MIT6_042JF10_rec13

MIT6_042JF10_rec13 - equality. Hint an = a 2 log 2 n . 1 1...

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6.042/18.062J Mathematics for Computer Science October 22, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 13 1 Asymptotic Notation Which of these symbols Θ O Ω o ω can go in these boxes? (List all that apply.) 2 n + log n = ( n ) log n = ( n ) n = (log 300 n ) n 2 n = ( n ) n 7 = (1 . 01 n )
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Recitation 13 2 2 Asymptotic Equivalence Suppose f,g : Z + Z + and f g . 1. Prove that 2 f 2 g . 2. Prove that f 2 g 2 . 3. Give examples of f and g such that 2 f 2 g . 4. Show that is an equivalence relation 5. Show that Θ is an equivalence relation 3 More Asymptotic Notation 1. Show that ( an ) b/n 1 . where a,b are positive constants and denotes asymptotic
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Unformatted text preview: equality. Hint an = a 2 log 2 n . 1 1 n n . 2. You may assume that if f ( n ) ≥ 1 and g ( n ) ≥ 1 for all n , then f ∼ g ⇒ f ∼ g Show that n √ n ! = Θ( n ) . MIT OpenCourseWare http://ocw.mit.edu 6.042J / 18.062J Mathematics for Computer Science Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This note was uploaded on 01/19/2012 for the course CS 6.042J / 1 taught by Professor Tomleighton,dr.martenvandijk during the Fall '10 term at MIT.

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MIT6_042JF10_rec13 - equality. Hint an = a 2 log 2 n . 1 1...

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