Algorithms | Analysis of Algorithms (Recurrences) | Question 11

Consider the following recurrence.

T(n) = T(\sqrt{n}) + \Theta(Log Log n)

What is the value of recurrence?



(A) \Theta( (Log Log n) ^ 2)
(B) \Theta(Log Log n)
(B) \Theta(n)
(B) \Theta(Log Log Log n)

(A) A
(B) B
(C) C
(D) D


Answer: (A)

Explanation:  Change of variables: let m = lg n. Recurrence becomes S(m) = S(m/2) + theta(lgm). Case 2 of master’s theorem applies, so T(n) = theta( (log Log n) ^ 2).

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