I. FUNDAMENTALS.
1. Introduction. Algorithms.
Outline of Topics.
2. C. Example: Euclid's Algorithm.
Types of Data.
Input/Output.
Concluding Remarks.
3. Elementary Data Structures. Arrays.
Linked Lists.
Storage Allocation.
Pushdown Stacks.
Queues.
Abstract Data Types.
4. Trees. Glossary.
Properties.
Representing Binary Trees.
Representing Forests.
Traversing Trees.
5. Recursion. Recurrences.
Divide-and-Conquer.
Recursive Tree Traversal.
Removing Recursion.
Perspective.
6. Analysis of Algorithms. Framework.
Classification of Algorithms.
Computational Complexity.
Average-Case Analysis.
Approximate and Asymptotic Results.
Basic Recurrences.
Perspective.
7. Implementation of Algorithms. Selecting an Algorithm.
Empirical Analysis.
Program Optimization.
Algorithms and Systems.
II. SORTING ALGORITHMS.
8. Elementary Sorting Methods. Rules of the Game.
Selection Sort.
Insertion Sort.
Digression: Bubble Sort.
Performance Characteristics of Elementary Sorts.
Sorting Files with Large Records.
Shellsort.
Distribution Counting.
9. Quicksort. The Basic Algorithm.
Performance Characteristics of Quicksort.
Removing Recursion.
Small Subfiles.
Median-of-Three Partitioning.
Selection.
10. Radix Sorting. Bits.
Radix Exchange Sort.
Straight Radix Sort.
Performance Characteristics of Radix Sorts.
A Linear Sort.
11. Priority Queues. Elementary Implementations.
Heap Data Structure.
Algorithms on Heaps.
Heapsort.
Indirect Heaps.
Advanced Implementations.
12. Mergesort. Merging.
Mergesort.
List Mergesort.
Bottom-up Mergesort.
Performance Characteristics.
Optimized Implementations.
Recursion Revisited.
13. External Sorting. Sort-Merge.
Balanced Multiway Merging.
Replacement Selection.
Practical Considerations.
Polyphase Merging.
An Easier Way.
III. SEARCHING ALGORITHMS.
14. Elementary Searching Methods. Sequential Searching.
Binary Search.
Binary Tree Search.
Deletion.
Indirect Binary Search Trees.
15. Balanced Trees. Top-Down 2-3-4 Trees.
Red-Black Trees.
Other Algorithms.
16. Hashing. Hash Functions.
Separate Chaining.
Linear Probing.
Double Hashing.
Perspective.
17. Radix Searching. Digital Search Trees.
Radix Search Tries.
Multiway Radix Searching.
Patricia.
18. External Searching. Indexed Sequential Access.
B-Trees.
Extendible Hashing.
Virtual Memory.
IV. STRING PROCESSING.
19. String Searching. A Short History.
Brute-Force Algorithm.
Knuth-Morris-Pratt Algorithm.
Boyer-Moore Algorithm.
Rabin-Karp Algorithm.
Multiple Searches.
20. Pattern Matching. Describe Patterns.
Pattern Matching Machines.
Representing the Machine.
Simulating the Machine.
21. Parsing. Context-Free Grammars.
Top-Down Parsing.
Bottom-Up Parsing.
Compilers.
Compiler-Compilers.
22. File Compression. Run-Length Encoding.
Variable-Length Encoding.
Building the Huffman Code.
Implementation.
23. Cryptology. Rules of Game.
Simple Methods.
Encryption/Decryption Machines.
Public-Key Cryptosystems.
V. GEOMETRIC ALGORITHMS.
24. Elementary Geometric Methods. Points, Lines, and Polygons.
Line Segment Intersection.
Simple Closed Path.
Inclusion in a Polygon.
Perspective.
25. Finding the Convex Hull. Rules of the Game.
Package-Wrapping.
The Graham Scan.
Interior Elimination.
Performance Issues.
26. Range Searching. Elementary Methods.
Grid Method.
Two-Dimensional Trees.
Multidimensional Range Searching.
27. Geometric Intersection. Horizontal and Vertical Lines.
Implementation.
General Line Intersection
28. Closest-Point Problems. Closest-Pair Problem.
Voronoi Diagrams.
VI. GRAPH ALGORITHMS.
29. Elementary Graph Algorithms. Glossary.
Representation.
Depth-First Search.
Nonrecursive Depth-First Search.
Breadth-First Search.
Mazes.
Perspective.
30. Connectivity. Connected Components.
Biconnectivity.
Union-Find Algorithms.
31. Weighted Graphs Minimum Spanning Tree.
Priority-First Search.
Kruskal's Method.
Shortest Path.
Minimum Spanning Tree and Shortest Paths in Dense Graphs.
Geometric Problems.
32. Network Flow. The Network Flow Problem.
Ford-Fulkerson Method.
Network Searching.
33. Matching. Bipartite Graphs.
Stable Marriage Problem.
Advanced Algorithms.
VII. MATHEMATICAL ALGORITHMS.
34. Random Numbers. Applications.
Linear Congruential Method.
Additive Congruential Method.
Testing Randomness.
Implementation Notes.
35. Arithmetic. Polynomial Arithmetic.
Polynomial Evaluation and Interpolation.
Polynomial Multiplication.
Arithmetic Operations with Large Integers.
Matrix Arithmetic.
36. Gaussian Elimination. A Simple Example.
Outline of the Method.
Variations and Extensions.
37. Curve Fitting. Polynomial Interpolation.
Spline Interpolation.
Method of Least Squares.
38. Integration. Symbolic Integration.
Simple Quadrature Methods.
Compound Methods.
Adaptive Quadrature.
VIII. ADVANCED TOPICS
39. Parallel Algorithms. General Approaches.
Perfect Shuffles.
Systolic Arrays.
Perspective.
40. The Fast Fourier Transform. Evaluate, Multiply, Interpolate.
Complex Roots of Unity.
Evaluation of the Roots of Unity.
Interpolation at the Roots of Unity.
Implementation.
41. Dynamic Programming. Knapsack Problem.
Matrix Chain Product.
Optimal Binary Search Trees.
Time and Space Requirements.
42. Linear Programming. Linear Programs.
Geometric Interpretation.
The Simplex Method.
Implementation.
43. Exhaustive Search. Exhaustive Search in Graphs.
Backtracking.
Digression: Permutation Generation.
Approximation Algorithms.
44. NP-Complete Problems. Deterministic and Nondeterministic Polynomial-Time
Algorithms.
NP-Completeness.
Cook's Theorem.
Some NP-Complete Problems. 0201514257T04062001
