![Theorem 4.1 (Master theorem) Let a 1 and b 1 be constants, let f(n) be a function, and let T(n) be defined on the nonnegative integers by the recurrence where we interpret n/b to mean either [n/b] or [n/b]. Then T(n) has the follow- ing asymptotic bounds: 1. If f(n) O(nogb-) for some constant >0, then T(n) e(n 2. If f(n) = ?(nlogba), then T(n)= ?(nogb algn). 3. If f(n) = ?(nlogba4e) for some constant E > 0, and if af(n/b) cf(n) for some constant c < 1 and all sufficiently large n, then T(n) - S(f(n). -](https://media.cheggcdn.com/media%2F2a9%2F2a9ac39c-faf7-4553-8762-77719f7556da%2FphpRKGC4z.png)
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