What is the time complexity of the following function?

Question

    int func(int n){
       if(n==1)
         return 0;
       else
         return sqrt(n);
    }

Where sqrt(n) is a C math.h library function.

Answer 1

Let n=2^m
Given T(n)=T(sqrt(n))+1
T(2^m)=T(2^m-1)+1
Let T(2^m)=S(m)
then,
S(m)=2S(m/2)+1
using master theorem-
S(m)=theta(m)
=theta(log(n))
Hence, time complexity is theta(log(n)).