Problem 14: Problem 26-5, Page 694; (CLRS) Let G = (V, E) be a ow network with source .9, sink t, and an integer capacity C(u, v) on each edge (um) E E. Let C = maxmnaeE c(u,v). a. b. Argue that a minimum cut of G has capacity at most 0 IE I For a given number K, show that an augmenting path of capacity at least K can be found in 0(E) time, if such a path exists. Argue that MAX-FIOW-BYSCALING return a maximum ow. Show that the capacity of a minimum cut of the residual graph G f us at most 2K IE I each time line 4 is executed. Argue that inner while loop of line 5-6 executed 0(E) times for each value of K. Conclude that MAX-FLOWBYSCALING can be implemented so that it runs in 0(E2lgC) time. The following modication of FORD-FULKERSONMETHOD can be used to compute the maximum ow in G