Data Structures and Algorithms

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Contents1 Introduction 11.1 What this book is, and what it isn’t . . . . . . . . . . . . . . . . 11.2 Assumed knowledge . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Big Oh notation . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Imperative programming language . . . . . . . . . . . . . 31.2.3 Object oriented concepts . . . . . . . . . . . . . . . . . . 41.3 Pseudocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Tips for working through the examples . . . . . . . . . . . . . . . 61.5 Book outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.7 Where can I get the code? . . . . . . . . . . . . . . . . . . . . . . 71.8 Final messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7I Data Structures 82 Linked Lists 92.1 Singly Linked List . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.1 Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.2 Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.3 Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.4 Traversing the list . . . . . . . . . . . . . . . . . . . . . . 122.1.5 Traversing the list in reverse order . . . . . . . . . . . . . 132.2 Doubly Linked List . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Reverse Traversal . . . . . . . . . . . . . . . . . . . . . . . 162.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Binary Search Tree 193.1 Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.4 Finding the parent of a given node . . . . . . . . . . . . . . . . . 243.5 Attaining a reference to a node . . . . . . . . . . . . . . . . . . . 243.6 Finding the smallest and largest values in the binary search tree 253.7 Tree Traversals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.7.1 Preorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26I
3.7.2 Postorder . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.7.3 Inorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.7.4 Breadth First . . . . . . . . . . . . . . . . . . . . . . . . . 303.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Heap 324.1 Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3 Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4 Traversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Sets 445.1 Unordered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.1.1 Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Ordered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Queues 486.1 A standard queue . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.2 Priority Queue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.3 Double Ended Queue . . . . . . . . . . . . . . . . . . . . . . . . . 496.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 AVL Tree 547.1 Tree Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567.2 Tree Rebalancing . . . . . . . . . . . . . . . . . . . . . . . . . . . 577.3 Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587.4 Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61II Algorithms 628 Sorting 638.1 Bubble Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638.2 Merge Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638.3 Quick Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658.4 Insertion Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678.5 Shell Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688.6 Radix Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 Numeric 729.1 Primality Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729.2 Base conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . 729.3 Attaining the greatest common denominator of two numbers . . 739.4 Computing the maximum value for a number of a specific baseconsisting of N digits . . . . . . . . . . . . . . . . . . . . . . . . . 749.5 Factorial of a number . . . . . . . . . . . . . . . . . . . . . . . . 749.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75II
Page 1 and 2: Data Structures and AlgorithmsDSAAn
Page 3: This book is made exclusively avail
Page 7 and 8: PrefaceEvery book has a story as to
Page 9 and 10: AcknowledgementsWriting this short
Page 11 and 12: Page intentionally left blank.
Page 13 and 14: CHAPTER 1. INTRODUCTION 2Figure 1.1
Page 15 and 16: CHAPTER 1. INTRODUCTION 4The reason
Page 17 and 18: CHAPTER 1. INTRODUCTION 61.4 Tips f
Page 19 and 20: Part IData Structures8
Page 21 and 22: CHAPTER 2. LINKED LISTS 10Figure 2.
Page 23 and 24: CHAPTER 2. LINKED LISTS 121) algori
Page 25 and 26: CHAPTER 2. LINKED LISTS 14Figure 2.
Page 27 and 28: CHAPTER 2. LINKED LISTS 161) algori
Page 29 and 30: CHAPTER 2. LINKED LISTS 18list.
Page 31 and 32: CHAPTER 3. BINARY SEARCH TREE 203.1
Page 37 and 38: CHAPTER 3. BINARY SEARCH TREE 261)
Page 39 and 40: CHAPTER 3. BINARY SEARCH TREE 28232
Page 43 and 44: Chapter 4HeapA heap can be thought
Page 45 and 46: CHAPTER 4. HEAP 34Figure 4.3: Conve
Page 47 and 48: CHAPTER 4. HEAP 36Figure 4.5: Inser
Page 49 and 50: CHAPTER 4. HEAP 381) algorithm Remo
Page 51 and 52: CHAPTER 4. HEAP 401) algorithm Cont
Page 53 and 54: CHAPTER 4. HEAP 42Figure 4.7: Deter
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Chapter 5SetsA set contains a numbe
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CHAPTER 5. SETS 461) algorithm Inte
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Chapter 6QueuesQueues are an essent
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CHAPTER 6. QUEUES 50Figure 6.1: Que
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CHAPTER 6. QUEUES 52Figure 6.2: Deq
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Chapter 7AVL TreeIn the early 60’
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CHAPTER 7. AVL TREE 567.1 Tree Rota
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CHAPTER 7. AVL TREE 581) algorithm
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CHAPTER 7. AVL TREE 601) algorithm
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Part IIAlgorithms62
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CHAPTER 8. SORTING 644 75 74 2 540
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CHAPTER 8. SORTING 664 75 74 2 54Pi
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CHAPTER 8. SORTING 688.5 Shell Sort
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CHAPTER 8. SORTING 701. Ones2. Tens
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Chapter 9NumericUnless stated other
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CHAPTER 9. NUMERIC 749.4 Computing
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Chapter 10Searching10.1 Sequential
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CHAPTER 10. SEARCHING 78the reader
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CHAPTER 11. STRINGS 801) algorithm
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CHAPTER 11. STRINGS 82Figure 11.2:
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CHAPTER 11. STRINGS 84Figure 11.4:
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Appendix AAlgorithm WalkthroughLear
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APPENDIX A. ALGORITHM WALKTHROUGH 8
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APPENDIX A. ALGORITHM WALKTHROUGH 9
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APPENDIX B. TRANSLATION WALKTHROUGH
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APPENDIX C. RECURSIVE VS. ITERATIVE
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APPENDIX C. RECURSIVE VS. ITERATIVE
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APPENDIX D. TESTING 98unstructured
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APPENDIX D. TESTING 100a PersonTest
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