6ehw1 - T n is Θ(1 for n ≤ 4(a T n = √ 2 T n 2 √...

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National Taiwan University Handout #4 Department of Electrical Engineering October 8, 2009 Algorithms, Fall 2009 Yao-Wen Chang Name: Student ID: Web ID: Problem 1. (12 pts) For the following functions, rank them from the slowest (with the lowest complexity) to the fastest growing. n 1 / 3 , n · (lg n ) 3 , ( n ) lg n , (lg n ) 30 Problem 2. (18 pts) For each of the following recurrence relations, give the asymptotic growth rate of the solution using the Θ notation. Assume in each case that
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Unformatted text preview: T ( n ) is Θ(1) for n ≤ 4. (a) T ( n ) = √ 2 · T ( n/ 2) + √ n . (b) T ( n ) = 3 · T ( n/ 2) + n/ lg n . (c) T ( n ) = T ( n/ 2) + T ( n/ 3) + n . Problem 3. (12 pts) Is 2 n 2 + 5 n-8 = O ( n 2 ) correct? Disprove the statement, or prove it by determining the smallest integer constant c and then the smallest integer constant n in the definition of O-notation....
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