Unformatted text preview: 100n for even n and f(n) = n 2 for odd n, then
f(n) = O(n2). Also f(n) = Ω (n). n is not O(n2). Demonstrate proof styles in class. 6 [email protected] Properties
If f(n) = O(h(n)) and g(n) = O(h(n)), then f(n)
+g(n)=O(h(n)). If f(n) = O(g(n)) and g(n) = O(h(n)), then f(n)=O(h(n)). If f(n) = O(g(n)) and c is a nonnegative constant,
then c f(n) = O(g(n)). What can you say about Ω ? If f(n)=O(g(n)), then g(n)= Ω (f(n)). 7 [email protected] Theta Notation
θ (g(n)) = { f(n): ∃ positive constants c1, c2 and N s.t.
c1• g(...
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 Fall '08
 Davulcu,H
 Algorithms, Data Structures, Big O notation, Analysis of algorithms, Asymptotic analysis, Random access machine

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