Open Data Structures
344 pages, 6 x 9
88 figures
Paperback
Release Date:01 Jun 2013
ISBN:9781927356388
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Open Data Structures

An Introduction

Athabasca University Press

Offered as an introduction to the field of data structures andalgorithms, Open Data Structures covers the implementation and analysisof data structures for sequences (lists), queues, priority queues,unordered dictionaries, ordered dictionaries, and graphs. Focusing on amathematically rigorous approach that is fast, practical, andefficient, Morin clearly and briskly presents instruction along withsource code.

Analyzed and implemented in Java, the data structures presented inthe book include stacks, queues, deques, and lists implemented asarrays and linked-lists; space-efficient implementations of lists; skiplists; hash tables and hash codes; binary search trees includingtreaps, scapegoat trees, and red-black trees; integer searchingstructures including binary tries, x-fast tries, and y-fast tries;heaps, including implicit binary heaps and randomized meldable heaps;and graphs, including adjacency matrix and adjacency listrepresentations; and B-trees.

A modern treatment of an essential computer science topic, Open DataStructures is a measured balance between classical topics andstate-of-the art structures that will serve the needs of allundergraduate students or self-directed learners.

Pat Morin is Professor in the School of ComputerScience at Carleton University as well as founder and managing editorof the open access Journal of Computational Geometry. He is the authorof numerous conference papers and journal publications on the topics ofcomputational geometry, algorithms, and data structures. 

Acknowledgments- xi

Why This Book?- xiii

1. Introduction- 1

    1.1 The Need for Efficiency- 2

    1.2 Interfaces- 4

    1.3 Mathematical Background- 9

    1.4 The Model of Computation- 18

    1.5 Correctness, Time Complexity, and Space Complexity- 19

    1.6 Code Samples- 22

    1.7 List of Data Structures- 22

    1.8 Discussion and Exercises- 26

2. Array-Based Lists- 29

    2.1 ArrayStack: Fast Stack Operations Using an Array- 30

2.2 FastArrayStack: An Optimized ArrayStack- 35

2.3 ArrayQueue: An Array-Based Queue- 36

2.4 ArrayDeque: Fast Deque Operations Using an Array- 40

2.5 DualArrayDeque: Building a Deque from Two Stacks- 43

2.6 RootishArrayStack: A Space-Efficient Array Stack- 49

2.7 Discussion and Exercises- 59

3. Linked Lists- 63

    3.1 SLList: A Singly-Linked List- 63

    3.2 DLList: A Doubly-Linked List- 67

    3.3 SEList: A Space-Efficient Linked List- 71

    3.4 Discussion and Exercises- 82

4. Skiplists- 87

    4.1 The Basic Structure- 87

    4.2 SkiplistSSet: An Efficient Sset- 90

    4.3 SkiplistList: An Efficient Random-Access List- 93

    4.4 Analysis of Skiplists- 98

    4.5 Discussion and Exercises- 102

5. Hash Tables- 107

    5.1 ChainedHashTable: Hashing with Chaining- 107

    5.2 LinearHashTable: Linear Probing- 114

    5.3 Hash Codes- 122

    5.4 Discussion and Exercises- 128

6. Binary Trees- 133

    6.1 BinaryTree: A Basic Binary Tree- 135

    6.2 BinarySearchTree: An Unbalanced Binary Search Tree- 140

    6.3 Discussion and Exercises- 147

7. Random Binary Search Trees- 153

    7.1 Random Binary Search Trees- 153

    7.2 Treap: A Randomized Binary Search Tree- 159

    7.3 Discussion and Exercises- 168

8. Scapegoat Trees- 173

    8.1 ScapegoatTree: A Binary Search Tree with Partial Rebuilding-173

    8.2 Discussion and Exercises- 181

9. Red-Black Trees- 185

    9.1 2-4 Trees- 186

    9.2 RedBlackTree: A Simulated 2-4 Tree- 190

    9.3 Summary- 205

    9.4 Discussion and Exercises- 206

10. Heaps- 211

    10.1 BinaryHeap: An Implicit Binary Tree- 211

    10.2 MeldableHeap: A Randomized Meldable Heap- 217

    10.3 Discussion and Exercises- 222

11. Sorting Algorithms- 225

    11.1 Comparison-Based Sorting- 226

    11.2 Counting Sort and Radix Sort- 238

    11.3 Discussion and Exercises- 243

12. Graphs- 247

    12.1 AdjacencyMatrix: Representing a Graph by a Matrix- 249

    12.2 AdjacencyLists: A Graph as a Collection of Lists- 252

    12.3 Graph Traversal- 256

    12.4 Discussion and Exercises- 261

13. Data Structures for Integers- 265

    13.1 BinaryTrie: A digital search tree- 266

    13.2 XFastTrie: Searching in Doubly-Logarithmic Time- 272

    13.3 YFastTrie: A Doubly-Logarithmic Time SSet- 275

    13.4 Discussion and Exercises- 280

14. External Memory Searching- 283

    14.1 The Block Store- 285

    14.2 B-Trees- 285

    14.3 Discussion and Exercises- 304

Bibliography- 309

Index- 317

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