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Big Omicron and big Omega and big Theta Jiaheng Lu Renmin University of China

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Big Omicron O(f(n)) denotes the set of all g(n) that there exist positive constants C and m with g(n) =m O(f(n)) can be read as “order at most f(n)”. E.g. g(n) = n 3 +n 2, f(n)=n 3

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Big Omega Ω(f(n)) denotes the set of all g(n) that there exist positive constants C and m with g(n) >= C*f(n) for all n >=m Ω(f(n)) can be read as “order at least f(n)”. E.g. g(n) = n 3 +n 2, f(n)=n 3

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Big Theta Θ(f(n)) denotes the set of all g(n) that there exist positive constants C, C’ and m with C*f(n) =m Θ(f(n)) can be read as “order exactly f(n)”. E.g. g(n) = log 10 n, f(n)= log 2 n

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