Question: Suppose that we have a directed graph with no directed cycles. We are given a length dij for each directed arc (i, j) and we want to compute a shortest path to node I from all other nodes, assuming there exists at least one such path. Show that nodes 2,3, ... , N can be renumbered so that there is an arc from i to j only if i > j. Show that once the nodes are renumbered, Bellmans equation can be solved with O(N2) operations at worst.