What is the Big O of that pseudocode?

Question

x <--1
for i <--0 to n do
    k <-- i
   while k> 0 do
         x <-- x*2
         k <-- k-1
return x

Is it O (n)? Do while loop increase the complexity?

Answer 1

When i = 0, inner loop runs 0 time
When i = 1, inner loop runs 1 time
When i = 2, inner loop runs 2 times
When i = 3, inner loop runs 3 times
...
When i = n, inner loop runs n times
Adding it all up: 0+1+2+3+...+n = n*(n+1)/2
So the time complexity is O(n^2)