/*
 * Return the index of element x within array A if present,
 * and return -1 if not found
 */
static public int BinarySearch (int [] A, int x, int size)
{
    return BoundedBinarySearch(A, x, 0, size-1);
}


/*
 * Return the index of element x within A[left...right] if present,
 * and return -1 if not found
 */
static public int BoundedBinarySearch (int [] A, int x, int left, int right)
{
    if (left > right) {    /* base case:  zero size */
        return -1;
    }
    if (left == right) {   /* base case:  size one */
	if (A[left] == x) return left;
	else return -1;
    }
    int mid = (left + right) / 2;
    if (A[mid] == x)  {
	return mid;
    }

    else if (A[mid] > x) {  /* look in left half  */
	return BoundedBinarySearch (A, x, left, mid-1);
    }	

    else {   /* A[mid] < x --- recurse on right half  */
	return BoundedBinarySearch (A, x, mid+1, right);
    }
}

/* Editor's note:  the size one base case is not necessary   */
/* It is worth your while to verify that it's ok to drop it. */