GATE | GATE-CS-2003 | Question 70

Let G (V, E) be a directed graph with n vertices. A path from v_i to v_j in G is sequence of vertices (v_i, v_i+1, ......., v_j) such that (vk, v_k+1) ∈ E for all k in i through j - 1. A simple path is a path in which no vertex appears more than once. Let A be an n x n array initialized as follow

Consider the following algorithm.

for i = 1 to n
   for j = 1 to n
      for k = 1 to n
         A [j , k] = max (A[j, k] (A[j, i] + A [i, k]);

Which of the following statements is necessarily true for all j and k after terminal of the above algorithm ?

(A)

A[j, k] ≤ n

(B)

If A[j, k] ≥ n - 1, then G has a Hamiltonian cycle

(C)

If there exists a path from j to k, A[j, k] contains the longest path lens from j to k

(D)

If there exists a path from j to k, every simple path from j to k contain most A[j, k] edges

Answer

Please comment below if you find anything wrong in the above post
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