Asymptotic_Notation

# Asymptotic_Notation - Asymptotic Notation& Review of...

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Asymptotic Notation& eview of Functions Review of Functions 8 October 2008 CS 570

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Θ -notation For function g ( n ), we define Θ ( g ( n )), big-Theta of n , as the set: Θ ( g ( n )) = { f ( n ) : positive constants c 1 , c 2 , and n 0, such that n n 0 , we have 0 c 1 g ( n ) f ( n ) c 2 g ( n ) } Intuitively : Set of all functions that isan symptotically tight bound r have the same rate of growth as g ( n ). asymp - 1 Comp 122 g ( n ) is an asymptotically tight bound for f ( n ).
-notation For function g ( n ), we define O ( g ( n )), big-O of n , as the set: O ( g ( n )) = { f ( n ) : positive constants c and n 0, such that n n 0 , we have 0 f ( n ) c g ( n ) } Intuitively : Set of all functions whose rate of growth is the same as r lower than that of g ( n ) is an asymptotic upper bound for f ( n ). or lower than that of g ( n ). = = asymp - 2 Comp 122 f ( n ) = Θ ( g ( n )) f ( n ) = O ( g ( n )). Θ

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## This note was uploaded on 01/24/2011 for the course CS 570 at USC.

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Asymptotic_Notation - Asymptotic Notation& Review of...

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