day3supp

day3supp - COP 3503 CS II CLASS NOTES - DAY #3 Supplemental...

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CLASS NOTES - DAY #3 – Supplemental Asymptotic Notation Big Oh Notation Definition: Let p(n) and q(n) be two nonnegative functions. The function p(n) is asymptotically bigger [p(n) asymptotically dominates q(n)] than the function q(n) iff The function q(n) is asymptotically smaller than p(n) iff p(n) is asympotically bigger than q(n). Functions p(n) and q(n) are asymptotically equal iff neither is asymptotically bigger than the other. Example 1: Let p(n) = 3n 2 + 2n + 6 and q(n) = 10n + 7. divide both functions by n 2 (to reduce dominant term to a constant) which will produce: Thus, 3n 2 + 2n + 6 is asymptotically bigger than 10n + 7. Similarly, 10n + 7 is asymptotically smaller than 3n 2 + 2n + 6. Example 2: Let p(n) = 6n + 2 and q(n) = 12n + 6 Day #3 Supplemental Material - 1 0 ) n ( p ) n ( q lim n = 2 / 1 12 / 6 n / 6 12 n 2 / 6 ) n by divide ( 6 n 12 2 n 6 lim 2 3 / 6 n / 2 6 n / 6 12 ) n by divide ( 2 n 6 6 n 12 lim n n = = + + = = + + = = + + = = + + 6
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day3supp - COP 3503 CS II CLASS NOTES - DAY #3 Supplemental...

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