# a4 - relations T(1 = 3 T(2 = 7 and T n ≤ T b n 2 c T d n...

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York University EECS 3101 September 30, 2015 Homework Assignment #4 Due: October 8, 2015 at 4:00 p.m. 1. Is log n O (log n )? Prove your answer is correct. 2. Is n ! O (2 n )? Prove your answer is correct. 3. Willemina has devised a recursive algorithm. Let T ( n ) be the worst-case running time of her algorithm on inputs of size n . Willemina determines that T ( n ) satisfies the following
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Unformatted text preview: relations. T (1) = 3 , T (2) = 7 , and T ( n ) ≤ T ( b n/ 2 c ) + T ( d n/ 6 e + 1) + 3 n, for n ≥ 3 (a) What is max { T ( n ) /n : 1 ≤ n ≤ 200 } ? You do not have to prove your answer is correct. (b) Give a careful proof that T ( n ) ∈ O ( n ). Hint: The Master Theorem does not apply to T . 1...
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