Explanation : Recurrance relation for procedure A (n) is
T(n) = T √n + 1 if n > 2
T(n) = 1 if n ≤ 2
T(n) = 1
Now, T (n) = T √n + 1
Put n = 2k, T (2k)= T (2k/2) + 1
Use S(K) for T (2k) then
S(K) = S(k/2) + 1
Apply masters method.
Klog21 ≅ 1
So θ (log k)
Now we know that
n = 2k so, k= log2n
So, O(log logn).