HW2_Solution - HW1 SOLUTION 1. Chapter 2 Problem 2: Suppose...

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Unformatted text preview: HW1 SOLUTION 1. Chapter 2 Problem 2: Suppose you have algorithms with the six running times listed below.(Assume these are the exact number of operations performed as a function of the input size n .) Suppose you have a computer that can perform 10 10 operations per second, and you need to compute a result in at most an hour of computation. For each of the algorithms, what is the largest input size n for which you would be able to get the result within an hour. (a) n 2 (b) n 3 (c) 100 n 2 (d) n log n (e) 2 n (f) 2 2 n Solution : The operations that a computer can perform within an hour is 10 10 * 3600 (a) n 2 = 10 10 * 3600, we have n = 6 * 10 6 (b) n 3 = 10 10 * 3600, we have n = 3 . 302 * 10 4 (c) 100 n 2 = 10 10 * 3600, we have n = 6 * 10 5 (d) n log n = 10 10 * 3600, we have n ≈ 1 . 291 * 10 12 (e) 2 n = 10 10 * 3600, we have n = log 2 (10 10 * 3600) ≈ 45 (f) 2 2 n = 10 10 * 3600, we have n = log 2 (log 2 (10 10 * 3600)) ≈ 5 Problem 3: Take the following list of functions and arrange them in ascending...
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HW2_Solution - HW1 SOLUTION 1. Chapter 2 Problem 2: Suppose...

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