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Lecture04 - Announcements CSE 421 Algorithms Richard...

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1 CSE 421 Algorithms Richard Anderson Lecture 4 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 Formalizing growth rates T(n) is O(f(n)) [T : Z + Æ R + ] – If sufficiently large n, 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 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 )

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2 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
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Lecture04 - Announcements CSE 421 Algorithms Richard...

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