# hw7-review - (f If f n = Θ g n and h n = Θ g n then f n h...

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CS 173: Discrete Structures, Spring 2010 Review problems for second quiz You should do these problems to help prepare for the second quiz. Solutions will be posted but you don’t have to turn them in. 1. Big-O notation For each of the following pairs of functions state whether f ( n ) = O ( g ( n )) or f ( n ) = Ω( g ( n )) or f ( n ) = Θ( g ( n )) (a) f ( n ) = n 2 and g ( n ) = n 2 . (b) f ( n ) = ( log 10 ( n )) 2 and g ( n ) = n. (c) f ( n ) = n 2 n and g ( n ) = n n 2 (d) f ( n ) = n ! and g ( n ) = n n (e) f ( n ) = 2 n + n and g ( n ) = 3 n Determine whether each statement below is true or false.
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Unformatted text preview: (f) If f ( n ) = Θ( g ( n )) and h ( n ) = Θ( g ( n )) then f ( n ) h ( n ) = Θ( g ( n )). (g) If f ( n ) = Ω( g ( n )) and h ( n ) = Ω( g ( n )) then f ( n ) + h ( n ) = Ω( g ( n )). (h) If f ( n ) = O ( g ( n )) then g ( n ) = Ω( f ( n )). (i) If f ( n ) = Θ( g ( n )) then g ( n ) = Θ( f ( n )) (j) If f ( n ) = log a ( n ) for a > 2 then f ( n ) n = Θ( log 2 ( n )). 1...
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