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Floyd Warshall Algorithm is a Dynamic Programming based algorithm.

It finds all pairs shortest paths using following recursive nature of problem.

For every pair (i, j) of source and destination vertices respectively, there are two possible cases.

1) k is not an intermediate vertex in shortest path from i to j. We keep the value of dist[i][j] as it is.

2) k is an intermediate vertex in shortest path from i to j. We update the value of dist[i][j] as dist[i][k] + dist[k][j].

Reference :-http://www.geeksforgeeks.org/gate-gate-cs-2016-set-2-question-24/

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