lecture 5 (big-oh)

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Calculus - Geometry

user_hodr Created by 6 mon ago

Cards in this deck(15)

a = b^c

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log(a) + log(c)

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log(a) - log(c)

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c log(a)

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log c (a) / log c (b)

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c is the constant of g(n) n0 is the n in which f(n) <= cg(n) for all n after n0

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find a g(n) such that f(n) <= g(n) and use that to find c and n0 - lim n->infinity (f(n) / g(n)) = 0 or C

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can prove by multiplying d(n) <= f(n) by constant a and setting ac = c so that ????????(????) <= ????(????)

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can prove by adding inequalities d(n) <= c1f(n) and e(n) <= c2g(n) to get d(n) + e(n) <= c1c2 f(n)+g(n)

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similar technique to prev

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d(n) <= c1f(n) <= c2g(n) so ????(????) <= c3????(????)

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d is the highest power of f(n) and since g(n) is of the same degree, f(n) <= cg(n)

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find a g(n) such that f(n) >= g(n) and use that to find c and n0 - lim n->infinity (f(n) / g(n)) = c or infinity

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find a g(n) such that f(n) = g(n) and use that to find c and n0 - lim n->infinity (f(n) / g(n)) = 0

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O(1) O(loglogn) O(logn) O(sqrt n) O(n) O(nlogn) O(n^k) O(a^n) O(n!) O(n^n)

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