算法设计手册

Ⅰ Practical Algorithm Design

1 Introduction to Algorithm Design

1.1 Robot Tour Optimization

1.2 Selecting the Right Jobs

1.3 Reasoning about Correctness

1.4 Modeling the Problem

1.5 About the Wax Stories

1.6 War Story： Psychic Modeling

1.7 Exercises

2 Algorithm Analysis

2.1 The RAM Model of Computation

2.2 The Big Oh Notation

2.3 Growth Rates and Dominance Relations

2.4 Working with the Big Oh

2.5 Reasoning About Efficiency

2.6 Logarithms and Their Applications

2.7 Properties of Logarithms

2.8 War Story： Mystery of the Pyramids

2.9 Advanced Analysis (*)

2.10 Exercises

3 Data Structures

3.1 Contiguous vs. Linked Data Structures

3.2 Stacks and Queues

3.3 Dictionaries

3.4 Binary Search Trees

3.5 Priority Queues

3.6 War Story： Stripping Triangulations

3.7 Hashing and Strings

3.8 Specialized Data Structures

3.9 War Story： Stringem Up

3.10 Exercises

4 Sorting and Searching

4.1 Applications of Sorting

4.2 Pragmatics of Sorting

4.3 Heapsort： Fast Sorting via Data Structures

4.4 War Story： Give me a Ticket on an Airplane

4.5 Mergesort： Sorting by Divide-and-Conquer

4.6 Quicksort： Sorting by Randomization

4.7 Distribution Sort： Sorting via Bucketing

4.8 War Story： Skiena for the Defense

4.9 Binary Search and Related Algorithms

4.10 Divide-and-Conquer

4.11 Exercises

5 Graph Traversal

5.1 Flavors of Graphs

5.2 Data Structures for Graphs

5.3 War Story： I was a Victim of Moores Law

5.4 War Story： Getting the Graph

5.5 Traversing a Graph

5.6 Breadth-First Search

5.7 Applications of Breadth-First Search

5.8 Depth-First Search

5.9 Applications of Depth-First Search

5.10 Depth-First Search on Directed Graphs

5.11 Exercises

6 Weighted Graph Algorithms

6.1 Minimum Spanning Trees

6.2 War Story： Nothing but Nets

6.3 Shortest Paths

6.4 War Story： Dialing for Documents

6.5 Network Flows and Bipartite Matching

6.6 Design Graphs， Not Algorithms

6.7 Exercises

7 Combinatorial Search and Heuristic Methods

7.1 Backtracking

7.2 Search Pruning

7.3 Sudoku

7.4 War Story： Covering Chessboards

7.5 Heuristic Search Methods

7.6 War Story： Only it is Not a Radio

7.7 War Story： Annealing Arrays

7.8 Other Heuristic Search Methods

7.9 Parallel Algorithms

7.10 War Story： Going Nowhere Fast

7.11 Exercises

8 Dynamic Programming

8.1 Caching vs. Computation

8.2 Approximate String Matching

8.3 Longest Increasing Sequence

8.4 War Story： Evolution of the Lobster

8.5 The Partition Problem

8.6 Parsing Context-Free Grammars

8.7 Limitations of Dynamic Programming： TSP

8.8 War Story： Whats Past is Prolog

8.9 War Story： Text Compression for Bar Codes

8.10 Exercises

9 Intractable Problems and Approximation Algorithms

9.1 Problems and Reductions

9.2 Reductions for Algorithms

9.3 Elementary Hardness Reductions ..

9.4 Satisfiability

9.5 Creative Reductions

9.6 The Art of Proving Hardness

9.7 War Story： Hard Against the Clock

9.8 War Story： And Then I Failed

9.9 P vs. NP

9.10 Dealing with NP-complete Problems

9.11 Exercises

10 How to Design Algorithms

Ⅱ The Hitchhikers Guide to Algorithms

11 A Catalog of Algorithmic Problems

12 Data Structures

12.1 Dictionaries

12.2 Priority Queues

12.3 Suffix Trees and Arrays

12.4 Graph Data Structures

12.5 Set Data Structures

12.6 Kd-Trees

13 Numerical Problems

13.1 Solving Linear Equations

13.2 Bandwidth Reduction

13.3 Matrix Multiplication

13.4 Determinants and Permanents

13.5 Constrained and Unconstrained Optimization

13.6 Linear Programming

13.7 Random Number Generation

13.8 Factoring and Primality Testing

13.9 Arbitrary-Precision Arithmetic

13.10 Knapsack Problem

13.11 Discrete Fourier Transform

14 Combinatorial Problems

14.1 Sorting

14.2 Searching

14.3 Median and Selection

14.4 Generating Permutations

14.5 Generating Subsets

14.6 Generating Partitions

14.7 Generating Graphs

14.8 Calendrical Calculations

14.9 Job Scheduling

14.10 Satisfiability

15 Graph Problems： Polynomial-Time

15.1 Connected Components

15.2 Topological Sorting

15.3 Minimum Spanning Tree

15.4 Shortest Path

15.5 Transitive Closure and Reduction

15.6 Matching

15.7 Eulerian Cycle/Chinese Postman

15.8 Edge and Vertex Connectivity

15.9 Network Flow

15.10 Drawing Graphs Nicely

15.11 Drawing Trees

15.12 Planarity Detection and Embedding

16 Graph Problems： Hard Problems

16.1 Clique

16.2 Independent Set

16.3 Vertex Cover

16.4 Traveling Salesman Problem

16.5 Hamiltonian Cycle

16.6 Graph Partition

16.7 Vertex Coloring

16.8 Edge Coloring

16.9 Graph Isomorphism

16.10 Steiner Tree

16.11 Feedback Edge/Vertex Set

17 Computational Geometry

17.1 Robust Geometric Primitives

17.2 Convex Hull

17.3 Triangulation

17.4 Voronoi Diagrams

17.5 Nearest Neighbor Search

17.6 Range Search

17.7 Point Location

17.8 Intersection Detection

17.9 Bin Packing

17.10 Medial-Axis Transform

17.11 Polygon Partitioning

17.12 Simplifying Polygons

17.13 Shape Similarity

17.14 Motion Planning

17.15 Maintaining Line Arrangements

17.16 Minkowski Sum

18 Set and String Problems

18.1 Set Cover

18.2 Set Packing

18.3 String Matching

18.4 Approximate String Matching

18.5 Text Compression

18.6 Cryptography

18.7 Finite State Machine Minimization

18.8 Longest Common Substring/Subsequence

18.9 Shortest Common Superstring

19 Algorithmic Resources

19.1 Software Systems

19.2 Data Sources

19.3 Online Bibliographic Resources

19.4 Professional Consulting Services

Bibliography

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