UGC-NET | UGC NET CS 2017 Jan – III | Question 31

The asymptotic upper bound solution of the recurrence relation given by

(A) O(n²)
(B) O(n lg n)
(C) O(n lg lg n)
(D) O(lg lg n)


Answer: (C)

Explanation:
We will apply master theorem in this question:
a = 2, b = 2 and k =1 and p = -1.
we will compare a and b^k
ie

2 = 21 and we have p = -1
Then T(n) = Θ(nlog22log log n)
     T(n) = Θ(nlog log n)   
and Θ(n log log n) >= O(n log log n)

So, option (C) is correct.

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