Suppose that we are given a weighted, directed graph G=(V, E) in which edges that leave the source vertex s may have negative weights, all other edge weights are nonnegative, and there are no negative-weight cycles. Argue that Dijkstra's algorithm correctly finds shortest paths from s in this graph. | Numerade
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Let G=(V, E) be a weighted, directed graph with source vertex s, and let G be initialized by INITIALIZE-SINGLE-SOURCE (G, s) . Prove that if a sequence of relaxation steps sets π[s] to a non-NIL value, then G contains a negative-weight cycle. | Numerade
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