0

I'm trying to understand the upper bound complexity for a Rush Hour game puzzle. I'm dealing with a 9x9 board, with 22 vehicles, including trucks (3 grids long) and cars (2 grids long).

By my logic, given the fact that a car can move 8 times over a 9x9 board in one direction, the calculation would be 8^22, which results in 7.34e+19. This implies that the upper bound is 7.34e+19 different states for this puzzle.

It seems too excessive to me, for I want to calculate how close my algorithm to a solution is, given the number of iterated board states. Even supposing that all vehicles are trucks and therefore could only move 7 times seems too large.

Is my upper bound overestimated? Perhaps I should consider that the amount of movable space is the only space not occupied by a vehicle.

Bjoern Rennhak
  • 6,766
  • 1
  • 16
  • 21
R A
  • 95
  • 3
  • 13
  • What exactly is a "complexity" for a game puzzle? Are you trying to solve the puzzle efficiently, simply calculate all "distinct" (in some sense) states, or something else? – yeputons Jun 22 '18 at 15:44
  • @yeputons I added the keyword 'complexity' in my edit as the original just mentioned 'upper bound' which I assumed related to probably some kind of upper bound complexity (computational, logic, etc). My apologies if the edit caused some confusion. Please see here the revision of the original post https://stackoverflow.com/posts/50990910/revisions – Bjoern Rennhak Jun 22 '18 at 16:02
  • 2
    This might be useful: https://arxiv.org/pdf/cs/0502068.pdf – Bjoern Rennhak Jun 22 '18 at 16:05
  • 1
    https://www.michaelfogleman.com/rush/ – Bjoern Rennhak Jul 12 '18 at 17:07

0 Answers0