I'm trying to implement a solver of an 8-puzzle. The puzzle board is represented as a list. For example, the goal state:
1 | 2 | 3
---------
4 | 5 | 6
---------
7 | 8 | 0
is represented as [1,2,3,4,5,6,7,8,0], where 0 represents the empty space.
I've implemented move(+Board,-Move) that succeeds with Move as all the possible states of the board one move away from Board. In addition I've implemented solvable(+Board) that gives true or false as to whether the board can be solved.
I've also implemented two heuristics, manhattan(+Board,+Goal,-H) and hamming(+Board,+Goal,-H), which calculates the heuristics cost from Board to Goal. For example:
?- hamming([1,2,3,8,0,4,7,6,5],[1,2,3,8,0,4,7,6,5],H).
H = 0.
?- hamming([1,2,3,4,0,8,7,6,5],[1,2,3,8,0,4,7,6,5],H).
H = 2.
?- manhattan([1,2,3,8,0,4,7,6,5],[1,2,3,8,0,4,7,6,5],H).
H = 0.
?- manhattan([1,2,3,4,0,8,7,6,5],[1,2,3,8,0,4,7,6,5],H).
H = 4.
I want to implment solve(+Board,+Heuristic,-Solution) that succeeds with Solution as one optimal solution to Board using the Heuristic given, and it must terminate deterministically with precisely one solution. For example:
?- solve([0,1,3,4,2,5,7,8,6],manhattan,Solution).
Solution = [
[0, 1, 3, 4, 2, 5, 7, 8, 6],
[1, 0, 3, 4, 2, 5, 7, 8, 6],
[1, 2, 3, 4, 0, 5, 7, 8, 6],
[1, 2, 3, 4, 5, 0, 7, 8, 6],
[1, 2, 3, 4, 5, 6, 7, 8, 0]
].
I wrote out the pseudo code for the A* algorithm:
For each Child of Board do:
If Child in Closed do:
Continue
If Child not in Closed or G(Board) + 1 < G(Child) do:
G(Child) := G(Board) + 1
F(Child) := G(Child) + Heuristic(Child,Goal)
If Child not in Open do:
Open := Open + {Child}
Where G(Board) is the actual cost of Board, defined as the length of the optimal path to Board from the initial board. F(Board) is the combined cost of Board, defined as the sum of G(Board) and the estimated cost of Board (defined by a heuristic function). And of course Closed and Open are the two sets maintained by the A* algorithm, with Closed containing boards that have been visited, Open containing boards that have not.
Issue is I have no idea how to do this in Prolog. I suppose that some heap datastructure is necessary to maintain the two list, but have no idea what or how. Any help would be great.
