'Fibonacci heap' diaporamas de présentation

CS XXX -Algorithms X

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Shortest Path Problems

Shortest Path Problems. Directed weighted graph. Path length is sum of weights of edges on path. The vertex at which the path begins is the source vertex. The vertex at which the path ends is the destination vertex. 1. 7. Example. 8. 6. 2. 1. 3. A path from 1 to 7 . 3. 1. 16.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. Fibonacci Heaps: A collection of heap-ordered trees. trees : rooted but unordered Each node x : P[x] points to its parent child[x] points to any one of its children,children of x are linked together in a circular doubly linked list

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Fibonacci Heaps

Fibonacci Heaps. Analysis. FibonacciAnalysis.ppt Video http://www.cise.ufl.edu/academics/courses/preview/cop5536sahni Same as: www.cise.ufl.edu/~sahni/cop5536 ; Internet Lectures; not registered COP5536_FHA.rm. 8. 6. 2. 1. 3. 3. 1. 16. 7. 5. 6. 4. 10. 4. 2. 4. 7. 5. 3.

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Fibonacci Heaps

Fibonacci Heaps. Analysis. FibonacciAnalysis.ppt Video www.cise.ufl.edu/~sahni/cop5536 ; Internet Lectures; not registered COP5536_FHA.rm. 8. 6. 2. 1. 3. 3. 1. 16. 7. 5. 6. 4. 10. 4. 2. 4. 7. 5. 3. 14. Single Source All Destinations Shortest Paths.

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Prim's Algorithm

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Priority Queues

Priority Queues. MakeQueue create new empty queue Insert ( Q , k , p ) insert key k with priority p Delete ( Q, k ) delete key k (given a pointer) DeleteMin (Q) delete key with min priority Meld( Q 1 , Q 2 ) merge two sets Empty ( Q ) returns if empty Size ( Q ) returns # keys

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Priority Queues

Priority Queues. MakeQueue create new empty queue Insert ( Q , k , p ) insert key k with priority p Delete ( Q, k ) delete key k (given a pointer) DeleteMin (Q) delete key with min priority Meld( Q 1 , Q 2 ) merge two sets Empty ( Q ) returns if empty Size ( Q ) returns # keys

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The single-source shortest path problem

The single-source shortest path problem. ???. The Single-Source Shortest Path Problem. The single-source shortest path problem ???????????????????????????? . ??????????? G =( V , E ), ???????????? . This weight can be considered as the length of this edge.

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