data structure time complexity solve problem

Question

I want to make sure that it's the right answer. answer :

T(n) = (n log n +1 ) 
big 0 = O(n log n)

sum = 0;      ---- 1
for( i=1; i<=n ; i*=2) ---- log n ? 
 for(j=1; j<=n ; j++) --- n 
   sum++; ----1

Answer 1

1. The number of iterations of the outer loop is the index of the most significant bit in n. So, it is indeed floor(log₂(n))

2. The number of iterations of the inner loop is exactly n.

Then, the total number of iterations of the body of the inner loop is n * floor(log₂(n)), the test, increment and body all execute in constant time.

Hence, the time complexity of this code is O(n.log(n))