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%(SWI-Prolog)You can run the program by: ?- bestfs([8,1,3,7,0,2,6,5,4],P).
initial([8,1,3,7,0,2,6,5,4]).
goal([1,2,3,8,0,4,7,6,5]).
operators([left, right, up, down]).
% 8-puzzle solution
% initial([8,1,3,7,0,2,6,5,4]).
% goal([1,2,3,8,0,4,7,6,5]).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Best-first Search %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bestfs(Start,Path):-
heuristic(Start, Distance),
bestfs_path([ node(Start, Distance, []) ], Path).
bestfs_path([node(Goal, _, Path)| _], Path):-
goal(Goal).
bestfs_path([node(Current, _, Path) | Queue],
GoalPath) :-
findall(node(Child, Distance, PathToChild),
(
apply(Operator, Current, Child),
heuristic(Child, Distance),
append(Path, [Operator], PathToChild)
), ChildNodes),
add_to_list(ChildNodes, Queue, NewQueue),
bestfs_path(NewQueue, GoalPath).
% add_to_list adds a new list into an old (ordered) list
% by recursively adding members of the new list at their
% appropriate position in the old list. The returned list
% is also ordered.
add_to_list([], L, L).
add_to_list([H|T], OldList, NewList):-
insert_at_place(H, OldList, TempList),
add_to_list(T, TempList, NewList).
% insert_at_place simply adds a new element at the right
% place of an ordered list so as to return another
% ordered list (provisions have been made for the node
% datastructure that is used in out implementation of
% best-first search)
insert_at_place(X, [], [X]).
insert_at_place(node(NodeX, X, PathX),
[node(NodeY, Y, PathY) | L],
[node(NodeX, X, PathX),
node(NodeY, Y, PathY) | L]) :-
X =< Y.
insert_at_place(node(NodeX, X, PathX),
[node(Node, Y, PathY) | L],
[node(Node, Y, PathY) | NewL]) :-
X > Y,
insert_at_place(node(NodeX, X, PathX), L, NewL).
% Of course, we need to choose our heuristic
% change this to use any other heuristic, such as
% manhattan distance
heuristic(X, Y) :-
displaced(X, Y).
% manhattan(X,Y).
%=====================================================================
%Implementation of 8-Puzzle Operators
%====================================================================
% move_left in the top row
move_left([X1,0,X3, X4,X5,X6, X7,X8,X9], [0,X1,X3, X4,X5,X6, X7,X8,X9]).
move_left([X1,X2,0, X4,X5,X6, X7,X8,X9], [X1,0,X2, X4,X5,X6, X7,X8,X9]).
% move_left in the middle row
move_left([X1,X2,X3, X4,0,X6, X7,X8,X9], [X1,X2,X3, 0,X4,X6, X7,X8,X9]).
move_left([X1,X2,X3, X4,X5,0, X7,X8,X9], [X1,X2,X3, X4,0,X5, X7,X8,X9]).
% move_left in the bottom row
move_left([X1,X2,X3, X4,X5,X6, X7,0,X9], [X1,X2,X3, X4,X5,X6, 0,X7,X9]).
move_left([X1,X2,X3, X4,X5,X6, X7,X8,0], [X1,X2,X3, X4,X5,X6, X7,0,X8]).
% move_right in the top row
move_right([0,X2,X3, X4,X5,X6, X7,X8,X9], [X2,0,X3, X4,X5,X6, X7,X8,X9]).
move_right([X1,0,X3, X4,X5,X6, X7,X8,X9], [X1,X3,0, X4,X5,X6, X7,X8,X9]).
% move_right in the middle row
move_right([X1,X2,X3, 0,X5,X6, X7,X8,X9], [X1,X2,X3, X5,0,X6, X7,X8,X9]).
move_right([X1,X2,X3, X4,0,X6, X7,X8,X9], [X1,X2,X3, X4,X6,0, X7,X8,X9]).
% move_right in the bottom row
move_right([X1,X2,X3, X4,X5,X6, 0,X8,X9], [X1,X2,X3, X4,X5,X6, X8,0,X9]).
move_right([X1,X2,X3, X4,X5,X6, X7,0,X9], [X1,X2,X3, X4,X5,X6, X7,X9,0]).
% move_up from the middle row
move_up([X1,X2,X3, 0,X5,X6, X7,X8,X9], [0,X2,X3, X1,X5,X6, X7,X8,X9]).
move_up([X1,X2,X3, X4,0,X6, X7,X8,X9], [X1,0,X3, X4,X2,X6, X7,X8,X9]).
move_up([X1,X2,X3, X4,X5,0, X7,X8,X9], [X1,X2,0, X4,X5,X3, X7,X8,X9]).
% move_up from the bottom row
move_up([X1,X2,X3, X4,X5,X6, 0,X8,X9], [X1,X2,X3, 0,X5,X6, X4,X8,X9]).
move_up([X1,X2,X3, X4,X5,X6, X7,0,X9], [X1,X2,X3, X4,0,X6, X7,X5,X9]).
move_up([X1,X2,X3, X4,X5,X6, X7,X8,0], [X1,X2,X3, X4,X5,0, X7,X8,X6]).
% move_down from the top row
move_down([0,X2,X3, X4,X5,X6, X7,X8,X9], [X4,X2,X3, 0,X5,X6, X7,X8,X9]).
move_down([X1,0,X3, X4,X5,X6, X7,X8,X9], [X1,X5,X3, X4,0,X6, X7,X8,X9]).
move_down([X1,X2,0, X4,X5,X6, X7,X8,X9], [X1,X2,X6, X4,X5,0, X7,X8,X9]).
% move_down from the middle row
move_down([X1,X2,X3, 0,X5,X6, X7,X8,X9], [X1,X2,X3, X7,X5,X6, 0,X8,X9]).
move_down([X1,X2,X3, X4,0,X6, X7,X8,X9], [X1,X2,X3, X4,X8,X6, X7,0,X9]).
move_down([X1,X2,X3, X4,X5,0, X7,X8,X9], [X1,X2,X3, X4,X5,X9, X7,X8,0]).
% Applying an operator
apply(left,S1,S2) :- move_left(S1,S2).
apply(right,S1,S2) :- move_right(S1,S2).
apply(up,S1,S2) :- move_up(S1,S2).
apply(down,S1,S2) :- move_down(S1,S2).
%======================================================================
%Implementation of 8-Puzzle Heuristic Functions
%======================================================================
% displacement heuristic
displaced(State, Number) :-
goal(Goal),
misplaced(State,Goal,Number).
% misplaced returns the number of tiles found in the wrong position
misplaced([],[],0).
misplaced([0|T1],[0|T2],Number) :- !,
misplaced(T1,T2,Number).
misplaced([H|T1],[H|T2],Number) :- !,
misplaced(T1,T2,Number).
misplaced([H1|T1],[H2|T2],Number) :- !,
H1\==H2,
misplaced(T1,T2,N),
Number is N+1.
% Manhattan Distance heuristic
manhattan(State, Number) :-
manh(State,State,0,Number).
manh([], _, X, X).
manh([H|T], State, Acc, Result) :-
nth1(Position, State, H),
NewPos is Position - 1,
Xaux1 is NewPos mod 3,
X1 is integer(Xaux1),
Y1 is NewPos // 3,
goal(Goal),
nth1(GoalPosition, Goal, H),
NewGPos is GoalPosition - 1,
Xaux2 is NewGPos mod 3,
X2 is integer(Xaux2),
Y2 is NewGPos // 3,
S1 is abs(X1-X2),
S2 is abs(Y1-Y2),
N is S1+S2,
NewAcc is Acc+N,
manh(T, State, NewAcc, Result).
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