Java数据结构与算法分析（影印版）

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