CS70_Exam%202%20Summer%202007%20Solution

CS70_Exam%202%20Summer%202007%20Solution - CS570 Analysis...

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CS570 Analysis of Algorithms Summer 2007 Exam 2 Name: _____________________ Student ID: _________________ Maximum Received Problem 1 10 Problem 2 20 Problem 3 20 Problem 4 10 Problem 5 20 Problem 6 20 Note: The exam is closed book closed notes.
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1) 10 pts Mark the following statements as TRUE or FALSE . No need to provide any justification. True [ TRUE/FALSE ] Binary search could be called a divide and conquer technique False [ TRUE/FALSE ] If you have non integer edge capacities, then you cannot have an integer max flow Ture [ TRUE/FALSE ] The Ford Fulkerson algorithm with real valued capacities can run forever Ture [ TRUE/FALSE ] If we have a 0-1 valued s-t flow in a graph of value f, then we have f edge disjoint s- t paths in the graph Ture [ TRUE/FALSE ] Merge sort works because at each level of the algorithm, the merge step assumes that the two lists are sorted
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2) 20pts Prove or disprove the following for a given graph G(V,E) with integer edge capacities Ci a. If the capacities on each edge are unique then there is a unique min cut Disprove : b. If we multiply each edge with the same multiple “f”, the max flow also gets multiplied by the same factor Prove: For each cut (A, B) of the graph G, the capacity c(A, B) will be multiplied by “f”
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CS70_Exam%202%20Summer%202007%20Solution - CS570 Analysis...

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