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fall_2007_midterm1

# fall_2007_midterm1 - CS570 Analysis of Algorithms Fall 2007...

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CS570 Analysis of Algorithms Fall 2007 Exam I Name: _____________________ Student ID: _________________ Maximum Received Problem 1 20 Problem 2 20 Problem 3 12 Problem 4 12 Problem 5 12 Problem 6 12 Problem 7 12 Note: The exam is closed book closed notes.

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1) 20 pts Mark the following statements as TRUE , FALSE . No need to provide any justification. [ TRUE/FALSE ] A greedy algorithm is any algorithm that follows the heuristic of making the locally optimum choice at each stage with the hope of finding the global optimum. T [ TRUE/FALSE] BFS can be used to find the shortest path between any two nodes in a weighted graph. F [ TRUE/FALSE] DFS can be used to find the shortest path between any two nodes in a non-weighted graph. F [ TRUE/FALSE] BFS can be used to test whether a graph is bipartite T [ TRUE/FALSE ] If T is a spanning tree of G and e an edge in G which is not in T, then the graph T+e has a unique cycle. T [ TRUE/FALSE ] Let T be a spanning tree of a graph G and e an edge of G which is not in T. For any edge f that is on a cycle in graph T+e, the graph T + e f is a spanning tree. T [ TRUE/FALSE ] Given a graph G(V,E) with distinct costs on edges and a set S V, let (u, v) be an edge such that (u, v) is the minimum cost edge between any vertex in S and any vertex in V-S. Then, the minimum spanning tree of G must include the edge (u, v). T [ TRUE/FALSE ] If f, g, and h are positive increasing functions with f in O(h) and g in (h), then the function f+g must be in Θ (h). F [ TRUE/FALSE ] If a divide and conquer algorithm divides the problem is half at every step, the log(n) factor related to the depth of the recursion tree will cause the algorithm to have a lower bound of (n log(n)) F [ TRUE/FALSE ] Suppose that in an instance of the original Stable Marriage problem with n couples, there is a man M who is last on every woman's list and a woman W who is last on
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fall_2007_midterm1 - CS570 Analysis of Algorithms Fall 2007...

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