ps1sol

# Ps1sol - CS161 Design and Analysis of Algorithms Summer 2004 Problem Set#1 Solutions General Notes Regrade Policy If you believe an error has been

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Problem Set #1 Solutions 2 Answer: Most of the ranking is fairly straightforward. Several identities are helpful: n lg lg n = (lg n ) lg n n 2 = 4 lg n n = 2 lg n 2 2 lg n = n 2 / lg n 1 = n 1 / lg n lg * (lg n ) = lg * n - 1 for n > 1 In addition, asymptotic bounds for Stirling’s formula are helpful in ranking the expressions with factorials: n ! = Θ( n n +1 / 2 e - n ) lg( n !) = Θ( n lg n ) (lg n )! = Θ((lg n ) lg n +1 / 2 e - lg n ) Each term gives a diFerent equivalence class, where the > symbol means ω .
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Ps1sol - CS161 Design and Analysis of Algorithms Summer 2004 Problem Set#1 Solutions General Notes Regrade Policy If you believe an error has been

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