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# Lecture04 - CSE 421 Algorithms Richard Anderson Lecture 4...

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CSE 421 Algorithms Richard Anderson Lecture 4

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Announcements Homework 2, Due October 11, 1:30 pm. Reading Chapter 2.1, 2.2 Chapter 3 (Mostly review) Start on Chapter 4
Today Finish discussion of asymptotics O, , Θ Graph theory terminology Basic graph algorithms

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Formalizing growth rates T(n) is O(f(n)) [T : Z + R + ] If n is sufficiently large, T(n) is bounded by a constant multiple of f(n) – Exist c, n 0 , such that for n > n 0 , T(n) < c f(n) T(n) is O(f(n)) will be written as: T(n) = O(f(n)) Be careful with this notation
Order the following functions in increasing order by their growth rate a) n log 4 n b) 2n 2 + 10n c) 2 n/100 d) 1000n + log 8 n e) n 100 f) 3 n g) 1000 log 10 n h) n 1/2

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Ordering growth rates For b > 0 and x > 0 log b n is O(n x ) For r > 1 and d > 0 n d is O(r n )
Lower bounds T(n) is (f(n)) T(n) is at least a constant multiple of f(n) – There exists an n 0 , and ε > 0 such that T(n) > ε f(n) for all n > n 0 Warning: definitions of vary T(n) is Θ (f(n)) if T(n) is O(f(n)) and T(n) is (f(n))

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Lecture04 - CSE 421 Algorithms Richard Anderson Lecture 4...

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