17. You've been called in to help some network administrators diagnose the extent of a failure in their network. The network is designed to carry traffic from a designated source node s to a designated target node t, so we will model the network as a directed graph G= (V,E), in which the capacity of each edge is 1 and in which each node lies on at least one path from s to t. Now, when everything is running smoothly in the network, the max imum s-t flow in G has value k. However, the current situation (and the reason you're here) is that an attacker has destroyed some of the edges irn the network, so that there is now no path from s to t using the remaining (surviving) edges. For reasons that we won't go into here, they believe the attacker has destroyed only k edges, the minimum number needed to separate s from t (i.e., the size of a minimum s-t cut); and we'll assume they're correct in believing this. The network administrators are running a monitoring tool on node s, which has the following behavior. If you issue the command ping(v), for a given node v, it will tell you whether there is currently a path from s to u(SO ping() reports that no path currently exists; on the other hand