L18-shortestPaths

L18-shortestPaths - L18 4102 abhi shelat 10.29.2013...

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L18 4102 10.29.2013 abhi shelat Shortest paths, negative weights
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implementation use a priority queue to keep track of light edges makequeue: insert: extractmin: decreasekey: priority queue Fbonacci heap O(log n) O(log n ) O(log n ) n log n log n O(1) n amortized amortized
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 sh o rtest paths
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0 10 12 18
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0 10 12 18 15 13 19
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0 10 12 18 15 13 19
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0 10 12 18 15 13 19 26
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0 10 12 18 15 13 19 26 30
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8 3 7 3 5 9 11 2 8 6 b a 9 12 e d f c 1 i g h 10 0 10 12 18 15 13 19 26 30 28
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Dijkstra ( G =( V,E ) ,s ) 1 for all v V 2 do d u ←⇥ 3 u nil 4 d s 0 5 Q makequeue ( V ) ± use d u as key 6 while Q = 7 do u extractmin ( Q ) 8 for each v Adj ( u ) 9 do if d v >d u + w ( u,v ) 10 then d v d u + w ( ) 11 v u 12 decreasekey ( Q,v )
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prim ( G =( V,E )) 1 Q ←⇧ ± Q is a Priority Queue 2 Initialize each v V with key k v ←⇥ , π v nil 3 Pick a starting node r and set k r 0 4 Insert all nodes into Q with key k v .
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L18-shortestPaths - L18 4102 abhi shelat 10.29.2013...

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