20_Shortest_path.pptx

# 8 1 5 5 5 9 7 2 14 4 8 8 10 6 5 6 3 10 7 example at

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8 1 5 0 5 5 9 0 7 2 14 0 4 8 8 0 10 6 5 6 0 3 10 7 0

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Example At step 3, we find: A path (7, 3, 2) of length 19 A path (7, 3, 6) of length 12 We update d 7,2 = 19 , p 7,2 = 3 and c 7,2 = T d 7,6 = 12 , p 7,6 = 3 and c 7,6 = T T T T T T T F F T F F T F T T F T T F F F F F F F T T T T T F T F T F T F T T T F T 2 3 4 5 6 7 4 7 2 4 6 2 2 3 4 6 7 2 4 7 3 3 4 3 0 11 7 9 8 1 5 0 5 5 9 0 7 2 14 0 4 8 8 0 10 6 5 6 0 3 19 10 7 12 0
Example At step 4, there are no paths out of vertex v 4 , so we are finished T T T T T T F F T F F T F T T F T T F F F F F F F T T T T T F T F T F T F T T T F T 2 3 4 5 6 7 4 7 2 4 6 2 2 3 4 6 7 2 4 7 3 3 4 3 0 11 7 9 8 1 5 0 5 5 9 0 7 2 14 0 4 8 8 0 10 6 5 6 0 3 19 10 7 12 0

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Example At step 5, there is one incoming edge from v 1 to v 5 , and it doesn’t make any paths out of vertex v 1 any shorter... T T T T T T F F T F F T F T T F T T F F F F F F F T T T T T F T F T F T F T T T F T 2 3 4 5 6 7 4 7 2 4 6 2 2 3 4 6 7 2 4 7 3 3 4 3 0 11 7 9 8 1 5 0 5 5 9 0 7 2 14 0 4 8 8 0 10 6 5 6 0 3 19 10 7 12 0
Example At step 6, we find: A path (1, 6, 2) of length 6 A path (1, 6, 4) of length 7 A path (1, 6, 7) of length 4 A path (3, 6, 2) of length 7 A path (3, 6, 7) of length 5 A path (7, 3, 6, 2) of length 17 T T T T T T F F T F F T F T T F T T F F F F F F F T T T T T F T F T F T F T T T F T 2 3 4 5 6 7 4 7 2 4 6 2 2 3 4 6 7 2 4 7 3 3 4 3

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