Question

So given x, and power, n, solve for X^n.
There’s the easy way that’s O(n)…
I can get it down to O(n/2), by doing

numSquares = n/2;
numOnes = n%2;
return (numSquares * x * x + numOnes * x);

Now there’s a O(log(n)) solution, does anyone know how to do it? It can be done recursively.

Answer 1

Well, you know that x^a+b = x^a x^b so…

int pow(int x, unsigned int y)
{
  if (y == 0) return 1;
  if (y == 1) return x;
  int a = y / 2;
  int xa = pow(x, a);
  if (a + a == y) // y even
    return xa * xa;
  else
    return xa * xa * x;
}