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November 10

# November 10 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 10, 2005

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November 10, 2005 Agenda Today Continue Section 7.1 Next week Finish Section 7.1 Do Section 7.2
November 10, 2005 Announcement Quiz next Tuesday (11/15) Big-O and small-o notation Identify Bit-O and small-o relationships Importance of proper encoding (today’s material) This is simplified material from Section 6.4

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November 10, 2005 n, logn, log(log n), and n*log n -50 0 50 100 150 200 250 0 50 100 150 n f(n) n log n log log n n log n
November 10, 2005 log n and log log n -1 -0.5 0 0.5 1 1.5 2 2.5 0 50 100 150 n f(n) log n log log n

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November 10, 2005 n, n log n, n^2, n^2 log n 0 5000 10000 15000 20000 25000 1 12 23 34 45 56 67 78 89 n f(n) n n log n n^2 n^2 log n
November 10, 2005 Small-o vs. big-O Small-o is strictly less than Big-O is less than or equal to For any function f, is f(n) = o(f(n))? No … never! For any function f, is f(n) = O(f(n))? Yes … always!

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November 10, 2005 Some identities n i  = o(n k ) for every i < k log n = o(n) log log n = o(log n)
November 10, 2005 Analyzing algorithms We examine an algorithm to determine how long it will  take to halt on an input of length n

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