(Shortest-paths optimality criteria) Demonstrate Proposition P. Let G be an edge-weighted digraph, with s as a source vertex in G and distTo[] a vertex-indexed array of path lengths in G such that the value of distTo[v] is the length of some path from s to v for all v accessible from s, and distTo[v] equal to infinity for all v not reachable from s. These are the lengths of the shortest routes if and only if they meet distTo[w] = distTo[v] + e.weight() for each edge e from v to w (or no edge is eligible).

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A:

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