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Merge pull request TheAlgorithms#349 from c-utkarsh/add-floyd-warshall
Added FloydWarshall All Pairs Shortest Path Algo
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Graphs/FloydWarshall.js

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/*
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Source:
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https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm
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Complexity:
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O(|V|^3) where V is the set of vertices
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*/
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const FloydWarshall = (dist) => {
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// Input:- dist: 2D Array where dist[i][j] = edge weight b/w i and j
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// Output:- dist: 2D Array where dist[i][j] = shortest dist b/w i and j
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const n = dist.length
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for (let k = 0; k < n; k++) {
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for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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if (dist[i][j] > dist[i][k] + dist[k][j]) {
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// dist from i to j via k is lesser than the current distance
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dist[i][j] = dist[i][k] + dist[k][j]
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}
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}
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}
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}
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return dist
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}
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const main = () => {
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// For the following graph (edge weights are shown in brackets)
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// 4 1 dist[1][2] = dist[2][1] = 1
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// \ (2)/ \ dist[1][3] = dist[3][1] = 2
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// \ / \(1) dist[1][4] = dist[4][1] = Infinity
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// (1)\ / \ dist[3][4] = dist[4][3] = 1
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// 3 2 dist[2][4] = dist[4][2] = Infinity
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// dist[2][3] = dist[3][2] = Infinity
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// Output should be:
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// [ [0, 1, 2, 3],
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// [1, 0, 3, 4],
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// [2, 3, 0, 1],
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// [3, 4, 1, 0] ]
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console.log(FloydWarshall(
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[[0, 1, 2, Infinity],
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[1, 0, Infinity, Infinity],
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[2, Infinity, 0, 1],
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[Infinity, Infinity, 1, 0]
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]
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))
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}
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main()

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