Table Of Content

www.it-ebooks.info www.it-ebooks.info Data Structures and Algorithms in Java™ Sixth Edition Michael T. Goodrich Department of Computer Science University of California, Irvine Roberto Tamassia Department of Computer Science Brown University Michael H. Goldwasser Department of Mathematics and Computer Science Saint Louis University www.it-ebooks.info Vice President and Executive Publisher Don Fowley Executive Editor Beth Lang Golub Assistant Marketing Manager Debbie Martin Sponsoring Editor Mary O’Sullivan Project Editor Ellen Keohane Associate Production Manager Joyce Poh Cover Designer Kenji Ngieng This book was set in LATEX by the authors, and printed and bound by RR Donnelley. The cover was printed by RR Donnelley. Trademark Acknowledgments: Java is a trademark of Oracle Corporation. Unix ® is a registered trademark in the United States and other countries, licensed through X/Open Company, Ltd. PowerPoint ® is a trademark of Microsoft Corporation. All other product names mentioned herein are the trademarks of their respective owners. This book is printed on acid free paper. Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work. In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business. Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support. For more information, please visit our website: www.wiley.com/go/citizenship. Copyright © 2014, 2010 John Wiley & Sons, Inc. All rights reserved. No part of this publi- cation may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, with- out either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, website http://www.wiley.com/go/ permissions. Evaluation copies are provided to qualified academics and professionals for review pur- poses only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instructions and a free of charge return mailing label are available at www.wiley.com/go/returnlabel. If you have chosen to adopt this textbook for use in your course, please accept this book as your complimentary desk copy. Outside of the United States, please contact your local sales representative. ISBN: 978-1-118-77133-4 (paperback) Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 www.it-ebooks.info To Karen, Paul, Anna, and Jack – Michael T. Goodrich To Isabel – Roberto Tamassia To Susan, Calista, and Maya – Michael H. Goldwasser www.it-ebooks.info www.it-ebooks.info Preface to the Sixth Edition Data Structures and Algorithms in Java provides an introduction to data structures and algorithms, including their design, analysis, and implementation. The major changes in this sixth edition include the following: • We redesigned the entire code base to increase clarity of presentation and consistency in style and convention, including reliance on type inference, as introduced in Java 7, to reduce clutter when instantiating generic types. • We added 38 new figures, and redesigned 144 existing figures. • We revised and expanded exercises, bringing the grand total to 794 exercises! We continue our approach of dividing them into reinforcement, creativity, and project exercises. However, we have chosen not to reset the number- ing scheme with each new category, thereby avoiding possible ambiguity between exercises such as R-7.5, C-7.5, P-7.5. • The introductory chapters contain additional examples of classes and inheritance, increased discussion of Java’s generics framework, and expanded coverage of cloning and equivalence testing in the context of data structures. • A new chapter, dedicated to the topic of recursion, provides comprehensive coverage of material that was previously divided within Chapters 3, 4, and 9 of the fifth edition, while newly introducing the use of recursion when processing file systems. • We provide a new empirical study of the efficiency of Java’s StringBuilder class relative to the repeated concatenation of strings, and then discuss the theoretical underpinnings of its amortized performance. • We provide increased discussion of iterators, contrasting between so-called lazy iterators and snapshot iterators, with examples of both styles of implementation for several data structures. • We have increased the use of abstract base classes to reduce redundancy when providing multiple implementations of a common interface, and the use of nested classes to provide greater encapsulation for our data structures. • We have included complete Java implementations for many data structures and algorithms that were only described with pseudocode in earlier editions. These new implementations include both array-based and linked-list-based queue implementations, a heap-based adaptable priority queue, a bottom-up heap construction, hash tables with either separate chaining or linear probing, splay trees, dynamic programming for the least-common subsequence problem, a union-find data structure with path compression, breadth-first search of a graph, the Floyd-Warshall algorithm for computing a graph’s transitive closure, topological sorting of a DAG, and both the Prim-Jarn´ık and Kruskal algorithms for computing a minimum spanning tree. v www.it-ebooks.info vi Preface Prerequisites We assume that the reader is at least vaguely familiar with a high-level programming language, such as C, C++, Python, or Java, and that he or she understands the main constructs from such a high-level language, including: • Variables and expressions • Methods (also known as functions or procedures) • Decision structures (such as if-statements and switch-statements) • Iteration structures (for-loops and while-loops) For readers who are familiar with these concepts, but not with how they are ex- pressed in Java, we provide a primer on the Java language in Chapter 1. Still, this book is primarily a data structures book, not a Java book; hence, it does not provide a comprehensive treatment of Java. Nevertheless, we do not assume that the reader is necessarily familiar with object-oriented design or with linked structures, such as linked lists, for these topics are covered in the core chapters of this book. In terms of mathematical background, we assume the reader is somewhat familiar with topics from high-school mathematics. Even so, in Chapter 4, we discuss the seven most-important functions for algorithm analysis. In fact, sections that use something other than one of these seven functions are considered optional, and are indicated with a star (⋆). Online Resources This book is accompanied by an extensive set of online resources, which can be found at the following website: www.wiley.com/college/goodrich Included on this website is a collection of educational aids that augment the topics of this book, for both students and instructors. For all readers, and especially for students, we include the following resources: • All Java source code presented in this book • An appendix of useful mathematical facts • PDF handouts of PowerPoint slides (four-per-page) • A study guide with hints to exercises, indexed by problem number For instructors using this book, we include the following additional teaching aids: • Solutions to hundreds of the book’s exercises • Color versions of all figures and illustrations from the book • Slides in PowerPoint and PDF (one-per-page) format The slides are fully editable, so as to allow an instructor using this book full free- dom in customizing his or her presentations. www.it-ebooks.info Preface vii Use as a Textbook The design and analysis of efficient data structures has long been recognized as a core subject in computing. We feel that the central role of data structure design and analysis in the curriculum is fully justified, given the importance of efficient data structures and algorithms in most software systems, including the Web, operating systems, databases, compilers, and scientific simulation systems. This book is designed for use in a beginning-level data structures course, or in an intermediate-level introduction to algorithms course. The chapters for this book are organized to provide a pedagogical path that starts with the basics of Java programming and object-oriented design. We then discuss concrete structures including arrays and linked lists, and foundational techniques like algorithm analysis and recursion. In the main portion of the book we present fundamental data structures and algorithms, concluding with a discussion of memory management. A detailed table of contents follows this preface, beginning on page x. To assist instructors in designing a course in the context of the IEEE/ACM 2013 Computing Curriculum, the following table describes curricular knowledge units that are covered within this book. Knowledge Unit Relevant Material AL/Basic Analysis Chapter 4 and Sections 5.2 & 12.1.4 AL/Algorithmic Strategies Sections 5.3.3, 12.1.1, 13.2.1, 13.4.2, 13.5, 14.6.2 & 14.7 AL/Fundamental Data Structures and Algorithms Sections 3.1.2, 5.1.3, 9.3, 9.4.1, 10.2, 11.1, 13.2, and Chapters 12 & 14 AL/Advanced Data Structures Sections 7.2.1, 10.4, 11.2–11.6, 12.2.1, 13.3, 14.5.1 & 15.3 AR/Memory System Organization and Architecture Chapter 15 DS/Sets, Relations, and Functions Sections 9.2.2 & 10.5 DS/Proof Techniques Sections 4.4, 5.2, 7.2.3, 9.3.4 & 12.3.1 DS/Basics of Counting Sections 2.2.3, 6.2.2, 8.2.2 & 12.1.4. DS/Graphs and Trees Chapters 8 and 14 DS/Discrete Probability Sections 3.1.3, 10.2, 10.4.2 & 12.2.1 PL/Object-Oriented Programming Chapter 2 and Sections 7.3, 9.5.1 & 11.2.1 SDF/Algorithms and Design Sections 2.1, 4.3 & 12.1.1 SDF/Fundamental Programming Concepts Chapters 1 & 5 SDF/Fundamental Data Structures Chapters 3 & 6, and Sections 1.3, 9.1 & 10.1 SDF/Developmental Methods Sections 1.9 & 2.4 SE/Software Design Section 2.1 Mapping the IEEE/ACM 2013 Computing Curriculum knowledge units to coverage within this book. www.it-ebooks.info viii Preface About the Authors Michael Goodrich received his Ph.D. in Computer Science from Purdue University in 1987. He is currently a Chancellor’s Professor in the Department of Computer Science at University of California, Irvine. Previously, he was a professor at Johns Hopkins University. He is a Fulbright Scholar and a Fellow of the American As- sociation for the Advancement of Science (AAAS), Association for Computing Machinery (ACM), and Institute of Electrical and Electronics Engineers (IEEE). He is a recipient of the IEEE Computer Society Technical Achievement Award, the ACM Recognition of Service Award, and the Pond Award for Excellence in Undergraduate Teaching. Roberto Tamassia received his Ph.D. in Electrical and Computer Engineering from the University of Illinois at Urbana–Champaign in 1988. He is the Plastech Professor of Computer Science and the Chair of the Department of Computer Sci- ence at Brown University. He is also the Director of Brown’s Center for Geometric Computing. His research interests include information security, cryptography, analysis, design, and implementation of algorithms, graph drawing, and computational geometry. He is a Fellow of the American Association for the Advancement of Science (AAAS), Association for Computing Machinery (ACM) and Institute for Electrical and Electronic Engineers (IEEE). He is a recipient of the IEEE Computer Society Technical Achievement Award. Michael Goldwasser received his Ph.D. in Computer Science from Stanford University in 1997. He is currently Professor and Director of the Computer Science program in the Department of Mathematics and Computer Science at Saint Louis University. He was previously a faculty member in the Department of Computer Science at Loyola University Chicago. His research interests focus on the design and implementation of algorithms, having published work involving approximation algorithms, online computation, computational biology, and computational geometry. He is also active in the computer science education community. Additional Books by These Authors • Di Battista, Eades, Tamassia, and Tollis, Graph Drawing, Prentice Hall • Goodrich, Tamassia, and Goldwasser, Data Structures and Algorithms in Python, Wiley • Goodrich, Tamassia, and Mount, Data Structures and Algorithms in C++, Wiley • Goodrich and Tamassia, Algorithm Design: Foundations, Analysis, and Internet Examples, Wiley • Goodrich and Tamassia, Introduction to Computer Security, Addison-Wesley • Goldwasser and Letscher, Object-Oriented Programming in Python, Prentice Hall www.it-ebooks.info Preface ix Acknowledgments There are so many individuals who have made contributions to the development of this book over the past decade, it is difficult to name them all. We wish to reit- erate our thanks to the many research collaborators and teaching assistants whose feedback shaped the previous versions of this material. The benefits of those contributions carry forward to this book. For the sixth edition, we are indebted to the outside reviewers and readers for their copious comments, emails, and constructive criticisms. We therefore thank the following people for their comments and suggestions: Sameer O. Abufardeh (North Dakota State University), Mary Boelk (Marquette University), Frederick Crabbe (United States Naval Academy), Scot Drysdale (Dartmouth College), David Eisner, Henry A. Etlinger (Rochester Institute of Technology), Chun-Hsi Huang (Univer- sity of Connecticut), John Lasseter (Hobart and William Smith Colleges), Yupeng Lin, Suely Oliveira (University of Iowa), Vincent van Oostrom (Utrecht Univer- sity), Justus Piater (University of Innsbruck), Victor I. Shtern (Boston University), Tim Soethout, and a number of additional anonymous reviewers. There have been a number of friends and colleagues whose comments have led to improvements in the text. We are particularly thankful to Erin Chambers, Karen Goodrich, David Letscher, David Mount, and Ioannis Tollis for their insightful comments. In addition, contributions by David Mount to the coverage of recursion and to several figures are gratefully acknowledged. We appreciate the wonderful team at Wiley, including our editor, Beth Lang Golub, for her enthusiastic support of this project from beginning to end, and the Product Solutions Group editors, Mary O’Sullivan and Ellen Keohane, for carrying the project to its completion. The quality of this book is greatly enhanced as a result of the attention to detail demonstrated by our copyeditor, Julie Kennedy. The final months of the production process were gracefully managed by Joyce Poh. Finally, we would like to warmly thank Karen Goodrich, Isabel Cruz, Susan Goldwasser, Giuseppe Di Battista, Franco Preparata, Ioannis Tollis, and our parents for providing advice, encouragement, and support at various stages of the prepa- ration of this book, and Calista and Maya Goldwasser for offering their advice regarding the artistic merits of many illustrations. More importantly, we thank all of these people for reminding us that there are things in life beyond writing books. Michael T. Goodrich Roberto Tamassia Michael H. Goldwasser www.it-ebooks.info Contents 1 Java Primer 1 1.1 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Base Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Classes and Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Creating and Using Objects . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Defining a Class . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Strings, Wrappers, Arrays, and Enum Types . . . . . . . . . . . . . 17 1.4 Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.1 Literals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.2 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.3 Type Conversions . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5 Control Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.5.1 The If and Switch Statements . . . . . . . . . . . . . . . . . . 30 1.5.2 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.5.3 Explicit Control-Flow Statements . . . . . . . . . . . . . . . . . 37 1.6 Simple Input and Output . . . . . . . . . . . . . . . . . . . . . . . . 38 1.7 An Example Program . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1.8 Packages and Imports . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.9 Software Development . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.9.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.9.2 Pseudocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 1.9.3 Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1.9.4 Documentation and Style . . . . . . . . . . . . . . . . . . . . . 50 1.9.5 Testing and Debugging . . . . . . . . . . . . . . . . . . . . . . 53 1.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2 Object-Oriented Design 59 2.1 Goals, Principles, and Patterns . . . . . . . . . . . . . . . . . . . . 60 2.1.1 Object-Oriented Design Goals . . . . . . . . . . . . . . . . . . 60 2.1.2 Object-Oriented Design Principles . . . . . . . . . . . . . . . . 61 2.1.3 Design Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.2 Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.2.1 Extending the CreditCard Class . . . . . . . . . . . . . . . . . . 65 2.2.2 Polymorphism and Dynamic Dispatch . . . . . . . . . . . . . . 68 2.2.3 Inheritance Hierarchies . . . . . . . . . . . . . . . . . . . . . . 69 2.3 Interfaces and Abstract Classes . . . . . . . . . . . . . . . . . . . . 76 2.3.1 Interfaces in Java . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.3.2 Multiple Inheritance for Interfaces . . . . . . . . . . . . . . . . 79 2.3.3 Abstract Classes . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.4 Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.4.1 Catching Exceptions . . . . . . . . . . . . . . . . . . . . . . . . 82 2.4.2 Throwing Exceptions . . . . . . . . . . . . . . . . . . . . . . . 85 2.4.3 Java’s Exception Hierarchy . . . . . . . . . . . . . . . . . . . . 86 2.5 Casting and Generics . . . . . . . . . . . . . . . . . . . . . . . . . . 88 x www.it-ebooks.info Contents xi 2.5.1 Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.5.2 Generics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.6 Nested Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3 Fundamental Data Structures 103 3.1 Using Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.1.1 Storing Game Entries in an Array . . . . . . . . . . . . . . . . . 104 3.1.2 Sorting an Array . . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.1.3 java.util Methods for Arrays and Random Numbers . . . . . . . 112 3.1.4 Simple Cryptography with Character Arrays . . . . . . . . . . . 115 3.1.5 Two-Dimensional Arrays and Positional Games . . . . . . . . . 118 3.2 Singly Linked Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.2.1 Implementing a Singly Linked List Class . . . . . . . . . . . . . 126 3.3 Circularly Linked Lists . . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.3.1 Round-Robin Scheduling . . . . . . . . . . . . . . . . . . . . . 128 3.3.2 Designing and Implementing a Circularly Linked List . . . . . . 129 3.4 Doubly Linked Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 3.4.1 Implementing a Doubly Linked List Class . . . . . . . . . . . . 135 3.5 Equivalence Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 3.5.1 Equivalence Testing with Arrays . . . . . . . . . . . . . . . . . 139 3.5.2 Equivalence Testing with Linked Lists . . . . . . . . . . . . . . 140 3.6 Cloning Data Structures . . . . . . . . . . . . . . . . . . . . . . . . 141 3.6.1 Cloning Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 3.6.2 Cloning Linked Lists . . . . . . . . . . . . . . . . . . . . . . . . 144 3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4 Algorithm Analysis 149 4.1 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.1.1 Moving Beyond Experimental Analysis . . . . . . . . . . . . . . 154 4.2 The Seven Functions Used in This Book . . . . . . . . . . . . . . . 156 4.2.1 Comparing Growth Rates . . . . . . . . . . . . . . . . . . . . . 163 4.3 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 4.3.1 The “Big-Oh” Notation . . . . . . . . . . . . . . . . . . . . . . 164 4.3.2 Comparative Analysis . . . . . . . . . . . . . . . . . . . . . . . 168 4.3.3 Examples of Algorithm Analysis . . . . . . . . . . . . . . . . . 170 4.4 Simple Justification Techniques . . . . . . . . . . . . . . . . . . . . 178 4.4.1 By Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 4.4.2 The “Contra” Attack . . . . . . . . . . . . . . . . . . . . . . . 178 4.4.3 Induction and Loop Invariants . . . . . . . . . . . . . . . . . . 179 4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 5 Recursion 189 5.1 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.1.1 The Factorial Function . . . . . . . . . . . . . . . . . . . . . . 191 5.1.2 Drawing an English Ruler . . . . . . . . . . . . . . . . . . . . . 193 5.1.3 Binary Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 www.it-ebooks.info xii Contents 5.1.4 File Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 5.2 Analyzing Recursive Algorithms . . . . . . . . . . . . . . . . . . . . 202 5.3 Further Examples of Recursion . . . . . . . . . . . . . . . . . . . . . 206 5.3.1 Linear Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . 206 5.3.2 Binary Recursion . . . . . . . . . . . . . . . . . . . . . . . . . 211 5.3.3 Multiple Recursion . . . . . . . . . . . . . . . . . . . . . . . . 212 5.4 Designing Recursive Algorithms . . . . . . . . . . . . . . . . . . . . 214 5.5 Recursion Run Amok . . . . . . . . . . . . . . . . . . . . . . . . . . 215 5.5.1 Maximum Recursive Depth in Java . . . . . . . . . . . . . . . . 218 5.6 Eliminating Tail Recursion . . . . . . . . . . . . . . . . . . . . . . . 219 5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6 Stacks, Queues, and Deques 225 6.1 Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 6.1.1 The Stack Abstract Data Type . . . . . . . . . . . . . . . . . . 227 6.1.2 A Simple Array-Based Stack Implementation . . . . . . . . . . 230 6.1.3 Implementing a Stack with a Singly Linked List . . . . . . . . . 233 6.1.4 Reversing an Array Using a Stack . . . . . . . . . . . . . . . . 234 6.1.5 Matching Parentheses and HTML Tags . . . . . . . . . . . . . 235 6.2 Queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 6.2.1 The Queue Abstract Data Type . . . . . . . . . . . . . . . . . 239 6.2.2 Array-Based Queue Implementation . . . . . . . . . . . . . . . 241 6.2.3 Implementing a Queue with a Singly Linked List . . . . . . . . . 245 6.2.4 A Circular Queue . . . . . . . . . . . . . . . . . . . . . . . . . 246 6.3 Double-Ended Queues . . . . . . . . . . . . . . . . . . . . . . . . . . 248 6.3.1 The Deque Abstract Data Type . . . . . . . . . . . . . . . . . 248 6.3.2 Implementing a Deque . . . . . . . . . . . . . . . . . . . . . . 250 6.3.3 Deques in the Java Collections Framework . . . . . . . . . . . . 251 6.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 7 List and Iterator ADTs 257 7.1 The List ADT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 7.2 Array Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 7.2.1 Dynamic Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . 263 7.2.2 Implementing a Dynamic Array . . . . . . . . . . . . . . . . . . 264 7.2.3 Amortized Analysis of Dynamic Arrays . . . . . . . . . . . . . . 265 7.2.4 Java’s StringBuilder class . . . . . . . . . . . . . . . . . . . . . 269 7.3 Positional Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 7.3.1 Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 7.3.2 The Positional List Abstract Data Type . . . . . . . . . . . . . 272 7.3.3 Doubly Linked List Implementation . . . . . . . . . . . . . . . . 276 7.4 Iterators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 7.4.1 The Iterable Interface and Java’s For-Each Loop . . . . . . . . 283 7.4.2 Implementing Iterators . . . . . . . . . . . . . . . . . . . . . . 284 7.5 The Java Collections Framework . . . . . . . . . . . . . . . . . . . 288 7.5.1 List Iterators in Java . . . . . . . . . . . . . . . . . . . . . . . 289 7.5.2 Comparison to Our Positional List ADT . . . . . . . . . . . . . 290 www.it-ebooks.info Contents xiii 7.5.3 List-Based Algorithms in the Java Collections Framework . . . . 291 7.6 Sorting a Positional List . . . . . . . . . . . . . . . . . . . . . . . . 293 7.7 Case Study: Maintaining Access Frequencies . . . . . . . . . . . . 294 7.7.1 Using a Sorted List . . . . . . . . . . . . . . . . . . . . . . . . 294 7.7.2 Using a List with the Move-to-Front Heuristic . . . . . . . . . . 297 7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 8 Trees 307 8.1 General Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 8.1.1 Tree Definitions and Properties . . . . . . . . . . . . . . . . . . 309 8.1.2 The Tree Abstract Data Type . . . . . . . . . . . . . . . . . . 312 8.1.3 Computing Depth and Height . . . . . . . . . . . . . . . . . . . 314 8.2 Binary Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 8.2.1 The Binary Tree Abstract Data Type . . . . . . . . . . . . . . . 319 8.2.2 Properties of Binary Trees . . . . . . . . . . . . . . . . . . . . 321 8.3 Implementing Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 8.3.1 Linked Structure for Binary Trees . . . . . . . . . . . . . . . . . 323 8.3.2 Array-Based Representation of a Binary Tree . . . . . . . . . . 331 8.3.3 Linked Structure for General Trees . . . . . . . . . . . . . . . . 333 8.4 Tree Traversal Algorithms . . . . . . . . . . . . . . . . . . . . . . . 334 8.4.1 Preorder and Postorder Traversals of General Trees . . . . . . . 334 8.4.2 Breadth-First Tree Traversal . . . . . . . . . . . . . . . . . . . 336 8.4.3 Inorder Traversal of a Binary Tree . . . . . . . . . . . . . . . . 337 8.4.4 Implementing Tree Traversals in Java . . . . . . . . . . . . . . 339 8.4.5 Applications of Tree Traversals . . . . . . . . . . . . . . . . . . 343 8.4.6 Euler Tours . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 8.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 9 Priority Queues 359 9.1 The Priority Queue Abstract Data Type . . . . . . . . . . . . . . . 360 9.1.1 Priorities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 9.1.2 The Priority Queue ADT . . . . . . . . . . . . . . . . . . . . . 361 9.2 Implementing a Priority Queue . . . . . . . . . . . . . . . . . . . . 362 9.2.1 The Entry Composite . . . . . . . . . . . . . . . . . . . . . . . 362 9.2.2 Comparing Keys with Total Orders . . . . . . . . . . . . . . . . 363 9.2.3 The AbstractPriorityQueue Base Class . . . . . . . . . . . . . . 364 9.2.4 Implementing a Priority Queue with an Unsorted List . . . . . . 366 9.2.5 Implementing a Priority Queue with a Sorted List . . . . . . . . 368 9.3 Heaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 9.3.1 The Heap Data Structure . . . . . . . . . . . . . . . . . . . . . 370 9.3.2 Implementing a Priority Queue with a Heap . . . . . . . . . . . 372 9.3.3 Analysis of a Heap-Based Priority Queue . . . . . . . . . . . . . 379 9.3.4 Bottom-Up Heap Construction ⋆ . . . . . . . . . . . . . . . . 380 9.3.5 Using the java.util.PriorityQueue Class . . . . . . . . . . . . . . 384 9.4 Sorting with a Priority Queue . . . . . . . . . . . . . . . . . . . . . 385 9.4.1 Selection-Sort and Insertion-Sort . . . . . . . . . . . . . . . . . 386 9.4.2 Heap-Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 www.it-ebooks.info