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Question: let g s t c be a flow network g...

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Let (G, s, t, c) be a flow network, G V,E).A directed edge e (u, v) is called always fullif f(e) c( for all maximum flows f: it is called sometimes full if f()for some but not all maximum flows; it is called never fulliff(e) < c(e) for all maximum flows. Let (S,V \ S be a cut. That is, s E S, t e V \ S. We say the edge e = (u, u)s crossing the cut if u E Sand v EV S. We say e is always crossing if it crosses every minimum cut sometimes crossing if it crosses some, but not all minimum cuts; never crossing if it crosses no minimum cut. For example, look at this flow network e 1 f 2 h:1 The edges e,g are sometimes full and never crossing f is never full and never crossing h is always full and always crossing. Alright, now its your turn. Consider this networik The fat edge a has capcity 2, all other edges have capacity 1. Let r be the number of always full edges, y that of sometimes full edges, that of never full edges. Determine what these numbers are and enter 100z 10y + as the answer. For example, if (, y, ) (2, 3, 4) answer 234: if (z,y,) (0,4, 5), answer 45: if (r, y,)(0,0,9). answer 9 Enter answer here Again refer to the above flow network on eight vertices. Now let z be the number of always crossing edges in the above picture, y that of sometimes crossing edges, and that of never crossing edges. Again, compute 100 10y and enter it as your answer. Enter answer here

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