Floyd-Warshall

November 17, 2022

Science

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Floyd-Warshall

Chen

November 17, 2022

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Transcript

Floyd-Warshall: Dynamic Programming Floyd-Warshall computes all pairs, but let us
focus on 5 to 6. 62 / 71
Floyd-Warshall: Dynamic Programming We start by considering only start(5) and
dest(6) when k is 0. 63 / 71
Floyd-Warshall: Dynamic Programming Then we also consider node 1 when
k is 1. 64 / 71
Floyd-Warshall: Dynamic Programming And node 2 when k is 2.
65 / 71
Floyd-Warshall: Dynamic Programming And node 3 when k is 3.....
66 / 71
Floyd-Warshall: Dynamic Programming And node 4 when k is 4....
And so on. Note that I have just been ﬁlling in the answers for recursive calls But we actually need to compute those. 67 / 71
Floyd-Warshall: Dynamic Programming Hmm it looks like some of those
recursive calls will recompute the same thing... 68 / 71