Question

I don’t see how this method would be used 31 times when I try to recursively calculate 2^8.

Does this method calculate powers in O(logN) complexity?

When I run it the output is:

0
1
2
3
4
5
...
29
30
2^8 is: 256

Code

private static int power(int x, int y)
{
    System.out.println(step++);

    if (y == 0)
        return 1;

    return power(x, y/2) * power(x, y/2);
}

Answer 1

Here you’re actually making two calls to the power method with the same values:

return power(x, y/2) * power(x, y/2);

Instead, you could make half as many calls if you write it like this:

int toReturn = power(x, y/2);
return toReturn * toReturn;

If we walk through your original example, we will make 31 calls, which is what you see (0 to 30). Walk through your code to see why:

power(2, 8)

power(2, 4)
power(2, 4)

power(2, 2)
power(2, 2)
power(2, 2)
power(2, 2)

power(2, 1)
power(2, 1)
power(2, 1)
power(2, 1)
power(2, 1)
power(2, 1)
power(2, 1)
power(2, 1)

power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)
power(2, 0)