Let G=(V,E) be the following weighted undirected graph: V={1,2,3,4,5} and

E={[(4, 2) 5], [(1, 2) 10], [(5, 2) 3], [(4, 1) 2], [(1, 3) 2], [(5, 1) 5], [(3, 5) 2]} where [(i,j) a] means that (i,j) is an edge of weight a.

Apply the all pairs shortest path algorithm to find the distance between every pair of nodes in G. (Represent the weights by a matrix A, and show the matrix A(k) after each step, for k=1,2,3,4,5.