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Write an algorithm: Even length paths: We are given the 0/1 adjacency matrix A[V, V] of an n vertex directed graph G = (V, E). Assume all diagonal...

Write an algorithm: Even length paths: We are given the 0/1 adjacency matrix A[V, V] of an n vertex directed graph G = (V, E). Assume all diagonal entries of A are 0 (i.e., G has no self-loops). We want to compute the 0/1 matrix P[V, V], such that for all vertices u and v in G, P[u,v] = 1 if and only if there is a path of even length from vertex u to v in G, where the length of a path is the number of edges on it. Design and analyze an efficient algorithm for this problem. [Hint: also think about odd length paths.]


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