HW01 - N ≥ 0 such that f N ≤ g N but f N 1> g N 1...

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CSE450/598 Design And Analysis of Algorithms HW01, Wednesday, 09/02/2009, Due: Monday, 09/14/2009 Please note that you have to typeset your assignment using either L A T E X or Microsoft Word. Hand-written assignment will not be graded. Please submit a hard copy in class before the lecture, and submit an e-copy using the drop box at the class website. 1. (10 pts) Let f ( n ) = 0 . 01 n 2 and g ( n ) = 1000 × n × log 2 ( n + 3). Find the smallest integer
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Unformatted text preview: N ≥ 0 such that f ( N ) ≤ g ( N ) but f ( N + 1) > g ( N + 1). Show the values of N , f ( N ), g ( N ), f ( N + 1) and g ( N + 1). ( CSE450 students only .) 2. (10 pts) Prove or disprove Θ( n 3 ) + O ( n 4 ) = Θ( n 4 ). 3. (10 pts) Exercise 3.5 (p.108) 4. (10 pts) Exercise 3.8 (p.109) 5. (10 pts) Exercise 3.10 (p.110) 6. (10 pts) Exercise 3.11 (p.111) ( CSE598 students only .) 1...
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