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ex2-sol08

# ex2-sol08 - AMS 301.3(Fall 2008 Estie Arkin Exam 2 Solution...

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AMS 301.3 (Fall, 2008) Estie Arkin Exam 2 – Solution sketch Mean 77.8, median 80, high 98, low 50. 1. (10 points) Let T be a balanced 7-ary tree with 100 internal nodes. Show your work! (A correct guess with no work shown will recieve very partial credit.) (a). How many nodes does the tree have? n = mi + 1, m = 7, i = 100, so n = 701, (b). How many edges does the tree have? n 1 = 700. (c). What is the height l = n i = 601, so the height of the tree is log 7 601 = 4. 2. (10 points) (a). Highlight the edges of a minimum spanning tree of the graph. A B C D E F 0 1 5 4 1 (b). Edge (A,D) of cost 4 is added to the graph. Will it be part of the minimum spanning tree? Explain. Yes, it will replace the edge (C,D) of cost 5 as a way to connect D. 3. (8 points) I wish to model the following word problem as a graph problem: The Maytag repairman has been called to repair washers and dryers at several customer’s homes. Assume travel times between locations are known. The repairman starts and ends his day at his home, and would like to complete his work as quickly as possible. (a). What do the nodes of the graph to be constructed represent? repair locations and home. (b). What do the edges of the graph to be constructed represent? Possible travel between locations. (c). State which graph problem it is: Traveling Salesman Problem. 4. (12 points) True or False? If true, give a short proof. If false, give a counterexample: (a). For every connected graph G , the DFS tree on G and the BFS tree on G have the same number of edges. True, since number of edges of any spanning tree is n 1.

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