Analysis 2.2

# Analysis 2.2 - Definition of Theta 3n2 + 7n + 8 = (n2) True...

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Last Updated: 10/01/12 5:45 AM CSE 2011 Prof. J. Elder - 56 - Definition of Theta 3n 2 + 7n + 8 = θ (n 2 ) 3 4 8 n 8 True > ∀ ≥ ,, 1 2 0 0 1 2 0 : , ( ) ( ) ( ) c c n n n c g n f n c g n 3 2 ! 3 2 + 7 + 8 ! 4 2

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Last Updated: 10/01/12 5:45 AM CSE 2011 Prof. J. Elder - 57 - Notations Theta f(n) = θ (g(n)) f(n) c g(n) Big Oh f(n) = O(g(n)) f(n) c g(n) Big Omega f(n) = Ω (g(n)) f(n) c g(n) Little Oh f(n) = o(g(n)) f(n) << c g(n) Little Omega f(n) = ω (g(n)) f(n) >> c g(n)
Last Updated: 10/01/12 5:45 AM CSE 2011 Prof. J. Elder - 58 - Time Complexity of an Algorithm O(n 2 ): For any input size n n 0 , the algorithm takes no more than cn 2 time on every input. Ω (n 2 ): For any input size n n 0 , the algorithm takes at least cn 2 time on at least one input. θ (n 2 ): Do both. The time complexity of an algorithm is the largest time required on any input of size n.

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## This note was uploaded on 02/14/2012 for the course CSE 2011Z taught by Professor Elder during the Fall '11 term at York University.

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Analysis 2.2 - Definition of Theta 3n2 + 7n + 8 = (n2) True...

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