Sams Teach Yourself Data Structures and Algorithms in 24 Hours

548 Pages·1999·11.76 MB·English

by  Robert Lafore

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Robert Lafore
Teach Yourself
Data Structures
and Algorithms
24
in Hours
201 West 103rd St.,Indianapolis,Indiana,46290 USA
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Sams Teach Yourself Data Structures and EXECUTIVEEDITOR
Algorithms in 24 Hours Brian Gill
Copyright ©1999 by Sams Publishing DEVELOPMENTEDITOR
Jeff Durham
All rights reserved. No part of this book shall be reproduced,stored in a
MANAGINGEDITOR
retrieval system,or transmitted by any means,electronic,mechanical,photo-
Jodi Jensen
copying,recording,or otherwise,without written permission from the pub-
lisher. No patent liability is assumed with respect to the use of the information PROJECTEDITOR
contained herein. Although every precaution has been taken in the preparation Tonya Simpson
of this book,the publisher and author assume no responsibility for errors or
omissions. Neither is any liability assumed for damages resulting from the use COPYEDITOR
of the information contained herein. Mike Henry
International Standard Book Number:0-672-31633-1 INDEXER
Larry Sweazy
Library of Congress Catalog Card Number:98-83221
PROOFREADERS
Printed in the United States of America Mona Brown
Jill Mazurczyk
First Printing:May 1999
TECHNICALEDITOR
01 00 99 4 3 2 1
Richard Wright
Trademarks SOFTWAREDEVELOPMENT
All terms mentioned in this book that are known to be trademarks or service SPECIALIST
marks have been appropriately capitalized. Sams Publishing cannot attest to Dan Scherf
the accuracy of this information. Use of a term in this book should not be INTERIORDESIGN
regarded as affecting the validity of any trademark or service mark.
Gary Adair
Warning and Disclaimer COVERDESIGN
Aren Howell
Every effort has been made to make this book as complete and as accurate as
possible,but no warranty or fitness is implied. The information provided is on COPYWRITER
an “as is”basis. The authors and the publisher shall have neither liability or Eric Borgert
responsibility to any person or entity with respect to any loss or damages aris-
ing from the information contained in this book or from the use of the CD- LAYOUTTECHNICIANS
ROM or programs accompanying it. Brian Borders
Susan Geiselman
TeamLRN
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Contents at a Glance
Introduction 1
PART I INTRODUCING DATA STRUCTURES AND ALGORITHMS 9
Hour 1 Overview of Data Structures and Algorithms 11
2 Arrays 31
3 Ordered Arrays 51
4 The Bubble Sort 75
5 The Insertion Sort 89
PART II ABSTRACT DATA TYPES 105
Hour 6 Stacks 107
7 Queues and Priority Queues 125
8 Linked Lists 145
9 Abstract Data Types 165
10 Specialized Lists 183
PART III RECURSION AND QUICKSORT 205
Hour 11 Recursion 207
12 Applied Recursion 233
13 Quicksort 257
14 Improving Quicksort 279
PART IV TREES 295
Hour 15 Binary Trees 297
16 Traversing Binary Trees 317
17 Red-Black Trees 337
18 Red-Black Tree Insertions 359
19 2-3-4 Trees 379
20 Implementing 2-3-4 Trees 395
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PART V HASH TABLES 415
Hour 21 Hash Tables 417
22 Quadratic Probing 441
23 Separate Chaining 457
24 When to Use What 475
PART VI APPENDIXES 487
Appendix A Quiz Answers 489
B How to Run the Workshop Applets and Sample Programs 505
C Further Reading 509
Index 513
TeamLRN
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Table of Contents
INTRODUCTION 1
What This Book Is About........................................................................................1
What’s Different About This Book..........................................................................2
Easy to Understand............................................................................................2
Workshop Applets..............................................................................................2
C++ Sample Code..............................................................................................3
Who This Book Is For ............................................................................................3
What You Need to Know Before You Read This Book..........................................4
The Software You Need to Use This Book..............................................................4
How This Book Is Organized..................................................................................4
Enjoy Yourself!........................................................................................................6
Conventions Used in This Book..............................................................................6
PART I INTRODUCING DATA STRUCTURES AND ALGORITHMS 9
HOUR1 OVERVIEWOFDATASTRUCTURESANDALGORITHMS 11
Some Uses for Data Structures and Algorithms....................................................12
Real-World Data Storage..................................................................................12
Programmer’s Tools..........................................................................................14
Real-World Modeling ......................................................................................14
Overview of Data Structures ................................................................................14
Overview of Algorithms........................................................................................15
Some Initial Definitions........................................................................................16
Datafile ............................................................................................................16
Record..............................................................................................................16
Field..................................................................................................................16
Key....................................................................................................................16
Search Key........................................................................................................17
A Quick Introduction to Object-Oriented Programming......................................18
Problems with Procedural Languages..............................................................18
Objects in a Nutshell........................................................................................19
A Runnable Object-Oriented Program ............................................................21
Inheritance and Polymorphism........................................................................24
New C++ Features ................................................................................................25
The stringClass..............................................................................................25
The vectorClass..............................................................................................26
Software Engineering............................................................................................26
Summary................................................................................................................27
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vi Sams Teach Yourself Data Structures and Algorithms in 24 Hours
Q&A......................................................................................................................28
Workshop ..............................................................................................................28
Quiz..................................................................................................................28
Exercise............................................................................................................29
HOUR2 ARRAYS 31
The Array Workshop Applet..................................................................................31
Deletion............................................................................................................34
The Duplicates Problem ..................................................................................35
Slow Array Algorithms....................................................................................37
An Array Example ................................................................................................37
Inserting a New Item........................................................................................39
Searching for an Item ......................................................................................39
Deleting an Item ..............................................................................................39
Displaying the Array Contents ........................................................................40
Program Organization......................................................................................40
Dividing a Program into Classes ..........................................................................40
The LowArrayClass and main() ......................................................................42
Class Interfaces......................................................................................................43
Making main()’s Job Easier ............................................................................43
Who’s Responsible for What?..........................................................................44
The highArray.cppExample ..........................................................................44
The User’s Life Made Easier............................................................................48
Abstraction........................................................................................................48
Summary................................................................................................................48
Q&A......................................................................................................................49
Workshop ..............................................................................................................49
Quiz..................................................................................................................49
Exercise............................................................................................................50
HOUR3 ORDEREDARRAYS 51
The Ordered Workshop Applet..............................................................................51
Demonstrating the Linear Search ....................................................................52
Demonstrating the Binary Search....................................................................53
C++ Code for an Ordered Array............................................................................55
Conducting a Binary Search with the find()Member Function....................56
Investigating the OrdArrayClass......................................................................57
The Advantages of Using Ordered Arrays ......................................................60
Logarithms ............................................................................................................61
An Equation Relating Range Size and Number of Steps................................62
The Opposite of Raising Two to a Power........................................................63
Storing Objects......................................................................................................64
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Contents vii
Implementing the PersonClass........................................................................64
Examining the classDataArray.cppProgram ................................................65
Big O Notation......................................................................................................69
Inserting into an Unordered Array:Constant ..................................................69
Linear Searching:Proportional to N................................................................69
Binary Searching:Proportional to log(N)........................................................70
Eliminating the Constant K..............................................................................70
Why Not Use Arrays for Everything? ..................................................................72
Summary................................................................................................................72
Q&A......................................................................................................................72
Workshop ..............................................................................................................73
Quiz..................................................................................................................73
Exercise............................................................................................................73
HOUR4 THEBUBBLESORT 75
Sorting....................................................................................................................75
Inventing Your Own Sorting Algorithm................................................................76
Bubble-Sorting the Baseball Players ....................................................................77
The bubbleSort Workshop Applet..........................................................................79
Sorting at Full Speed with the Run Button......................................................80
Starting a New Sort with the New Button........................................................80
Single-Stepping with the Step Button..............................................................81
Changing the Array Size with the Size Button................................................81
Fixing the Picture with the Draw Button ........................................................82
Implementing C++ Code for a Bubble Sort..........................................................83
Invariants................................................................................................................86
Efficiency of the Bubble Sort................................................................................86
Summary................................................................................................................87
Q&A......................................................................................................................87
Workshop ..............................................................................................................88
Quiz..................................................................................................................88
Exercise............................................................................................................88
HOUR5 THEINSERTIONSORT 89
Insertion Sort on the Baseball Players..................................................................90
Demonstrating Partial Sorting..........................................................................90
Inserting the Marked Player in the Appropriate Location ..............................90
The insertSort Workshop Applet............................................................................92
Implementing the Insertion Sort in C++................................................................94
Invariants in the Insertion Sort ........................................................................97
Efficiency of the Insertion Sort..............................................................................97
Sorting Objects......................................................................................................98
Implementing C++ Code to Sort Objects........................................................98
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viii Sams Teach Yourself Data Structures and Algorithms in 24 Hours
Another Feature of Sorting Algorithms:Stability ..............................................101
Comparing the Simple Sorts................................................................................102
Summary..............................................................................................................102
Q&A....................................................................................................................103
Workshop ............................................................................................................103
Quiz................................................................................................................103
Exercise..........................................................................................................103
PART II ABSTRACT DATA TYPES 105
HOUR6 STACKS 107
A Different Way to Think About Data Structure................................................107
Uses for Stacks and Queues:Programmer’s Tools........................................108
Stacks and Queues:Restricted Access to Data..............................................108
Stacks and Queues:More Abstract................................................................108
Understanding Stacks..........................................................................................109
Two Real-World Stack Analogies..................................................................109
The Stack Workshop Applet ..........................................................................111
Implementing a Stack in C++..............................................................................113
StackXClass Member Functions....................................................................114
Error Handling................................................................................................116
Stack Example 1:Reversing a Word ..................................................................116
Stack Example 2:Delimiter Matching................................................................118
Opening Delimiters on the Stack ..................................................................119
C++ Code for brackets.cpp..........................................................................120
Using the Stack as a Conceptual Aid ............................................................123
Efficiency of Stacks ............................................................................................123
Summary..............................................................................................................123
Q&A....................................................................................................................124
Workshop ............................................................................................................124
Quiz................................................................................................................124
Exercise..........................................................................................................124
HOUR7 QUEUESANDPRIORITYQUEUES 125
Queues..................................................................................................................125
The Queue Workshop Applet ........................................................................126
A Circular Queue............................................................................................130
C++ Code for a Queue ..................................................................................132
Efficiency of Queues......................................................................................137
Priority Queues....................................................................................................137
The PriorityQ Workshop Applet....................................................................138
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Contents ix
C++ Code for a Priority Queue......................................................................141
Efficiency of Priority Queues ........................................................................143
Summary..............................................................................................................143
Q&A....................................................................................................................144
Workshop ............................................................................................................144
Quiz................................................................................................................144
Exercise..........................................................................................................144
HOUR8 LINKEDLISTS 145
Understanding Links............................................................................................146
Structure Defined by Relationship,Not Position ..........................................147
The LinkList Workshop Applet ..........................................................................147
Inserting a New Link......................................................................................147
Using the Find Button....................................................................................148
Using the Del Button......................................................................................149
Creating Unsorted and Sorted Lists ..............................................................149
Implementing a Simple Linked List....................................................................149
The LinkClass................................................................................................150
The LinkListClass........................................................................................151
The insertFirst()Member Function..........................................................151
The removeFirst()Member Function..........................................................153
The displayList()Member Function..........................................................153
The linkList.cppProgram............................................................................155
Finding and Removing Specified Links..............................................................157
The find()Member Function........................................................................160
The remove()Member Function....................................................................161
Avoiding Memory Leaks................................................................................162
The Efficiency of Linked Lists............................................................................162
Summary..............................................................................................................163
Q&A....................................................................................................................163
Workshop ............................................................................................................164
Quiz................................................................................................................164
Exercise..........................................................................................................164
HOUR9 ABSTRACTDATATYPES 165
A Stack Implemented By a Linked List..............................................................166
Implementing push()and pop()....................................................................166
Implementing a Stack Based on a Linked List..............................................167
Focusing on Class Relationships....................................................................170
Double-Ended Lists ............................................................................................170
Accessing Both Ends of a List ......................................................................170
Implementing a Double-Ended List ..............................................................171
Pointers to Both Ends of the List ..................................................................174
Insertion and Deletion Routines ....................................................................174