A Practical Introduction to Data Structures and Algorithm Analysis

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PrefacexixVirginia Tech helped make this whole thing possible through sabbatical researchleave during Fall 1994, enabling me to get the project off the ground. My departmentheads during the time I have written the various editions of this book, DennisKafura and Jack Carroll, provided unwavering moral support for this project.Mike Keenan, Lenny Heath, and Jeff Shaffer provided valuable input on early versionsof the chapters. I also wish to thank Lenny Heath for many years of stimulatingdiscussions about algorithms and analysis (and how to teach both to students).Steve Edwards deserves special thanks for spending so much time helping me onvarious redesigns of the C++ and Java code versions for the second and third editions,and many hours of discussion on the principles of program design. Thanksto Layne Watson for his help with Mathematica, and to Bo Begole, Philip Isenhour,Jeff Nielsen, and Craig Struble for much technical assistance. Thanks to Bill Mc-Quain, Mark Abrams and Dennis Kafura for answering lots of silly questions aboutC++ and Java.I am truly indebted to the many reviewers of the various editions of this manuscript.For the first edition these reviewers included J. David Bezek (University ofEvansville), Douglas Campbell (Brigham Young University), Karen Davis (Universityof Cincinnati), Vijay Kumar Garg (University of Texas – Austin), Jim Miller(University of Kansas), Bruce Maxim (University of Michigan – Dearborn), JeffParker (Agile Networks/Harvard), Dana Richards (George Mason University), JackTan (University of Houston), and Lixin Tao (Concordia University). Without theirhelp, this book would contain many more technical errors and many fewer insights.For the second edition, I wish to thank these reviewers: Gurdip Singh (KansasState University), Peter Allen (Columbia University), Robin Hill (University ofWyoming), Norman Jacobson (University of California – Irvine), Ben Keller (EasternMichigan University), and Ken Bosworth (Idaho State University). In addition,I wish to thank Neil Stewart and Frank J. Thesen for their comments and ideas forimprovement.Third edition reviewers included Randall Lechlitner (University of Houstin,Clear Lake) and Brian C. Hipp (York Technical College). I thank them for theircomments.Without the hard work of many people at Prentice Hall, none of this would bepossible. Authors simply do not create printer-ready books on their own. Foremostthanks go to Kate Hargett, Petra Rector, Laura Steele, and Alan Apt, my editorsover the years. My production editors, Irwin Zucker for the second edition, KathleenCaren for the original C++ version, and Ed DeFelippis for the Java version,kept everything moving smoothly during that horrible rush at the end. Thanks toBill Zobrist and Bruce Gregory (I think) for getting me into this in the first place.
xxPrefaceOthers at Prentice Hall who helped me along the way include Truly Donovan, LindaBehrens, and Phyllis Bregman. I am sure I owe thanks to many others at PrenticeHall for their help in ways that I am not even aware of.I wish to express my appreciation to Hanan Samet for teaching me about datastructures. I learned much of the philosophy presented here from him as well,though he is not responsible for any problems with the result. Thanks to my wifeTerry, for her love and support, and to my daughters Irena and Kate for pleasantdiversions from working too hard. Finally, and most importantly, to all of the datastructures students over the years who have taught me what is important and whatshould be skipped in a data structures course, and the many new insights they haveprovided. This book is dedicated to them.Clifford A. ShafferBlacksburg, Virginia
Page 15 and 16: xviPrefacemake the examples as clea
Page 17: xviiiPrefaceOne of the most importa
Page 22 and 23: 1Data Structures and AlgorithmsHow
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Sec. 2.8 Further Reading 49typical
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Sec. 2.9 Exercises 51(f) {〈2, 1
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Sec. 2.9 Exercises 532.17 Prove by
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Sec. 2.9 Exercises 552.38 When buyi
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3Algorithm AnalysisHow long will it
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Sec. 3.1 Introduction 59compiled wi
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Sec. 3.1 Introduction 61Example 3.3
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Sec. 3.2 Best, Worst, and Average C
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Sec. 3.3 A Faster Computer, or a Fa
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Sec. 3.4 Asymptotic Analysis 67comp
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Sec. 3.4 Asymptotic Analysis 69fast
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Sec. 3.4 Asymptotic Analysis 71Exam
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Sec. 3.4 Asymptotic Analysis 73Rule
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Sec. 3.5 Calculating the Running Ti
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Sec. 3.6 Analyzing Problems 79binar
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Sec. 3.7 Common Misunderstandings 8
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Sec. 3.9 Space Bounds 83pixel. Assu
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Sec. 3.9 Space Bounds 85A classic e
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Sec. 3.10 Speeding Up Your Programs
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Sec. 3.11 Empirical Analysis 893.11
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Sec. 3.13 Exercises 913.3 Arrange t
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Sec. 3.13 Exercises 93(f) sum = 0;f
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Sec. 3.14 Projects 95a summation fo
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4Lists, Stacks, and QueuesIf your p
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Sec. 4.1 Lists 101The next step is
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Sec. 4.1 Lists 103mentations, asser
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Sec. 4.1 Lists 105/** Array-based l
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Sec. 4.1 Lists 107Insert 23:1312 20
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Sec. 4.1 Lists 109currtailheadFigur
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Sec. 4.1 Lists 111// Linked list im
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Sec. 4.1 Lists 113curr... 23 12 ...
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Sec. 4.1 Lists 115// Singly linked
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Sec. 4.1 Lists 117determined size.
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Sec. 4.1 Lists 119pointer to each e
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Sec. 4.1 Lists 121// Insert "it" at
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Sec. 4.1 Lists 123curr... 20curr23
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Sec. 4.2 Stacks 125/** Stack ADT */
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Sec. 4.2 Stacks 127// Linked stack
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Sec. 4.2 Stacks 129Currptr β 1Curr
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Sec. 4.2 Stacks 131Example 4.3 The
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Sec. 4.3 Queues 133/** Queue ADT */
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Sec. 4.3 Queues 135frontfront20 512
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Sec. 4.3 Queues 137// Array-based q
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Sec. 4.4 Dictionaries 139enqueue pl
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Sec. 4.4 Dictionaries 141Method cle
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Sec. 4.4 Dictionaries 143// Contain
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Sec. 4.4 Dictionaries 145/** Dictio
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Sec. 4.5 Further Reading 1474.5 Fur
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Sec. 4.6 Exercises 149(a) The data
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Sec. 4.7 Projects 1514.3 Use singly
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5Binary TreesThe list representatio
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Sec. 5.1 Definitions and Properties
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Sec. 5.1 Definitions and Properties
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Sec. 5.2 Binary Tree Traversals 159
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Sec. 5.2 Binary Tree Traversals 161
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Sec. 5.3 Binary Tree Node Implement
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Sec. 5.4 Binary Search Trees 171Thi
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Sec. 5.4 Binary Search Trees 173120
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Sec. 5.4 Binary Search Trees 175/**
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Sec. 5.4 Binary Search Trees 177min
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Sec. 5.5 Heaps and Priority Queues
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Sec. 5.6 Huffman Coding Trees 189Le
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Sec. 5.6 Huffman Coding Trees 191St
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Sec. 5.6 Huffman Coding Trees 193/*
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Sec. 5.6 Huffman Coding Trees 195//
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Sec. 5.6 Huffman Coding Trees 197A
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Sec. 5.8 Exercises 199Many techniqu
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Sec. 5.8 Exercises 2015.19 Write a
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Sec. 5.9 Projects 203(d) The record
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6Non-Binary TreesMany organizations
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Sec. 6.1 General Tree Definitions a
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Sec. 6.3 General Tree Implementatio
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Sec. 6.4 K-ary Trees 221RRABABCDEFC
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Sec. 6.5 Sequential Tree Implementa
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Sec. 6.7 Exercises 2276.2 Write an
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Sec. 6.7 Exercises 229CAFBEHGDIFigu
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Sec. 6.8 Projects 231proved perform
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7Internal SortingWe sort many thing
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Sec. 7.2 Three Θ(n 2 ) Sorting Alg
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Sec. 7.3 Shellsort 24559 20 17 13 2
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Sec. 7.4 Mergesort 24736 20 17 13 2
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Sec. 7.5 Quicksort 249static
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Sec. 7.5 Quicksort 251static
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Sec. 7.5 Quicksort 253InitialPass 1
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Sec. 7.5 Quicksort 255The initial c
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Sec. 7.6 Heapsort 257and fast. The
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Sec. 7.7 Binsort and Radix Sort 259
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Sec. 7.8 An Empirical Comparison of
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Sec. 7.9 Lower Bounds for Sorting 2
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Sec. 7.10 Further Reading 271• A
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Sec. 7.11 Exercises 2737.7 Recall t
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Sec. 7.12 Projects 2757.16 (a) Devi
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Sec. 7.12 Projects 277classmates? W
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280 Chap. 8 File Processing and Ext
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318 Chap. 9 SearchingThis and the f
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320 Chap. 9 Searchingelement in L,
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322 Chap. 9 SearchingThis is equal
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324 Chap. 9 Searching9.2 Self-Organ
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326 Chap. 9 SearchingWhen a frequen
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328 Chap. 9 Searchingand the total
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330 Chap. 9 SearchingThe set differ
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332 Chap. 9 Searchingprobability th
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334 Chap. 9 SearchingExample 9.6 A
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336 Chap. 9 Searchingand the next f
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338 Chap. 9 Searching01HashTable100
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340 Chap. 9 Searching/** Insert rec
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344 Chap. 9 SearchingExample 9.9 Co
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346 Chap. 9 Searchingproject at the
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350 Chap. 9 SearchingDepending on t
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352 Chap. 9 SearchingBentley et al.
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354 Chap. 9 Searching(c) How many s
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356 Chap. 9 Searching9.5 Implement
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358 Chap. 10 Indexingfile is create
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368 Chap. 10 Indexing/** 2-3 tree n
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382 Chap. 10 IndexingAs mentioned e
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PART IVAdvanced Data Structures387
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390 Chap. 11 Graphs04123147123(a)(b
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392 Chap. 11 Graphs0 1 2 3 40201 11
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394 Chap. 11 GraphsThe adjacency ma
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396 Chap. 11 Graphsedge list. Funct
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398 Chap. 11 Graphspublic int weigh
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400 Chap. 11 Graphs}// Store edge w
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402 Chap. 11 GraphsABABCCDDFFEE(a)(
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404 Chap. 11 Graphs// Breadth first
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406 Chap. 11 GraphsAInitial call to
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408 Chap. 11 Graphsstatic void tops
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410 Chap. 11 Graphs// Compute short
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412 Chap. 11 Graphs// Dijkstra’s
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414 Chap. 11 Graphs// Compute a min
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418 Chap. 11 GraphsInitialA B C D E
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420 Chap. 11 Graphs2 511032041032 6
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422 Chap. 11 Graphstriangular matri
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424 Chap. 12 Lists and Arrays Revis
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PART VTheory of Algorithms479
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484 Chap. 14 Analysis TechniquesExa
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490 Chap. 14 Analysis TechniquesHow
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492 Chap. 14 Analysis Techniques= 2
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15Lower BoundsHow do I know if I ha
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Sec. 15.1 Introduction to Lower Bou
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Sec. 15.2 Lower Bounds on Searching
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Sec. 15.3 Finding the Maximum Value
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Sec. 15.4 Adversarial Lower Bounds
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Sec. 15.4 Adversarial Lower Bounds
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Sec. 15.5 State Space Lower Bounds
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Sec. 15.5 State Space Lower Bounds
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Sec. 15.6 Finding the ith Best Elem
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Sec. 15.7 Optimal Sorting 525search
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Sec. 15.8 Further Reading 527Merge
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Sec. 15.9 Exercises 52915.10 Show t
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16Patterns of AlgorithmsThis chapte
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Sec. 16.2 Randomized Algorithms 537
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Sec. 16.3 Numerical Algorithms 555b
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Sec. 16.6 Projects 55716.8 What is
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560 Chap. 17 Limits to Computations
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594 BIBLIOGRAPHY[BG00] Sara Baase a
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596 BIBLIOGRAPHY[LLKS85] E.L. Lawle
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598 BIBLIOGRAPHY[WMB99][Zei07]I.H.
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600 INDEXbest fit, see memory manag
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602 INDEXrelation, 27, 50estimating
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604 INDEXinteger representation, 5,
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606 INDEXpath compression, 215-216,
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608 INDEXterminology, 236-237spatia
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