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Open Data Structures

By Pat Morin

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Book Description

Table of Contents

Front Matter
Contents
Acknowledgments
Why This Book?
1. Introduction
- 1.1 The Need for Efficiency
- 1.2 Interfaces
  - 1.2.1 The Queue, Stack, and Deque Interfaces
  - 1.2.2 The List Interface: Linear Sequences
  - 1.2.3 The USet Interface: Unordered Sets
  - 1.2.4 The SSet Interface: Sorted Sets
- 1.3 Mathematical Background
  - 1.3.1 Exponentials and Logarithms
  - 1.3.2 Factorials
  - 1.3.3 Asymptotic Notation
  - 1.3.4 Randomization and Probability
- 1.4 The Model of Computation
- 1.5 Correctness, Time Complexity, and Space Complexity
- 1.6 Code Samples
- 1.7 List of Data Structures
- 1.8 Discussion and Exercises
2. Array-Based Lists
- 2.1 ArrayStack: Fast Stack Operations Using an Array
  - The Basics
  - Growing and Shrinking
  - Summary
- 2.2 FastArrayStack: An Optimized ArrayStack
- 2.3 ArrayQueue: An Array-Based Queue
  - 2.3.1 Summary
- 2.4 ArrayDeque: Fast Deque Operations Using an Array
  - 2.4.1 Summary
- 2.5 DualArrayDeque: Building a Deque from Two Stacks
  - 2.5.1 Balancing
  - 2.5.2 Summary
- 2.6 RootishArrayStack: A Space-Efficient Array Stack
  - 2.6.1 Analysis of Growing and Shrinking
  - 2.6.2 Space Usage
  - 2.6.3 Summary
  - 2.6.4 Computing Square Roots
- 2.7 Discussion and Exercises
3. Linked Lists
- 3.1 SLList: A Singly-Linked List
  - 3.1.1 Queue Operations
  - 3.1.2 Summary
- 3.2 DLList: A Doubly-Linked List
  - 3.2.1 Adding and Removing
  - 3.2.2 Summary
- 3.3 SEList: A Space-Efficient Linked List
  - 3.3.1 Space Requirements
  - 3.3.2 Finding Elements
  - 3.3.3 Adding an Element
  - 3.3.4 Removing an Element
  - 3.3.5 Amortized Analysis of Spreading and Gathering
  - 3.3.6 Summary
- 3.4 Discussion and Exercises
4. Skiplists
- 4.1 The Basic Structure
- 4.2 SkiplistSSet: An Efficient SSet
  - 4.2.1 Summary
- 4.3 SkiplistList: An Efficient Random-Access List
  - 4.3.1 Summary
- 4.4 Analysis of Skiplists
- 4.5 Discussion and Exercises
5. Hash Tables
- 5.1 ChainedHashTable: Hashing with Chaining
  - 5.1.1 Multiplicative Hashing
  - 5.1.2 Summary
- 5.2 LinearHashTable: Linear Probing
  - 5.2.1 Analysis of Linear Probing
  - 5.2.2 Summary
  - 5.2.3 Tabulation Hashing
- 5.3 Hash Codes
  - 5.3.1 Hash Codes for Primitive Data Types
  - 5.3.2 Hash Codes for Compound Objects
  - 5.3.3 Hash Codes for Arrays and Strings
- 5.4 Discussion and Exercises
6. Binary Trees
- 6.1 BinaryTree: A Basic Binary Tree
  - 6.1.1 Recursive Algorithms
  - 6.1.2 Traversing Binary Trees
- 6.2 BinarySearchTree: An Unbalanced Binary Search Tree
  - 6.2.1 Searching
  - 6.2.2 Addition
  - 6.2.3 Removal
  - 6.2.4 Summary
- 6.3 Discussion and Exercises
7. Random Binary Search Trees
- 7.1 Random Binary Search Trees
  - 7.1.1 Proof of Lemma 7.1
  - 7.1.2 Summary
- 7.2 Treap: A Randomized Binary Search Tree
  - 7.2.1 Summary
- 7.3 Discussion and Exercises
8. Scapegoat Trees
- 8.1 ScapegoatTree: A Binary Search Tree with Partial Rebuilding
  - 8.1.1 Analysis of Correctness and Running-Time
  - 8.1.2 Summary
- 8.2 Discussion and Exercises
9. Red-Black Trees
- 9.1 2-4 Trees
  - 9.1.1 Adding a Leaf
  - 9.1.2 Removing a Leaf
- 9.2 RedBlackTree: A Simulated 2-4 Tree
  - 9.2.1 Red-Black Trees and 2-4 Trees
  - 9.2.2 Left-Leaning Red-Black Trees
  - 9.2.3 Addition
  - 9.2.4 Removal
- 9.3 Summary
- 9.4 Discussion and Exercises
10. Heaps
- 10.1 BinaryHeap: An Implicit Binary Tree
  - 10.1.1 Summary
- 10.2 MeldableHeap: A Randomized Meldable Heap
  - 10.2.1 Analysis of merge(varh1,varh2)
  - 10.2.2 Summary
- 10.3 Discussion and Exercises
11. Sorting Algorithms
- 11.1 Comparison-Based Sorting
  - 11.1.1 Merge-Sort
  - 11.1.2 Quicksort
  - 11.1.3 Heap-sort
  - 11.1.4 A Lower-Bound for Comparison-Based Sorting
- 11.2 Counting Sort and Radix Sort
  - 11.2.1 Counting Sort
  - 11.2.2 Radix-Sort
- 11.3 Discussion and Exercises
12. Graphs
- 12.1 AdjacencyMatrix: Representing a Graph by a Matrix
- 12.2 AdjacencyLists: A Graph as a Collection of Lists
- 12.3 Graph Traversal
  - 12.3.1 Breadth-First Search
  - 12.3.3 Depth-First Search
- 12.4 Discussion and Exercises
13. Data Structures for Integers
- 13.1 BinaryTrie: A digital search tree
- 13.2 XFastTrie: Searching in Doubly-Logarithmic Time
- 13.3 YFastTrie: A Doubly-Logarithmic Time SSet
- 13.4 Discussion and Exercises
14. External Memory Searching
- 14.1 The Block Store
- 14.2 B-Trees
  - 14.2.1 Searching
  - 14.2.2 Addition
  - 14.2.3 Removal
  - 14.2.4 Amortized Analysis of B-Trees
- 14.3 Discussion and Exercises
Bibliography
Index