What is the big O notation of this function

Question

 result = 0
 i = 0
 while i < 2**n:
      result = result + i
      i += 1
 # end while

I'm assuming O(2^n). Python code.

Answer 1

I think your code's time complexity is O(2^n log n) because you are computing 2^n, for 2^n times.
a^b can compute in O(log b) for exponentiation by squaring and I think the exponential algorithm in python is O(log n) algorithm.
So, the time complexity is O(2^n log n).