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Unformatted text preview: Midterm I, Part 1 – Version B Oct. 10, 2011 2:00pm  2:50pm CS431 CS531 (Please circle one) First Name (Print): Last Name (Print): UB ID number: 1. This is a closed book, closed notes exam. 2. You must support your answer. 3. Write your name on the top righthand corner of every page. 4. There are 5 problems and 18 points. in this exam. Name 1. (4 points) Relate the following functions by using Θ ,ω or o notations: g 1 ( n ) = n/ log n , g 2 ( n ) = n 1 . 5 log n , g 3 ( n ) = 4 log 2 n . Answer: g 1 ( n ) = o ( g 2 ( n )) ,g 2 ( n ) = o ( g 3 ( n )) Proof: 1. lim n →∞ n/ log n n 1 . 5 log n = lim n →∞ 1 n . 5 log 2 n = 0 ⇒ n/ log n = o ( n 1 . 5 log n ) 2. lim n →∞ n 1 . 5 log n 4 log 2 n = lim n →∞ n 1 . 5 log n n 2 = lim n →∞ log n n . 5 = lim n →∞ 1 n · 1 ln 2 . 5 n . 5 = lim n →∞ 2 ln 2 · 1 n . 5 = 0 ⇒ n 1 . 5 log n = o (4 log 2 n ) 1 Name 2 (3 points). Suppose that we have the following algorithm for solving the matrix multiplication problem. We divide each of the matricesproblem....
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This note was uploaded on 02/27/2012 for the course CSE 431/531 taught by Professor Xinhe during the Fall '11 term at SUNY Buffalo.
 Fall '11
 XINHE
 Algorithms

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