Recall the little master theorem

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Reference no: EM133550300

Question: In this problem, when the base of a logarithm is left unspecified, it is taken to be base-2. So, log n means log2 n.

(a) Recall the Little Master Theorem (LMT). It was shown there, using the iteration method, that T(n) = Θ(n log_b a ) if a > b. Use a similar approach to establish that T(n) = Θ(n log n) if a = b and T(n) = Θ(n) if a < b. Assume that n = b^k for some k ≥ 0, (Note that a Θ(·) bound is sought here, not O(·).)

(b) Use the Master Theorem (MT) to solve the following recurrence: T(1) = Θ(1) and, for n > 1, T(n) = 2T(n/4) + n log n. Be sure to identify clearly which case of the MT applies.

(c) Use the Master Theorem (MT) to solve the following recurrence: T(1) = Θ(1) and, for n > 1, T(n) = 2T(n^(1/4) ) + 1. Be sure to identify clearly which case of the MT applies.

Reference no: EM133550300

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