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algoritmi

Contents
Introduction . . . . . . . . . . . . . . . . . . . . .  . .  .  . 3
Algorithms, Outline of Topics
1. Preview. . . . . . . . . . . . . . . . . . . . . .  . . . .  . 9
Pascal,  Euclid’s  Algorithm,  Recursion,  Analysis  of  Algorithms
Implementing Algorithms
MATHEMATICAL ALGORITHMS
2. Arithmetic . . . . . . . . . . . . . . . . . . . .  . . . .  . 21
Polynomials, Matrices, Data  Structures
3. Random Numbers . . . . . . . . . . . . . . . . . .  . . . .  . 33
Applications, Linear Congruential Method, Additive
Congruential Method, Testing Randomness, Implementation  Notes
4. Polynomials . . . . . . . . . . . . . . . . . . . . .  . . . .  . 45
Evaluation, Interpolation, Multiplication, Divide-and-conquer
Recurrences, Matriz Multiplication
5. Gaussian Elimination . . . . . . . . . . . . . . . . .  . . . .  . 57
A  Simple Example, Outline  of  the  Method, Variations and  Extensions
6. Curve Fitting . . . . . . . . . . . . . . . . . . . .  . . . .  . 67
Polynomaal  Interpolation,  Spline Interpolation, Method  of  Least Squares
7. Integration . . . . . . . . . . . . . . . . . . . . .  . . . .  . 79
Symbolac  Integration, Simple Quadrature Methods, Compound Methods,
Adaptive Quadrature
SORTING
8. Elementary Sorting Methods . . . . . . . . . . . . .  . . . .  . 91
Rules of the  Game, Selection Sort, Insertion Sort,  Shellsort,
Bubble  Sort,  Distribution Counting, Non-Random  Files
9. Quicksort . . . . . . . . . . . . . . , , . , . . . .  . * .  . 103
The  Baszc  Algorithm, Removing Recursion, Small  Subfiles,
Median-of-  Three  Partitioning
10. Radix Sorting . . . . . . . . . . . , . . . . . . . .  . . .  . 115
Radiz  Ezchange  Sort, Straight Radix  Sort,  A Linear Sort
11. Priority Queues . . . . . . . . . . . . . . . . . . .  . .  . 127
Elementary Implementations, Heap Data Structure, Algorithms
on Heaps, Heapsort, Indirect Heaps, Advanced Implementations
12. Selection and Merging . . . . . . . . . . . . . . . .  . . .  . 143
Selection,  Mergang, Recursion Revisited
13. External Sorting . . . . . . . . . . . . . . . . . . .  . .  . 155
Sort-Merge, Balanced  Multiway  Merging,  Replacement  Selectzon,
Practical Considerations, Polyphase Merging,  An  Easier  Way

vii
SEARCHING
14. Elementary Searching Methods . . . . . . . . . . . . . . .  . 171
Sequential Searching,  Sequential  List  Searchang,  Binary  Search,
Binary  ‘Pree  Search, Indirect Binary Search Trees
15. Balanced Trees . . . . . . . . . . . . . . . . . . . . .  . 187
Top-Down  2-9-4 Trees, Red-Black  Trees,  Other Algorithms
16. Hashing . . . . . . . . . . . . . . . . . , . . . . . .  . 201
Hash  Functions,  Separate  Chaining, Open  Addresszng, Analytic Results
17. Radix Searching . . . . . . . . . . . . . . . . . . . . .  . 213
Digital Search  Trees,   Radix Search  Wes,   M&iway   Radar  Searching,
Patricia
18. External Searching . . . . . . . .  ,, . . . . . . . . . . . . . 225
Indexed Sequential  Access, B-  nees,   Extendible Hashing, Virtual Memory
STRING PROCESSING
19. String Searching . . . . . . . . . . . . . . . . . . . . . . 241
A Short History, Brute-Force Algorithm, Knuth-Morris-Pratt  Algorzthm,
Bayer-Moore  Algorithm,  Rabin-Karp  Algorithm, Multiple Searches
20. Pattern Matching . . . . . . . . . . . . . . . . . . . . . 257
Describing  Patterns, Pattern Matching  Machznes,  Representzng
the  Machine, Simulating  the  Machine
21. Parsing , . . . . . . . . . . . . . . . . . . . . . . . .  . 269
Conteti-Free   Grammars, Top-Down  Parsing,  Bottom-Up Parsing,
Compilers, Compiler-Compilers
22. File Compression . . . . . . . . . . . . . . . . . . . . .  . 283
Run-Length  Encoding,  Variable-Length  Encoding
23. Cryptology . . . . . . . . . . . . . . . . . . . . . . . . . 295
Rules  of the  Game, Simple  Methods, Encrypt:!on/Decryption
Machines,  Publzc-Key  Cryptosystems
GEOMETRIC ALGORITHMS
24. Elementary Geometric Methods . . . . . . . . . . . . . . . . 307
Poznts,  Lines,  and  Polygons, Line  Intersection, Simple
Closed Path,  Inclusaon  in  4  Polygon,  Perspective
25. Finding the Convex Hull . . . . . . . . . . . . . . . . . .  . 321
Rules  of the  Game,  Package  Wrapping,  The Graham  Scan,
Hull  Selection, Performance  Issues
26. Range Searching . . . . . . . . . . . . . . . . . . . . . . . 335
Elementary Methods,  Grad  Method,  2D  Trees,
Multidimensaonal  Range  Searching
27. Geometric Intersection . , . . . . . . . . . . . . . . . . . . 349
Horizontal and Vertical  Lines, General Line Intersection
28. Closest Point Problems . . . . . . . . . . . . . . . . . . . 361
Closest  Paar,   Voronoi  Diagrams

GRAPH ALGORITHMS
29. Elementary Graph Algorithms . . . . . . . . . . . . . .  . . . 373
Glossary, Representation, Depth-First Search,  Mazes,  Perspectzve
30. Connectivity . . . . . . . . . . . . . . . . . . . .  . . . 389
Biconnectivity,  Graph Traversal  Algorzthms, Union-Find Algorithms
31. Weighted Graphs . . . . . . . . . . . . . . . . . .  . . . 407
Mmimum  Spanning  Tree, Shortest Path, Dense Graphs,  Geometrzc   Problems
32. Directed Graphs . . . . . . . . . . . . . . . . . . .  . . 421
Depth-Farst   Search,  Transitwe   Closure,  Topological Sorting,
Strongly Connected Components
33. Network Flow . . . . . . . . . . . . . . . . . .  . . . 433
The Network Flow Problem,  Ford-Adkerson   Method, Network  Searching
34. Matching . . . . . . . . . . . . . . . . . . , . . . .  . . . 443
Bapartite Graphs,  Stable Marriage Problem,  Advanced  Algorathms
ADVANCED TOPICS
35. Algorithm Machines . . . . . . . . . . . . . . . . . .  . . . 457
General  Approaches>  Perfect  ShujIes, Systolic  Arrays
36. The Fast Fourier Transform . . . . . . . . . . . . . .  . . . 471
Evaluate,  Multiply,  Interpolate,  Complez  Roots  of  Unity,  Evaluation
at the Roots of Unity,  Interpolatzon  at  the Roots of Unity,  Implementation
37. Dynamic Programming . . . . . . . . . . . . . . . . .  . . . 483
Knapsack  Problem,  Matriz  Chain  Product,  Optimal Binary Search  Trees,
Shortest Paths, Time  and Space  Requirements
38. Linear Programming . . . . . . . . . . . . . . . . .  . . . 497
Lznear   Programs, Geometric  Interpretation,  The  Simplex  Method,
Implementation
39. Exhaustive Search . . . . . . . . . . . . . . . . . .  . . . 513
Exhaustive Search in Graphs,  Backtrackzng,  Permutation Generation,
Approximation  Algorithms
40. NP-complete Problems . . . . . . . . . . . . . . .  . . . 527
Deterministic and Nondeterministic Polynomial- Time Algorzthms,
NP-Completeness, Cook’s  Theorem,  Some NP-Complete Problems

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