midtermI1a-sol-2011

midtermI1a-sol-2011 - Midterm I Part 1 – Version A Oct 10...

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Unformatted text preview: Midterm I, Part 1 – Version A 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 right-hand 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: f 1 ( n ) = n log n , f 2 ( n ) = 4 log 2 n , f 3 ( n ) = n 1 . 5 / log n . Answer: f 1 ( n ) = o ( f 3 ( n )) ,f 3 ( n ) = o ( f 2 ( n )) Proof: 1. lim n →∞ n log n n 1 . 5 / log n = lim n →∞ log 2 n n . 5 = lim n →∞ 2 log n 1 n . 5 ln 2 n- . 5 = 4 ln 2 lim n →∞ log n n . 5 = 4 (ln 2) 2 lim n →∞ 1 /n . 5 n- . 5 = 8 (ln 2) 2 lim n →∞ 1 n . 5 = 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 →∞ 1 n . 5 log n = 0 ⇒ n 1 . 5 log n = o (4 log 2 n ) 1 Name 2. (4 points) Let f (...
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midtermI1a-sol-2011 - Midterm I Part 1 – Version A Oct 10...

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