Can someone help solve this recurrence relation? [closed]

Answer 1

For part 1, you can use Master Theorem as @Prasoon Saurav suggested.

For part 2, just expand the recurrence:

T(n) = T(n ^ 1/2) + O(1)         // sqrt(n) = n ^ 1/2
     = T(n ^ 1/4) + O(1) + O(1)  // sqrt(sqrt(n)) = n ^ 1/4
     etc.

The series will continue to k terms until n ^ 1/(2^k) <= 1, i.e. 2^k = log n or k = log log n. That gives T(n) = k * O(1) = O(log log n).