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master theorem

A three-case rule that reads off a divide-and-conquer recurrence's growth rate directly from its parameters.

For $T(n)=aT(n/b)+f(n)$ with $f(n)=\Theta(n^d)$ , the master theorem compares $d$ to $\log_b a$ to name $T(n)$ 's growth rate in one of three cases, no recursion tree required.