Prelim1_q3sol - 3. (30) Consider a n u ndirected g raph G =...

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3. (30) Consider an undirected graph G = (V, E), where each undirected edge {i,j} has a corre- sponding cost c{ i, j}, which is an input to the minimum spanning tree problem. Suppose that V {I, 2, . .. ,20}. You have already computed a minimum spanning tree in the graph G, but have lost part of the answer. You still know all of the edges with both endpoints among the nodes {I, 2, . .. , 10} (there are k of them). You also still know all of the edges with both endpoints among the nodes {ll, 12, ... ,20} (there are C of them). What you have lost are all of the edges that have one endpoint among the nodes {I, 2, ... , 1O} and one endpoint among the nodes {ll, 12, ... , 20} . (a) (15) How many edges have you los~~Hint: how many edges are there in the minimum spanning tree?) A ItA S T "Uob 1i.:;'6'" \-:: 1,0-1 ~ (9 t.O'jt'!l. We. .,.",.,. .... k +1 eJ.j~ 1. C We need tq-~ .... J r-1&lrL (b) (15) Suppose that the following table gives a complete list of all of the edges in G with one endpoint in {I, 2, . .. ,10} and one endpoint in {ll, 12,
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