Time Complexity of multiple nested loops

Question

What would be the complexity of the below code : Since the increment is not by 1 and the conditions are not direct, how to calculate the complexity ?

for(int h =0; h<n;h+=2)
    {
       for (int j =1; j<=n*n; j*=3)
       {
          for (int k =2; k+k <=n;++k)
          { 
          } 
       } 
    }

Answer 1

There are 3 nested loops. Let's analyze each of them (keep in mind that we don't care about any constants, no matter how large they are):

for(int h=0; h<n; h+=2) - O(¹⁄₂N) -> O(N)

for (int j=1; j<=n*n; j*=3) - O(log₃N²) -> O(logN2)

for (int k=2; k+k<=n; ++k)- O(¹⁄₂N) -> O(N)

Since all the loops are nested O(N * logN² * N) -> O(N2*logN2)