Computer Algorithms: Introduction to Design

Drawing upon combined decades of teaching experience, Professors Sara Baase and Allen Van Gelder have extensively revised this best seller to make it the most current and accessible choice for any algorithms course. The new Third Edition features the addition of new topics and exercises and an increased emphasis on algorithm design techniques such as divide-and-conquer and greedy algorithms. It continues the tradition of solid mathematical analysis and clear writing style that made it so popular in previous editions.

Sara Baase is a Professor of Computer Science at San Diego State University and has been teaching CS for 25 years. Dr. Baase is a three-time recipient of the San Diego State University Alumni Association's Outstanding Faculty Award, and she has written a number of textbooks in the areas of algorithms, assembly language, and social and ethical issues related to computing. She earned her doctorate at the University of California, Berkeley. Allen Van Gelder is a Professor of Computer Science at the University of California at Santa Cruz, where he has been teaching CS for 12 years. He received his Ph.D. in Computer Science at Stanford University and is a past recipient of the Presidential Young Investigator Award.

Preface

vii

Analyzing Algorithms and Problems: Principles and Examples

1

(68)

Introduction

2

(1)

Java as an Algorithm Language

3

(8)

Mathematical Background

11

(19)

Analyzing Algorithms and Problems

30

(13)

Classifying Functions by Their Asymptotic Groth Rates

43

(10)

Searching an Ordered Array

53

(16)

Exercises

61

(6)

Notes and References

67

(2)

Data Abstraction and Basic Data Structures

69

(32)

Introduction

70

(1)

ADT Specification and Design Techniques

71

(2)

Elementary ADTs---Lists and Trees

73

(13)

Stacks and Queues

86

(3)

ADTs for Dynamic Sets

89

(12)

Exercises

95

(5)

Notes and References

100

(1)

Recursion and Induction

101

(48)

Introduction

102

(1)

Recursive Procedures

102

(6)

What Is a Proof?

108

(3)

Induction Proofs

111

(7)

Proving Correctness of Procedures

118

(12)

Recurrence Equations

130

(4)

Recursion Trees

134

(15)

Exercises

141

(5)

Notes and References

146

(3)

Sorting

149

(74)

Introduction

150

(1)

Insertion Sort

151

(6)

Divide and Conquer

157

(2)

Quicksort

159

(12)

Merging Sorted Sequences

171

(3)

Mergesort

174

(4)

Lower Bounds for Sorting by Comparison of Keys

178

(4)

Heapsort

182

(15)

Comparison of Four Sorting Algorithms

197

(1)

Shellsort

197

(4)

Radix Sorting

201

(22)

Exercises

206

(15)

Programs

221

(1)

Notes and References

221

(2)

Selection and Adversary Arguments

223

(26)

Introduction

224

(2)

Finding max and min

226

(3)

Finding the Second-Largest Key

229

(4)

The Selection Problem

233

(5)

A Lower Bound for Finding the Median

238

(2)

Designing Against an Adversary

240

(9)

Exercises

242

(4)

Notes and References

246

(3)

Dynamic Sets and Searching

249

(64)

Introduction

250

(1)

Array Doubling

250

(1)

Amortized Time Analysis

251

(2)

Red-Black Trees

253

(22)

Hashing

275

(8)

Dynamic Equivalence Relations and Union-Find Programs

283

(12)

Priority Queues with a Decrease Key Operation

295

(18)

Exercises

302

(7)

Programs

309

(1)

Notes and References

309

(4)

Graphs and Graph Traversals

313

(74)

Introduction

314

(1)

Definitions and Represantations

314

(14)

Traversing Graphs

328

(8)

Depth-First Search on Directed Graphs

336

(21)

Strongly Connected Components of a Directed Graph

357

(7)

Depth-First Search on Undirected Graphs

364

(2)

Biconnected Components of an Undirected Graph

366

(21)

Exercises

375

(9)

Programs

384

(1)

Notes and References

385

(2)

Graph Optimization Problems and Greedy Algorithms

387

(38)

Introduction

388

(1)

Prim's Minimum Spanning Tree Algorithm

388

(15)

Single-Source Shortest Paths

403

(9)

Kruskal's Minimum Spanning Tree Algorithm

412

(13)

Exercises

416

(5)

Programs

421

(1)

Notes and References

422

(3)

Transitive Closure, All-Pairs Shortest Paths

425

(26)

Introduction

426

(1)

The Transitive Closure of a Binary Relation

426

(4)

Warshall's Algorithm for Transitive Closure

430

(3)

All-Pairs Shortest Paths in Graphs

433

(3)

Computing Transitive Closure by Matrix Operations

436

(3)

Multiplying Bit Matrices---Kronrod's Algorithm

439

(12)

Exercises

446

(3)

Programs

449

(1)

Notes and References

449

(2)

Dynamic Programming

451

(32)

Introduction

452

(1)

Subproblem Graphs and Their Traversal

453

(4)

Multiplying a Sequence of Matrices

457

(9)

Constructing Optimal Binary Search Trees

466

(5)

Separating Sequences of Words into Lines

471

(3)

Developing a Dynamic Programming Algorithm

474

(9)

Exercises

475

(6)

Programs

481

(1)

Notes and References

482

(1)

String Matching

483

(32)

Introduction

484

(1)

A Straightforward Solution

485

(2)

The Knuth-Morris-Pratt Algorithm

487

(8)

The Boyer-Moore Algorithm

495

(9)

Approximate String Matching

504

(11)

Exercises

508

(4)

Programs

512

(1)

Notes and References

512

(3)

Polynomials and Matrices

515

(32)

Introduction

516

(1)

Evaluating Polynomial Functions

516

(6)

Vector and Matrix Multiplication

522

(6)

The Fast Fourier Transform and Convolution

528

(19)

Exercises

542

(4)

Programs

546

(1)

Notes and References

546

(1)

NP-Complete Problems

547

(64)

Introduction

548

(1)

P and NP

548

(11)

NP-Complete Problems

559

(11)

Approximation Algorithms

570

(2)

Bin Packing

572

(5)

The Knapsack and Subset Sum Problems

577

(4)

Graph Coloring

581

(8)

The Traveling Salesperson Problem

589

(3)

Computing with DNA

592

(19)

Exercises

600

(8)

Notes and References

608

(3)

Parallel Algorithms

611

(38)

Introduction

612

(1)

Parallelism, the PRAM, and Other Models

612

(4)

Some Simple PRAM Algorithms

616

(6)

Handling Write Conflicts

622

(2)

Merging and Sorting

624

(4)

Finding Connected Components

628

(13)

A Lower Bound for Adding n Integers

641

(8)

Exercises

643

(4)

Notes and References

647

(2)

A Java Examples and Techniques

649

(20)

A.1 Introduction

650

(1)

A.2 A Java Main Program

651

(5)

A.3 A Simple Input Library

656

(2)

A.4 Documenting Java Classes

658

(1)

A.5 Generic Order and the ``Comparable'' Interface

659

(4)

A.6 Subclasses Extend the Capability of Their Superclass

663

(4)

A.7 Copy via the ``Cloneable'' Interface

667

(2)

Bibliography

669

(10)

Index

679

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Computer Algorithms: Introduction to Design and Analysis

Summary

Author Biography

Table of Contents

Supplemental Materials