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How would you modify the Floyd-Warshall algorithm on a weighted, directed graph G = (V,E) to solve the following problems? Carefully justify your answer in each case:a) Find the number of shortest paths between each pair of vertices.b) Find the number of simple paths of even length and of odd length between each pair of vertices.

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(a) Run the Floyd-Warshall algorithm on the weighted, directed graph given in Figure 4. Show the matrix D^(k) that result for EACH iteration of the outer loop. [15 points]12123-42-1710-854563Figure 4(b) Use Johnson's algorithm to find the shortest paths between all pairs of vertices in Figure 4. Show the values of h and wh computed by the algorithm in a tabular form. [15 points]

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