i, Theorem 4.1 (Master Theorem). Let > 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 T(n) - aT(n/b)+(n) where we take n/b to be either floor(n/b) or ceil(n/b). Then T(n) has the following asymptotic bounds 1. If f(n) O(no() for some constante >0, then T(n)- e()) 2. If f(n) = ((a)), then T(n) = (nlog.(a) Ig(n)). 3. If f(n) = (nlo.(.)+-) fr some constant > 0, and if af(n/b) cf(n) for some constant e