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CS223-0122-Analysis

# CS223-0122-Analysis - Algorithm Analysis Neil Tang CS223...

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CS223 Advanced Data Structures and Algorithms 1 Algorithm Analysis Algorithm Analysis Neil Tang Neil Tang 01/22/2008 01/22/2008

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CS223 Advanced Data Structures and Algorithms 2 Algorithm and Complexity Algorithm and Complexity Algorithm : A clearly specified set of instructions to be followed to solve a problem. Characteristics of an algorithm: - input - output - stop on any input Time complexity: The number of operations required. Best vs. average vs. worst case complexity. Space complexity: The amount of memory required.
3 Asymptotic Notations Asymptotic Notations T(N) = O(f(N)) if there exist positive constants c and n 0 , s.t. T(N) cf(N) when N n 0 T(N) = (g(N)) if there exist positive constants c and n 0 , s.t. T(N) cg(N) when N n 0 T(N) = Θ (h(N)) iff T(N) = O(h(N)) and T(N) = (h(N)) T(N) = o(p(N)) if T(N) = O(p(N)) and T(N) Θ (p(N)) O-notation is used to determine an upper bound on the order of growth

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CS223-0122-Analysis - Algorithm Analysis Neil Tang CS223...

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