Consider the following recurrence relation:

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What will be complexity of above relation?
(A) O(n)
(B) O(√n )
(C) O(log2n)
(D) O(nlog2n)


Answer: (C)

Explanation:

T(n) = T(n / 2) + C
= T(n / 4) + C + C
= T(n / 8) + 3*C
.
.
. 

N will be divided until it becomes 1. So,

= T(n / 2k) + (k-1) * C
That means, n / 2k = 1 
= k = log2n 

T(n) = 1 + (log2n - 1) * C
T(n) = O(log2n) 

So, option (C) is correct.

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  • Last Updated : 19 Nov, 2018

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