/*
 * Compute x^n using repeated squaring.
 *
 * Version 1:  inefficient, since each call makes *2* recursive calls
 */
static public int pow(int x, int n)
{
    if (n == 0) return 1;

    if (n%2 == 0)  {  /* n is even */
	return pow(x, n/2) * pow (x, n/2);
    }

    else  {  /* n is odd, so n/2 rounds down */
             /* thus, x^11 = x^5 * x^5 * x   */

	return pow(x, n/2) * pow (x, n/2) * x;
    }
}




/*
 * Compute x^n using repeated squaring.
 *
 * Version 2:  efficient, each call makes *1* recursive call,
 *   and reuses the result of that call.
 */
static public int pow(int x, int n)
{
    if (n == 0) return 1;

    int halfway = pow (x, n/2);

    if (n%2 == 0)  {  /* n is even */
	return halfway * halfway; 
    }

    else  {  /* n is odd */
	return halfway * halfway * x;
    }
}


/*  Our textbook devises a different solution on pp. 47-48.  */