Title : A Practical Introduction to Data Structures and Algorithm Analysis

Practical Introduction to Data Structures and Algorithm Analysis
Edition 3.1 (Java Version)
Clifford A. Shaffer
Department of Computer Science
Virginia Tech
Blacksburg, VA 24061

Table Of Content

I Preliminaries
1 Data Structures and Algorithms
1.1 A Philosophy of Data Structures
1.2 Abstract Data Types and Data Structures
1.3 Design Patterns
1.4 Problems, Algorithms, and Programs
1.5 Further Reading
1.6 Exercises

2 Mathematical Preliminaries
2.1 Sets and Relations
2.2 Miscellaneous Notation
2.3 Logarithms
2.4 Summations and Recurrences
2.5 Recursion
2.6 Mathematical Proof Techniques
2.7 Estimating
2.8 Further Reading
2.9 Exercises

3 Algorithm Analysis
3.1 Introduction
3.2 Best, Worst, and Average Cases
3.3 A Faster Computer, or a Faster Algorithm?
3.4 Asymptotic Analysis
3.5 Calculating the Running Time for a Program
3.6 Analyzing Problems
3.7 Common Misunderstandings
3.8 Multiple Parameters
3.9 Space Bounds
3.10 Speeding Up Your Programs
3.11 Empirical Analysis
3.12 Further Reading
3.13 Exercises
3.14 Projects

II Fundamental Data Structures
4 Lists, Stacks, and Queues
4.1 Lists
4.1.1 Array-Based List Implementation
4.1.2 Linked Lists
4.1.3 Comparison of List Implementations
4.1.4 Element Implementations
4.1.5 Doubly Linked Lists
4.2 Stacks
4.2.1 Array-Based Stacks
4.2.2 Linked Stacks
4.2.3 Comparison of Array-Based and Linked Stacks
4.2.4 Implementing Recursion
4.3 Queues
4.3.1 Array-Based Queues
4.3.2 Linked Queues
4.3.3 Comparison of Array-Based and Linked Queues
4.4 Dictionaries
4.5 Further Reading
4.6 Exercises
4.7 Projects

5.1 Definitions and Properties
5.2 Binary Tree Traversals
5.3 Binary Tree Node Implementations
5.4 Binary Search Trees
5.5 Heaps and Priority Queues
5.6 Huffman Coding Trees
5.6.1 Building Huffman Coding Trees
5.6.2 Assigning and Using Huffman Codes
5.7 Further Reading
5.8 Exercises
5.9 Projects

6 Non-Binary Trees
6.1 General Tree Definitions and Terminology
6.1.1 An ADT for General Tree Nodes
6.1.2 General Tree Traversals
6.2 The Parent Pointer Implementation
6.3 General Tree Implementations
6.3.1 List of Children
6.3.2 The Left-Child/Right-Sibling Implementation
6.3.3 Dynamic Node Implementations
6.3.4 Dynamic “Left-Child/Right-Sibling” Implementation
6.4 K-ary Trees
6.5 Sequential Tree Implementations
6.6 Further Reading
6.7 Exercises
6.8 Projects

III Sorting and Searching
7 Internal Sorting
7.1 Sorting Terminology and Notation
7.2 Three (n2) Sorting Algorithms
7.3 Shellsort
7.4 Mergesort
7.5 Quicksort
7.6 Heapsort
7.7 Binsort and Radix Sort
7.8 An Empirical Comparison of Sorting Algorithms
7.9 Lower Bounds for Sorting
7.10 Further Reading
7.11 Exercises
7.12 Projects

8 File Processing and External Sorting
8.1 Primary versus Secondary Storage
8.2 Disk Drives
8.2.1 Disk Drive Architecture
8.2.2 Disk Access Costs
8.3 Buffers and Buffer Pools
8.4 The Programmer’s View of Files
8.5 External Sorting
8.5.1 Simple Approaches to External Sorting
8.5.2 Replacement Selection
8.5.3 Multiway Merging
8.6 Further Reading
8.7 Exercises
8.8 Projects

9 Searching
9.1 Searching Unsorted and Sorted Arrays
9.2 Self-Organizing Lists
9.3 Bit Vectors for Representing Sets
9.4 Hashing
9.4.1 Hash Functions
9.4.2 Open Hashing
9.4.3 Closed Hashing
9.4.4 Analysis of Closed Hashing
9.4.5 Deletion
9.5 Further Reading
9.6 Exercises
9.7 Projects

10 Indexing
10.1 Linear Indexing
10.2 ISAM
10.3 Tree-based Indexing
10.4 2-3 Trees
10.5 B-Trees
10.5.1 B+-Trees
10.5.2 B-Tree Analysis
10.6 Further Reading
10.7 Exercises
10.8 Projects

IV Advanced Data Structures
11 Graphs
11.1 Terminology and Representations
11.2 Graph Implementations
11.3 Graph Traversals
11.4 Shortest-Paths Problems
11.4.1 Single-Source Shortest Paths
11.5 Minimum-Cost Spanning Trees
11.5.1 Prim’s Algorithm
11.5.2 Kruskal’s Algorithm
11.6 Further Reading
11.7 Exercises
11.8 Projects

12 Lists and Arrays Revisited
12.1 Multilists
12.2 Matrix Representations
12.3 Memory Management
12.3.1 Dynamic Storage Allocation
12.3.2 Failure Policies and Garbage Collection
12.4 Further Reading
12.5 Exercises
12.6 Projects

13 Advanced Tree Structures
13.1 Tries
13.2 Balanced Trees
13.2.1 The AVL Tree
13.2.2 The Splay Tree
13.3 Spatial Data Structures
13.3.1 The K-D Tree
13.3.2 The PR quadtree
13.3.3 Other Point Data Structures
13.3.4 Other Spatial Data Structures
13.4 Further Reading
13.5 Exercises
13.6 Projects

V Theory of Algorithms
14 Analysis Techniques
14.1 Summation Techniques
14.2 Recurrence Relations
14.2.1 Estimating Upper and Lower Bounds
14.2.2 Expanding Recurrences
14.2.3 Divide and Conquer Recurrences
14.2.4 Average-Case Analysis of Quicksort
14.3 Amortized Analysis
14.4 Further Reading
14.5 Exercises
14.6 Projects

15 Lower Bounds
15.1 Introduction to Lower Bounds Proofs
15.2 Lower Bounds on Searching Lists
15.3 Finding the Maximum Value
15.4 Adversarial Lower Bounds Proofs
15.5 State Space Lower Bounds Proofs
15.6 Finding the ith Best Element
15.7 Optimal Sorting
15.8 Further Reading
15.9 Exercises
15.10 Projects

16 Patterns of Algorithms
16.1 Dynamic Programming
16.1.1 The Knapsack Problem
16.1.2 All-Pairs Shortest Paths
16.2 Randomized Algorithms
16.3 Numerical Algorithms
16.3.1 Exponentiation
16.3.2 Largest Common Factor
16.3.3 Matrix Multiplication
16.3.4 Random Numbers
16.3.5 The Fast Fourier Transform
16.4 Further Reading
16.5 Exercises
16.6 Projects

17 Limits to Computation
17.1 Reductions
17.2 Hard Problems
17.2.1 The Theory of NP-Completeness
17.2.2 NP-Completeness Proofs
17.2.3 Coping with NP-Complete Problems
17.3 Impossible Problems
17.3.1 Uncountability
17.3.2 The Halting Problem Is Unsolvable
17.4 Further Reading
17.5 Exercises
17.6 Projects

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