This sounds like a graph theory problem. (Though, given that I've been using Graph a bunch, and even submitted patches to it, recently, everything's been looking kinda like a nail right now.)

Here's what I mean

  1. Create an undirected graph of X x Y vertices, presumably labeled a1, a2, b1, etc.
  2. Create edges between all the squares that are connected to one another by means of how a rook can move. So, a1 has an edge to both a2 and b1, but a2 and b1 don't have an edge between them.
  3. Put all the vertex names into a hash to mark if you've been there or not.
  4. Pick a starting point. Mark it as being seen.
  5. Find all the neighbors.
  6. Iterate through them, recursively calling this function until you have touched every square.

The problem statement (as I read it) doesn't make mention of going back and forth between two squares (though it would be a valid variation upon a given walk), so you could probably prune a bunch of possibilities because you've already been there.

I would look at writing a better problem statement. Basically, are you only counting walks that minimize the number of squares touched? I would add the stipulation that you can only touch any square a maximum of two times. (One could add the once-per-square stipulation, but that may eliminate desired outcomes. I don't know enough about the problem domain to say with any certainty.)

The reason I suggest this option is because it sounds like you're not happy with your data structure which, in turn, is causing serious headaches with your algorithm.

------
We are the carpenters and bricklayers of the Information Age.

Then there are Damian modules.... *sigh* ... that's not about being less-lazy -- that's about being on some really good drugs -- you know, there is no spoon. - flyingmoose

I shouldn't have to say this, but any code, unless otherwise stated, is untested

In reply to Re^3: better algorithm: bitwise reordering by dragonchild
in thread better algorithm: bitwise reordering by hv

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