Recent questions tagged cormen

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Prove that the running time of an algorithm is $\Theta (g(n))$ if and only if its worst-case running time is $O(g(n))$ and its best-case running time is $\Omega(g(n))$.
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Let $f(n)$ and $g(n)$ be asymptotically nonnegative functions. Using the basic definition of $\Theta$ notation, prove that $max(f(n),g(n)) = \Theta(f(n)+g(n))$.
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