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In computer science, the Floyd–Warshall algorithm is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights. A single execution of the algorithm will find the lengths of shortest paths between all pairs of vertices. Although it does not return details of the paths themselves, it is possible to reconstruct the paths with simple modifications to the algorithm. Versions of the algorithm can also be used for finding the transitive closure of a relation, or widest paths between all pairs of vertices in a weighted graph.
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