Exam1s05 - COT 5405 Analysis of Algorithms On-Campus Exam#1...

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COT 5405 Analysis of Algorithms Spring 2005 On-Campus Exam #1 Name: __________________________________________ UFID: ____________ - ____________ E-mail: _________________________________________ Instructions: 1. Write neatly and legibly. 2. While grading, not only your final answer but also your approach to the problem will be evaluated. 3. You have to attempt only TWO problems. If you attempt more than two problems, we will grade ANY two of OUR choice. 4. Each problem carries 10 points. 5. Total time for the exam is 60 minutes. 6. You are not allowed to use a calculator for this exam. I have read carefully, and have understood the above instructions. On my honor, I have neither given nor received unauthorized aid on this examination. Signature: _____________________________________ Date: ____ (MM) / ____ (DD) / ___________ (YYYY) Analysis of Algorithms Spring 2005 On-Campus Exam #1 Page 1 of 7
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Question 1: Solve the recurrence relation ( without using Masters theorem) T ( n ) = 2 T ( n /2) + log n 2 n [the last term is log of 2 n to the base of n ] Make any reasonable assumptions. Find an exact formula for T ( n ) and then give an asymptotic expression.
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