an integer as a parameter and returns an integer: . etc. A truly circular definition is typically not very useful: frabjuous: an adjective used to describe something that is frabjuous. Accordingly.. If you saw that definition in the dictionary. which is 6. since we never call main ourselves. you might be annoyed. Any program ever written could be rewritten using only the language features we have used so far (actually. it starts by calling main in pretty much the same way it calls all the other functions. some would argue that he was a mathematician.
return result.. } } Otherwise. we take the first branch and return the value 1 immediately without making any more recursive calls. If we call factorial with the value 3: Since 3 is not zero. } else { int recurse = factorial (n-1). int result = n * recurse.. The return value (1) gets multiplied by n. we take the second branch and calculate the factorial of n − 1.. all we have to do is return 1: int factorial (int n) { if (n == 0) { return 1. Since 2 is not zero. Since 0 is zero. we take the second branch and calculate the factorial of n − 1. MORE RECURSION 49 int factorial (int n) { } If the argument happens to be zero. it is similar to nLines from the previous chapter. and the result is returned. and this is the interesting part.5. Since 1 is not zero. which is 1. which is 2. we take the second branch and calculate the factorial of n − 1. and the result is returned. and then multiply it by n. } } If we look at the flow of execution for this program.10.. int factorial (int n) { if (n == 0) { return 1.. The return value (1) gets multiplied by n.. we have to make a recursive call to find the factorial of n − 1. .
instead of following the flow of execution. is returned to main. you should assume that the recursive call works (yields the correct result).8 we wrote a function called isSingleDigit that determines whether a number is between 0 and 9. the local variables recurse and result do not exist because when n=0 the branch that creates them does not execute. For example. which is 3. Once we have convinced ourselves that this function is correct—by testing and examination of the code—we can use the function without ever looking at the code again. FRUITFUL FUNCTIONS The return value (2) gets multiplied by n. and the result. you don't examine the implementations of those functions. "Assuming that I can find the factorial of n − 1. 5. it is clear that you can. or whoever called factorial (3). Here is what the stack diagram looks like for this sequence of function calls: main 6 n: 2 n: 3 2 1 0 recurse: recurse: recurse: 2 1 1 result: result: result: 6 2 1 factorial factorial factorial factorial 1 n: 1 n: The return values are shown being passed back up the stack.11 Leap of faith Following the flow of execution is one way to read programs. You just assume that they work. it can quickly become labarynthine. the same is true when you call one of your own functions." When you come to a function call. 6. can I compute the factorial of n?" In this case. When you get to the recursive call. An alternative is what I call the "leap of faith. In fact. Well. you assume that the function works correctly and returns the appropriate value. by multiplying by n. it is a bit strange to assume that the function works correctly . Of course. The same is true of recursive programs. When you call cos or exp. Notice that in the last instance of factorial. but as you saw in the previous section.50 CHAPTER 5. because the people who wrote the built-in libraries were good programmers. instead of following the flow of execution. in Section 5. and then ask yourself. you are already practicing this leap of faith when you use built-in functions.
you can tighten it up.13 Glossary return type: The type of value a function returns. But according to the leap of faith.12. but I recommend that you use the more explicit version while you are developing code. Translated into C++. you can make two recursive calls) work correctly. . 5. this is int fibonacci (int n) { if (n == 0 || n == 1) { return 1. but that's why it's called a leap of faith! 5. When you have it working. } else { return fibonacci (n-1) + fibonacci (n-2). if we assume that the two recursive calls (yes. if you are feeling inspired.5. your head explodes. } } If you try to follow the flow of execution here. which has the following definition: f ibonacci(0) = 1 f ibonacci(1) = 1 f ibonacci(n) = f ibonacci(n − 1) + f ibonacci(n − 2). ONE MORE EXAMPLE 51 when you have not even finished writing it. then it is clear that we get the right result by adding them together. } } From now on I will tend to use the more concise version. } else { return n * factorial (n-1). the classic example of a recursively-defined mathematical function is fibonacci.12 One more example In the previous example I used temporary variables to spell out the steps. even for fairly small values of n. and to make the code easier to debug. After factorial. but I could have saved a few lines: int factorial (int n) { if (n == 0) { return 1.
dead code: Part of a program that can never be executed. often because it appears after a return statement. When you call an overloaded function. overloading: Having more than one function with the same name but different parameters. C++ knows which version to use by looking at the arguments you provide. boolean values can be stored in a variable type called bool. . flag: A variable (usually type bool) that records a condition or status information. FRUITFUL FUNCTIONS return value: The value provided as the result of a function call. one that does not return a value.52 CHAPTER 5. scaffolding: Code that is used during program development but is not part of the final version. that is. In C++. logical operator: An operator that combines boolean values in order to test compound conditions. comparison operator: An operator that compares two values and produces a boolean that indicates the relationship between the operands. boolean: A value or variable that can take on one of two states. void: A special return type that indicates a void function. often called true and f alse.
it is tempting to interpret a statement like a = b as a statement of equality. cout << fred. The output of this program is 57. But in C++ the statement a = 7. It is not! First of all. This kind of multiple assignment is the reason I described variables as a container for values. because the first time we print fred his value is 5. and the second time his value is 7. For example.1 Multiple assignment I haven't said much about it. 53 . in mathematics if a = 7 then 7 = a. and 7 = a. fred fred = 7. fred 5 5 7 When there are multiple assignments to a variable. it is especially important to distinguish between an assignment statement and a statement of equality. but it is legal in C++ to make more than one assignment to the same variable. is not. When you assign a value to a variable.Chapter 6 Iteration 6. fred = 7. as shown in the figure: int fred = 5. The effect of the second assignment is to replace the old value of the variable with a new value. you change the contents of the container. is legal. equality is commutative. cout << fred. int fred = 5. Because C++ uses the = symbol for assignment. and assignment is not.
the flow of execution for a while statement is as follows: 1. such as nLines and countdown. If a = b now. In C++. continue displaying the value of n and then reducing the value of n by 1. such as <. When you get to zero. .54 CHAPTER 6. but they don't have to stay that way! int a = 5. output the word 'Blastoff!"' More formally. and C++ provides several language features that make it easier to write iterative programs. a statement of equality is true for all time. in order to avoid confusion. ITERATION Furthermore. we can rewrite countdown: void countdown (int n) { while (n > 0) { cout << n << endl. yielding true or false. 6. The two features we are going to look at are the while statement and the for statement. and so they are no longer equal. This type of repetition is called iteration. then a will always equal b. it can make the code difficult to read and debug. // a and b are now equal // a and b are no longer equal The third line changes the value of a but it does not change the value of b. 6. Evaluate the condition in parentheses. "While n is greater than zero. Although multiple assignment is frequently useful.3 The while statement Using a while statement. In many programming languages an alternate symbol is used for assignment. We have seen programs that use recursion to perform repetition. you should use it with caution.or :=. a = 3. n = n-1. an assignment statement can make two variables equal. What this means is. } You can almost read a while statement as if it were English. If the values of variables are changing constantly in different parts of the program.2 Iteration One of the things computers are often used for is the automation of repetitive tasks. in mathematics. } cout << "Blastoff!" << endl. Repeating identical or similar tasks without making errors is something that computers do well and people do poorly. int b = a.
This type of flow is called a loop because the third step loops back around to the top. and then go back to step 1." are an infinite loop. Particular values aside. If the condition is true. until we get to 1. eventually. The body of the loop should change the value of one or more variables so that. For some particular values of n. If it is odd. 1. then the value of n will be even every time through the loop. which will make the condition false. Otherwise the loop will repeat forever. there is no obvious proof that n will ever reach 1. which is called an infinite loop. or that the program will terminate. } } } // n is even // n is odd The condition for this loop is n != 1. An endless source of amusement for computer scientists is the observation that the directions on shampoo. and we can see that the value of n gets smaller each time through the loop (each iteration). Since n sometimes increases and sometimes decreases. "Lather. starting with 16. execute each of the statements between the squiggly-braces. At each iteration. In other cases it is not so easy to tell: void sequence (int n) { while (n != 1) { cout << n << endl. 8. rinse. repeat. 16. 5. the resulting sequence is 3. If the condition is false. the interesting question is whether we can prove that this program terminates for all values of n. we can prove that the loop will terminate because we know that the value of n is finite. 10. Notice that if the condition is false the first time through the loop. if the starting value (the argument passed to sequence) is 3. THE WHILE STATEMENT 55 2. exit the while statement and continue execution at the next statement. So far. so eventually we have to get to zero. the statements inside the loop are never executed. the value is replaced by 3n + 1. no one has been able to prove it or disprove it! . The previous example ends with such a sequence. so the loop will continue until n is 1. 2. the value of n is divided by two. For example. we can prove termination. The statements inside the loop are called the body of the loop. 4. In the case of countdown. if (n%2 == 0) { n = n / 2. if the starting value is a power of two. If it is even. } else { n = n*3 + 1. For example.6.3. 3. the condition becomes false and the loop terminates. the program outputs the value of n and then checks whether it is even or odd.
4 Tables One of the things loops are good for is generating tabular data. and the result tended to be full of errors.38629 1. When computers appeared on the scene. The sequence \n represents a newline character. A newline character has exactly the same effect as endl. which are normally every eight characters. sines and cosines. The output of this program is 1 2 3 4 5 6 7 8 0 0. In some cases. } The sequence \t represents a tab character. "This is great! We can use the computers to generate the tables. As we will see in a minute. x = x + 1. but shortsighted. Creating these tables was slow and boring.0. there were books containing long tables where you could find the values of various functions. it still makes a good example of iteration. while (x < 10. A tab character causes the cursor to shift to the right until it reaches one of the tab stops. These sequences can be included anywhere in a string. there have been errors in the underlying tables. Well. I use endl. and then perform computations to improve the approximation.07944 . but if it appears as part of a string.0. Soon thereafter computers and calculators were so pervasive that the tables became obsolete. one of the initial reactions was. so there will be no errors. before computers were readily available.60944 1. It turns out that for some operations. and other common mathematical functions by hand. although in these examples the sequence is the whole string. tabs are useful for making columns of text line up.693147 1. it causes the cursor to move on to the next line. ITERATION 6.09861 1.0) { cout << x << "\t" << log(x) << "\n".56 CHAPTER 6. To make that easier. Although a "log table" is not as useful as it once was. people had to calculate logarithms. computers use tables of values to get an approximate answer.79176 1. almost." That turned out to be true (mostly). Usually if a newline character appears by itself.94591 2. I use \n. The following program outputs a sequence of values in the left column and their logarithms in the right column: double x = 1. most famously in the table the original Intel Pentium used to perform floating-point division. For example.
while (x < 100.4. 2.58496 2. Since powers of two are so important in computer science. . we often want to find logarithms with respect to base 2.0) { cout << x << "\t" << log(x) / log(2.0) << endl. we can use the following formula: log2 x = Changing the output statement to cout << x << "\t" << log(x) / log(2. 4 and 8 are powers of two. yielding a geometric sequence. knowing the powers of two is! As an exercise. Log tables may not be useful any more. If we wanted to find the logarithms of other powers of two.80735 3 3. Print it out and memorize it.0. but for computer scientists. TABLES 57 9 2. yields 1 2 3 4 5 6 7 8 9 0 1 1. } Now instead of adding something to x each time through the loop. modify this program so that it outputs the powers of two up to 65536 (that's 216 ). we could modify the program like this: double x = 1. because their logarithms base 2 are round numbers.16993 loge x loge 2 We can see that 1. x = x * 2. which yields an arithmetic sequence. To do that.0) << endl.58496 2 2. remember that the log function uses base e.19722 If these values seem odd.0. the position of the second column does not depend on the number of digits in the first column. we multiply x by something. The result is: 1 2 4 8 16 32 64 0 1 2 3 4 5 6 Because we are using tab characters between the columns.32193 2.6.
i = i + 1. we print the value 2*i followed by three spaces. A good way to start is to write a simple loop that prints the multiples of 2. the value of i increases from 1 to 6. like printing the multiples of any integer. ITERATION 6. Each time through the loop. A multiplication table is a good example. while (i <= 6) { cout << 2*i << " i = i + 1.3 and isSingleDigit in Section 5. By omitting the endl from the first output statement.5 Two-dimensional tables A two-dimensional table is a table where you choose a row and a column and read the value at the intersection. As the loop executes. allowing you to take advantage of all the things functions are good for. We have seen two examples of encapsulation. Here's a function that encapsulates the loop from the previous section and generalizes it to print multiples of n. ". or loop variable. we get all the output on a single line.8. Generalization means taking something specific. and then when i is 7. all on one line. int i = 1. and making it more general. The output of this program is: 2 4 6 8 10 12 So far.6 Encapsulation and generalization Encapsulation usually means taking a piece of code and wrapping it up in a function.58 CHAPTER 6. } . like printing multiples of 2. the loop terminates. } cout << endl. The next step is to encapsulate and generalize. The first line initializes a variable named i. } cout << endl. so good. void printMultiples (int n) { int i = 1. when we wrote printParity in Section 4. Let's say you wanted to print a multiplication table for the values from 1 to 6. which is going to act as a counter. while (i <= 6) { cout << n*i << " ". 6.
To encapsulate, all I had to do was add the first line, which declares the name, parameter, and return type. To generalize, all I had to do was replace the value 2 with the parameter n. If we call this function with the argument 2, we get the same output as before. With argument 3, the output is: 3 6 9 12 15 18
and with argument 4, the output is 4 8 12 16 20 24
By now you can probably guess how we are going to print a multiplication table: we'll call printMultiples repeatedly with different arguments. In fact, we are going to use another loop to iterate through the rows. int i = 1; while (i <= 6) { printMultiples (i); i = i + 1; } First of all, notice how similar this loop is to the one inside printMultiples. All I did was replace the print statement with a function call. The output of this program is 1 2 3 4 5 6 2 4 6 8 10 12 3 4 5 6 6 8 10 12 9 12 15 18 12 16 20 24 15 20 25 30 18 24 30 36
which is a (slightly sloppy) multiplication table. If the sloppiness bothers you, try replacing the spaces between columns with tab characters and see what you get.
In the last section I mentioned "all the things functions are good for." About this time, you might be wondering what exactly those things are. Here are some of the reasons functions are useful: • By giving a name to a sequence of statements, you make your program easier to read and debug. • Dividing a long program into functions allows you to separate parts of the program, debug them in isolation, and then compose them into a whole.
• Functions facilitate both recursion and iteration. • Well-designed functions are often useful for many programs. Once you write and debug one, you can reuse it.
More encapsulation
To demonstrate encapsulation again, I'll take the code from the previous section and wrap it up in a function: void printMultTable () { int i = 1; while (i <= 6) { printMultiples (i); i = i + 1; } } The process I am demonstrating is a common development plan. You develop code gradually by adding lines to main or someplace else, and then when you get it working, you extract it and wrap it up in a function. The reason this is useful is that you sometimes don't know when you start writing exactly how to divide the program into functions. This approach lets you design as you go along.
Local variables
About this time, you might be wondering how we can use the same variable i in both printMultiples and printMultTable. Didn't I say that you can only declare a variable once? And doesn't it cause problems when one of the functions changes the value of the variable? The answer to both questions is "no," because the i in printMultiples and the i in printMultTable are not the same variable. They have the same name, but they do not refer to the same storage location, and changing the value of one of them has no effect on the other. Remember that variables that are declared inside a function definition are local. You cannot access a local variable from outside its "home" function, and you are free to have multiple variables with the same name, as long as they are not in the same function. The stack diagram for this program shows clearly that the two variables named i are not in the same storage location. They can have different values, and changing one does not affect the other.
main i: n:
1 3
printMultTable printMultiples
Notice that the value of the parameter n in printMultiples has to be the same as the value of i in printMultTable. On the other hand, the value of i in printMultiple goes from 1 up to n. In the diagram, it happens to be 3. The next time through the loop it will be 4. It is often a good idea to use different variable names in different functions, to avoid confusion, but there are good reasons to reuse names. For example, it is common to use the names i, j and k as loop variables. If you avoid using them in one function just because you used them somewhere else, you will probably make the program harder to read.
More generalization
As another example of generalization, imagine you wanted a program that would print a multiplication table of any size, not just the 6x6 table. You could add a parameter to printMultTable: void printMultTable (int high) { int i = 1; while (i <= high) { printMultiples (i); i = i + 1; } } I replaced the value 6 with the parameter high. If I call printMultTable with the argument 7, I get 1 2 3 4 5 6 7 2 4 6 8 10 12 14 3 4 5 6 6 8 10 12 9 12 15 18 12 16 20 24 15 20 25 30 18 24 30 36 21 28 35 42
which is fine, except that I probably want the table to be square (same number of rows and columns), which means I have to add another parameter to printMultiples, to specify how many columns the table should have.
Just to be annoying, I will also call this parameter high, demonstrating that different functions can have parameters with the same name (just like local variables): void printMultiples (int n, int high) { int i = 1; while (i <= high) { cout << n*i << " "; i = i + 1; } cout << endl; } void printMultTable (int high) { int i = 1; while (i <= high) { printMultiples (i, high); i = i + 1; } } Notice that when I added a new parameter, I had to change the first line of the function (the interface or prototype), and I also had to change the place where the function is called in printMultTable. As expected, this program generates a square 7x7 table: 1 2 3 4 5 6 7 2 4 6 8 10 12 14 3 4 5 6 7 6 8 10 12 14 9 12 15 18 21 12 16 20 24 28 15 20 25 30 35 18 24 30 36 42 21 28 35 42 49
When you generalize a function appropriately, you often find that the resulting program has capabilities you did not intend. For example, you might notice that the multiplication table is symmetric, because ab = ba, so all the entries in the table appear twice. You could save ink by printing only half the table. To do that, you only have to change one line of printMultTable. Change printMultiples (i, high); to printMultiples (i, i); and you get
generalize: To replace something unnecessarily specific (like a constant value) with something appropriately general (like a variable or parameter). Local variables cannot be accessed from outside their home function. by using local variables). infinite loop: A loop whose condition is always true. written as \t in C++. and sometimes even easier to write. encapsulate: To divide a large complex program into components (like functions) and isolate the components from each other (for example. more likely to be reused. . that causes the cursor to move to the next tab stop on the current line. and do not interfere with any other functions.11. Generalization makes code more versatile. I demonstrated a style of development based on developing code to do simple.11 Glossary loop: A statement that executes repeatedly while a condition is true or until some condition is satisfied. body: The statements inside the loop. specific things. including the evaluation of the condition. GLOSSARY 63 1 2 3 4 5 6 7 4 6 8 10 12 14 9 12 15 18 21 16 20 24 28 25 30 35 36 42 49 I'll leave it up to you to figure out how it works. In this chapter. development plan: A process for developing a program. tab: A special character.6. iteration: One pass through (execution of) the body of the loop. and then encapsulating and generalizing. 6. local variable: A variable that is declared inside a function and that exists only within that function.
it is not possible to avoid C strings altogether. sometimes called "a native C string. In a few places in this chapter I will warn you about some problems you might run into using apstrings instead of C strings. which is a type created specifically for the Computer Science AP Exam. so for the most part we are going to avoid them. 65 . and using them requires some concepts we have not covered yet. there are several kinds of variables in C++ that can store strings." The syntax for C strings is a bit ugly. Educational Testing service. int and double. characters.1 Unfortunately. integers.Chapter 7 Strings and things 7. It will be a few more chapters before I can give a complete definition. 1 In order for me to talk about AP classes in this book.1 Containers for strings We have seen five types of values—booleans. I have to include the following text: "Inclusion of the C++ classes defined for use in the Advanced Placement Computer Science courses does not constitute endorsement of the other material in this textbook by the College Board. or the AP Computer Science Development Committee. but for now a class is a collection of functions that defines the operations we can perform on some type. The string type we are going to use is called apstring. In fact. So far we have no way to store a string in a variable or perform operations on strings. The apstring class contains all the functions that apply to apstrings. The versions of the C++ classes defined for use in the AP Computer Science courses included in this textbook were accurate as of 20 July 1999. floating-point numbers and strings—but only four types of variables—bool. Revisions to the classes may have been made since that time. One is a basic type that is part of the C++ language. char." You might be wondering what they mean by class.
2 apstring variables You can create a variable with type apstring in the usual ways: apstring first. cout << letter << endl. The letter ("zeroeth") of "banana" is b. " or "world. The expression fruit[1] indicates that I want character number 1 from the string named fruit. The first line creates an apstring without giving it a value. For 0th 2th the . 7.66 CHAPTER 7. When I output the value of letter. you will have to include the header file for the apstring class." The third line is a combined declaration and assignment. you have to put zero in square brackets: char letter = fruit[0]. Unless you are a computer scientist. In order to compile this code. you should type in the program above and make sure you can compile and run it. In this case."." appear. when we assign them to an apstring variable. first = "Hello. We can output strings in the usual way: cout << first << second << endl. STRINGS AND THINGS 7. also called an initialization. The first operation we are going to perform on a string is to extract one of the characters. ". The details of how to do this depend on your programming environment. char letter = fruit[1]. The result is stored in a char named letter. The 1th letter ("oneth") is a and the ("twoeth") letter is n.cpp to the list of files you want to compile. and you will have to add the file apstring. they are converted automatically to apstring values. Normally when string values like "Hello. I get a surprise: a a is not the first letter of "banana". perverse reasons. Before proceeding. C++ uses square brackets ([ and ]) for this operation: apstring fruit = "banana".3 Extracting characters from a string Strings are called "strings" because they are made up of a sequence. apstring second = "world. If you want the the zereoth letter of a string. The second line assigns it the string value "Hello. computer scientists always start counting from zero. or string. of characters. they are treated as C strings.
length(). fruit. which means that when index is equal to the length of the string. length takes no arguments. select each character in turn.4 Length To find the length of a string (number of characters). 7.length(). A natural way to encode a traversal is with a while statement: int index = 0. // WRONG!! That won't work. The syntax for function invocation is called "dot notation. while (index < fruit. from the name of the function. char last = fruit[length]. char last = fruit[length-1]. we can use the length function. we would say that we are invoking the length function on the string named fruit. The return value is an integer.length(). do something to it. This vocabulary may seem strange. Notice that the condition is index < fruit. the condition is false and the body of the .length()) { char letter = fruit[index]. Since we started counting at 0. LENGTH 67 7. in this case 6. as indicated by the empty parentheses (). length = fruit. This pattern of processing is called a traversal.4. cout << letter << endl. The syntax for calling this function is a little different from what we've seen before: int length. the 6 letters are numbered from 0 to 5. Notice that it is legal to have a variable with the same name as a function. and continue until the end. but we will see many more examples where we invoke a function on an object. int length = fruit.7. To get the last character. index = index + 1. To describe this function call.length(). you might be tempted to try something like int length = fruit. The reason is that there is no 6th letter in "banana". length. To find the last letter of a string.5 Traversal A common thing to do with a string is start at the beginning. } This loop traverses the string and outputs each letter on a line by itself." because the dot (period) separates the name of the object. you have to subtract 1 from length.
find returns -1. If the given letter does not appear in the string. STRINGS AND THINGS loop is not executed. The find function is like the opposite the [] operator. This example finds the index of the letter 'a' in the string. so it is not obvious what find should do. An index is a variable or value used to specify one member of an ordered set. the letter appears three times. As an exercise. apstring fruit = "banana". The set has to be ordered so that each letter has an index and each index refers to a single character.7 The find function The apstring class provides several other functions that you can invoke on strings. According to the documentation. you will get a run-time error and a message something like this: index out of range: 6. For example.find("nan"). .68 CHAPTER 7. there is a version of find that takes another apstring as an argument and that finds the index where the substring appears in the string. The name of the loop variable is index. write a function that takes an apstring as an argument and that outputs the letters backwards.2 I talked about run-time errors. find takes a character and finds the index where that character appears.3. int index = fruit.length()-1. Well. apstring fruit = "banana". If you use the [] operator and you provide an index that is negative or greater than length-1. 7. now we are. because we haven't been doing many things that can cause one.find('a'). So far. 7. string: banana Try it in your development environment and see how it looks.6 A run-time error Way back in Section 1. it returns the index of the first appearance. in this case the set of characters in the string. The last character we access is the one with the index fruit. Instead of taking an index and extracting the character at that index. In addition. The index indicates (hence the name) which one you want. all on one line. int index = fruit. you probably haven't seen many run-time errors. which are errors that don't appear until a program has started running. In this case. so the result is 1.
int find (apstring s. } Instead of invoking this function on an apstring. One way to generalize the find function is to write a version that takes an additional parameter—the index where we should start looking.4 that there can be more than one function with the same name. } return -1. This program demonstrates a common idiom.9 Looping and counting The following program counts the number of times the letter 'a' appears in a string: apstring fruit = "banana". C++ knows which version of find to invoke by looking at the type of the argument we provide. called a counter. (To . we have to pass the apstring as the first argument. int length = fruit. The other arguments are the character we are looking for and the index where we should start. int i) { while (i<s. char c. 7. 7. int count = 0. like the first version of find. while (index < length) { if (fruit[index] == 'a') { count = count + 1. int index = 0. } index = index + 1. The variable count is initialized to zero and then incremented each time we find an 'a'. we may not want to start at the beginning of the string. Here is an implementation of this function. i = i + 1. as long as they take a different number of parameters or different types.8 Our own version of find If we are looking for a letter in an apstring.length().7. You should remember from Section 5.length()) { if (s[i] == c) return i. In this case. OUR OWN VERSION OF FIND 69 This example returns the value 2.8. } cout << count << endl.
or you can write index++. Looking at this. while (index < length) { if (fruit[index] == 'a') { count++. I would discourage you from using them. Neither operator works on apstrings. and neither should be used on bools. rewrite this function so that instead of traversing the string. As a second exercise. you might see something like: cout << i++ << endl. count contains the result: the total number of a's. 7. we can rewrite the letter-counter: int index = 0. and generalize it so that it accepts the string and the letter as arguments.) When we exit the loop.. you can try it. it is not clear whether the increment will take effect before or after the value is displayed. and -. but you shouldn't mix them. char or double. Remember. it is legal to increment a variable and use it in an expression at the same time. STRINGS AND THINGS increment is to increase by one. // WRONG!! Unfortunately. encapsulate this code in a function named countLetters.. Technically. which is a noun.subtracts one. As an exercise. to discourage you even more. Because expressions like this tend to be confusing. Using the increment operators. For example. } index++. This is often a difficult bug to track down. If you really want to know. } It is a common error to write something like index = index++.70 CHAPTER 7. The effect of this statement is to leave the value of index unchanged. it uses the version of find we wrote in the previous section. so the compiler will not warn you. this is syntactically legal. I'm not going to tell you what the result is. . In fact. it is the opposite of decrement. and unrelated to excrement. The ++ operator adds one to the current value of an int.10 Increment and decrement operators Incrementing and decrementing are such common operations that C++ provides special operators for them. you can write index = index +1.
Mack.7. "Abecedarian" refers to a series or list in which the elements appear in alphabetical order. cout << dessert << endl. apstring dessert = fruit + bakedGood. Unfortunately. Nack.11. To concatenate means to join the two operands end to end. It is also possible to concatenate a character onto the beginning or end of an apstring. char letter = 'J'. Lack. For example: apstring fruit = "banana". apstring bakedGood = " nut bread". C++ will automatically convert the other. the + operator can be used on strings. Pack and Quack. } The output of this program is: Jack Kack Lack Mack Nack Oack Pack Qack . letter++. though. In the following example. As long as one of the operands is an apstring. For example. the names of the ducklings are Jack. in Robert McCloskey's book Make Way for Ducklings.11 String concatenation Interestingly. Ouack. the + operator does not work on native C strings. The output of this program is banana nut bread. it performs string concatenation. because both operands are C strings. STRING CONCATENATION 71 7. Kack. Here is a loop that outputs these names in order: apstring suffix = "ack". so you cannot write something like apstring dessert = "banana" + " nut bread". while (letter <= 'Q') { cout << letter + suffix << endl. we will use concatenation and character arithmetic to output an abecedarian series.
if you want to know if two strings are equal: if (word == "banana") { cout << "Yes. Zebra. that the apstring class does not handle upper and lower case letters the same way that people do. Your word. if (word < "banana") { cout << "Your word. that's not quite right because I've misspelled "Ouack" and "Quack. an expression like letter + "ack" is syntactically legal in C++. we have no bananas!" << endl. " << word << ". though. which is making the program realize that zebras are not fruit. } else { cout << "Yes. be careful to use string concatenation only with apstrings and not with native C strings. modify the program to correct this error.72 CHAPTER 7. } The other comparison operations are useful for putting words in alphabetical order." << endl. For example. STRINGS AND THINGS Of course. world!. apstring greeting = "Hello. greeting[0] = 'J'." << endl. at least in my development environment. world!". The next sections explains how. All the upper case letters come before all the lower case letters.13 apstrings are comparable All the comparison operators that work on ints and doubles also work on apstrings. cout << greeting << endl. " << word << ". comes before banana. 7. A common way to address this problem is to convert strings to a standard format. . Again. comes before banana. like all lower-case. } else if (word > "banana") { cout << "Your word. 7." As an exercise. comes after banana. we have no bananas!" << endl. For example. Unfortunately. before performing the comparison. I will not address the more difficult problem. although it produces a very strange result. } You should be aware.12 apstrings are mutable You can change the letters in an apstring one at a time using the [] operator on the left side of an assignment. produces the output Jello. As a result.
newlines.15 Other apstring functions This chapter does not cover all the apstring functions. if (isalpha(letter)) { cout << "The character " << letter << " is a letter.14 Character classification It is often useful to examine a character and test whether it is upper or lower case.7. there are two functions that convert letters from one case to the other.14. use the character classification and conversion library to write functions named apstringToUpper and apstringToLower that take a single apstring as a parameter. Other character classification functions include isdigit. because it is legal to use this kind of integer in a conditional. this sort of thing should not be allowed—integers are not the same thing as boolean values. There are also isupper and islower. are covered in Section 15. In order to use these functions. and isspace. cout << letter << endl. and some non-zero value if it is." << endl. and that modify the string by converting all the letters to upper or lower case. which distinguish upper and lower case letters.4. but for reasons I don't even want to think about. Two additional ones. which identifies all kinds of "white" space. c str and substr. char letter = 'a'.2 and Section 15. . Finally. the C++ habit of converting automatically between types can be useful. Nevertheless. Both take a single character as a parameter and return a (possibly converted) character. and a few others. CHARACTER CLASSIFICATION 73 7. } You might expect the return value from isalpha to be a bool. Technically. it is actually an integer that is 0 if the argument is not a letter. you have to include the header file ctype. including spaces. C++ provides a library of functions that perform this kind of character classification. as shown in the example. The value 0 is treated as false. As an exercise. This oddity is not as inconvenient as it seems. tabs.h. char letter = 'a'. The output of this code is A. The return type should be void. and all non-zero values are treated as true. or whether it is a character or a digit. which identifies the digits 0 through 9. called toupper and tolower. letter = toupper (letter). 7.
traverse: To iterate through all the elements of a set performing a similar operation on each.16 Glossary object: A collection of related data that comes with a set of functions that operate on it. decrement: Decrease the value of a variable by one. counter: A variable used to count something. The decrement operator in C++ is --. The increment operator in C++ is ++. because it is meant to be one better than C. and apstrings. STRINGS AND THINGS 7. index: A variable or value used to select one of the members of an ordered set. like a character from a string. usually initialized to zero and then incremented. concatenate: To join two operands end-to-end. In fact. . increment: Increase the value of a variable by one.74 CHAPTER 7. The objects we have used so far are the cout object provided by the system. that's why C++ is called C++.
For example. a boolean value. consider the concept of a mathematical point. The answer is a struct definition: struct Point { double x. A natural way to represent a point in C++ is with two doubles. with a comma separating the coordinates. or structure. It is also useful to be able to create your own compound values. (0. y) indicates the point x units to the right and y units up from the origin. This ambiguity is useful. is how to group these two values into a compound object. C++ provides two mechanisms for doing that: structures and classes. In mathematical notation. a point is two numbers (coordinates) that we treat collectively as a single object. Thus. points are often written in parentheses. Depending on what we are doing. 75 . The question. then. }. apstrings are different in the sense that they are made up of smaller pieces. We will start out with structures and get to classes in Chapter 14 (there is not much difference between them). a floating-point number.1 Compound values Most of the data types we have been working with represent a single value—an integer. 0) indicates the origin. apstrings are an example of a compound type.Chapter 8 Structures 8. the characters. At one level. 8. and (x. we may want to treat a compound type as a single thing (or object). or we may want to access its parts (or instance variables). y.2 Point objects As a simple example of a compound structure.
Once you have defined the new structure. blank. The first line is a conventional variable declaration: blank has type Point.0.length(). for reasons I will explain a little later.0. This definition indicates that there are two elements in this structure. named x and y. These elements are called instance variables. Notice that there is no conflict between the local variable named x and the instance variable named x. Of course. even if it is empty. It might seem odd to put a semi-colon after a squiggly-brace. The expression blank.3 Accessing instance variables You can read the values of an instance variable using the same syntax we used to write them: int x = blank.x. STRUCTURES struct definitions appear outside of any function definition. that value is a compound object with two named instance variables. as in fruit. blank. It is a common error to leave off the semi-colon at the end of a structure definition. In this case. The "dot notation" used here is similar to the syntax for invoking a function on an object. usually at the beginning of the program (after the include statements). The result of these assignments is shown in the following state diagram: blank x: y: 3 4 As usual. you can create variables with that type: Point blank. The next two lines initialize the instance variables of the structure." In this case we assign that value to a local variable named x. The purpose of dot notation is to identify which variable you are referring to unambiguously.x means "go to the object named blank and get the value of x.76 CHAPTER 8. one difference is that function names are always followed by an argument list. .y = 4.x = 3. the name of the variable blank appears outside the box and its value appears inside the box. but you'll get used to it. 8.
do not work on structures. " << p2.x + blank.x << ". %.0 }. " << blank.0 }.x << ". the second line calculates the value 25. 4. Actually. If you add a typecast: Point blank.y * blank. It is legal to assign one structure to another.8. 8. 4. // WRONG !! You might wonder why this perfectly reasonable statement should be illegal.0.0. 4.0. An initialization looks like this: Point blank = { 3. On the other hand. this syntax can be used only in an initialization. For example: Point p1 = { 3. 4.).y << endl. it is possible to define the meaning of these operators for the new type.0 }.y.0. 4. 4. Point blank. x gets the first value and y gets the second. double distance = blank. The output of this program is 3.y << endl. like mathematical operators ( +. It can be used in two ways: to initialize the instance variables of a structure or to copy the instance variables from one structure to another. not in an assignment statement. The first line outputs 3. blank = (Point){ 3.) and comparison operators (==.4. So the following is illegal.x * blank. but we won't do that in this book. I'm not sure.4 Operations on structures Most of the operators we have been using on other types. Unfortunately. The values in squiggly braces get assigned to the instance variables of the structure one by one.0 }. cout << p2. etc. . etc. OPERATIONS ON STRUCTURES 77 You can use dot notation as part of any C++ expression. the assignment operator does work for structures. That works. blank = { 3. in order. >. So in this case. cout << blank. but I think the problem is that the compiler doesn't know what type the right hand side should be. so the following are legal. Point p2 = p1.
" << p. we can rewrite the distance function from Section 5. } printPoint takes a point as an argument and outputs it in the standard format.6 Call by value When you pass a structure as an argument.y << ")" << endl. Point p2) { double dx = p2. the stack diagram looks like this: main blank x: y: 3 4 printPoint p x: y: 3 4 .y .x . } 8. there are two variables (one in the caller and one in the callee) that have the same value. double dy = p2.y. when we call printPoint.5 Structures as parameters You can pass structures as parameters in the usual way. it will output (3.x << ".p1.2 so that it takes two Points as parameters instead of four doubles. STRUCTURES 8. If you call printPoint (blank).78 CHAPTER 8. Instead.x. void printPoint (Point p) { cout << "(" << p. For example. 4). For example. double distance (Point p1. As a second example. remember that the argument and the parameter are not the same variable.p1. return sqrt (dx*dx + dy*dy). at least initially.
y = temp. The output of this program is as expected: (3. reflect (blank). Of course. we have to specify that we want to pass the parameter by reference. p. This kind of parameter-passing is called "pass by value" because it is the value of the structure (or other type) that gets passed to the function. We do that by adding an ampersand (&) to the parameter declaration: void reflect (Point& p) { double temp = p. there is no reason for printPoint to modify its parameter.x = p. p.y.y.7." This mechanism makes it possible to pass a structure to a procedure and modify it. } Now we can call the function in the usual way: printPoint (blank). you can reflect a point around the 45-degree line by swapping the two coordinates. The most obvious (but incorrect) way to write a reflect function is something like this: void reflect (Point p) { double temp = p. 4) (4. it would have no effect on blank. Instead.7 Call by reference An alternative parameter-passing mechanism that is available in C++ is called "pass by reference.x. so this isolation between the two functions is appropriate. because the changes we make in reflect will have no effect on the caller. For example. p. printPoint (blank). 3) .y = temp. p. } // WRONG !! But this won't work. 8.x.8. CALL BY REFERENCE 79 If printPoint happened to change one of the instance variables of p.x = p.
. almost all structures are passed by reference almost all the time. On the other hand. The usual representation for a reference is a dot with an arrow that points to whatever the reference refers to. it is less safe. Nevertheless. because the callee can modify the structure. 8. struct Rectangle { Point corner. The important thing to see in this diagram is that any changes that reflect makes in p will also affect blank. Passing structures by reference is more versatile than passing by value. It is also faster. In this book I will follow that convention. since it is harder to keep track of what gets modified where.80 CHAPTER 8. because the system does not have to copy the whole structure. }. The question is. To do that in C++. we will define a structure that contains a Point and two doubles. never at an angle. or I could specify two opposing corners. or I could specify one of the corners and the size. what information do I have to provide in order to specify a rectangle? To keep things simple let's assume that the rectangle will be oriented vertically or horizontally. There are a few possibilities: I could specify the center of the rectangle (two coordinates) and its size (width and height). STRUCTURES Here's how we would draw a stack diagram for this program: main blank x: y: 3 4 4 3 reflect p The parameter p is a reference to the structure named blank. height. The most common choice in existing programs is to specify the upper left corner of the rectangle and the size. double width. in C++ programs.8 Rectangles Now let's say that we want to create a structure to represent a rectangle.
It makes the most sense to read this statement from right to left: "Extract x from the corner of the box.x. 0.0. we can compose the two statements: double x = box. Alternatively.height << endl. this sort of thing is quite common. 200. double x = temp.0.0. in fact." While we are on the subject of composition. In order to access the instance variables of corner. cout << box. The innermost squiggly braces are the coordinates of the corner point.width += 50. and assign it to the local variable x. together they make up the first of the three values that go into the new Rectangle. create the Point and the Rectangle at the same time: Rectangle box = { { 0.0 }. this means that in order to create a Rectangle. 0. 100. The figure shows the effect of this assignment. Rectangle box = { corner. we have to create a Point first: Point corner = { 0.0 }. we can use a temporary variable: Point temp = box. I should point out that you can.8. This code creates a new Rectangle structure and initializes the instance variables. RECTANGLES 81 Notice that one structure can contain another. This statement is an example of nested structure. Of course.x.8. .corner. box corner: x: y: 0 0 100 200 width: height: We can access the width and height in the usual way: box.corner. 100.0. 200.0 }. In fact.0.0 }.
When people start passing things like integers by reference.9 Structures as return types You can write functions that return structures.10 Passing other types by reference It's not just structures that can be passed by reference. x = y.x + box. For example. we could write something like: void swap (int& x. } We would call this function in the usual way: int i = 7. int j = 9. y = temp. return result.corner. y}. int& y) { int temp = x. The output of this program is 97.82 CHAPTER 8. to swap two integers.0. we have to pass a box as an argument (notice that it is being passed by reference). 8.width/2. findCenter takes a Rectangle as an argument and returns a Point that contains the coordinates of the center of the Rectangle: Point findCenter (Rectangle& box) { double x = box. The output of this program is (50. It would modify x and y and have no effect on i and j.height/2. 100. 200 }. For example: . If the parameters x and y were declared as regular parameters (without the &s). too. cout << i << j << endl.y + box. swap would not work. } To call this function. Draw a stack diagram for this program to convince yourself this is true.0}. All the other types we've seen can. swap (i. 0. double y = box. Point center = findCenter (box). STRUCTURES 8. j).corner. Point result = {x. they often try to use an expression as a reference argument. 100). and assign the return value to a Point variable: Rectangle box = { {0. For example. printPoint (center).
We can invoke the good function on cin to check what is called the stream state.8. There are many ways to get input. or anything sensible like that. as well as more exotic mechanisms like voice control and retinal scanning. the program converts it into an integer value and stores it in x. Most of the time. The >> operator causes the program to stop executing and wait for the user to type something. If the user types a valid integer. Fortunately. 8. To get an integer value from the user: int x. Thus. we know that some previous operation failed. int j = 9. If the user types something other than an integer. In the header file iostream. It is a little tricky to figure out exactly what kinds of expressions can be passed by reference. C++ doesn't report an error. they do the same thing every time they run. swap (i. // WRONG!! This is not legal because the expression j+1 is not a variable—it does not occupy a location that the reference can refer to. . and also that the next operation will fail. Instead. For now a good rule of thumb is that reference arguments have to be variables. including keyboard input. mouse movements and button clicks. In this text we will consider only keyboard input. we want programs that take input from the user and respond accordingly. cin >> x. j+1). there is a way to check and see if an input statement succeeds. getting input from the user might look like this: int main () { int x.h. GETTING USER INPUT 83 int i = 7. it puts some meaningless value in x and continues. If not. // prompt the user for input cout << "Enter an integer: ". though. then the last input statement succeeded.11 Getting user input The programs we have written so far are pretty predictable. // get input cin >> x. C++ defines an object named cin that handles input in much the same way that cout handles output.11. good returns a bool: if true.
you can print an error message and ask the user to try again." << endl.good() == false) { cout << "That was not an integer. Because of these problems (inability to handle errors and funny behavior). So. If not. We will get to that in Section 15. if you run this program and type your full name. I avoid using the >> operator altogether. apstring name. . you can convert it to an integer value. cout << "What is your name? ". Unfortunately. getline reads the entire line until the user hits Return or Enter. STRUCTURES // check and see if the input statement succeeded if (cin. Instead. if you wanted the user to type an integer. unless I am reading data from a source that is known to be error-free. cin >> name. } cin can also be used to input an apstring: apstring name. For example. this statement only takes the first word of input.84 CHAPTER 8.4. } // print the value we got from the user cout << x << endl. I use a function in the apstring called getline. If so. return 0. and leaves the rest for the next input statement. In fact. The first argument to getline is cin. it will only output your first name. This is useful for inputting strings that contain spaces. To convert a string to an integer you can use the atoi function defined in the header file stdlib. getline (cin. cout << name << endl.h. you could input a string and then check to see if it is a valid integer. getline is generally useful for getting input of any kind. which is where the input is coming from. cout << name << endl. name). return -1. The second argument is the name of the apstring where you want the result to be stored. cout << "What is your name? ".
. Changes to the parameter also affect the argument variable. instance variable: One of the named pieces of data that make up a structure. pass by value: A method of parameter-passing in which the value provided as an argument is copied into the corresponding parameter. reference: A value that indicates or refers to a variable or structure. GLOSSARY 85 8.8. but the parameter and the argument occupy distinct locations.12. pass by reference: A method of parameter-passing in which the parameter is a reference to the argument variable. In a state diagram. a reference appears as an arrow.12 Glossary structure: A collection of data grouped together and treated as a single object.
The state diagram for this object looks like this: time hour: minute: second: 11 59 3. let's make second a double.14159 }.1 Time As a second example of a user-defined structure. 3. The various pieces of information that form a time are the hour. minute and second. The first step is to decide what type each instance variable should be.14159 87 . double second. We can create a Time object in the usual way: Time time = { 11. we will define a type called Time. minute. 59. Here's what the structure definition looks like: struct Time { int hour. }.Chapter 9 More structures 9. which is used to record the time of day. so we can record fractions of a second. so these will be the instance variables of the structure. Just to keep things interesting. It seems clear that hour and minute should be integers.
14159. . Technically. and it has no side effects like modifying an argument or outputting something.hour) return true.4 Pure functions A function is considered a pure function if the result depends only on the arguments. For some operations. is 11:59:3. because every object is an instance (or example) of some type. 9. The return value is either a basic type or a new object created inside the function. One example is after. Often returns void. The only result of calling a pure function is the return value.hour > time2. this is a type of modifier. } The output of this function.minute << ":" << t. Time& time2) { if (time1. if we pass time an argument.second << endl.hour < time2.3 Functions for objects In the next few sections.hour) return false. 9. you will have a choice of several possible interfaces. if (time1.2 printTime When we define a new type it is a good idea to write function that displays the instance variables in a human-readable form. 9. fill-in function: One of the parameters is an "empty" object that gets filled in by the function.88 CHAPTER 9. The reason that instance variables are so-named is that every instance of a type has a copy of the instance variables for that type. I will demonstrate several possible interfaces for functions that operate on objects. which compares two Times and returns a bool that indicates whether the first operand comes after the second: bool after (Time& time1. MORE STRUCTURES The word "instance" is sometimes used when we talk about objects. modifier: Takes objects as parameters and modifies some or all of them.hour << ":" << t. so you should consider the pros and cons of each of these: pure function: Takes objects and/or basic types as arguments but does not modify the objects. For example: void printTime (Time& t) { cout << t.
35. . then you could use addTime to figure out when the bread will be done. if (time1. sum. which calculates the sum of two times.minute + t2. Can you think of one? The problem is that this function does not deal with cases where the number of seconds or minutes adds up to more than 60. = t1.0 }. there are cases where the result is not correct.minute) return false.second = t1.9.second) return true.second.hour. On the other hand. or extra minutes into the hours column. return false.second (Time& t1.minute = t1.minute) return true. which is correct. if (time1. would you mention that case specifically? A second example is addTime. 14. For example.hour + t2.minute < time2.minute. return sum. Time& t2) { t1. you could use addTime to figure out when the bread will be done. sum. if it is 9:14:30. breadTime). sum.second + t2. Time& t2) { Time sum. When that happens we have to "carry" the extra seconds into the minutes column. corrected version of this function.hour = sum.minute > time2. } Here is an example of how to use this function. PURE FUNCTIONS 89 if (time1. sum. Time doneTime = addTime (currentTime. Time addTime Time sum. 0. Here's a second.0 }.second > time2. Time breadTime = { 3.minute sum.hour = t1. = t1.hour. The output of this program is 12:49:30.second.minute + t2. and your breadmaker takes 3 hours and 35 minutes. } What is the result of this function if the two times are equal? Does that seem like the appropriate result for this function? If you were writing the documentation for this function.hour + t2.4. If currentTime contains the current time and breadTime contains the amount of time it takes for your breadmaker to make bread. printTime (doneTime).minute.second + t2. Here is a rough draft of this function that is not quite right: Time addTime (Time& t1. Time currentTime = { 9. 30.
Furthermore. is equivalent to sum.. . there is a nice feature in C++. sum. For example. The syntax looks like this: void printTime (const Time& time) . you should get a compiler error. sum.. These operators provide a concise way to increment and decrement variables. 9.second >= 60. If you are writing a function and you do not intend to modify a parameter. the statement sum.6 Modifiers Of course. += and -=. it's starting to get big.0) { sum. because it avoids copying the argument.5 const parameters You might have noticed that the parameters for after and addTime are being passed by reference.minute += 1. } if (sum. const Time& t2) .0. Time addTime (const Time& t1. passing by reference usually is more efficient.hour += 1. } Although it's correct.second -= 60. it can help remind you. On the other hand.. they do not modify the parameters they receive. except by affecting the return value. The advantage of passing by value is that the calling function and the callee are appropriately encapsulated—it is not possible for a change in one to affect the other.minute >= 60) { sum. Since these are pure functions. Functions that do are called modifiers. I've included only the first line of the functions.second . 9.second -= 60. that can make reference parameters just as safe as value parameters.. I will suggest an alternate approach to this problem that will be much shorter.90 CHAPTER 9. } return sum. called const.60. you can declare that it is a constant reference parameter. This code demonstrates two operators we have not seen before. If you tell the compiler that you don't intend to change a parameter. sometimes you want to modify one of the arguments. Later.0.second = sum. MORE STRUCTURES if (sum. so I could just as well have passed them by value.minute -= 60. or at least a warning. If you try to change one.
Can you think of a solution that does not require iteration? 9.second -= 60.0) { time. time.second += secs.second += secs. it is not enough to subtract 60 once.hour += 1. Instead of creating a new object every time addTime is called. Again. time.0) { time.minute += 1. } } This solution is correct.9. Compare the following with the previous version: .0. } } The first line performs the basic operation. } while (time. } if (time. We can do that by replacing the if statements with while statements: void increment (Time& time. double secs) { time. we could require the caller to provide an "empty" object where addTime can store the result. if (time.minute -= 60. which adds a given number of seconds to a Time object. a rough draft of this function looks like: void increment (Time& time.hour += 1.second -= 60. double secs) { time. FILL-IN FUNCTIONS 91 As an example of a modifier.second >= 60. time. we have to keep doing it until second is below 60. consider increment.minute -= 60. Is this function correct? What happens if the argument secs is much greater than 60? In that case. the remainder deals with the special cases we saw before. while (time.minute >= 60) { time.7. but not very efficient. time.minute >= 60) { time.0.minute += 1.second >= 60.7 Fill-in functions Occasionally you will see functions like addTime written with a different interface (different arguments and return values).
second = t1.hour + t2.second + t2. In general. For the vast majority of programming. 9.minute -= 60. This approach might be called a functional programming style. This can be slightly more efficient.second. called functional programming languages. } if (sum. although it can be confusing enough to cause subtle errors. Nevertheless. .minute + t2. and cases where functional programs are less efficient. I recommend that you write pure functions whenever it is reasonable to do so. sum. In each case.hour += 1. if (sum. that only allow pure functions. and resort to modifiers only if there is a compelling advantage.minute = t1. I wrote a rough draft (or prototype) that performed the basic calculation.0) { sum. it can lead to code that is unnecessarily complicated—since it deals with many special cases—and unreliable— since it is hard to know if you have found all the errors.92 CHAPTER 9.minute >= 60) { sum.minute.minute += 1. there are programming languages.9 Incremental development versus planning In this chapter I have demonstrated an approach to program development I refer to as rapid prototyping with iterative improvement. Some programmers believe that programs that use pure functions are faster to develop and less error-prone than programs that use modifiers.0. correcting flaws as I found them. sum.second -= 60. there are times when modifiers are convenient. but the third cannot. sum. } } One advantage of this approach is that the caller has the option of reusing the same object repeatedly to perform a series of additions. MORE STRUCTURES void addTimeFill (const Time& t1.hour = t1. and then tested it on a few cases. Although this approach can be effective. Time& sum) { sum.8 Which is best? Anything that can be done with modifiers and fill-in functions can also be done with pure functions. Notice that the first two parameters can be declared const. sum. In fact. 9. const Time& t2.hour.second >= 60. it is worth a spending a little run time to avoid a lot of debugging time.
Here is a function that converts a Time into a double: double convertToSeconds (const Time& t) { int minutes = t.0). in which a little insight into the problem can make the programming much easier. and the hour is the "3600's column.9. return time. secs -= time. our intuition for dealing with times is better. Assuming you are convinced. as usual. double seconds = minutes * 60 + t. time. secs -= time. time.minute * 60.hour = int (secs / 3600.0). that the functions it calls are correct). const Time& t2) { double seconds = convertToSeconds (t1) + convertToSeconds (t2). we were effectively doing addition in base 60. } You might have to think a bit to convince yourself that the technique I am using to convert from one base to another is correct. As an exercise.second.hour * 3600. time. and it is much easier to demonstrate that it is correct (assuming." When we wrote addTime and increment.hour * 60 + t." the minute is the "60's column".second = secs. Thus an alternate approach to the whole problem is to convert Times into doubles and take advantage of the fact that the computer already knows how to do arithmetic with doubles. GENERALIZATION 93 An alternative is high-level planning.0.10. In this case the insight is that a Time is really a three-digit number in base 60! The second is the "ones column. } Now all we need is a way to convert from a double to a Time object: Time makeTime (double secs) { Time time. which is why we had to "carry" from one column to the next. } This is much shorter than the original version. . 9. rewrite increment the same way.minute = int (secs / 60.minute. we can use these functions to rewrite addTime: Time addTime (const Time& t1. return seconds. Base conversion is more abstract.10 Generalization In some ways converting from base 60 to base 10 and back is harder than just dealing with times. return makeTime (seconds).
I mentioned this word in Chapter 1. you can write n − 1 as the first digit and 10 − n as the second digit. the process of designing algorithms is interesting. It is also easier to add more features later. That's an algorithm! Similarly. fewer opportunities for error). to find the product of n and 9. without difficulty or conscious thought. require no intelligence. but did not define it carefully. and useful algorithms computer science has produced. sometimes making a problem harder (more general) makes is easier (fewer special cases. and make the investment of writing the conversion functions (convertToSeconds and makeTime). For example. consider something that is not an algorithm. Understanding natural language is a good example. Data Structures. and more reliable. In effect. MORE STRUCTURES But if we have the insight to treat times as base 60 numbers. One of the characteristics of algorithms is that they do not require any intelligence to carry out. . We all do it. If you take the next class in the Computer Science sequence. But if you were "lazy. On the other hand. but so far no one has been able to explain how we do it. This trick is a general solution for multiplying any single-digit number by 9. First. you probably memorized the multiplication table. as opposed to a specific solution to a single problem. It is not easy to define. quite literally. are the most difficult to express algorithmically. the techniques you learned for addition with carrying. and long division are all algorithms. you have written an algorithm. That kind of knowledge is not really algorithmic.11 Algorithms When you write a general solution for a class of problems. clever. For example. at least not in the form of an algorithm. so I will try a couple of approaches. In my opinion. Some of the things that people do naturally. we get a program that is shorter. you will see some of the most interesting. The naive approach would be to implement subtraction with borrowing. and a central part of what we call programming.94 CHAPTER 9. 9. subtraction with borrowing. intellectually challenging. They are mechanical processes in which each step follows from the last according to a simple set of rules. Ironically. easier to read and debug. you memorized 100 specific solutions. Using the conversion functions would be easier and more likely to be correct. When you learned to multiply single-digit numbers. it is embarrassing that humans spend so much time in school learning to execute algorithms that. imagine subtracting two Times to find the duration between them. you will have the opportunity to design simple algorithms for a variety of problems. Later in this book." you probably cheated by learning a few tricks.
Each structure has its own copy of the instance variables for its type.12 Glossary instance: An example from a category. constant reference parameter: A parameter that is passed by reference but that cannot be modified. and that has so effects other than returning a value. functional programming style: A style of program design in which the majority of functions are pure. pure function: A function whose result depends only on its parameters. unintelligent process. modifier: A function that changes one or more of the objects it receives as parameters. and usually returns void. My cat is an instance of the category "feline things.9. instance variable: One of the named data items that make up an structure.12. algorithm: A set of instructions for solving a class of problems by a mechanical. . GLOSSARY 95 9." Every object is an instance of some type. fill-in function: A function that takes an "empty" object as a parameter and fills it its instance variables instead of generating a return value.
again. the second creates a vector of doubles. they are not very useful because they create vectors that have no elements (their length is zero). An apstring is similar to a vector. which is the size of the new vector. The type that makes up the vector appears in angle brackets (< and >). In fact.h. the constructor takes a single argument.Chapter 10 Vectors A vector is a set of values where each value is identified by a number (called an index). The syntax here is a little odd. including basic types like ints and doubles. A constructor is a special function that creates new objects and initializes their instance variables. The function we are invoking is an apvector constructor. It is more common to specify the length of the vector in parentheses: apvector<int> count (4). since it is made up of an indexed set of characters. You can create a vector the same way you create other variable types: apvector<int> count. Although these statements are legal. apvector<double> doubleVector. that's exactly what it is. it looks like a combination of a variable declarations and a function call. you have to include the header file apvector. In this case. In order to use it. and user-defined types like Point and Time. The first line creates a vector of integers named count. The vector type that appears on the AP exam is called apvector. the details of how to do that depend on your programming environment. The nice thing about vectors is that they can be made up of any type of element. The following figure shows how vectors are represented in state diagrams: 97 .
so count[0] refers to the "zeroeth" element of the vector. 0). the elements are not initialized. and count[1] refers to the "oneth" element. The small numbers outside the boxes are the indices used to identify each box. This statement creates a vector of four elements and initializes all of them to zero. count[2]++. count[1] = count[0] * 2. They could contain any values.1 Accessing elements The [] operator reads and writes the elements of a vector in much the same way it accesses the characters in an apstring.98 CHAPTER 10. count[3] -= 60. All of these are legal assignment statements. VECTORS count 0 1 2 3 0 0 0 0 The large numbers inside the boxes are the elements of the vector. the indices start at zero." the value that will be assigned to each of the elements. apvector<int> count (4. Here is the effect of this code fragment: count 0 1 2 3 7 14 1 -60 . You can use the [] operator anywhere in an expression: count[0] = 7. the second is a "fill value. When you allocate a new vector. 10. There is another constructor for apvectors that takes two parameters. As with apstrings.
Each time through the loop we use i as an index into the vector. This type of vector traversal is very common. as long as it has type int. it is almost never used for apvectors because there is a better alternative: apvector<int> copy = count. i++. 1. It is a common error to go beyond the bounds of a vector. Although this syntax is legal. there is no element with the index 4. One of the most common ways to index a vector is with a loop variable. called for. The general syntax looks like this: for (INITIALIZER. All of them start by initializing a variable.2. 2 and 3. For example: int i = 0. INCREMENTOR) { BODY } . } This while loop counts from 0 to 4. the condition fails and the loop terminates. You can use any expression as an index.10. 10. outputting the ith element. Thus. Vectors and loops go together like fava beans and a nice Chianti. when the loop variable i is 4. which is called a copy constructor because it takes one apvector as an argument and creates a new vector that is the same size. and then quits.3 for loops The loops we have written so far have a number of elements in common. or condition. they have a test. that depends on that variable. which causes a run-time error.2 Copying vectors There is one more constructor for apvectors. that expresses it more concisely. with the same elements. and inside the loop they do something to that variable. 10. COPYING VECTORS 99 Since elements of this vector are numbered from 0 to 3. like increment it. CONDITION. the body of the loop is only executed when i is 0. This type of loop is so common that there is an alternate loop statement. apvector<int> copy (count). The program outputs an error message like "Illegal vector index". The = operator works on apvectors in pretty much the way you would expect. while (i < 4) { cout << count[i] << endl.
length().1. you won't have to go through the program changing all the loops. i++) { cout << count[i] << endl. } The last time the body of the loop gets executed. determinism is a good thing. For example: for (int i = 0. though: length. That way. i < count. It is a good idea to use this value as the upper bound of a loop. } is equivalent to int i = 0. which is the index of the last element. since it puts all the loop-related statements in one place. Not surprisingly. i < 4. One of them is very useful. the value of i is count. while (CONDITION) { BODY INCREMENTOR } except that it is more concise and.100 CHAPTER 10. which is a good thing. while (i < 4) { cout << count[i] << endl. When i is equal to count. Usually.length() . since . it returns the length of the vector (the number of elements). it is easier to read. they will work correctly for any size vector. i++. 10. the condition fails and the body is not executed. VECTORS This statement is exactly equivalent to INITIALIZER. if the size of the vector changes. for (int i = 0. since it would cause a run-time error. i++) { cout << count[i] << endl.5 Random numbers Most computer programs do the same thing every time they are executed.length(). } 10. so they are said to be deterministic.4 Vector length There are only a couple of functions you can invoke on an apvector. rather than a constant.
. you might want to think about how to generate a random floating-point value in a given range. Pseudorandom numbers are not truly random in the mathematical sense. between 100. } On my machine I got the following output: 1804289383 846930886 1681692777 1714636915 You will probably get something similar. It is declared in the header file stdlib. Since y is the remainder when x is divided by upperBound. Making a program truly nondeterministic turns out to be not so easy. The return value from random is an integer between 0 and RAND MAX. hence the name. For some applications.h.0. run this loop: for (int i = 0. To see a sample. the only possible values for y are between 0 and upperBound . we would like the computer to be unpredictable. but different. A common way to do that is by dividing by RAND MAX.0 and 200. For example: int x = random (). including both end points. cout << x << endl. double y = double(x) / RAND_MAX. Games are an obvious example. More often we want to generate integers between 0 and some upper bound. including both end points. where RAND MAX is a large number (about 2 billion on my computer) also defined in the header file. they will do. though.1.10. C++ provides a function called random that generates pseudorandom numbers. Keep in mind. for example. but for our purposes. i < 4. which contains a variety of "standard library" functions. For example: int x = random (). on yours. Of course. RANDOM NUMBERS 101 we expect the same calculation to yield the same result. Each time you call random you get a different randomly-generated number.0 and 1. As an exercise.5. though. This code sets y to a random value between 0. A simple way to do that is with the modulus operator. we don't always want to work with gigantic integers. i++) { int x = random ().0. int y = x % upperBound. but there are ways to make it at least seem nondeterministic. It is also frequently useful to generate random floating-point values. that y will never be equal to upperBound. One of them is to generate pseudorandom numbers and use them to determine the outcome of the program.
void printVector (const apvector<int>& vec) { for (int i = 0.6 Statistics The numbers generated by random are supposed to be distributed uniformly. The following function takes a single argument. and fills it with random values between 0 and upperBound-1. provided that we generate a large number of values. apvector<int> vector = randomVector (numValues.7 Vector of random numbers The first step is to generate a large number of random values and store them in a vector. and then increase it later. . the size of the vector. } The return type is apvector<int>. To test this function. i++) { vec[i] = random () % upperBound. apvector<int> randomVector (int n. The following code generates a vector and outputs it: int numValues = 20. In fact it is quite common.102 CHAPTER 10. which means that this function returns a vector of integers. to help with debugging.length(). In the next few sections. i++) { cout << vec[i] << " ". since it makes it unnecessary to copy the vector. That means that each value in the range should be equally likely. it is convenient to have a function that outputs the contents of a vector." of course. } } Notice that it is legal to pass apvectors by reference. I mean 20. printVector (vector). int upperBound) { apvector<int> vec (n). we declare the parameter const. It's always a good idea to start with a manageable number. i<vec. If we count the number of times each value appears. By "large number. we will write programs that generate a sequence of random numbers and check whether this property holds true.length(). for (int i = 0. 10. } return vec. upperBound). It allocates a new vector of ints. it should be roughly the same for all values. VECTORS 10. i<vec. int upperBound = 10. Since printVector does not modify the vector.
9 we looked at a loop that traversed a string and counted the number of times a given letter appeared. Also. If these numbers are really random. Of course. COUNTING 103 On my machine the output is 3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2 6 which is pretty random-looking.8 Counting A good approach to problems like this is to think of simple functions that are easy to write.10. Back in Section 7. You can think of this program as an example of a pattern called "traverse and count.8. This approach is sometimes called bottom-up design. the number 6 appears five times. Do these results mean the values are not really uniform? It's hard to tell. and the numbers 4 and 8 never appear at all. The parameters are the vector and the integer value we are looking for. I have a function in mind called howMany that counts the number of elements in a vector that equal a given value. In fact. but a good approach is to look for subproblems that fit a pattern you have seen before. int howMany (const apvector<int>& vec. for (int i=0.length()." The elements of this pattern are: • A set or container that can be traversed. • A counter that keeps track of how many elements pass the test. it is not always obvious what sort of things are easy to write. i< vec. The return value is the number of times the value appears. and then see what happens when we increase numValues. 10. To test this theory. we expect each digit to appear the same number of times—twice each. but as you gain experience you will have a better idea. • A test that you can apply to each element in the container. int value) { int count = 0. } . and that might turn out to be useful. But as the number of values increases. Your results may differ. } return count. In this case. With so few values. it is not easy to know ahead of time which functions are likely to be useful. we'll write some programs that count the number of times each value appears. like a string or a vector. Then you can combine them into a solution. the chances are slim that we would get exactly what we expect. the outcome should be more predictable. i++) { if (vec[i] == value) count++.
you will get a compiler error. If we increase numValues to 100. If you try to refer to i later. but you should be aware that a variable declared inside a loop only exists inside the loop. in order.000 we get the following: value 0 1 2 3 4 5 6 7 howMany 10130 10072 9990 9842 10174 9930 10059 9954 . cout << "value\thowMany". upperBound). it is hard to tell if the digits are really appearing equally often. This syntax is sometimes convenient. for (int i = 0. i<upperBound. and we are interested in seeing how many times each value appears.9 Checking the other values howMany only counts the occurrences of a particular value. in order to check each value between 0 and 9. i++) { cout << i << '\t' << howMany (vector. i) << endl. int upperBound = 10. This code uses the loop variable as an argument to howMany. apvector<int> vector = randomVector (numValues. We can solve that problem with a loop: int numValues = 20. VECTORS 10. The result is: value 0 1 2 3 4 5 6 7 8 9 howMany 2 1 3 3 0 2 5 2 0 2 Again. } Notice that it is legal to declare a variable inside a for statement.104 CHAPTER 10.
i). In this example we have to traverse the vector ten times! It would be better to make a single pass through the vector. 10. First. the number of appearances is within about 1% of the expected value (10. Here's how: int numValues = 100000. 10. Every time it calls howMany. . specifying which value I am interested in. That way we can create all ten storage locations at once and we can access them using indices.11 A single-pass solution Although this code works. We could create 10 integer variables with names like howManyOnes. Second. histogram[i] = count. howManyTwos. 0). etc. we can use the value from the vector as an index into the histogram. But that would require a lot of typing. rather than ten different names. so we conclude that the random numbers are probably uniform. apvector<int> histogram (upperBound). i++) { int count = howMany (vector. specifying which location I should store the result in. } I called the vector histogram because that's a statistical term for a vector of numbers that counts the number of appearances of a range of values. apvector<int> vector = randomVector (numValues. and it would be a real pain later if we decided to change the range of values. it is not as efficient as it could be. i<upperBound. it traverses the entire vector. For each value in the vector we could find the corresponding counter and increment it.10.000).10 A histogram It is often useful to take the data from the previous tables and store them for later access. A HISTOGRAM 105 8 9 9891 9958 In each case. rather than just print them. it is an index into the histogram. In other words. for (int i = 0. upperBound). Here's what that looks like: apvector<int> histogram (upperBound. The tricky thing here is that I am using the loop variable in two different ways. A better solution is to use a vector with length 10. What we need is a way to store 10 integers.10. int upperBound = 10. it is an argument to howMany.
when you make a change to the program you can compare the output before and after the change. i++) { int index = vector[i]. you can use the srand function. That way. VECTORS for (int i = 0. histogram[index]++. Forgetting to initialize counters is a common error. That's not very random! One of the properties of pseudorandom number generators is that if they start from the same place they will generate the same sequence of values. index: An integer variable or value used to indicate an element of a vector.106 CHAPTER 10. when we use the increment operator (++) inside the loop. you might have noticed that you are getting the same "random" values every time. The starting place is called a seed. which is an integer between 0 and RAND MAX. by default. While you are debugging. it is often helpful to see the same sequence over and over. It takes a single argument. and use that number as a seed. . and each value is identified by an index. C++ uses the same seed every time you run the program. element: One of the values in a vector. The [] operator selects elements of a vector.12 Random seeds If you have run the code in this chapter a few times. } The first line initializes the elements of the histogram to zeroes. 10. like games. As an exercise. A common way to do that is to use a library function like gettimeofday to generate something reasonably unpredictable and unrepeatable. encapsulate this code in a function called histogram that takes a vector and the range of values in the vector (in this case 0 through 10). like the number of milliseconds since the last second tick. For many applications. The details of how to do that depend on your development environment. If you want to choose a different seed for the random number generator. That way.13 Glossary vector: A named collection of values. 10. you want to see a different random sequence every time the program runs. and that returns a histogram of the values in the vector. i<numValues. where all the values have the same type. we know we are starting from zero.
useful functions and then assembling them into larger solutions. but which are actually the product of a deterministic computation. bottom-up design: A method of program development that starts by writing small. deterministic: A program that does the same thing every time it is run.10. pseudorandom: A sequence of numbers that appear to be random.13. . seed: A value used to initialize a random number sequence. GLOSSARY 107 constructor: A special function that creates a new object and initializes its instance variables. Using the same seed should yield the same sequence of values. histogram: A vector of integers where each integer counts the number of values that fall into a certain range.
the Point and Rectangle structures correspond to the mathematical concept of a point and a rectangle. With some examination. So far. we have not taken advantage of the features C++ provides to support object-oriented programming.1 Objects and functions C++ is generally considered an object-oriented programming language. Programs are made up of a collection of structure definitions and function definitions. Strictly speaking. where most of the functions operate on specific kinds of structures (or objecs). though. For example. For the most part they provide an alternate syntax for doing things we have already done. these features are not necessary. For example. 2. and the functions that operate on that structure correspond to the ways real-world objects interact. but in many cases the alternate syntax is more concise and more accurately conveys the structure of the program. but we have already seen some features of it: 1. Each structure definition corresponds to some object or concept in the real world. it is apparent that every function takes at least one Time structure as a parameter. It's not easy to define object-oriented programming. and the operations we defined correspond to the sorts of things people do with recorded times.Chapter 11 Member functions 11. This observation is the motivation for member functions. Member function differ from the other functions we have written in two ways: 109 . the Time structure we defined in Chapter 9 obviously corresponds to the way people record the time of day. which means that it provides features that support object-oriented programming. Similarly. in the Time program. there is no obvious connection between the structure definition and the function definitions that follow.
30.hour << ":" << time. we are going to invoke the function on an object. rather than a structure itself. As a result. The function is declared inside the struct definition. One thing you should realize is that this transformation is purely mechanical." or "sending a message to an object. together they indicate that this is a function named print that can be invoked on a Time structure. When we call the function. the first step is to change the name of the function from printTime to Time::print. anything that can be done with a member function can also be done with a nonmember function (sometimes called a free-standing function). 11. A pointer is similar to a reference. 14. One thing that makes life a little difficult is that this is actually a pointer to a structure. you will be able to choose the best form for whatever you are doing. As I said. we will take the functions from Chapter 9 and transform them into member functions. we invoke it on an object. }. void printTime (const Time& time) { cout << time.minute << ":" << time. } To call this function. in order to make the relationship between the structure and the function explicit.second << endl. The next step is to eliminate the parameter. in other words. Time currentTime = { 9. inside the function. In the next few sections.0 }. which is the object the function is invoked on. Instead of passing an object as an argument. People sometimes describe this process as "performing an operation on an object. we no longer have a parameter named time." 2. But sometimes there is an advantage to one over the other. The :: operator separates the name of the structure from the name of the function. you can do it just by following a sequence of steps. Instead.2 print In Chapter 9 we defined a structure named Time and wrote a function named printTime struct Time { int hour. If you are comfortable converting from one form to another. To make printTime into a member function. minute. rather than just call it. double second.110 CHAPTER 11. we have a current object. we had to pass a Time object as a parameter. . We can refer to the current object using the C++ keyword this. MEMBER FUNCTIONS 1. printTime (currentTime).
all by themselves with no dot notation. minute. and the type of the return value.0 }.hour << ":" << time. The declaration describes the interface of the function. or second. double second. The last step of the transformation process is that we have to declare the new function inside the structure definition: struct Time { int hour. you are making a promise to the compiler that you will. If you omit the definition.3 Implicit variable access Actually. In order to invoke the new version of print.print (). since it contains the details of how the function works. This definition is sometimes called the implementation of the function. or provide a definition that has an interface different from what you promised. we use it to assign the value of this to a local variable named time: void Time::print () { Time time = *this. the number and types of the arguments.11. C++ knows that it must be referring to the current object. the compiler will complain. 11. 30.minute << ":" << time.second << endl. When you declare a function.3. If the function refers to hour. void Time::print (). IMPLICIT VARIABLE ACCESS 111 but I don't want to go into the details of using pointers yet. 14. In the following function. except that it has a semi-colon at the end. } The first two lines of this function changed quite a bit as we transformed it into a member function. }. that is. provide a definition for the function. the new version of Time::print is more complicated than it needs to be. The only pointer operation we need for now is the * operator. currentTime. but notice that the output statement itself did not change at all. minute. A function declaration looks just like the first line of the function definition. cout << time. We don't really need to create a local variable in order to refer to the instance variables of the current object. at some point later on in the program. which converts a structure pointer into a structure. So we could have written: . we have to invoke it on a Time object: Time currentTime = { 9.
increment (500. 11.0). MEMBER FUNCTIONS void Time::print () { cout << hour << ":" << minute << ":" << second << endl. void Time::increment (double secs) { second += secs. while (second >= 60. }.4 Another example Let's convert increment to a member function. currentTime. The output of this program is 9:22:50. And again. 14. . hour += 1. Features like this are one reason member functions are often more concise than nonmember functions. } } By the way. you should write a more efficient version now.0. void Time::increment (double secs). 30. void Time::print (). To declare the function. Again.print (). } This kind of variable access is called "implicit" because the name of the object does not appear explicitly.0. Then we can go through the function and make all the variable accesses implicit. we are going to transform one of the parameters into the implicit parameter called this. currentTime.112 CHAPTER 11. we can just copy the first line into the structure definition: struct Time { int hour.0 }.0) { second -= 60. we have to invoke it on a Time object: Time currentTime = { 9. minute += 1. to call it. double second. minute. } while (minute >= 60) { minute -= 60. remember that this is not the most efficient implementation of this function. If you didn't do it back in Chapter 9.
second. return false. For example. we have to invoke the function on one of them and pass the other as an argument. we can refer to one of the them implicitly.second) return true. double seconds = minutes * 60 + second.6 A more complicated example Although the process of transforming functions into member functions is mechanical.minute) return false.11.hour) return false. and we can't make both of them implicit. return seconds.5.hour) return true. return seconds.minute. Inside the function. not just one. if (hour < time2. since we don't modify it in this function. } It is straightforward to convert this to a member function: double Time::convertToSeconds () const { int minutes = hour * 60 + minute. if (minute > time2. The print function in the previous section should also declare that the implicit parameter is const. as you can see in the example. Instead. The answer. is after the parameter list (which is empty in this case).minute) return true. But it is not obvious where we should put information about a parameter that doesn't exist. 11. but to access the instance variables of the other we continue to use dot notation.5 Yet another example The original version of convertToSeconds looked like this: double convertToSeconds (const Time& time) { int minutes = time. } To invoke this function: . after operates on two Time structures.hour * 60 + time. bool Time::after (const Time& time2) const { if (hour > time2. if (minute < time2. there are some oddities. YET ANOTHER EXAMPLE 113 11. double seconds = minutes * 60 + time. if (second > time2. } The interesting thing here is that the implicit parameter should be declared const.
0)." << endl. then. notice that the constructor has the same name as the class. though. } You can almost read the invocation like English: "If the done-time is after the current-time. time. These functions are called constructors and the syntax looks like this: Time::Time (double secs) { hour = int (secs / 3600. To invoke the constructor. The arguments haven't changed.hour * 3600. secs -= time.114 CHAPTER 11. and no return type.minute = int (secs / 60. for every new type. time. we need to be able to create new objects. return time. functions like makeTime are so common that there is a special function syntax for them. MEMBER FUNCTIONS if (doneTime. When we write values to hour.second = secs. Both of these steps are handled automatically..7 Constructors Another function we wrote in Chapter 9 was makeTime: Time makeTime (double secs) { Time time.hour = int (secs / 3600.0. and we don't have to return anything.minute * 60.0). . second = secs.0). secs -= hour * 3600. the compiler knows we are referring to the instance variables of the new object. In fact. secs -= time. secs -= minute * 60. you use syntax that is a cross between a variable declaration and a function call: Time time (seconds).0. or implicitly as shown here." 11. We can refer to the new object—the one we are constructing—using the keyword this. minute = int (secs / 60.after (currentTime)) { cout << "The bread will be done after it starts. Second. } First.0.0. } Of course.0). minute and second. time. notice that we don't have to create a new time object..
and not both in the same program. the C++ compiler requires that you use one or the other. INITIALIZE OR CONSTRUCT? 115 This statement declares that the variable time has type Time.8. In other words. 0. we use the same funny syntax as before. passing the value of seconds as an argument. 11. double s) { hour = h. 35. 14. using constructors." as long as they take different parameters. second = s. and different points in the history of C++. it is legal to overload constructors in the same way we overloaded functions. 30. If you define a constructor for a structure. For example. int m. and that assigns the values of the parameters to the instance variables: Time::Time (int h. then you have to use the constructor to initialize all new structures of that type. } To invoke this constructor. 11. Now.8 Initialize or construct? Earlier we declared and initialized some Time structures using squiggly-braces: Time currentTime = { 9.0 }. The alternate syntax using squiggly-braces is no longer allowed. Fortunately.11. 30. Then. it is common to have a constructor that takes one parameter for each instance variable. The system allocates space for the new object and the constructor initializes its instance variables. we have a different way to declare and initialize: Time time (seconds). there can be more than one constructor with the same "name. Time breadTime = { 3. and it invokes the constructor we just wrote.9 One last example The final example we'll look at is addTime: . Maybe for that reason. 14. These two functions represent different programming styles. The result is assigned to the variable time. when we initialize a new object the compiler will try to find a constructor that takes the appropriate parameters.0 }.0). minute = m. except that the arguments have to be two integers and a double: Time currentTime (9.
The next line of the function invokes the constructor that takes a single double as a parameter. the compiler assumes that we want to invoke the function on the current object. There is a reason for the hassle. minute. Replace the first parameter with an implicit parameter.10 Header files It might seem like a nuisance to declare functions inside the structure definition and then define the functions later. Replace the use of makeTime with a constructor invocation. there is no apparent object! Inside a member function. which contains the structure definition. For the example we have been looking at. Here's the result: Time Time::add (const Time& t2) const { double seconds = convertToSeconds () + t2. the last line returns the resulting object. . but with the suffix . and the implementation file. which contains the functions. 2. you have to change it in two places.convertToSeconds (). the header file is called Time. MEMBER FUNCTIONS Time addTime2 (const Time& t1. and it contains the following: struct Time { // instance variables int hour.116 CHAPTER 11. return makeTime (seconds). which is that it is now possible to separate the structure definition and the functions into two files: the header file. Thus.cpp. double second. 3. return time. though. which should be declared const. } The first time we invoke convertToSeconds.h instead of . the second invocation acts on t2. Change the name from addTime to Time::add. Any time you change the interface to a function. const Time& t2) { double seconds = convertToSeconds (t1) + convertToSeconds (t2). 11. Header files usually have the same name as the implementation file. the first invocation acts on this. even if it is a small change like declaring one of the parameters const. including: 1. } We have to make several changes to this function.h. Time time (seconds).
void Time::increment (double secs) .h" Time::Time (int h. // functions void print () const. The compiler knows that we are declaring functions that are members of the Time structure. it knows enough about the structure to check the code and catch errors.. Notice that in the structure definition I don't really have to include the prefix Time:: at the beginning of every function name.. Time (double secs). HEADER FILES 117 // constructors Time (int hour. }. . In this case the definitions in Time. it is necessary to include the header file using an include statement.cpp appear in the same order as the declarations in Time.h. Time add (const Time& t2) const.. double s) Time::Time (double secs) . double convertToSeconds () const.. although it is not necessary.10. main. Finally. double secs). double Time::convertToSeconds () const . void Time::print () const .cpp contains the definitions of the member functions (I have elided the function bodies to save space): #include <iostream. while the compiler is reading the function definitions. bool after (const Time& time2) const.11. bool Time::after (const Time& time2) const ..cpp contains the function main along with any functions we want that are not members of the Time structure (in this case there are none): #include <iostream. Time. On the other hand. int min.... Time Time::add (const Time& t2) const .h> #include "Time.. // modifiers void increment (double secs). That way.h> .. int m.....
As the program gets large. 0. separate compilation can save a lot of time.cpp from the programs that use them. By separating the definition of Time from main. .h is the header file that contains declarations for cin and cout and the functions that operate on them. } } Again. if (doneTime. 30.0). Time doneTime = currentTime.cpp has to include the header file.print ().0). Time breadTime (3. doneTime.increment (500. 14. When you compile your program. The details of how to do this depend on your programming environment. But it is good for you to know about this feature. Managing interactions: As systems become large. most of the advantages come when we are working with larger programs: Reuse: Once you have written a structure like Time. In fact. the number of interactions between components grows and quickly becomes unmanageable.after (currentTime)) { cout << "The bread will be done after it starts. main.118 CHAPTER 11.0). MEMBER FUNCTIONS #include "Time.h" void main () { Time currentTime (9. since you usually need to compile only a few files at a time. For small programs like the ones in this book. currentTime.cpp. there is no great advantage to splitting up programs.print (). It is often useful to minimize these interactions by separating modules like Time. Separate compilation: Separate files can be compiled separately and then linked into a single program later.add (breadTime). currentTime. It may not be obvious why it is useful to break such a small program into three pieces. you make is easy to include the Time structure in another program." << endl. you need the information in that header file. 35. you might find it useful in more than one program. especially since it explains one of the statements that appeared in the first program we wrote: #include <iostream.h> iostream.
or by using the keyword this. For the most part the library doesn't change. this is a pointer. current object: The object on which a member function is invoked. sometimes called the "Standard Library" that gets linked to your program automatically. in order to pass the object as an implicit parameter. we can refer to the current object implicitly. which makes it difficult to use. this: A keyword that refers to the current object. so there is no reason to recompile it. function declaration: A statement that declares the interface to a function without providing the body. The nice thing is that you don't have to recompile the library every time you compile a program. invoke: To call a function "on" an object. since we do not cover pointers in this book. including the number and types of the parameters and the type of the return value. 11. or the details of how a function works. Inside the member function. interface: A description of how a function is used. GLOSSARY 119 The implementations of those functions are stored in a library. implementation: The body of a function.11.11 Glossary member function: A function that operates on an object that is passed as an implicit parameter named this. nonmember function: A function that is not a member of any structure definition.11. Declarations of member functions appear inside structure definitions even if the definitions appear outside. . Also called a "free-standing" function. constructor: A special function that initializes the instance variables of a newly-created object.
7. One possibility is apstrings. Hearts. 5. Depending on what game you are playing. now would be a good time to get a deck. the rank of the Ace may be higher than King or lower than 2. Diamonds and Clubs (in descending order in Bridge). In fact. Jack.Chapter 12 Vectors of Objects 12. 4. 9. 2. 10. you should not be surprised to learn that you can have vectors of objects. and having learned about vectors and objects. There are 52 cards in a deck. One problem with this implementation is that it would not be easy to compare cards to see which had higher rank or suit. 12. 8. 6. One of the first examples we saw was using a function invocation as part of an expression. In the next two chapters we will look at some examples of these combinations. you can also have objects that contain vectors (as instance variables). The ranks are Ace. or within another if statement. If we want to define a new object to represent a playing card. 3. Queen and King. It is not as obvious what type the instance variables should be. or else this chapter might not make much sense.1 Composition By now we have seen several examples of composition (the ability to combine language features in a variety of arrangements).2 Card objects If you are not familiar with common playing cards. The suits are Spades. using Card objects as a case study. containing things like "Spade" for suits and "Queen" for ranks. Having seen this pattern. you can have vectors that contain vectors. you can have objects that contain objects. 121 . each of which belongs to one of four suits and one of 13 ranks. etc. Another example is the nested structure of statements: you can put an if statement within a while loop. and so on. it is pretty obvious what the instance variables should be: rank and suit.
int r). rank = r. rank. It takes two parameters." I do not mean what some people think. each of the numerical ranks maps to the corresponding integer. Card::Card () { suit = 0. the suit and rank of the card. . Card (int s. but they never appear explicitly in the code. Spades Hearts Diamonds Clubs → → → → 3 2 1 0 The symbol → is mathematical notation for "maps to. The mapping for ranks is fairly obvious. } Card::Card (int s. and for face cards: Jack Queen King → → → 11 12 13 The reason I am using mathematical notation for these mappings is that they are not part of the C++ program. They are part of the program design. You can tell that they are constructors because they have no return type and their name is the same as the name of the structure. int r) { suit = s. By "encode. VECTORS OF OBJECTS An alternative is to use integers to encode the ranks and suits." For example. Card (). The first constructor takes no arguments and initializes the instance variables to a useless value (the zero of clubs).122 CHAPTER 12. rank = 0. } There are two constructors for Cards. The second constructor is more useful." The obvious feature of this mapping is that the suits map to integers in order. }. so we can compare suits by comparing integers. The class definition for the Card type looks like this: struct Card { int suit. or translate into a secret code. What a computer scientist means by "encode" is something like "define a mapping between a sequence of numbers and the things I want to represent. which is to encrypt.
"Hearts". "human-readable" means that we have to map the internal representation of the rank and suit onto words. represents the rank 3.h. 12. naturally. THE PRINTCARD FUNCTION 123 The following code creates an object named threeOfClubs that represents the 3 of Clubs: Card threeOfClubs (0. it is usually sufficient to include the header file apvector. you will have to include the header files for both1 . A state diagram for this vector looks like this: 1 apvectors are a little different from apstrings in this regard. the compiler generates code to support that kind of vector. "Diamonds". I hope this footnote helps you avoid an unpleasant surprise. the compiler generates different code to handle that kind of vector.3. In the case of Card objects. "Spades". To initialize the elements of the vector. but the details in your development environment may differ. The first time you use a vector of integers. If you use a vector of apstrings. A natural way to do that is with a vector of apstrings. we can use a series of assignment statements. . Of course. the first step is usually to declare the instance variables and write constructors. You can create a vector of apstrings the same way you create an vector of other types: apvector<apstring> suits (4). As a result. 0 represents the suit Clubs. in order to use apvectors and apstrings. you do not have to compile apvector. The second step is often to write a function that prints the object in human-readable form. suits[0] suits[1] suits[2] suits[3] = = = = "Clubs".12.3 The printCard function When you create a new type.cpp at all! Unfortunately.cpp contains a template that allows the compiler to create vectors of various kinds. the second. The first argument. The file apvector. 3). you are likely to get a long stream of error messages. if you do.
ranks[1] = "Ace". Finally. ranks[13] = "King". ranks[3] = "3". suits[1] = "Diamonds". ranks[8] = "8"." . ranks[12] = "Queen". VECTORS OF OBJECTS suits "Clubs" "Diamonds" "Hearts" "Spades" We can build a similar vector to decode the ranks. ranks[10] = "10".124 CHAPTER 12. ranks[7] = "7". suits[0] = "Clubs". suits[3] = "Spades". } The expression suits[suit] means "use the instance variable suit from the current object as an index into the vector named suits. ranks[5] = "5". ranks[11] = "Jack". ranks[4] = "4". ranks[6] = "6". and select the appropriate string. ranks[9] = "9". apvector<apstring> ranks (14). cout << ranks[rank] << " of " << suits[suit] << endl. Then we can select the appropriate elements using the suit and rank as indices. we can write a function called print that outputs the card on which it is invoked: void Card::print () const { apvector<apstring> suits (4). ranks[2] = "2". suits[2] = "Hearts".
if (card1. 11). What I ." << endl. 12. it looks like this: bool Card::equals (const Card& c2) const { return (rank == c2.print (). From the point of view of the user. the == operator does not work for user-defined types like Card. } To use this function. 3 maps to "3". The output of this code Card card (1. in which the two arguments are symmetric. it can refer to the instance variables of the current object implicitly (without having to use dot notation to specify the object). 11). } This method of invocation always seems strange to me when the function is something like equals.12.equals(card2)) { cout << "Yup. that's the same card. but we will not cover that in this book. it doesn't matter what the encoding is. On the other hand. THE EQUALS FUNCTION 125 Because print is a Card member function. etc. we get an encoding where 2 maps to "2". It is clear that the return value from equals should be a boolean that indicates whether the cards are the same.4. We'll call it equals. card. 11). You might notice that we are not using the zeroeth element of the ranks vector.suit).4 The equals function In order for two cards to be equal. Unfortunately. we have to invoke it on one of the cards and pass the other as an argument: Card card1 (1. But we have one more choice: should equals be a member function or a free-standing function? As a member function. It is also possible to write a new definition for the == operator. is Jack of Diamonds. it is often helpful for the programmer if the mappings are easy to remember. since all input and output uses human-readable formats. That's because the only valid ranks are 1–13. they have to have the same rank and the same suit. Card card2 (1.rank && suit == c2. so we have to write a function that compares two cards. By leaving an unused element at the beginning of the vector. It is also clear that there have to be two Cards as parameters.
so that you can choose the interface that works best depending on the circumstance. the arguments appear side-by-side in a way that makes more logical sense.5 The isGreater function For basic types like int and double. but the other has a higher suit. } Of course. the choice is completely arbitrary. In order to make cards comparable. the fruits are unordered." << endl. VECTORS OF OBJECTS mean by symmetric is that it does not matter whether I ask "Is A equal to B?" or "Is B equal to A?" In this case. followed by all the Diamonds. and the 3 of Diamonds is higher than the 3 of Clubs because it has higher suit. we will use this function to sort a deck of cards. For example. I know that the 3 of Clubs is higher than the 2 of Clubs because it has higher rank. const Card& c2) { return (c1. we will write a comparison function that plays the role of the > operator.rank && c1. My point here is that you should be comfortable writing both member and nonmember functions. For the sake of choosing. These operators (< and > and the others) don't work for user-defined types. For example. card2)) { cout << "Yup. the bool type is unordered. which means that there is no meaningful way to say that one element is bigger than another. we cannot say that true is greater than false. But which is better. rank or suit. because when you buy a new deck of cards. The set of playing cards is partially ordered. Some sets are unordered. Later. 12. and so on.suit). . we have to decide which is more important.suit == c2.rank == c2. I will say that suit is more important. this is a matter of taste. the 3 of Clubs or the 2 of Diamonds? One has a higher rank. which means that you can compare any two elements and tell which is bigger. the integers and the floatingpoint numbers are totally ordered. To be honest. to me at least. Just as we did for the == operator.126 CHAPTER 12. I think it looks better to rewrite equals as a nonmember function: bool equals (const Card& c1. it comes sorted with all the Clubs together. which means that sometimes we can compare cards and sometimes not. As another example. Some sets are totally ordered. that's the same card. if (equals (card1. there are comparison operators that compare values and determine when one is greater or less than another. } When we call this version of the function. which is why we cannot compare apples and oranges. For example.
cout << "is greater than" << endl. Here is some code that creates a new deck of 52 cards: .rank) return false. This time. we can write isGreater.print ().suit) return false. aces are less than deuces (2s).print ().suit) return true. It matters whether we want to know "Is A greater than B?" or "Is B greater than A?" Therefore I think it makes more sense to write isGreater as a member function: bool { // if if Card::isGreater (const Card& c2) const first check the suits (suit > c2. Card card2 (1. card2. As an exercise.. } You can almost read it like English: "If card1 isGreater card2 . return false return false.6. 11). VECTORS OF CARDS 127 With that decided.isGreater (card2)) { card1. 12. if (rank < c2. it is obvious from the syntax which of the two possible questions we are asking: Card card1 (2. (suit < c2." The output of this program is Jack of Hearts is greater than Jack of Diamonds According to isGreater. // if the suits are equal. and again we have to choose between a member function and a nonmember function.6 Vectors of cards The reason I chose Cards as the objects for this chapter is that there is an obvious use for a vector of cards—a deck. the arguments are not symmetric. as they are in most card games.. check the ranks if (rank > c2. Again. } Then when we invoke it. // if the ranks are also equal. the arguments (two Cards) and the return type (boolean) are obvious.12. if (card1. 11).rank) return true. fix it so that aces are ranked higher than Kings.
apvector<Card> deck (52. Since the outer loop iterates 4 times. from 0 to 3. aceOfSpades). Notice that we can compose the syntax for selecting an element from an array (the [] operator) with the syntax for selecting an instance variable from an object (the dot operator). For each suit. The outer loop enumerates the suits. the inner loop enumerates the ranks. VECTORS OF OBJECTS apvector<Card> deck (52). suit <= 3.suit = suit. like a special deck for a magic trick. } } I used the variable i to keep track of where in the deck the next card should go.rank = rank. . This code builds a deck with 52 identical cards. as shown in the figure. i++. suit++) { for (int rank = 1.suit means "the suit of the ith card in the deck". rank++) { deck[i]. 1). The expression deck[i]. In some environments. int i = 0. but in others they could contain any possible value. the total number of times the body is executed is 52 (13 times 4). To do that we use a nested loop.128 CHAPTER 12. and the inner loop iterates 13 times. Of course. Here is the state diagram for this object: deck 0 suit: rank: 1 2 51 0 0 suit: rank: 0 0 suit: rank: 0 0 suit: rank: 0 0 The three dots represent the 48 cards I didn't feel like drawing. they will get initialized to zero. for (int suit = 0. rank <= 13. it makes more sense to build a deck with 52 different cards in it. Keep in mind that we haven't initialized the instance variables of the cards yet. from 1 to 13. One way to initialize them would be to pass a Card as a second argument to the constructor: Card aceOfSpades (3. deck[i].
7 The printDeck function Whenever you are working with vectors. we return -1.length(). const apvector<Card>& deck) { for (int i = 0. a linear search and a bisection search.print (). i < deck. . If it is not in the deck. encapsulate this deck-building code in a function called buildDeck that takes no parameters and that returns a fully-populated vector of Cards. 12. it involves traversing the deck and comparing each card to the one we are looking for. We have seen the pattern for traversing a vector several times. it is convenient to have a function that prints the contents of the vector. } The loop here is exactly the same as the loop in printDeck. which means that we do not have to traverse the entire deck if we find the card we are looking for. In fact. Inside the loop. i < deck. I copied it. card)) return i. int find (const Card& card. 12. i++) { if (equals (deck[i]. The function returns as soon as it discovers the card. which searches through a vector of Cards to see whether it contains a certain card. Therefore. so the following function should be familiar: void printDeck (const apvector<Card>& deck) { for (int i = 0.length(). i++) { deck[i]. when I wrote the program. Linear search is the more obvious of the two. but it gives me a chance to demonstrate two ways to go searching for things. we compare each element of the deck to card. it is legal to invoke print on deck[i]. an element of deck has type Card. If we find it we return the index where the card appears. It may not be obvious why this function would be useful. } return -1. we know the card is not in the deck and return -1. If the loop terminates without finding the card. Since deck has type apvector<Card>. which saved me from having to write and debug it twice.7. } } By now it should come as no surprise that we can compose the syntax for vector access with the syntax for invoking a function. THE PRINTDECK FUNCTION 129 As an exercise.8 Searching The next function I want to write is find.12.
you can conclude that your word is not in the dictionary. . In the case of a deck of cards. I wrote the following: apvector<Card> deck = buildDeck (). and call it mid. The best way to write a bisection search is with a recursive function. The only alternative is that your word has been misfiled somewhere. Choose a word on the page and compare it to the word you are looking for.130 CHAPTER 12. We have to look at every card. flip to somewhere earlier in the dictionary and go to step 2. if we know that the cards are in order. To search the vector. but that contradicts our assumption that the words are in alphabetical order. As a result. If the word you are looking for comes after the word on the page. If the word you are looking for comes before the word on the page. since otherwise there is no way to be certain the card we want is not there. you probably use an algorithm that is similar to a bisection search: 1. The output of this code is I found the card at index = 17 12. The trick is to write a function called findBisect that takes two indices as parameters. 4. Start in the middle somewhere.9 Bisection search If the cards in the deck are not in order. 2.find (deck[17]). VECTORS OF OBJECTS To test this function. 1. That's because bisection is naturally recursive. int index = card. there is no way to search that is faster than the linear search. 3. flip to somewhere later in the dictionary and go to step 2. But when you look for a word in a dictionary. choose an index between low and high. we can write a version of find that is much faster. Compare the card at mid to the card you are looking for. cout << "I found the card at index = " << index << endl. If you found the word you are looking for. The reason is that the words are in alphabetical order. If you ever get to the point where there are two adjacent words on the page and your word comes between them. stop. indicating the segment of the vector that should be searched (including both low and high). low and high. you don't search linearly through every word. 5.
Here's what this all looks like translated into C++: int findBisect (const Card& card. it is still missing a piece. stop. it will recurse forever. If the card at mid is higher than your card. low. search in the range from low to mid-1. . const apvector<Card>& deck. mid+1. We need a way to detect this condition and deal with it properly (by returning -1). return its index if (equals (deck[mid]. If you found it. With that line added. if (high < low) return -1. The easiest way to tell that your card is not in the deck is if there are no cards in the deck. } else { // search the second half of the deck return findBisect (card. compare the card to the middle card if (deck[mid]. // otherwise. int low. search in the range from mid+1 to high. card)) return mid. there are still cards in the deck. which is the case if high is less than low. BISECTION SEARCH 131 2. If the card at mid is lower than your card. 4. mid-1). int mid = (high + low) / 2. int high) { cout << low << ". high). deck. int high) { int mid = (high + low) / 2. const apvector<Card>& deck. the function works correctly: int findBisect (const Card& card. if the card is not in the deck. As it is currently written.9. Well.isGreater (card)) { // search the first half of the deck return findBisect (card. of course. } } Although this code contains the kernel of a bisection search. Steps 3 and 4 look suspiciously like recursive invocations. " << high << endl. deck. 3. int low. // if we found the card.12. but what I mean is that there are no cards in the segment of the deck indicated by low and high.
And got the following output: 0. typically 6 or 7. 51 0. high). 24 22. no amount of testing can prove that a program is correct. in which case C++ will (eventually) generate a run-time error. 12 I found the card at index = -1 These tests don't prove that this program is correct. } else { return findBisect (card. 24 13. 51)). compared to up to 52 times if we did a linear search. you might be able to convince yourself. by looking at a few cases and examining the code. and tried to find it. . 17 13. 24 13.isGreater (card)) { return findBisect (card. I got the following: 0. if (deck[mid]. 24 I found the card at index = 23 Then I made up a card that is not in the deck (the 15 of Diamonds). 24 13. deck[23]. deck. Two common errors in recursive programs are forgetting to include a base case and writing the recursive call so that the base case is never reached. low.132 CHAPTER 12. } } I added an output statement at the beginning so I could watch the sequence of recursive calls and convince myself that it would eventually reach the base case. mid-1). deck. card)) return mid. 51 0. The number of recursive calls is fairly small. I tried out the following code: cout << findBisect (deck. On the other hand. Either error will cause an infinite recursion. bisection is much faster than a linear search. mid+1. 24 19. VECTORS OF OBJECTS if (equals (deck[mid]. especially for large vectors. 14 13. That means we only had to call equals and isGreater 6 or 7 times. In general. 0. In fact.
When you create them. as a single parameter that specifies a subdeck. in which a program comes to take on meaning beyond what is literally encoded. they are given default values. int low. you are really sending the whole deck.11 Glossary encode: To represent one set of values using another set of values. and I sometimes think of it as an abstract parameter. abstraction is a central idea in computer science (as well as many other fields). For example. int high) { it might make sense to treat three of the parameters.10 Decks and subdecks Looking at the interface to findBisect int findBisect (const Card& card. but which describes the function of the program at a higher level.3. when I referred to an "empty" data structure. . There is one other example of this kind of abstraction that you might have noticed in Section 9. DECKS AND SUBDECKS 133 12. by constructing a mapping between them. the word "abstract" gets used so often and in so many contexts that it is hard to interpret." This kind of thinking. But as long as the recipient plays by the rules. Nevertheless. Sometimes.12. All variables have values all the time. Abstractly. low and high. But if the program guarantees that the current value of a variable is never read before it is written. This kind of thing is quite common. What I mean by "abstract. then the current value is irrelevant. The reason I put "empty" in quotation marks was to suggest that it is not literally accurate." is something that is not literally part of the program text. deck. const apvector<Card>& deck. So there is no such thing as an empty object. there is nothing that prevents the called function from accessing parts of the vector that are out of bounds. it makes sense to think of it. when you call a function and pass a vector and the bounds low and high. is a very important part of thinking like a computer scientist. A more general definition of "abstraction" is "The process of modeling a complex system with a simplified description in order to suppress unnecessary details while capturing relevant behavior. abstract parameter: A set of parameters that act together as a single parameter.10. as a subdeck. it makes sense to think of such a variable as "empty." 12. So you are not literally sending a subset of the deck. abstractly.
QUEEN. I pointed out that the mapping itself does not appear as part of the program. For example. and so on. Once we have defined these types. For example. Suit suit. NINE.Chapter 13 Objects of Vectors 13. DIAMONDS. we can use them anywhere. the second to 1. The definition of Rank overrides the default mapping and specifies that ACE should be represented by the integer 1. etc. EIGHT. The other values follow in the usual way. THREE. and internal representations like integers and strings. FOUR.1 Enumerated types In the previous chapter I talked about mappings between real-world values like rank and suit. Actually. SPADES }. the first value in the enumerated type maps to 0. TEN. DIAMONDS is represented by 1. the value CLUBS is represented by the integer 0. By default. and (2) define the set of values that make up the mapping. Although we created a mapping between ranks and integers. KING }. Within the Suit type. HEARTS. here is the definition of the enumerated types Suit and Rank: enum Suit { CLUBS. SIX. 135 . SEVEN. and between suits and integers. TWO. enum Rank { ACE=1. C++ provides a feature called and enumerated type that makes it possible to (1) include a mapping as part of the program. the instance variables rank and suit are can be declared with type Rank and Suit: struct Card { Rank rank. FIVE. JACK.
deck[index]. JACK). }. rank <= KING. Rank r). we can use the values from the enumerated type as arguments: Card card (DIAMONDS. too. This code is much clearer than the alternative using integers: Card card (1. there is a better way to do this—we can define the ++ operator for enumerated types—but that is beyond the scope of this book. } } In some ways. OBJECTS OF VECTORS Card (Suit s. so suit++ is not legal. Now. That the types of the parameters for the constructor have changed. in the expression suit+1. we are not allowed to do arithmetic with enumerated types. because they often go hand in hand. On the other hand. for (Suit suit = CLUBS.2 switch statement It's hard to mention enumerated types without mentioning switch statements.rank = rank. index++. A switch statement is an alternative to a chained conditional that is syntactically prettier and often more efficient. using enumerated types makes this code more readable. 11). We have to make some changes in buildDeck. suit <= SPADES. suit = Suit(suit+1)) { for (Rank rank = ACE. Strictly speaking.suit = suit.136 CHAPTER 13. Therefore the old print function will work without modification. Because we know that the values in the enumerated types are represented as integers. C++ automatically converts the enumerated type to integer. but there is one complication. Actually. the values in enumerated types have names with all capital letters. to create a card. rank = Rank(rank+1). Then we can take the result and typecast it back to the enumerated type: suit = Suit(suit+1). It looks like this: . By convention. though: int index = 0. 13. rank = Rank(rank+1)) { deck[index]. we can use them as indices for a vector.
switch statements work with integers. "Diamonds". } This switch statement is equivalent to the following chained conditional: if (symbol == '+') { perform_addition (). "Hearts". Occasionally this feature is useful. "Spades". } else { cout << "I only know how to perform addition and multiplication" << endl. } else if (symbol == '*') { perform_multiplication ().2. break. Without the break statements. characters. default: cout << "I only know how to perform addition and multiplication" << endl. For example. . case '*': perform_multiplication (). } The break statements are necessary in each branch in a switch statement because otherwise the flow of execution "falls through" to the next case. break. and then print the error message. but most of the time it is a source of errors when people forget the break statements. and then perform multiplication. "Not a valid suit". break. and enumerated types. SWITCH STATEMENT 137 switch (symbol) { case '+': perform_addition (). In general it is good style to include a default case in every switch statement. we could use something like: switch (suit) { case CLUBS: case DIAMONDS: case HEARTS: case SPADES: default: } return return return return return "Clubs". the symbol + would make the program perform addition. to handle errors or unexpected values.13. In this case we don't need break statements because the return statements cause the flow of execution to return to the caller instead of falling through to the next case. to convert a Suit to the corresponding string.
Deck::Deck (int size) { apvector<Card> temp (size). Now we can create a deck of cards like this: Deck deck (52). passing the size as a parameter. OBJECTS OF VECTORS 13. but I also mentioned that it is possible to have an object that contains a vector as an instance variable. cards = temp. } The name of the instance variable is cards to help distinguish the Deck object from the vector of Cards that it contains. Here is a state diagram showing what a Deck object looks like: deck cards: 0 suit: rank: 1 2 51 0 0 suit: rank: 0 0 suit: rank: 0 0 suit: rank: 0 0 The object named deck has a single instance variable named cards. that contains a vector of Cards. The structure definition looks like this struct Deck { apvector<Card> cards. which is a vector of Card objects. we worked with a vector of objects. For now there is only one constructor. which it initializes by invoking the constructor for the apvector class. To access the cards in a deck we have to compose . called a Deck.138 CHAPTER 13. }. Deck (int n). In this chapter I am going to create a new object. It creates a local variable named temp.3 Decks In the previous chapter. Then it copies the vector from temp into the instance variable cards.
and deck.5 Deck member functions Now that we have a Deck object. Deck::Deck () { apvector<Card> temp (52). cards[i]. For example. . cards = temp. it would be useful to initialize the cards in it. suit <= SPADES. From the previous chapter we have a function called buildDeck that we could use (with a few adaptations).7).rank = rank. the expression deck.suit is its suit. i++) { deck. rewritten as a Deck member function: void Deck::print () const { for (int i = 0. } demonstrates how to traverse the deck and output each card. for (Suit suit = CLUBS.suit = suit. i<52. 13. Looking at the functions we have written so far. int i = 0.13. Here's how it looks. but it might be more natural to write a second Deck constructor. 13. Now we can create a standard 52-card deck with the simple declaration Deck deck. ANOTHER CONSTRUCTOR 139 the syntax for accessing an instance variable and the syntax for selecting an element from an array. it makes sense to put all the functions that pertain to Decks in the Deck structure definition.cards[i] is the ith card in the deck. The following loop for (int i = 0. except that we had to change the syntax to make it a constructor. one obvious candidate is printDeck (Section 12. suit = Suit(suit+1)) { for (Rank rank = ACE.4.length().print (). i < cards.cards[i]. } } } Notice how similar this function is to buildDeck. rank <= KING. i++) { cards[i].4 Another constructor Now that we have a Deck object. rank = Rank(rank+1)) { cards[i]. i++.cards[i].print().
// that way we can refer to it in the definition of Card struct Card { int suit. The problem is that when the compiler is reading the first structure definition. or nonmember functions that take Cards and Decks as parameters. int find (const Deck& deck) const. Card (). }. For example. *this)) return i.140 CHAPTER 13. int r). member functions of Deck. Card (int s. Here's my version: int Card::find (const Deck& deck) const { for (int i = 0. it is not obvious whether they should be member functions of Card. the version of find in the previous chapter takes a Card and a Deck as arguments. As an exercise. For some of the other functions. // and then later we provide the definition of Deck struct Deck { apvector<Card> cards. OBJECTS OF VECTORS } } As usual. but you could reasonably make it a member function of either type. i < deck. } The first trick is that we have to use the keyword this to refer to the Card the function is invoked on.cards. . rank.length(). The second trick is that C++ does not make it easy to write structure definitions that refer to each other. One solution is to declare Deck before Card and then define Deck afterwards: // declare that Deck is a structure. } return -1. we can refer to the instance variables of the current object without using dot notation. rewrite find as a Deck member function that takes a Card as a parameter. Writing find as a Card member function is a little tricky.cards[i]. i++) { if (equals (deck. it doesn't know about the second one yet. without defining it struct Deck. void print () const. bool isGreater (const Card& c2) const.
SHUFFLING 141 Deck (). although you will have to be careful about possibly generating indices that are out of range. we need something like randomInt. I am using a combination of C++ statements and English words that is sometimes called pseudocode: for (int i=0. 13.wiskit. which is usually by dividing the deck in two and then reassembling the deck by choosing alternately from each deck. You can probably figure out how to write randomInt by looking at Section 10. and at each iteration choose two cards and swap them. there is an algorithm for sorting that is very similar to the algorithm .7 Sorting Now that we have messed up the deck. You can also figure out swapCards yourself. i++) { // choose a random number between i and cards." A better shuffling algorithm is to traverse the deck one card at a time. Deck (int n). we need a way to put it back in order. which chooses a random integer between the parameters low and high. put the cards in a random order. }.com/marilyn/craig.length() // swap the ith card and the randomly-chosen card } The nice thing about using pseudocode is that it often makes it clear what functions you are going to need. Since humans usually don't shuffle perfectly.html or do a web search with the keywords "perfect shuffle.6. But a computer program would have the annoying property of doing a perfect shuffle every time. I will leave the remaining implementation of these functions as an exercise to the reader. Ironically. after 8 perfect shuffles. In fact. int find (const Card& card) const.5.6 Shuffling For most card games you need to be able to shuffle the deck. Here is an outline of how this algorithm works. you would find the deck back in the same order you started in. i<cards.5 we saw how to generate random numbers. that is.length(). 13. see http://www. One possibility is to model the way humans shuffle.13. after about 7 iterations the order of the deck is pretty well randomized. In Section 10. which is not really very random. void print () const. For a discussion of that claim. To sketch the program. and swapCards which takes two indices and switches the cards at the indicated positions. but it is not obvious how to use them to shuffle a deck. In this case.
cards[i] = cards[low+i]. that takes a vector of cards and a range of indices. i++) { // find the lowest card at or to the right of i // swap the ith card and the lowest card } Again." I mean cards that are at or to the right of the index i.cards. we are going to traverse the deck and at each location choose another card and swap.8 Subdecks How should we represent a hand or some other subset of a full deck? One easy choice is to make a Deck object that has fewer than 52 cards. we are going to find the lowest card remaining in the deck. By "remaining in the deck.142 CHAPTER 13. i<sub. We might want a function.length(). This sort of computation can be confusing. that takes a vector of cards and an index where it should start looking. The only difference is that this time instead of choosing the other card at random. is sometimes called top-down design. subdeck. In this case we can use swapCards again. i++) { sub. write a version of findBisect that takes a subdeck as an argument. Once again. called findLowestCard. for (int i=0. rather than a deck and an index range. int high) const { Deck sub (high-low+1). Which version is more errorprone? Which version do you think is more efficient? . the pseudocode helps with the design of the helper functions. OBJECTS OF VECTORS for shuffling. The length of the subdeck is high-low+1 because both the low card and high card are included.length(). using pseudocode to figure out what helper functions are needed. and lead to "off-by-one" errors. This process. The cards get initialized when they are copied from the original deck. I am going to leave the implementation up to the reader. } To create the local variable named subdeck we are using the Deck constructor that takes the size of the deck as an argument and that does not initialize the cards. Again. 13. i<cards. in contrast to the bottom-up design I discussed in Section 10.8. Drawing a picture is usually the best way to avoid them. for (int i = 0. and that returns a new vector of cards that contains the specified subset of the deck: Deck Deck::subdeck (int low. so we only need one new one. As an exercise. } return sub.
Shuffling and dealing
In Section 13.6 I wrote pseudocode for a shuffling algorithm. Assuming that we have a function called shuffleDeck that takes a deck as an argument and shuffles it, we can create and shuffle a deck: Deck deck; deck.shuffle (); // create a standard 52-card deck // shuffle it
Then, to deal out several hands, we can use subdeck: Deck hand1 = deck.subdeck (0, 4); Deck hand2 = deck.subdeck (5, 9); Deck pack = deck.subdeck (10, 51); This code puts the first 5 cards in one hand, the next 5 cards in the other, and the rest into the pack. When you thought about dealing, did you think we should give out one card at a time to each player in the round-robin style that is common in real card games? I thought about it, but then realized that it is unnecessary for a computer program. The round-robin convention is intended to mitigate imperfect shuffling and make it more difficult for the dealer to cheat. Neither of these is an issue for a computer. This example is a useful reminder of one of the dangers of engineering metaphors: sometimes we impose restrictions on computers that are unnecessary, or expect capabilities that are lacking, because we unthinkingly extend a metaphor past its breaking point. Beware of misleading analogies.
In Section 13.7, we saw a simple sorting algorithm that turns out not to be very efficient. In order to sort n items, it has to traverse the vector n times, and each traversal takes an amount of time that is proportional to n. The total time, therefore, is proportional to n2 . In this section I will sketch a more efficient algorithm called mergesort. To sort n items, mergesort takes time proportional to n log n. That may not seem impressive, but as n gets big, the difference between n2 and n log n can be enormous. Try out a few values of n and see. The basic idea behind mergesort is this: if you have two subdecks, each of which has been sorted, it is easy (and fast) to merge them into a single, sorted deck. Try this out with a deck of cards: 1. Form two subdecks with about 10 cards each and sort them so that when they are face up the lowest cards are on top. Place both decks face up in front of you.
2. Compare the top card from each deck and choose the lower one. Flip it over and add it to the merged deck. 3. Repeat step two until one of the decks is empty. Then take the remaining cards and add them to the merged deck. The result should be a single sorted deck. Here's what this looks like in pseudocode: Deck merge (const Deck& d1, const Deck& d2) { // create a new deck big enough for all the cards Deck result (d1.cards.length() + d2.cards.length()); // use the index i to keep track of where we are in // the first deck, and the index j for the second deck int i = 0; int j = 0; // the index k traverses the result deck for (int k = 0; k<result.cards.length(); k++) { // if d1 is empty, d2 wins; if d2 is empty, d1 wins; // otherwise, compare the two cards // add the winner to the new deck } return result; } I chose to make merge a nonmember function because the two arguments are symmetric. The best way to test merge is to build and shuffle a deck, use subdeck to form two (small) hands, and then use the sort routine from the previous chapter to sort the two halves. Then you can pass the two halves to merge to see if it works. If you can get that working, try a simple implementation of mergeSort: Deck // // // // } Deck::mergeSort () const { find the midpoint of the deck divide the deck into two subdecks sort the subdecks using sort merge the two halves and return the result
Notice that the current object is declared const because mergeSort does not modify it. Instead, it creates and returns a new Deck object. If you get that version working, the real fun begins! The magical thing about mergesort is that it is recursive. At the point where you sort the subdecks, why
should you invoke the old, slow version of sort? Why not invoke the spiffy new mergeSort you are in the process of writing? Not only is that a good idea, it is necessary in order to achieve the performance advantage I promised. In order to make it work, though, you have to add a base case so that it doesn't recurse forever. A simple base case is a subdeck with 0 or 1 cards. If mergesort receives such a small subdeck, it can return it unmodified, since it is already sorted. The recursive version of mergesort should look something like this: Deck Deck::mergeSort (Deck deck) const { // if the deck is 0 or 1 cards, return it // // // // } As usual, there are two ways to think about recursive programs: you can think through the entire flow of execution, or you can make the "leap of faith." I have deliberately constructed this example to encourage you to make the leap of faith. When you were using sort to sort the subdecks, you didn't feel compelled to follow the flow of execution, right? You just assumed that the sort function would work because you already debugged it. Well, all you did to make mergeSort recursive was replace one sort algorithm with another. There is no reason to read the program differently. Well, actually you have to give some thought to getting the base case right and making sure that you reach it eventually, but other than that, writing the recursive version should be no problem. Good luck! find the midpoint of the deck divide the deck into two subdecks sort the subdecks using mergesort merge the two halves and return the result
pseudocode: A way of designing programs by writing rough drafts in a combination of English and C++. helper function: Often a small function that does not do anything enormously useful by itself, but which helps another, more useful, function. bottom-up design: A method of program development that uses pseudocode to sketch solutions to large problems and design the interfaces of helper functions. mergesort: An algorithm for sorting a collection of values. Mergesort is faster than the simple algorithm in the previous chapter, especially for large collections.
we could have written the Card definition: struct Card { private: int suit. In C++.Chapter 14 Classes and invariants 14. Data encapsulation is based on the idea that each structure definition should provide a set of functions that apply to the structure. in order to separate the function's interface (how to use it) from its implementation (how it does what it does). including two integers. we have been using apstring and apvector objects without ever discussing their implementations. As another example. The keyword private is used to protect parts of a structure definition. there are many possible representations for a Card. and prevent unrestricted access to the internal representation.1 Private data and classes I have used the word "encapsulation" in this book to refer to the process of wrapping up a sequence of instructions in a function. but as "clients" of these libraries." which is the topic of this chapter. This kind of encapsulation might be called "functional encapsulation. For example. 147 . rank. two strings and two enumerated types. but someone using the Card structure should not have to know anything about its internal structure. the most common way to enforce data encapsulation is to prevent client programs from accessing the instance variables of an object. There are many possibilities." to distinguish it from "data encapsulation. The programmer who writes the Card member functions needs to know which implementation to use. One use of data encapsulation is to hide implementation details from users or programmers that don't need to know them. For example. we don't need to know.
But there is another feature in C++ that also meets this definition. public: Card (). structures in C++ meet the general definition of a class. which means that they can be read and written only by Card member functions. On the other hand. For example. int int int int }. Another advantage of using accessor functions is that we can change the internal representations of cards without having to change any client programs. The instance variables are private. { { { { return return rank = suit = rank.2 What is a class? In most object-oriented programming languages. it is called a class. a class is just a structure whose instance variables are private by default. Card (int s. int r). Card (int s. } (int r) { rank = r.148 CHAPTER 14. For example. To do that. which means that they can be invoked by client programs. rank. The functions are public. } (int s) { suit = s. I could have written the Card definition: class Card { int suit. As we have seen. } s. confusingly. it might be a good idea to make cards "read only" so that after they are constructed. } () const { return suit. It is still possible for client programs to read and write the instance variables using the accessor functions (the ones beginning with get and set). } suit. int r). In C++. it is now easy to control which operations clients can perform on which instance variables. a private part and a public part. } There are two sections of this definition. } . CLASSES AND INVARIANTS public: Card (). int getRank () const int getSuit () const void setRank (int r) void setSuit (int s) }. } r. getRank getSuit setRank setSuit () const { return rank. they cannot be changed. 14. a class is a user-defined type that includes a set of functions. all we have to do is remove the set functions.
and we have to include the label public: to allow client code to invoke the constructors. it is common to refer to all user-defined types in C++ as "classes. y is the imaginary part. then the point might be clearer. except that as a stylistic choice. }. Complex numbers are useful for many branches of mathematics and engineering. 14. imag. In fact. double i) { real = r. the instance variables real and imag are private. where x is the real part. imag = i. just by adding or removing labels. the other takes two parameters and uses them to initialize the instance variables. and i represents the square root of -1. Instead of specifying the real part and the imaginary part of a point in the complex plane.14. most C++ programmers use class. and many computations are performed using complex arithmetic. there are two constructors: one takes no parameters and does nothing. The following figure shows the two coordinate systems graphically. Also. and is usually written in the form x + yi. and the distance (or magnitude) of the point. public: Complex () { } Complex (double r. polar coordinates specify the direction (or angle) of the point relative to the origin. There is another common representation for complex numbers that is sometimes called "polar form" because it is based on polar coordinates. The following is a class definition for a user-defined type called Complex: class Complex { double real. There is no real reason to choose one over the other. Let's make things a little more complicated." regardless of whether they are defined as a struct or a class. So far there is no real advantage to making the instance variables private.3. } Because this is a class definition. As usual. anything that can be written as a struct can also be written as a class. COMPLEX NUMBERS 149 I replaced the word struct with the word class and removed the private: label. This result of the two definitions is exactly the same.3 Complex numbers As a running example for the rest of this chapter we will consider a class definition for complex numbers. . A complex number is the sum of a real part and an imaginary part.
and others are easier in polar coordinates (like multiplication). double i) polar = false. where r is the magnitude (radius). as needed.150 CHAPTER 14. x = r cos θ y = r sin θ So which representation should we use? Well. and θ is the angle in radians. To go from Cartesian to polar. it is easy to convert from one form to another. Fortunately. } . imag. theta. double mag. and that converts between them automatically. polar. public: Complex () { cartesian = false. Complex (double r. the whole reason there are multiple representations is that some operations are easier to perform in Cartesian coordinates (like addition). One option is that we can write a class definition that uses both representations. bool cartesian. CLASSES AND INVARIANTS Cartesian coordinates imaginary axis Polar coordinates magnitude angle real axis Complex numbers in polar coordinates are written reiθ . r θ = = x2 + y 2 arctan(y/x) To go from polar to Cartesian. class Complex { double real.
They contain the real part. There are now six instance variables. is the type of the corresponding instance variable. } If the cartesian flag is true then real contains valid data.4 Accessor functions By convention. The second constructor uses the parameters to initialize the real and imaginary parts.4. in either representation. the accessor functions give us an opportunity to make sure that the value of the variable is valid before we return it. For example. but we will see that it is very versatile. and we can just return it. Otherwise. ACCESSOR FUNCTIONS 151 { real = r.14. Setting the polar flag to false warns other functions not to access mag or theta until they have been set. The return type. return real. Here's what getReal looks like: double Complex::getReal () { if (cartesian == false) calculateCartesian (). 14. In the next few sections. Four of the instance variables are self-explanatory. imag = i. cartesian = true. The other two variables. In this case. cartesian and polar are flags that indicate whether the corresponding values are currently valid. which means that this representation will take up more space than either of the others. Now it should be clearer why we need to keep the instance variables private. the do-nothing constructor sets both flags to false to indicate that this object does not contain a valid complex number (yet). the imaginary part. } }. we have to call calculateCartesian to convert from polar coordinates to Cartesian coordinates: void Complex::calculateCartesian () { . accessor functions have names that begin with get and end with the name of the instance variable they fetch. the angle and the magnitude of the complex number. If client programs were allowed unrestricted access. we will develop accessor functions that will make those kinds of mistakes impossible. it would be easy for them to make errors by reading uninitialized values. but it does not calculate the magnitude or angle. naturally. polar = false.
we want to be able to output objects in a human-readable form. it is in Cartesian format only. CLASSES AND INVARIANTS real = mag * cos (theta). Initially. When we invoke printCartesian it accesses real and imag without having to do any conversions. Then we set the cartesian flag. the program is forced to convert to polar coordinates and store the results in the instance variables.152 CHAPTER 14.0). indicating that real and imag now contain valid data. write a corresponding function called calculatePolar and then write getMag and getTheta.5 Output As usual when we define a new class. and printPolar invokes getMag.printPolar(). 14. Since the output functions use the accessor functions.0. The following code creates a Complex object using the second constructor. When we invoke printPolar. As an exercise. The output of this code is: . The good news is that we only have to do the conversion once. we can calculate the Cartesian coordinates using the formulas from the previous section. because invoking them might modify the instance variables. cartesian = true. the program will compute automatically any values that are needed. } void Complex::printPolar () { cout << getMag() << " e^ " << getTheta() << "i" << endl. For Complex objects. } The nice thing here is that we can output any Complex object in either format without having to worry about the representation. c1. 3. } Assuming that the polar coordinates are valid. Complex c1 (2. When printPolar invokes getTheta. c1. we could use two functions: void Complex::printCartesian () { cout << getReal() << " + " << getImag() << "i" << endl.printCartesian(). One unusual thing about these accessor functions is that they are not const. it will see that the polar coordinates are valid and return theta immediately. imag = mag * sin (theta).
getImag() + b.14.getReal(). it is easiest to convert them to Cartesian coordinates and then add them. anyway). As usual. Complex& b) { double mag = a.0).7 Another function on Complex numbers Another operation we might want is multiplication. Again.printCartesian().getMag() . c2). Complex sum = add (c1.982794i 14. Complex mult (Complex& a. In polar coordinates.0). return sum. sum.getReal() + b. Complex c2 (3. double imag = a. a little harder. A FUNCTION ON COMPLEX NUMBERS 153 2 + 3i 3. multiplication is easy if the numbers are in polar coordinates and hard if they are in Cartesian coordinates (well. Complex sum (real.getMag() * b.6. we can just multiply the magnitudes and add the angles.60555 e^ 0.0. we would pass both operands as arguments: Complex c1 (2.0. it is easy to deal with these cases if we use the accessor functions: Complex add (Complex& a. If the numbers are in Cartesian coordinates. If the numbers are in polar coordinates. we can use the accessor functions without worrying about the representation of the objects. The output of this program is 5 + 7i 14. 4.6 A function on Complex numbers A natural operation we might want to perform on complex numbers is addition. 3.getImag(). addition is easy: you just add the real parts together and the imaginary parts together. imag). To invoke this function. Unlike addition. } Notice that the arguments to add are not const because they might be modified when we invoke the accessors. Complex& b) { double real = a.
0). } A small problem we encounter here is that we have no constructor that accepts polar coordinates. The result is also in polar format. and we can't have that. In this case. it's amazing that we get the right answer! 14.0. write the corresponding function named setCartesian. Complex product = mult (c1.setPolar (mag.0).printCartesian(). we have to make sure that when mag and theta are set. the cartesian coordinates are no longer valid. product.getTheta(). 3. though. Complex c2 (3. Really. cartesian = false. if both flags are set then we expect the other four variables to . product. Complex product. we have to make sure that the cartesian flag is unset. In order to do that properly.0. c2).getTheta() + b. we can try something like: Complex c1 (2. To test the mult function. } As an exercise. we would like a second constructor that also takes two doubles. theta = t. polar = true. For example. if polar is set. both arguments get converted to polar coordinates. Similarly. return product. When we call mult. we expect mag and theta to be valid. CLASSES AND INVARIANTS double theta = a. 4.154 CHAPTER 14. At the same time. if the cartesian flag is set then we expect real and imag to contain valid data. but remember that we can only overload a function (even a constructor) if the different versions take different parameters. An alternative it to provide an accessor function that sets the instance variables. so when we invoke printCartesian it has to get converted back. The output of this program is -6 + 17i There is a lot of conversion going on in this program behind the scenes. Finally. double t) { mag = m. we also set the polar flag. theta). That's because if we change the polar coordinates. void Complex::setPolar (double m.8 Invariants There are several conditions we expect to be true for a proper Complex object. It would be nice to write one.
The first step is to prevent unrestricted access to the instance variables by making them private. One of the primary things that data encapsulation is good for is helping to enforce invariants." That definition allows two loopholes. Otherwise. they should be specifying the same point in two different formats. document them as part of the program. If we examine all the accessors and modifiers. and in some cases unavoidable. it will still be true when the function is complete. though. What that means is "If the invariant is true when the function is called. 14. and maybe write code that checks them. We have to be a little careful. That's ok. The other loophole is that we only have to maintain the invariant if it was true at the beginning of the function. if not. One of the ways to write good quality code that contains few bugs is to figure out what invariants are appropriate for your classes. If those assumptions turn out to be true. output an error message. and write code that makes it impossible to violate them. PRECONDITIONS 155 be consistent. As long as the invariant is restored by the end of the function.14. To make your programs more robust. all bets are off. Is there an assumption we make about the current object? Yes. it is a good idea to think about your assumptions explicitly. we can list the functions that make assignments to one or more instance variables: the second constructor calculateCartesian calculatePolar setCartesian setPolar In each case. let's take another look at calculateCartesian. If the invariant was violated somewhere else in the program. Then the only way to modify the object is through accessor functions and modifiers. all is well. there may be some point in the middle of the function when the invariant is not true. Notice that I said "maintain" the invariant.9 Preconditions Often when you write a function you make implicit assumptions about the parameters you receive. your program might crash. then we can prove that it is impossible for an invariant to be violated. For example. First. Looking at the Complex class. usually the best we can do is detect the error. that is. and we can show that every one of them maintains the invariants. then everything is fine. it is straightforward to show that the function maintains each of the invariants I listed. and exit. These kinds of conditions are called invariants.9. for the obvious reason that they do not vary—they are always supposed to be true. we assume that the polar .
exit (1). One option is to add a comment to the function that warns programmers about the precondition. These comments are useful for people reading your programs. imag = mag * sin (theta). void Complex::calculateCartesian () // precondition: the current object contains valid polar coordinates and the polar flag is set // postcondition: the current object will contain valid Cartesian coordinates and valid polar coordinates. imag = mag * sin (theta).h header file. the things we know will be true when the function completes. } real = mag * cos (theta). assert does nothing. you get a function called assert that takes a boolean value (or a conditional expression) as an argument. } At the same time. As long as the argument is true. cartesian = true. If you include the assert. } The exit function causes the program to quit immediately. but it is an even better idea to add code that checks the preconditions. This kind of error-checking is so common that C++ provides a built-in function to check preconditions and print error messages. then this function will produce meaningless results. CLASSES AND INVARIANTS flag is set and that mag and theta contain valid data. cartesian = true. so that we can print an appropriate error message: void Complex::calculateCartesian () { if (polar == false) { cout << "calculateCartesian failed because the polar representation is invalid" << endl. and both the cartesian flag and the polar flag will be set { real = mag * cos (theta). If that is not true. assert prints an error message and quits. Here's how to use it: void Complex::calculateCartesian () . If the argument is false. The return value is an error code that tells the system (or whoever executed the program) that something went wrong. I also commented on the postconditions.156 CHAPTER 14.
Complex (double r. } The first assert statement checks the precondition (actually just part of it). Abort There is a lot of information here to help me track down the error. but that should not be invoked by client programs. real = mag * cos (theta).cpp:63: void Complex::calculatePolar(): Assertion 'cartesian' failed. imag. public: Complex () { cartesian = false. For example. there are member functions that are used internally by a class. I get the following message when I violate an assertion: Complex. imag = i. void calculateCartesian (). polar. the second assert statement checks the postcondition. In my development environment. the function name and the contents of the assert statement. In that case the complete class definition for Complex would look like: class Complex { private: double real.14. If we wanted to protect these functions. bool cartesian. including the file name and line number of the assertion that failed. double mag. PRIVATE FUNCTIONS 157 { assert (polar). } . cartesian = true. double i) { real = r. but there is probably no reason clients should call them directly (although it would not do any harm).10. theta. calculatePolar and calculateCartesian are used by the accessor functions. void calculatePolar (). we could declare them private the same way we do with instance variables. imag = mag * sin (theta). polar = false.10 Private functions In some cases. assert (polar && cartesian). 14.
The private label at the beginning is not necessary.158 CHAPTER 14. CLASSES AND INVARIANTS cartesian = true. invariant: A condition. void setPolar (double m. void setCartesian (double r. double t). accessor function: A function that provides access (read or write) to a private instance variable. that should be true at all times in client code. if possible. getImag (). usually pertaining to an object. getMag (). . postcondition: A condition that is true at the end of a function. getTheta (). If the precondition is not true. } polar = false. a class is a structure with private instance variables.11 Glossary class: In general use. void printPolar (). and that should be maintained by all member functions. a class is a user-defined type with member functions. In C++. It is often a good idea for functions to check their preconditions. void printCartesian (). but it is a useful reminder. double double double double getReal (). double i). the function may not work. }. precondition: A condition that is assumed to be true at the beginning of a function. 14.
A stream is an abstract object that represents the flow of data from a source like the keyboard or a file to a destination like the screen or a file. because the distance from A to B is the same as the distance from B to A. which you have to include.1 Streams To get input from a file or send output to a file. Also. We will also implement a data structure called Set that expands automatically as you add elements. Aside from demonstrating all these features.h.Chapter 15 File Input/Output and apmatrixes In this chapter we will develop a program that reads and writes files. 159 . These objects are defined in the header file fstream. 15. The output is a table that looks like this: Atlanta Chicago Boston Dallas Denver Detroit Orlando Phoenix Seattle 0 700 1100 800 1450 750 400 1850 2650 Atlanta 0 1000 900 1000 300 1150 1750 2000 Chicago 0 1750 2000 800 1300 2650 3000 Boston 0 800 1150 1100 1000 2150 Dallas 0 1300 1900 800 1350 Denver 0 1200 2000 2300 Detroit 0 2100 0 3100 1450 0 Orlando Phoenix Seattle The diagonal elements are all zero because that is the distance from a city to itself. and demonstrates the apmatrix class. you have to create an ifstream object (for input files) or an ofstream object (for output files). there is no need to print the top half of the matrix. the real purpose of the program is to generate a two-dimensional table of the distances between cities in the United States. parses input.
. but don't know how big it is. though. they are called good." Whenever you get data from an input stream.160 CHAPTER 15. There are member functions for ifstreams that check the status of the input stream.good() == false) { cout << "Unable to open the file named " << fileName.eof()) break. which has type istream. If the return value from eof is true then we have reached the end of the file and we know that the last attempt failed. cin represents the flow of data from the keyboard to the program. and cout. ifstream infile ("file-name"). fail and bad.c_str()).. if (infile. int x. Each time the program uses the >> operator or the getline function. line). // get a single integer and store in x // get a whole line and store in line If we know ahead of time how much data is in a file. you don't know whether the attempt succeeded until you check. We will use good to make sure the file was opened successfully and eof to detect the "end of file. line). infile >> x. 15. it adds a datum to the outgoing stream. We can do that using the ifstream constructor. Similarly. which has type ostream. } while (true) { getline (infile. we have to create a stream that flows from the file into the program. getline (infile.. if (infile. FILE INPUT/OUTPUT AND APMATRIXES We have already worked with two streams: cin. Here is a program that reads lines from a file and displays them on the screen: apstring fileName = . The argument for this constructor is a string that contains the name of the file you want to open.2 File input To get data from a file.. The result is an object named infile that supports all the same operations as cin. we want to read the entire file. when the program uses the << operator on an ostream. exit (1). it removes a piece of data from the input stream. apstring line. eof. it is straightforward to write a loop that reads the entire file and then stops. including >> and getline. ifstream infile (fileName. More often.
good() == false) { cout << "Unable to open one of the files. or you do not have permission to read it. For example. It is important to exit the loop between the input statement and the output statement.eof()) break." << endl. The return value is false if the system could not open the file. For example. Usually there will be a break statement somewhere in the loop so that the program does not really run forever (although some programs do). } while (true) { getline (infile.good() == false || outfile. if (infile.3. exit (1). line). so that when getline fails at the end of the file.4 I defined "parsing" as the process of analyzing the structure of a sentence in a natural language or a statement in a formal language. In addition. In this case. we could modify the previous program to copy lines from one file to another. ifstream infile ("input-file"). } 15. ofstream outfile ("output-file"). the compiler has to parse your program before it can translate it into machine language.3 File output Sending output to a file is similar.4 Parsing input In Section 1. 15. outfile << line << endl. } The function c str converts an apstring to a native C string. FILE OUTPUT 161 cout << line << endl. The statement while(true) is an idiom for an infinite loop. Because the ifstream constructor expects a C string as an argument. we invoke the good function. we have to convert the apstring. if (infile. most likely because it does not exist. we do not output the invalid data in line. Immediately after opening the file. when you read input from a file or from the keyboard you often have to parse it in order to extract the information you want and detect errors. the break statement allows us to exit the loop as soon as we detect the end of file.15. .
we can find the beginning and end of each city name.100 700 800 1. substr is an apstring member function. Parsing input lines consists of finding the beginning and end of each city name and using the substr function to extract the cities and distance. Interestingly. the sequence \' represents a single-quote. The backslash (\) indicates that we want to treat the next character literally. I have a file called distances that contains information about the distances between major cities in the United States. the sequence \\ represents a single backslash.162 CHAPTER 15.html so it may be wildly inaccurate. we have to write something like: int index = line. Searching for special characters like quotation marks can be a little awkward. a double quotation mark. it takes two arguments.jaring. but it represents a single character. The format of the file looks like this: "Atlanta" "Atlanta" "Atlanta" "Atlanta" "Atlanta" "Atlanta" "Atlanta" "Chicago" "Boston" "Chicago" "Dallas" "Denver" "Detroit" "Orlando" 700 1. FILE INPUT/OUTPUT AND APMATRIXES For example. like "San Francisco. . The sequence \" represents a quotation mark. void processLine (const apstring& line) { // the character we are looking for is a quotation mark char quote = '\"'.450 750 400 Each line of the file contains the names of two cities in quotation marks and the distance between them in miles. because the quotation mark is a special character in C++. The outermost single-quotes indicate that this is a character value." By searching for the quotation marks in a line of input. I got this information from a randomly-chosen web page http://www.find ('\"'). the starting index of the substring and the length. The first backslash indicates that we should take the second backslash seriously. but that doesn't matter.my/usiskl/usa/distance. The quotation marks are useful because they make it easy to deal with names that have more than one word. as usual. If we want to find the first appearance of a quotation mark. used to identify string values. The argument here looks like a mess. though.
quote.1. and the built-in functions for reading numbers usually can't handle them. atoi is defined in the header file stdlib.quoteIndex[2] . but it is a good starting place. quoteIndex[i-1]+1). 15. // output the extracted information cout << city1 << "\t" << city2 << "\t" << distString << endl.find (quote).quoteIndex[0] . city1 = line. i<s.h. we add it to the result string. one option is to traverse the string and check whether each character is a digit. Most of the time when computers write large numbers. At the end of the loop. they often use commas to group the digits.quoteIndex[2] .length() . // find the other quotation marks using the find from Chapter 7 for (int i=1. } Of course. the result string contains all the digits from the original string. we can use the library function atoi to convert to integer.1.750. distString = line.5. city2 = line. // find the first quotation mark using the built-in find quoteIndex[0] = line.5 Parsing numbers The next task is to convert the numbers in the file from strings to integers.1.length(). When people write large numbers. That makes the conversion a little more difficult. i++) { quoteIndex[i] = find (line. To get rid of the commas. len3). for (int i=0. PARSING NUMBERS 163 // store the indices of the quotation marks in a vector apvector<int> quoteIndex (4).substr (quoteIndex[3]+1. i<4. int convertToInt (const apstring& s) { apstring digitString = "". } // break int len1 apstring int len2 apstring int len3 apstring the line up into substrings = quoteIndex[1] . they don't include commas. as in 1. just displaying the extracted information is not exactly what we want. len1). len2). Once we get rid of the commas. = line. but it also provides an opportunity to write a comma-stripping function. If so.substr (quoteIndex[2]+1. in order.substr (quoteIndex[0]+1. so that's ok. i++) { .15. = quoteIndex[3] .
The expression digitString += s[i]. our implementation of an ordered set will have the following property: Arbitrary size: As we add elements to the set. } The variable digitString is an example of an accumulator. except that instead of getting incremented. .164 CHAPTER 15. In addition.9. Both apstrings and apvectors have an ordering. it expands to make room for new elements.c_str()). Since atoi takes a C string as a parameter. We have seen some examples already. it gets accumulates one new character at a time. using string concatentation. there is no effect. Here is the beginning of a class definition for a Set. we can take advantage of the resize function on apvectors. including apstrings. An ordered set is a collection of items with two defining properties: Ordering: The elements of the set have indices associated with them. 15. If you try to add an element to a set. we have to write an add function that searches the set to see if it already exists. We can use these indices to identify elements of the set. To make the set expand as elements are added. and apvectors which are collections on any type. we have to convert digitString to a C string before passing it as an argument. is equivalent to digitString = digitString + s[i]. It is similar to the counter we saw in Section 7. and it already exists.6 The Set data structure A data structure is a container for grouping a collection of data into a single object. Both statements add a single character onto the end of the existing string. To achieve uniqueness. Both none of the data structures we have seen so far have the properties of uniqueness or arbitrary size. Uniqueness: No element appears in the set more than once. every element has an index we can use to identify it. } } return atoi (digitString. FILE INPUT/OUTPUT AND APMATRIXES if (isdigit (s[i])) { digitString += s[i]. which are collections of characters.
int add (const apstring& s). int numElements. } Why do we have to prevent client programs from changing getNumElements? What are the invariants for this type. it checks to make sure the index is greater than or equal to zero and less than the length of the apvector. } The instance variables are an apvector of strings and an integer that keeps track of how many elements there are in the set. To access the elements of a set. }. As we look at the rest of the Set member function. which might be smaller than the length of the apvector. int Set::getNumElements () const { return numElements. we need to check a stronger condition. The Set constructor takes a single parameter. Set::Set (int n) { apvector<apstring> temp (n). and how could a client program break an invariant. numElements is a read-only variable.15. When we use the [] operator to access the apvector. Keep in mind that the number of elements in the set. see if you can convince yourself that they all maintain the invariants.6. elements = temp. numElements. The index has to be less than the number of elements. which is the initial size of the apvector. which are private. The initial number of elements is always zero. int find (const apstring& s) const. apstring getElement (int i) const. public: Set (int n). so we provide a get function but not a set function. int getNumElements () const. is not the same thing as the size of the apvector. apstring Set::getElement (int i) const . Usually it will be smaller. though. getNumElements and getElement are accessor functions for the instance variables. THE SET DATA STRUCTURE 165 class Set { private: apvector<apstring> elements. numElements = 0.
of course. exit (1). } So that leaves us with add. i<numElements. i++) { if (elements[i] == s) return i. it prints an error message (not the most useful message. } The tricky thing here is that numElements is used in two ways. the pattern for traversing and searching should be old hat: int Set::find (const apstring& s) const { for (int i=0. It is the number of elements in the set.length()) { elements. but it is also the index of the next element to be added. } // add the new elements and return its index index = numElements. elements[index] = s. int Set::add (const apstring& s) { // if the element is already in the set. } else { cout << "Set index out of range. if (index != -1) return index. but in this case it might be useful to make it return the index of the element. } return -1.166 CHAPTER 15. } } If getElement gets an index that is out of range. I admit). FILE INPUT/OUTPUT AND APMATRIXES { if (i < numElements) { return elements[i]. return its index int index = find (s). . By now. numElements++. // if the apvector is full. return index. and exits.length() * 2). The interesting functions are find and add. double its size if (numElements == elements.resize (elements." << endl. Often the return type for something like add would be void.
APMATRIX 167 It takes a minute to convince yourself that that works. there are four constructors: apmatrix<char> m1. Then in processLine we add both cities to the Set and store the index that gets returned.15. cols. 0. . 4). In main we create the Set with an initial size of 2: Set cities (2). and we have to allocate more space (using resize) before we can add the new element. int index1 = cities. the other the column number.add (city1). for "number of rows" and "number of columns.0).7. 15. int index2 = cities. apmatrix<double> m3 (rows. it has two dimensions.7 apmatrix An apmatrix is similar to an apvector except it is two-dimensional. but consider this: when the number of elements is zero. called numrows and numcols. that means that the vector is full. When the number of elements is equal to the length of the apvector. the index of the next element is 0." Each element in the matrix is indentified by two indices. Here is a state diagram showing a Set object that initially contains space for 2 elements. one specifies the row number. numElements: elements: 0 1 0 numElements: elements: 0 1 1 numElements: elements: 0 1 2 numElements: elements: 0 1 2 3 3 "element1" "element1" "element2" "element1" "element2" "element3" Now we can use the Set class to keep track of the cities we find in the file. To create a matrix. apmatrix<double> m4 (m3). Instead of a length.add (city2). I modified processLine to take the cities object as a second parameter. apmatrix<int> m2 (3.
.168 CHAPTER 15. 50. row++) { for (int col=0. } } This loop prints each row of the matrix with tabs between the elements and newlines between the rows: for (int row=0. row++) { for (int col=0. which are the initial number of rows and columns. } cout << endl.numrows(). col < m2. except that it takes an additional parameter that is used to initialized the elements of the matrix. Remember that the row indices run from 0 to numrows() -1 and the column indices run from 0 to numcols() -1. col++) { cout << m2[row][col] << "\t". row < m2. 0). row < m2. Just as with apvectors. the program prints an error message and quits.8 A distance matrix Finally. The third is the same as the second. the matrix will have one row and one column for each city.numcols(). FILE INPUT/OUTPUT AND APMATRIXES The first is a do-nothing constructor that makes a matrix with both dimensions 0.numcols(). and even apmatrixes).0 * m2[0][0]. with plenty of space to spare: apmatrix<int> distances (50. Specifically. we can make apmatrixes with any type of elements (including apvectors. This loop sets each element of the matrix to the sum of its two indices: for (int row=0. The numrows and numcols functions get the number of rows and columns. we use the [] operator to specify the row and column: m2[0][0] = 1. The second takes two integers. col++) { m2[row][col] = row + col. If we try to access an element that is out of range. col < m2. To access the elements of a matrix. The usual way to traverse a matrix is with a nested loop.numrows(). We'll create the matrix in main. } 15. The fourth is a copy constructor that takes another apmatrix as a parameter. m3[1][2] = 10. in that order. we are ready to put the data from the file into a matrix.
2. What are some of the problems with the existing code? 1. It . It would be better to allow the distance matrix to expand in the same way a Set does.getElement(i) << "\t".add (city2). } cout << endl. i<cities.add (city1). j++) { cout << distances[i][j] << "\t". i<cities. } cout << endl. distances[index2][index1] = distance. in main we can print the information in a human-readable form: for (int i=0. j<=i. We have to pass the set of city names and the matrix itself as arguments to processLine. The data in the distance matrix is not well-encapsulated. i++) { cout << cities. Finally.9 A proper distance matrix Although this code works. int index2 = cities. This code produces the output shown at the beginning of the chapter. we add new information to the matrix by getting the indices of the two cities from the Set and using them as matrix indices: int dist = convertToInt (distString). A PROPER DISTANCE MATRIX 169 Inside processLine. so we chose an arbitrary large number (50) and made it a fixed size. it is not as well organized as it should be. The original data is available from this book's web page. The apmatrix class has a function called resize that makes this possible.getNumElements(). int index1 = cities.9. use of the distance matrix is error prone because we have not provided accessor functions that perform error-checking. for (int j=0. distances[index1][index2] = distance. for (int i=0. We did not know ahead of time how big to make the distance matrix.getNumElements(). we are in a good position to evaluate the design and improve it. Also.getElement(i) << "\t". i++) { cout << cities. which is awkward.15. } cout << "\t". 15. Now that we have written a prototype.
}. processLine (line. distances). quoteIndex[i-1]+1). for (int i=1.eof()) break. apvector<int> quoteIndex (4). and combine them into a single object called a DistMatrix. ifstream infile ("distances"). FILE INPUT/OUTPUT AND APMATRIXES might be a good idea to take the Set of city names and the apmatrix of distances. if (infile. void print ().find (quote). const apstring& city2) const. int distance (int i. apmatrix<int> distances. const apstring& city2. } distances. } It also simplifies processLine: void processLine (const apstring& line. public: DistMatrix (int rows). i<4.print (). int j) const. . int numCities () const. int distance (const apstring& city1. while (true) { getline (infile. Here is a draft of what the header for a DistMatrix might look like: class DistMatrix { private: Set cities. Using this interface simplifies main: void main () { apstring line. DistMatrix distances (2). apstring cityName (int i) const. quote.170 CHAPTER 15. void add (const apstring& city1. i++) { quoteIndex[i] = find (line. quoteIndex[0] = line. DistMatrix& distances) { char quote = '\"'. int dist). line).
10. } I will leave it as an exercise to you to implement the member functions of DistMatrix. GLOSSARY 171 } // break the line up into substrings int len1 = quoteIndex[1] .1. int len2 = quoteIndex[3] . apstring city1 = line.10 Glossary ordered set: A data structure in which every element appears only once and every element has an index that identifies it. int len3 = line.substr (quoteIndex[2]+1. In C++ streams are used for input and output. accumulator: A variable used inside a loop to accumulate a result. apstring distString = line. len3). city2. len2).quoteIndex[2] .quoteIndex[0] . len1). // add the new datum to the distances matrix distances.substr (quoteIndex[3]+1.quoteIndex[2] .length() .add (city1. distance). 15.15. int distance = convertToInt (distString).substr (quoteIndex[0]+1. . often by getting something added or concatenated during each iteration.1.1. apstring city2 = line. stream: A data structure that represents a "flow" or sequence of data items from one place to another.
htm with minor formatting changes. ~apstring(). // public member functions // constructors/destructor apstring(). apstring(const char * s). http://www. apstring(const apstring & str).1 apstring // used to indicate not a position in the string extern const int npos. Revisions to the classes may have been made since that time. The versions of the C++ classes defined for use in the AP Computer Science courses included in this textbook were accurate as of 20 July 1999.Appendix A Quick reference for AP classes These class definitions are copied from the College Board web page. // assignment 173 // // // // construct empty string "" construct from string literal copy constructor destructor . This is probably a good time to repeat the following text. or the AP Computer Science Development Committee.org/ap/computer-science/html/quick_ref. Educational Testing service.collegeboard. also from the College Board web page." A. "Inclusion of the C++ classes defined for use in the Advanced Placement Computer Science courses does not constitute endorsement of the other material in this textbook by the College Board.
lhs. // comparison operators bool operator== ( const bool operator!= ( const bool operator< ( const bool operator<= ( const bool operator> ( const bool operator>= ( const apstring apstring apstring apstring apstring apstring & & & & & & lhs. ). // append str const apstring & operator+= (char ch). int len) const. ). char ch ). ). istream & operator>> ( istream & is. apstring & str ). // assign s const apstring & operator= (char ch). ). apstring operator+ ( char ch. ). const apstring & rhs ). // range-checked indexing // modifiers const apstring & operator+= (const apstring & str). const apstring & str ). // // // // // // number of chars index of first occurrence of str index of first occurrence of ch substring of len chars. int find(char ch) const. // append char // The following free (non-member) functions operate on strings // I/O functions ostream & operator<< ( ostream & os. apstring & str ). istream & getline( istream & is. // range-checked indexing char & operator[ ](int k). lhs. starting at pos explicit conversion to char * // indexing char operator[ ](int k) const. A. apstring substr(int pos. // concatenation operator + apstring operator+ ( const apstring & lhs.174 APPENDIX A. const const const const const const apstring apstring apstring apstring apstring apstring & & & & & & rhs rhs rhs rhs rhs rhs ). // assign ch // accessors int length() const. lhs. apstring operator+ ( const apstring & str. const apstring & str ). QUICK REFERENCE FOR AP CLASSES const apstring & operator= (const apstring & str). // assign str const apstring & operator= (const char * s). const char * c_str() const. lhs.2 apvector template <class itemType> class apvector . lhs. int find(const apstring & str) const.
// number of rows // number of columns . // modifiers void resize(int newSize).3. // copy constructor ~apmatrix( ). // destructor // assignment const apmatrix & operator = (const apmatrix & rhs). // initial size of vector is size apvector(int size. // all entries == fillValue apmatrix(const apmatrix & mat). int numcols() const. // accessors int length() const. // default size is 0 x 0 apmatrix(int rows. // capacity of vector // change size dynamically //can result in losing values A. int cols. // default constructor (size==0) apvector(int size). // indexing // indexing with range checking itemType & operator[ ](int index). // destructor // assignment const apvector & operator= (const apvector & vec). int cols). const itemType & fillValue).3 apmatrix template <class itemType> class apmatrix // public member functions // constructors/destructor apmatrix(). // all entries == fillValue apvector(const apvector & vec). // accessors int numrows() const. const itemType & operator[ ](int index) const. const itemType & fillValue). APMATRIX 175 // public member functions // constructors/destructor apvector(). // copy constructor ~apvector().A. // size is rows x cols apmatrix(int rows.
apvector<itemType> & operator[ ](int k). int newCols). // modifiers void resize(int newRows. QUICK REFERENCE FOR AP CLASSES // indexing // range-checked indexing const apvector<itemType> & operator[ ](int k) const. // resizes matrix to newRows x newCols // (can result in losing values) .176 APPENDIX A.
absolute value, 41 abstract parameter, 133 abstraction, 133 accessor function, 148, 151, 158 accumulator, 164, 171 algorithm, 94, 95 ambiguity, 6 apmatrix, 167 apstring, 72 length, 67 vector of, 123 argument, 23, 27, 30 arithmetic base 60, 93 complex, 149 floating-point, 22, 93 integer, 16 assert, 156 assignment, 13, 19, 53 atoi, 163 backslash, 162 bisection search, 130 body, 63 loop, 55 bool, 46, 52 boolean, 45 bottom-up design, 103, 142, 145 break statement, 137, 161 bug, 4 C string, 161 c str, 161 call, 30 call by reference, 79, 82 call by value, 78 Card, 121 Cartesian coordinate, 149 character classification, 163 special sequence, 162 character operator, 17 cin, 83, 160 class, 147, 148, 158 apstring, 72 Card, 121 Complex, 149 Time, 29 client programs, 147 cmath, 23 comment, 7 comparable, 126 comparison apstring, 72 operator, 31 comparison operator, 45, 126 compile, 2, 9 compile-time error, 4, 41 complete ordering, 126 Complex, 149 complex number, 149 composition, 18, 19, 24, 43, 81, 121 concatenate, 74 concatentation, 164 conditional, 31, 37 alternative, 32 chained, 33, 37 nested, 33, 37 constructor, 97, 107, 119, 122, 138, 139, 142, 149, 151, 165, 168 convention, 136 convert to integer, 163 coordinate, 149 177
Cartesian, 149 polar, 149 correctness, 132 counter, 70, 74, 103 cout, 83, 160 current object, 110 data encapsulation, 147, 155, 165 data structure, 164 dead code, 40, 52 dealing, 143 debugging, 4, 9, 41 deck, 127, 133, 138 declaration, 13, 76 decrement, 70, 74, 90 default, 137 detail hiding, 147 deterministic, 100, 107 diagram stack, 36, 50 state, 36, 50 distribution, 102 division floating-point, 56 integer, 16 double (floating-point), 21 Doyle, Arthur Conan, 5 efficiency, 143 element, 98, 107 encapsulation, 58, 60, 63, 70, 128 data, 147, 155, 165 functional, 147 encode, 121, 133 encrypt, 121 end of file, 160 enumerated type, 135 eof, 160 error, 9 compile-time, 4, 41 logic, 4 run-time, 4, 68, 90 exit, 156 expression, 16, 18, 19, 23, 24, 99 factorial, 51
file input, 160 file output, 161 fill-in function, 91 find, 68, 129, 162 findBisect, 130 flag, 46, 151 floating-point, 30 floating-point number, 21 for, 99 formal language, 5, 9 frabjuous, 48 fruitful function, 30, 39 function, 30, 59, 88 accessor, 148, 151 bool, 46 definition, 24 fill-in, 91 for objects, 88 fruitful, 30, 39 helper, 142, 145 main, 24 Math, 23 member, 109, 119, 139 modifier, 90 multiple parameter, 29 nonmember, 110, 119 pure function, 88 void, 39 functional programming, 95 generalization, 58, 61, 63, 70, 93 getline, 161 good, 160 header file, 23, 159 hello world, 7 helper function, 142, 145 high-level language, 2, 9 histogram, 105, 107 Holmes, Sherlock, 5 ifstream, 160 immutable, 72 implementation, 119, 147 increment, 70, 74, 90
incremental development, 41, 92 nested, 128, 139, 168 index, 68, 74, 99, 107, 128, 167 search, 129 infinite loop, 55, 63, 161 loop variable, 58, 61, 68, 99 infinite recursion, 36, 37, 132 low-level language, 2, 9 initialization, 21, 30, 45 main, 24 input map to, 121 keyboard, 83 mapping, 135 instance, 95 instance variable, 85, 95, 138, 149, 151 Math function, 23 math function integer division, 16 acos, 39 interface, 119, 147 exp, 39 interpret, 2, 9 fabs, 41 invariant, 154, 158 sin, 39 invoke, 119 matrix, 167 iostream, 23 mean, 102 isdigit, 163 member function, 109, 119, 139 isGreater, 126 mergesort, 143, 145 istream, 160 modifier, 90, 95 iteration, 54, 63 modulus, 31, 37 keyword, 15, 19 multiple assignment, 53 language complete, 48 formal, 5 high-level, 2 low-level, 2 natural, 5 programming, 1 safe, 4 leap of faith, 50, 145 length apstring, 67 vector, 100 linear search, 129 Linux, 5 literalness, 6 local variable, 60, 63 logarithm, 56 logic error, 4 logical operator, 46 loop, 55, 63, 99 body, 55 counting, 69, 103 for, 99 infinite, 55, 63, 161 natural language, 5, 9 nested loop, 128 nested structure, 34, 46, 81, 121 newline, 11, 36 nondeterministic, 100 nonmember function, 110, 119 object, 74, 88 current, 110 output, 88 vector of, 127 object-oriented programming, 148 ofstream, 161 operand, 16, 19 operator, 7, 16, 19 >>, 83 character, 17 comparison, 31, 45, 126 conditional, 52 decrement, 70, 90 increment, 70, 90 logical, 46, 52 modulus, 31 order of operations, 17
30. 106 random number. 85 pass by value. 129 seed. 53 break. 171 shuffling. 164 set ordered. 4. 76. 7 conditional. 39. 149 function. 143 sorting. 1 programming style. 167 statement. 171 counter. 123 vector of Cards. 137. 126 pass by reference. 88. 92 prose. 132 recursive. 2 postcondition. 19 assignment. 152 overloading. 141 representation. 76 . 48. 164 ostream. 132. 13. 125 scaffolding. 161 parsing number. 88. 44. 31 declaration. 149 portability. 162 stack. 29 parameter passing. 92 top-down. 85. 129 return type. 107 semantics. 145 infinite. 145 encapsulation. 90. 79. 145 pseudorandom. 36. 79. 129 printCard. 147. 78 abstract. 157 problem-solving. 36 redundancy. 164. 141. 78. 171 ordering. 92 planning. 80 recursion. 158 precedence.180 INDEX ordered set. 6 prototyping. 141. 6. 168 safe language. 22 run-time error. 161 comment. 107 public. 156. 141. 141 rank. 34. 36. 82 parse. 9 program development. 128. 153 random. 37. 158 print Card. 13. 100. 95. 52 return value. 39 poetry. 142 programming language. 133 multiple. 63 bottom-up. 27. 37. 110 polar coordinate. 9. 52. 123. 147 resize. 106. 76. 142. 52 rounding. 121 Rectangle. 139 private. 7. 103 eureka. 3. 4. 123 printDeck. 169 return. 160 output. 126. 92 pseudocode. 166. 50 state. 36. 143 special character. 39. 129 pi. 11. 103. 99. 131. 17 precondition. 34. 41. 68. 82. 75 pointer. 129. 52 searching. 138. 155. 82 inside loop. 4 same. 60 incremental. 85 pattern accumulator. 6 Point. 142 parameter. 163 partial ordering. 46 Set. 6 reference. 149 pure function. 155. 42. 76 state diagram. 9 parsing.
7. 4. 138 of object. 21 enumerated. 136 while. 132. 159. 63 loop. 19 boolean. 98 length. 52. 100 of apstring. 75 Rectangle. 11 vector. 45 output. 103 Turing. 87. 69. 48 type. 123 of Cards. 83. 142 traverse. 87 top-down design. 19 bool. 9 tab. 99 temporary. 16 String. 61. 144 this. 39. 67. 45 double. 171 status. 97. 142 suit. 19 instance. 76 operations. 74. 12. 77 Point. 160 String. 39. 136 syntax. 87 structure. 164 native C. 99 initialization. 78 as return type. 75. 141 switch statement.INDEX 181 for. 40 vector. 140 subdeck. 63 table. 11. 102 stream. 60. 80 Time. 68. 82. 54 . 58. 58 temporary variable. 56 two-dimensional. 12. 11 string concatentation. 88 while statement. 13. 22 value. 97 typecasting. 85 structure definition. 107 copying. 151 local. 133. Alan. 127 void. 161 struct. 135 int. 40 testing. 138. 129 counting. 82 instance variable. 121 swapCards. 110 Time. 13. 45 variable. 54 statistics. 34. 149. 129 switch. 99 element. 88 return. 148 as parameter.
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