Shortest paths are not always unique: sometimes there are two or more different paths with the minimum possible length. Show how to solve the following problem in O((|V| + |E |) log |V|) time.
Input: An undirected graph G = (V, E); edge lengths le > 0; starting vertex s ∈ V.
Output: A Boolean array u s p[.]: for each node u, the entry u s p[u] should be t r u e if and only if there is a unique shortest path from s to u. (Note: u s p[s] = t r u e.)
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