Problem 5 Suggest a modication of Dijkstraa method that is specically designed to solve the longest path problem. Here we want the algorithm to change to meet a new class of problem, rather than the other wayr around; hence it is not acceptable to have the rst step of your algorithm be to convert a longest path problem to a shortest path problem. Prove [with a logical argument] or disprove {with a counterexample} each of the following statements: [a] My algorithm always succeeds in solving the longest path problem when all are lengths are nonpositive. [in] My algorithm always succeeds in solving the longest path problem when all are lengths are nonnegative. [c] My algorithm alwan succeeds in solving the longest. path