Data Structures and Their Algorithms

525 Pages·1991·24.87 MB·English

by  Harry R. Lewis

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Data
Structures
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Harry R. Lewis
Harvard University
Larry Denenberg
Harvard University
m HarperCollinsPublisbers
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Sponsoring Editor: Don Childress
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Art Direction: Julie Anderson
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Data Structures and Their Algorithms
Copyright (1991 by Harry R. Lewis and Larry Denenberg
All rights reserved. Printed in the United States of America. No part of this book
may be used or reproduced in any manner whatsoever without written permis-
sion, except in the case of brief quotations embodied in critical articles and
reviews. For information address HarperCollins Publishers Inc., 10 East 53rd
Street, New York, NY 10022.
Library of Congress Cataloging-in-Publication Data
Lewis, Harry R.
Data structures and their algorithms / Harry R. Lewis, Larry Denenberg.
p. cm.
Includes bibliographical references and index.
ISBN 0-673-39736-X
1. Data structures (Computer science) 2. Algorithms.
I. Denenberg, Larry. II. Title.
QA76.9.D35L475 1991
005.7'3--dc2O 90-23290
CIP
90 91 92 93 9 8 7 6 5 4 3 2 1
To Eunice and Norman Denenberg, and to Elizabeth and Anne Lewis

Contents
Preface xiii
I INTRODUCTION
1.1 Programming as an Engineering Activity 1
1.2 Computer Science Background 3
Memory and Data in Von Neumann Computers
Notation for Programs
Locatives
Abstract Data Types
1.3 Mathematical Background 17
Finite and Infinite Series
Logarithms, Powers, and Exponentials
Order Notation
Recurrence Relations
Naive Probability Theory
Problems 36
References 44
ALGORITHM ANALYSIS 46
2.1 Properties of an Algorithm 46
Effectiveness
Correctness
Termination
Efficiency
Program Complexity
2.2 Exact vs. Growth-Rate Analysis 49
Principles of Mathematical Analysis
Expected-Case and Amortized Analysis
vii
Viii CONTENTS
2.3 Algorithm Paradigms 59
Brute-Force and Exhaustive Search
Greedy Algorithms
Dynamic Programming
NP-Completeness
Problems 65
References 71
LI[
LISTS 73
3.1 List Operations 73
3.2 Basic List Representations 75
Stack Representation in Contiguous Memory
Queue Representation in Contiguous Memory
Stack Representation in Linked Memory
Queue Representation in Linked Memory
3.3 Stacks and Recursion 79
3.4 List Representations for Traversals 84
3.5 Doubly Linked Lists 87
Problems 90
References 94
TREES 96
4.1 Basic Definitions 96
4.2 Special Kinds of Trees 100
4.3 Tree Operations and Traversals 103
4.4 Tree Implementations 108
Representation of Binary Trees
Representation of Ordered Trees
Representation of Complete Binary Trees
4.5 Implementing Tree Traversals and Scans 112
Stack-Based Traversals
Link-Inversion Traversal
Scanning a Tree in Constant Space
Threaded Trees
Implementing Level-Order Traversal
Summary
Problems 125
References 129
CONTENTS ix
ARRAYS AND STRINGS 130
5.1 Arrays as Abstract Data Types 130
Multidimensional Arrays
5.2 Contiguous Representation of Arrays 133
Constant-Time Initialization
5.3 Sparse Arrays 138
List Representations
Hierarchical Tables
Arrays with Special Shapes
5.4 Representations of Strings 143
Huffman Encoding
Lempel-Ziv Encoding
5.5 String Searching 154
The Knuth-Morris-Pratt Algorithm
The Boyer-Moore Algorithm
Fingerprinting and the Karp-Rabin Algorithm
Problems 165
References 173
LIST AND TREE IMPLEMENTATIONS OF SETS 175
6.1 Sets and Dictionaries as Abstract Data Types 175
6.2 Unordered Lists 177
6.3 Ordered Lists 181
Binary Search
Interpolation Search
Skip Lists
6.4 Binary Search Trees 193
Insertion
Deletion
6.5 Static Binary Search Trees 200
Optimal Trees
Probability-Balanced Trees
Median Split Trees
Problems 208
References 216
X CONTENTS
I IJTREE STRUCTURES FOR DYNAMIC DICTIONARIES 219
7.1 AVL Trees 219
Insertion
Deletion
7.2 2-3 Trees and B-Trees 229
2-3 Trees
Red-Black Trees
(a, b)-Trees and B-Trees
7.3 Self-Adjusting Binary Search Trees 243
Problems 251
References 256
I SETS OF DIGITAL DATA 257
8.1 Bit Vectors 257
8.2 Tries and Digital Search Trees 260
8.3 Hashing Techniques 265
Chaining Strategies
Open Addressing Strategies
Deletions
8.4 Extendible Hashing 280
8.5 Hashing Functions 284
Hashing by Division
Hashing by Multiplication
Perfect Hashing of Static Data
Universal Classes of Hash Functions
Problems 291
References 296
SETS WITH SPECIAL OPERATIONS 298
9.1 Priority Queues 298
Balanced Tree Implementations
Heaps
Leftist Trees