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If fn 100n for even n and fn n 2 for odd n then fn

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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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