Algorithms | Analysis of Algorithms (Recurrences) | Question 8
What is the time complexity of the following recursive function:
Explanation: Recursive relation for the DoSomething() is
T(n) = T() + C1 if n > 2
We have ignored the floor() part as it doesn’t matter here if it’s a floor or ceiling.
Let n = 2^m, T(n) = T(2^m) Let T(2^m) = S(m) From the above two, T(n) = S(m) S(m) = S(m/2) + C1 /* This is simply binary search recursion*/ S(m) = O(logm) = O(loglogn) /* Since n = 2^m */ Now, let us go back to the original recursive function T(n) T(n) = S(m) = O(LogLogn)