Factoring

["L. Todd Masco" <cactus@bb.com>]

I'm confused on a point, and I hope someone will clarify.  Factoring
 keeps being described as a 2^(n/2) problem, yet AFAIK (I wrote the code
 to do it the other morning before breakfast), it's doable in
 linear (O(n)) time.

What gives?

(The algorithm I'm thinking of is:

/* Algorithm:  To factor the number n, start with n boxes, each with one
   "marble."  Remove last box, put it's marble in box #1.  If all boxes
   have the same number of marbles, the number is factored.  If not,
   remove last box.  Put marble in box #2.  Compare.  Etc.

   possible optimizations: div by each prime l for a quicker starting
	point.  (2,3...)
   */

factor(int target)
{
  int place = target;
  int smallest = 0;
  int load = 1;

  while (place>1) {
    place--;       /* N-1 boxes. */
    smallest+=load;    /* Next box in line gets the marble */
    if (place <= smallest ) {
      load++;
      if (place == smallest) 
	printf(" Factor: %d by %d\n",place,load);
      smallest = smallest-place;
    }
  }
}
--
L. Todd Masco  | Bibliobytes books on computer, on any UNIX host with e-mail
cactus@bb.com  | "Information wants to be free, but authors want to be paid."