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Unformatted text preview: Computer Science I Summer 2011 Recitation #4: Algorithm Analysis (Solutions) 1)For an O(n 3 ) algorithm, one data set with n = 3 takes 54 seconds. How long will it take for a data set with n = 5? Solution Let T(n) be the function for the run time of the algorithm. Then, T(n) = cn 3 for some constant c. T(3) = c3 3 = 54 27c = 54, so c = 2 T(5) = c5 3 = 2(125) = 250 seconds. 2)For an O(2 n ) algorithm, a friend tells you that it took 17 seconds to run on her data set on a O(2 n ) algorithm. You run the same program, on the same machine, and your data set with n = 7 takes 68 seconds. What size was her data set? Solution Let T(n) be the function for the run time of the algorithm. Then, T(n) = c2 n for some constant c. T(7) = c2 7 = 68 128c = 68, so c = 68/128 = 17/32. T(n) = c2 n = 17(2 n )/32 = 17, so 2 n = 32 and n = 5. 3)For an O(N k ) algorithm, where k is a positive integer, an instance of size M takes 32 seconds to run. Suppose you run an instance of size 2M and find that it takes 512 seconds to run. What is to run....
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 Spring '08
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 Computer Science

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