All-pairs shortest paths in digraphs without negative cycles.Articulate an API like the one implemented on page 656 for the all-pairs shortest-paths problem in graphs with no negative cycles. Develop an implementation that runs a version of Bellman-Ford to identify real-valued weights pi[v] such that for any edge v->w, the edge weight plus the difference between pi[v] and pi[w] is nonnegative. Then use these weights to reweight the graph, so that Dijkstra’s algorithm is effective for finding all shortest paths in the reweighted graph.
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