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CS336f1012

# CS336f1012 - Lecture 12 CS336 S10 Asymptotic Dominance...

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10/13/10 1 Lecture 12 CS336 S10 Asymptotic Dominance Uses for Big‐O Give a big‐O estimate for (log(n!+2 n )). For your estimate, use the simplest function of the smallest order.

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10/13/10 2 Uses for Big‐O Give a big‐O estimate for (log(n!+2 n )). For your estimate, use the simplest function of the smallest order. nlogn Give a big‐O estimate for (n+3n 2 )(log n!+ 2 n + logn 3 ). For your estimate, use the simplest function of the smallest order.
10/13/10 3 Give a big‐O estimate for (n+3n 2 )(log n!+ 2 n + logn 3 ). For your estimate, use the simplest function of the smallest order. n 2 2 n Example Estimate the running time So the running time is O(n)

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10/13/10 4 For Algorithm 3 Before after time n n‐1 n n‐1 n‐2 n‐1 1 0 1 For Algorithm 4 Before after time n=2 p n/2 p n/2=2 p‐1 n/4 p‐1 2 1 1
10/13/10 5 Example First the inner loop Example Before after time 1 2 c 2 4 2c n=2 p 2 p c

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10/13/10 6 Prove that every nonempty, full binary tree has an odd number of nodes. Recall, with our
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CS336f1012 - Lecture 12 CS336 S10 Asymptotic Dominance...

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