I know that we can brute force it by placing an obstacle at every valid position in the path, but is there a more elegant / efficient solution?
I know that we can brute force it by placing an obstacle at every valid position in the path, but is there a more elegant / efficient solution?
That’s a neat idea, but isn’t it possible that adding an obstacle could send the guard into a loop in a previously unexplored part of the map? I think you’d miss that case.
I’m not sure I understand the concern, maybe a visualization would help describe what you’re talking about? I updated my comment to describe my process in better detail, it was confusing before. I’m only focused in checking unobstructed straight lines from places where the guard has turned, so I don’t think it could get into unexplored areas.
I’m imagining something like this:
.#........ ....#..#.. .O.......# .........# ......#... .^......#.The original path hits the leftmost two obstructions, whereas the new path avoids these but hits all the others (and loops).
Ois not on an intersection of any two turns in the original path. It is if you check all possible turning points, although there’s potentially a lot more of them.Ohh that is helpful, yeah, i don’t know how I’d get these counted. This is probably the ones I’m missing. The way I’ve been thinking about it is that all a loop is is a rectangle. So basically each guard’s turn is a corner of a rectangle. By taking opposite corners (every other turn the guard makes) we can see if we can draw a full rectangle without hitting any walls. If we can, then that would make a loop.
A few things I figured out playing with this:
So maybe the logic would be to ignore the rotations in part one when the guard walks unobstructed, and do a pass through the whole map and mark each point of a possible rotation, and then drawing possible rectangles where 3 corners exist, to find an obstruction point. Then you can check if the obstruction point is in the set of steps the guard made in part 1 when unobstructed. Still though, I think this doesn’t take into account the guards rotation, so will probably be wrong.
Rectangles don’t account for all loops though, right? Couldn’t you have a loop with, say, 6 points in an L shape?
Yeah you’re right. I keep focusing on the smaller example where everything is just rectangle loops, but the big map is way more complex. I do wonder though if an L shaped loop is just multiple rectangle loops combined though? Like if you can find all the rectangles, then find ones where combined they make bigger loops?
I mean, sure you can combine rectangles to make any path, but since there is no upper limit I don’t think that will help much. You may be on to something and I just can’t see it, though! Good luck!