Question

I am trying to find the running time O(n) for the block of code below:

int z=0;
int x=0; 
for (int i=1; i<=n; i=i*3){ //runs from 1->n, 1, 3, 9, 27... <- fcn that defines this?
   //constant running times below
   z = z+5;
   z++;
   x = 2*x;
}

if it was i=i*2, then it would be logn complexity running time. What is it for this case?

tia.

Answer 1

Notice that log_3 (n) = log_2 (n) / log_2 (3) . Here log_2 means log with base 2 and log_3 means log with base 3. So, log_2(n) is just log_3(n) times a constant.

So, by big O definition, any code which has running time O(log_3(n)) is also O(log(n)).