questions regarding the use of A* with the 15-square puzzle

Question

I\'m trying to build an A* solver for a 15-square puzzle.

The goal is to re-arrange the tiles so that they appear in their natural positions. You can only sli

Answer 1

An A-star search will find the optimal solution by proving that all paths that have not yet been solved are incapable of being solved with fewer moves than the current solution. You aren't looking for the best solution, but the fastest solution. Therefore, you can optimize your algorithm by returning the first solution, by weighting the number of moves lower than your heuristic function, and the heuristic can return an over-estimate.

The heuristic function itself is typically best modeled by the Manhattan distance and linear conflict. Manhattan distance is well explained in other answers and in the Wikipedia article, and you seem to have a handle on it. Linear conflict adds two to the manhattan distance for each pair of blocks that would have to be swapped to reach a solution. For example, if a row contains "3 2 1 4", then the one and the three have to be swapped, and one would have to be moved to another row to do so.

Using a pattern database is an option and could help your search avoid certain dead-ends, and the memory usage of doing so for a 15-puzzle should be manageable.