Contents
Chapter 1 Introduction
1.1. What's the Book About?
1.2. Mathematics Review
1.2.1. Exponents
1.2.2. Logarithms
1.2.3. Series
1.2.4. Modular Arithmetic
1.2.5. The P Word
1.3. A Brief Introduction to Recursion
1.4. Genetic Objects in Java
1.4.1. The IntCell Class
1.4.2. The MemoryCell Class
1.4.3. Implementing Genetic findMax
1.5. Exceptions
1.6. Input and Output
1.6.1. Basic Stream Operations
1.6.2. The StringTokenizer Object
1.6.3. Sequential Files
1.7. Code Organization
1.7.1. Packages
1.7.2. The MyInteger Class
1.7.3. Efficiency Considerations
Summary
Exercises
References
Chapter 2 Algorithm Analysis
2.1. Mathematical Background
2.2. Model
2.3. What to Analyze
2.4. Running Time Calculations
2.4.1. A Simple Example
2.4.2. General Rules
2.4.3. Solutions for the Maximum Subsequence
Sum Problem
2.4.4. Logarithms in the Running Time
2.4.5. Checking Your Analysis
2.4.6. A Grain of Salt
Summary
Exercises
References
Chapter 3 Lists, Stacks, and Queues
3.1. Abstract Data Types (ADTS)
3.2. The List ADT
3.2.1. Simple Array Implementation of Lists
3.2.2. Linked Lists
3.2.3. Programming Details
3.2.4. Doubly Linked Lists
3.2.5. Circular Linked Lists
3.2.6. Examples
3.2.7. Cursor Implementation of Linked Lists
3.3. The Stack ADT
3.3.1. Stack Model
3.3.2. Implementation of Stacks
3.3.3. Applications
3.4. The Queue ADT
3.4.1. Queue Model
3.4.2. Array Implementation of Queues
3.4.3. Applications of Queues
Summary
Exercises
Chapter 4 Trees
4.1. Preliminaries
4.1.1. Implementation of Trees
4.1.2. Tree Traversals with an Application
4.2. Binary Trees
4.2.1. Implementation
4.2.2. An Example: Expression Trees
4.3. The Search Tree ADT--Binary Search Trees
4.3.1. find
4.3.2. findMin and findMax
4.3.3. insert
4.3.4. remove
4.3.5. Average-Case Analysis
4.4. AVL Trees
4.4.1. Single Rotation
4.4.2. Double Rotation
4.5. Splay Trees
4.5.1. A Simple Idea (That Does Not Work)
4.5.2. Splaying
4.6. Tree Traversals (Revisited)
4.7. B-Trees
Summary
Exercises
References
Chapter 5 Hashing
5.1. General Idea
5.2. Hash Function
5.3. Separate Chaining
5.4. Open Addressing
5.4.1. Linear Probing
5.4.2. Quadratic Probing
5.4.3. Double Hashing
5.5. Rehashing
5.6. Extendible Hashing
Summary
Exercises
References
Chapter 6 Priority Queues (Heaps)
6.1. Model
6.2. Simple Implementations
6.3. Binary Heap
6.3.1. Structure Property
6.3.2. Heap Order Property
6.3.3. Basic Heap Operations
6.3.4. Other Heap Operations
6.4. Applications of Priority Queues
6.4.1. The Selection Problem
6.4.2. Event Simulation
6.5. d-Heaps
6.6. Leftist Heaps
6.6.1. Leftist Heap Property
6.6.2. Leftist Heap Operations
6.7. Skew Heaps
6.8. Binomial Queues
6.8.1. Binomial Queue Structure
6.8.2. Binomial Queue Operations
6.8.3. Implementation of Binomial Queues
Summary
Exercises
References
Chapter 7 Sorting
7.2. Insertion Sort
7.2.1. The Algorithm
7.2.2. Analysis of Insertion Sort
7.3. A Lower Bound for Simple Sorting Algorithms
7.4. Shellsort
7.4.1. Worst-Case Analysis of Shellsort
7.5. Heapsort
7.5.1. Analysis of Heapsort
7.6. Mergesort
7.6.1. Analysis of Mergesort
7.7. Quicksort
7.7.1. Picking the Pivot
7.7.2. Partitioning Strategy
7.7.3. Small Arrays
7.7.4. Actual Quicksort Routines
7.7.5. Analysis of Quicksort
7.7.6. A Linear-Expected-Time Algorithm for Selection
7.8. A General Lower Bound for Sorting
7.8.1. Decision Trees
7.9. Bucket Sort
7.10. External Sorting
7.10.1. Why We Need New Algorithms
7.10.2. Model for External Sorting
7.10.3. The Simple Algorithm
7.10.4. Multiway Merge
7.10.5. Polyphase Merge
7.10.6. Replacement Selection
Summary
Exercises
References
Chapter 8 The Disjoint Set ADT
8.1. Equivalence Relations
8.2. The Dynamic Equivalence Problem
8.3. Basic Data Structure
8.4. Smart Union Algorithms
8.5. Path Compression
8.6. Worst Case for Union-by-Rank and Path Compression
8.6.1. Analysis of the Union/Find Algorithm
8.7. An Application
Summary
Exercises
References
Chapter 9 Graph Algorithms
9.1. Definitions
9.1.1. Representation of Graphs
9.2. Topological Sort
9.3. Shortest-Path Algorithms
9.3.1. Unweighted Shortest Paths
9.3.2. Dijkstra's Algorithm
9.3.3. Graphs with Negative Edge Costs
9.3.4. Acyclic Graphs
9.3.5. All-Pairs Shortest Path
9.4. Network Flow Problems
9.4.1. A Simple Maximum-Flow Algorithm
9.5. Minimum Spanning Tree
9.5.1. Prim's Algorithm
9.5.2. Kruskal's Algorithm
9.6. Applications of Depth-First Search
9.6.1. Undirected Graphs
9.6.5. Biconnectivity
9.6.3. Euler Circuits
9.6.5. Finding Strong Components
9.7. Introduction to NP-Completeness
9.7.1. Easy vs. Hard
9.7.2. The Class NP
9.7.3. NP-Complete Problems
Summary
Exercises
References
Chapter 10 Algorithm Design Techniques
10.1. Greedy Algorithms
10.1.1. A Simple Scheduling Problem
10.1.2. Huffman Codes
10.1.3. Approximate Bin Packing
10.2. Divide and Conquer
10.2.1. Running Time of Divide
and Conquer Algorithms
10.2.2. Closest-Points Problem
10.2.3. The Selection Problem
10.2.4. Theoretical Improvements
for Arithmetic Problems
10.3. Dynamic Programming
10.3.1. Using a Table Instead of Recursion
10.3.2. Ordering Matrix Multiplications
10.3.3. Optimal Binary Search Tree
10.3.4. All-Pairs Shortest Path
10.4. Randomized Algorithms
10.4.1. Random Number Generators
10.4.2. Skip Lists
10.4.3. Primality Testing
10.5. Backtracking Algorithms
10.5.1. The Turnpike Reconstruction Problem
10.5.2. Games
Summary
Exercises
References
Chapter 11 Amortized Analysis
11.1. An Unrelated Puzzle
11.2. Binomial Queues
11.3. Skew Heaps
11.4. Fibonacci Heaps
11.4.1. Cutting Nodes in Leftist Heaps
11.4.2. Lazy Merging for Binomial Queues
11.4.3. The Fibonacci Heap Operations
11.4.4. Proof of the Time Bound
11.5 Splay Trees
Summary
Exercises
References
Chapter 12 Advanced Data Structures
and Implementation
12.1. Top-Down Splay Trees
12.2. Red-Black Trees
12.2.1. Bottom-Up Insertion
12.2.2. Top-Down Red-Black Trees
12.2.3. Top-Down Deletion
12.3. Deterministic Skip Lists
12.4. AA-Trees
12.5. Treaps
12.6. k-d Trees
12.7. Pairing Heaps
Summary
Exercises
References
Appendix A Some Library Routines
A. 1. Classes in Package java.lang
A.1.1. Character
A.1.2. Integer
A.1.3. Object
A.1.4. String
A.1.5. StringBuffer
A.1.6. System
A.1.7. Throwable
A.2. Classes in Package java.io
A.2.1. BufferedReader
A.2.2. BufferedWriter
A.2.3. File
A.2.4. FileReader
A.2.5. FileWriter
A.2.6. InputStreamReader
A.2.7. PrintWriter
A.2.8. PushbackReader
A.3. Classes in Package java.util
A.3.1. Random
A.3.2. StringTokenizer
Appendix B The Collections Library
B.1. Introduction
B.2. Basic Classes
B.2.1. Collection
B.2.2. Iterator
B.2.3. Comparable
B.2.4. Comparator
B.3. Lists
B.3.1. ArrayList vs. LinkedList
B.3.2. Stacks and Queues
B.3.3. ListIterator
B.4. Sets
B.5. Maps
B.5.1. put, get, remove, and contains
B.5.2. Getting a Collection from the Map
B.5.3. Map. Entry Pairs
B.6. Example: Generating a Concordance
B.6.1. Collections API Version
B.6.2. Version Using Package DataStructures
B.7. Example: Shortest-Path Calculation
B.7.1. Collections API Implementation
B.7.7. Version Using Package DataStructures
B.8. Priority Queues
Summary
Index
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