Please answer part c

Question 1 (25 points) We are given a directed flow network G (V, E), with positive integral capacities c(e) on edges e e E, a source s and a sink t. Recall that an s-t cut in G is a partition (A, B) of the vertices of V, such that s E A and te B. An s-t cut (A, B) is a minimum cut iff the value C(A, B) = {(u, v)EB: C(u, v) is minimal among all s-t cuts. Notice that it is possible for a graph to contain several minimum s-t cuts. UEA,VEB a. Show an example of a flow network that contains 29(n) minimum s-t cuts, where n = |V]. b. Show an example of a flow network that contains a unique minimum s-t cut (that is, the number of minimum s-t cuts in the flow network is 1). c. Show an efficient algorithm to determine whether G contains a unique minimum s-t cut, or the number of such cuts is greater than 1. Prove the algorithm's correctness