Practical Introduction to Data Structures and Algorithms with Java

621 Pages·2017·2.38 MB·English

by  Shaffer C.A.

A Practical Introduction to
Data Structures and Algorithm
Analysis
Third Edition (Java Version)
Clifford A. Shaffer
DepartmentofComputerScience
VirginiaTech
Blacksburg,VA24061
January19,2010
Copyright(cid:13)c 2009-2010byCliffordA.Shaffer.
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Contents
Preface xiii
I Preliminaries 1
1 DataStructuresandAlgorithms 3
1.1 APhilosophyofDataStructures 4
1.1.1 TheNeedforDataStructures 4
1.1.2 CostsandBenefits 6
1.2 AbstractDataTypesandDataStructures 8
1.3 DesignPatterns 12
1.3.1 Flyweight 13
1.3.2 Visitor 14
1.3.3 Composite 15
1.3.4 Strategy 16
1.4 Problems,Algorithms,andPrograms 17
1.5 FurtherReading 19
1.6 Exercises 21
2 MathematicalPreliminaries 25
2.1 SetsandRelations 25
2.2 MiscellaneousNotation 29
2.3 Logarithms 31
2.4 SummationsandRecurrences 33
iii
iv Contents
2.5 Recursion 36
2.6 MathematicalProofTechniques 39
2.6.1 DirectProof 40
2.6.2 ProofbyContradiction 40
2.6.3 ProofbyMathematicalInduction 41
2.7 Estimating 47
2.8 FurtherReading 49
2.9 Exercises 50
3 AlgorithmAnalysis 57
3.1 Introduction 57
3.2 Best,Worst,andAverageCases 63
3.3 AFasterComputer,oraFasterAlgorithm? 65
3.4 AsymptoticAnalysis 67
3.4.1 UpperBounds 68
3.4.2 LowerBounds 70
3.4.3 ΘNotation 71
3.4.4 SimplifyingRules 72
3.4.5 ClassifyingFunctions 73
3.5 CalculatingtheRunningTimeforaProgram 74
3.6 AnalyzingProblems 79
3.7 CommonMisunderstandings 81
3.8 MultipleParameters 83
3.9 SpaceBounds 84
3.10 SpeedingUpYourPrograms 86
3.11 EmpiricalAnalysis 89
3.12 FurtherReading 90
3.13 Exercises 91
3.14 Projects 95
II FundamentalDataStructures 97
4 Lists,Stacks,andQueues 99
Contents v
4.1 Lists 100
4.1.1 Array-BasedListImplementation 103
4.1.2 LinkedLists 106
4.1.3 ComparisonofListImplementations 117
4.1.4 ElementImplementations 119
4.1.5 DoublyLinkedLists 120
4.2 Stacks 125
4.2.1 Array-BasedStacks 125
4.2.2 LinkedStacks 128
4.2.3 ComparisonofArray-BasedandLinkedStacks 129
4.2.4 ImplementingRecursion 129
4.3 Queues 133
4.3.1 Array-BasedQueues 134
4.3.2 LinkedQueues 137
4.3.3 ComparisonofArray-BasedandLinkedQueues 140
4.4 DictionariesandComparators 140
4.5 FurtherReading 147
4.6 Exercises 147
4.7 Projects 150
5 BinaryTrees 153
5.1 DefinitionsandProperties 153
5.1.1 TheFullBinaryTreeTheorem 156
5.1.2 ABinaryTreeNodeADT 157
5.2 BinaryTreeTraversals 158
5.3 BinaryTreeNodeImplementations 162
5.3.1 Pointer-BasedNodeImplementations 163
5.3.2 SpaceRequirements 169
5.3.3 ArrayImplementationforCompleteBinaryTrees 170
5.4 BinarySearchTrees 171
5.5 HeapsandPriorityQueues 180
5.6 HuffmanCodingTrees 187
5.6.1 BuildingHuffmanCodingTrees 189
vi Contents
5.6.2 AssigningandUsingHuffmanCodes 195
5.7 FurtherReading 198
5.8 Exercises 198
5.9 Projects 202
6 Non-BinaryTrees 205
6.1 GeneralTreeDefinitionsandTerminology 205
6.1.1 AnADTforGeneralTreeNodes 206
6.1.2 GeneralTreeTraversals 207
6.2 TheParentPointerImplementation 208
6.3 GeneralTreeImplementations 216
6.3.1 ListofChildren 217
6.3.2 TheLeft-Child/Right-SiblingImplementation 218
6.3.3 DynamicNodeImplementations 218
6.3.4 Dynamic“Left-Child/Right-Sibling”Implementation 220
6.4 K-aryTrees 221
6.5 SequentialTreeImplementations 223
6.6 FurtherReading 226
6.7 Exercises 226
6.8 Projects 230
III SortingandSearching 233
7 InternalSorting 235
7.1 SortingTerminologyandNotation 236
7.2 ThreeΘ(n2)SortingAlgorithms 237
7.2.1 InsertionSort 238
7.2.2 BubbleSort 240
7.2.3 SelectionSort 241
7.2.4 TheCostofExchangeSorting 243
7.3 Shellsort 244
7.4 Mergesort 246
7.5 Quicksort 249
Contents vii
7.6 Heapsort 256
7.7 BinsortandRadixSort 259
7.8 AnEmpiricalComparisonofSortingAlgorithms 265
7.9 LowerBoundsforSorting 267
7.10 FurtherReading 271
7.11 Exercises 272
7.12 Projects 275
8 FileProcessingandExternalSorting 279
8.1 PrimaryversusSecondaryStorage 280
8.2 DiskDrives 282
8.2.1 DiskDriveArchitecture 283
8.2.2 DiskAccessCosts 286
8.3 BuffersandBufferPools 289
8.4 TheProgrammer’sViewofFiles 297
8.5 ExternalSorting 298
8.5.1 SimpleApproachestoExternalSorting 301
8.5.2 ReplacementSelection 304
8.5.3 MultiwayMerging 307
8.6 FurtherReading 310
8.7 Exercises 311
8.8 Projects 315
9 Searching 317
9.1 SearchingUnsortedandSortedArrays 318
9.2 Self-OrganizingLists 324
9.3 BitVectorsforRepresentingSets 329
9.4 Hashing 330
9.4.1 HashFunctions 331
9.4.2 OpenHashing 336
9.4.3 ClosedHashing 337
9.4.4 AnalysisofClosedHashing 346
9.4.5 Deletion 350
viii Contents
9.5 FurtherReading 351
9.6 Exercises 352
9.7 Projects 355
10 Indexing 357
10.1 LinearIndexing 359
10.2 ISAM 361
10.3 Tree-basedIndexing 364
10.4 2-3Trees 366
10.5 B-Trees 372
10.5.1 B+-Trees 375
10.5.2 B-TreeAnalysis 381
10.6 FurtherReading 382
10.7 Exercises 382
10.8 Projects 385
IV AdvancedDataStructures 387
11 Graphs 389
11.1 TerminologyandRepresentations 390
11.2 GraphImplementations 394
11.3 GraphTraversals 397
11.3.1 Depth-FirstSearch 400
11.3.2 Breadth-FirstSearch 401
11.3.3 TopologicalSort 405
11.4 Shortest-PathsProblems 407
11.4.1 Single-SourceShortestPaths 407
11.5 Minimum-CostSpanningTrees 411
11.5.1 Prim’sAlgorithm 412
11.5.2 Kruskal’sAlgorithm 415
11.6 FurtherReading 416
11.7 Exercises 416
11.8 Projects 420
Contents ix
12 ListsandArraysRevisited 423
12.1 Multilists 423
12.2 MatrixRepresentations 427
12.3 MemoryManagement 430
12.3.1 DynamicStorageAllocation 431
12.3.2 FailurePoliciesandGarbageCollection 438
12.4 FurtherReading 443
12.5 Exercises 444
12.6 Projects 445
13 AdvancedTreeStructures 447
13.1 Tries 447
13.2 BalancedTrees 452
13.2.1 TheAVLTree 453
13.2.2 TheSplayTree 455
13.3 SpatialDataStructures 459
13.3.1 TheK-DTree 461
13.3.2 ThePRquadtree 466
13.3.3 OtherPointDataStructures 471
13.3.4 OtherSpatialDataStructures 471
13.4 FurtherReading 473
13.5 Exercises 473
13.6 Projects 475
V TheoryofAlgorithms 479
14 AnalysisTechniques 481
14.1 SummationTechniques 482
14.2 RecurrenceRelations 487
14.2.1 EstimatingUpperandLowerBounds 487
14.2.2 ExpandingRecurrences 491
14.2.3 DivideandConquerRecurrences 492
14.2.4 Average-CaseAnalysisofQuicksort 495
x Contents
14.3 AmortizedAnalysis 496
14.4 FurtherReading 499
14.5 Exercises 500
14.6 Projects 504
15 LowerBounds 505
15.1 IntroductiontoLowerBoundsProofs 506
15.2 LowerBoundsonSearchingLists 508
15.2.1 SearchinginUnsortedLists 508
15.2.2 SearchinginSortedLists 510
15.3 FindingtheMaximumValue 511
15.4 AdversarialLowerBoundsProofs 513
15.5 StateSpaceLowerBoundsProofs 516
15.6 FindingtheithBestElement 519
15.7 OptimalSorting 522
15.8 FurtherReading 524
15.9 Exercises 525
15.10Projects 527
16 PatternsofAlgorithms 529
16.1 GreedyAlgorithms 529
16.2 DynamicProgramming 530
16.2.1 KnapsackProblem 531
16.2.2 All-PairsShortestPaths 532
16.3 RandomizedAlgorithms 534
16.3.1 SkipLists 536
16.4 NumericalAlgorithms 541
16.4.1 Exponentiation 542
16.4.2 LargestCommonFactor 543
16.4.3 MatrixMultiplication 543
16.4.4 RandomNumbers 546
16.4.5 FastFourierTransform 546
16.5 FurtherReading 551