1.)The following is the adjacency matrix representing a digraph.

?0 0 1 0 0 0?

?0 0 1 0 0 1 ?

? 0 0 0 0 1 0 ?

? 1 0 0 0 1 0 ?

?0 0 1 0 0 1 ?

? 0 0 0 0 0 0?

Use Warshalls algorithm to create the transitive closure of the digraph. Please represent the transitive closure as a matrix. You are required to show the intermediate results as well.

2)The following is the weight matrix representing a digraph of vertices a, b, c, d, e, and f.

?0 4 ? ? ? 2?

? 1 0 3 4 ? ? ?

? 6 3 0 7 ? ? ?

? 6 ? ? 0 2 ? ?

? ? ? ? 5 0 ??

|_ ? ? ? 2 3 0_|

2.1 Use the Floyds algorithm to solve the all-pairs shortest-path problem. Please repre-

sent the result as a distance matrix. You are required to show the intermediate results. 2.2 Use the Dijkstras algorithm to solve the single-source shortest-paths problem. The

source node is a. Break a tie using the alphabetic order.