Problem 1 Like our ordinary shortest path problem, the bottleneck shortest path. problem is dened on a directed network in which each arc has an associated length. The problem is to nd a path from a given node 3 to a given node t such that the length of the longest arc in that path is minimized. Show that if there exists a polynomial time algorithm for the ordinary shortest path problem: then there exists a polynomial time algorithm for the bottleneck shortest path problem. (Hint: treat the algorithm for ordinary shortest paths as a subroutine or 'hlack boa-cI and show how you would make {repeated} use of it to solve the bottleneck problem.)