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2 Q2 In general, a flow network G = (V, E, s, t, c) with integer edge capacities may not have a unique min-cut. a) (2 points) Describe an example G that has exponentially many (non-zero) min-cuts, i.e., the number of min-cuts is at least C\V for some constant C > 1. Your graph should contain at least 100 vertices and the capacity of the min-cut should be non-zero. For each of the following problems, your algorithm should take the network G as an input and output the set S containing s in the cut (S, T). Your algorithm should have the same asymptotic running time as Ford-Fulkerson algorithm. b) (4 points) We would like to find the min-cut in G with the fewest number of edges across the cut. Write pseudocode for an algorithm which solves this problem. 2 Q2 In general, a flow network G = (V, E, s, t, c) with integer edge capacities may not have a unique min-cut. a) (2 points) Describe an example G that has exponentially many (non-zero) min-cuts, i.e., the number of min-cuts is at least C\V for some constant C > 1. Your graph should contain at least 100 vertices and the capacity of the min-cut should be non-zero. For each of the following problems, your algorithm should take the network G as an input and output the set S containing s in the cut (S, T). Your algorithm should have the same asymptotic running time as Ford-Fulkerson algorithm. b) (4 points) We would like to find the min-cut in G with the fewest number of edges across the cut. Write pseudocode for an algorithm which solves this