CS70_Exam 2- Summer 2007 solution

CS70_Exam 2- Summer 2007 solution - CS570 Analysis of...

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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/FALSE ] TRUE Binary search could be called a divide and conquer technique [ TRUE/FALSE ] FALSE If you have non integer edge capacities, then you cannot have an integer max flow [ TRUE/FALSE ] TRUE The Ford Fulkerson algorithm with real valued capacities can run forever [ TRUE/FALSE ] TRUE 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 [ TRUE/FALSE ] TRUE 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 b.
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