# Sliding puzzle

## Description

Program solve scrabble shown on ukladanka.png

Source: PrologTutorial (on-line tutorial

Program source code: sliding_puzzle.pl

## Listing

```/* 8_puzzle.pl */

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%

%%%     A* Algorithm

%%%

%%%

%%%     Nodes have form    S#D#F#A

%%%            where S describes the state or configuration

%%%                  D is the depth of the node

%%%                  F is the evaluation function value

%%%                  A is the ancestor list for the node

:- op(400,yfx,'#').    /* Node builder notation */

solve(State,Soln) :- f_function(State,0,F),

search([State#0#F#[]],S), reverse(S,Soln).

f_function(State,D,F) :- h_function(State,H),

F is D + H.

search([State#_#_#Soln|_], Soln) :- goal(State).

search([B|R],S) :- expand(B,Children),

insert_all(Children,R,Open),

search(Open,S).

insert_all([F|R],Open1,Open3) :- insert(F,Open1,Open2),

insert_all(R,Open2,Open3).

insert_all([],Open,Open).

insert(B,Open,Open) :- repeat_node(B,Open), ! .

insert(B,[C|R],[B,C|R]) :- cheaper(B,C), ! .

insert(B,[B1|R],[B1|S]) :- insert(B,R,S), !.

insert(B,[],[B]).

repeat_node(P#_#_#_, [P#_#_#_|_]).

cheaper( _#_#F1#_ , _#_#F2#_ ) :- F1 < F2.

expand(State#D#_#S,All_My_Children) :-

bagof(Child#D1#F#[Move|S],

(D1 is D+1,

move(State,Child,Move),

f_function(Child,D1,F)),

All_My_Children).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%

%%%     8-puzzle solver

%%%

%%%

%%%     State have form    A/B/C/D/E/F/G/H/I

%%%            where {A,...,I} = {0,...,8}

%%%               0 represents the empty tile

%%%

goal(1/2/3/8/0/4/7/6/5).

%%% The puzzle moves

left( A/0/C/D/E/F/H/I/J , 0/A/C/D/E/F/H/I/J ).

left( A/B/C/D/0/F/H/I/J , A/B/C/0/D/F/H/I/J ).

left( A/B/C/D/E/F/H/0/J , A/B/C/D/E/F/0/H/J ).

left( A/B/0/D/E/F/H/I/J , A/0/B/D/E/F/H/I/J ).

left( A/B/C/D/E/0/H/I/J , A/B/C/D/0/E/H/I/J ).

left( A/B/C/D/E/F/H/I/0 , A/B/C/D/E/F/H/0/I ).

up( A/B/C/0/E/F/H/I/J , 0/B/C/A/E/F/H/I/J ).

up( A/B/C/D/0/F/H/I/J , A/0/C/D/B/F/H/I/J ).

up( A/B/C/D/E/0/H/I/J , A/B/0/D/E/C/H/I/J ).

up( A/B/C/D/E/F/0/I/J , A/B/C/0/E/F/D/I/J ).

up( A/B/C/D/E/F/H/0/J , A/B/C/D/0/F/H/E/J ).

up( A/B/C/D/E/F/H/I/0 , A/B/C/D/E/0/H/I/F ).

right( A/0/C/D/E/F/H/I/J , A/C/0/D/E/F/H/I/J ).

right( A/B/C/D/0/F/H/I/J , A/B/C/D/F/0/H/I/J ).

right( A/B/C/D/E/F/H/0/J , A/B/C/D/E/F/H/J/0 ).

right( 0/B/C/D/E/F/H/I/J , B/0/C/D/E/F/H/I/J ).

right( A/B/C/0/E/F/H/I/J , A/B/C/E/0/F/H/I/J ).

right( A/B/C/D/E/F/0/I/J , A/B/C/D/E/F/I/0/J ).

down( A/B/C/0/E/F/H/I/J , A/B/C/H/E/F/0/I/J ).

down( A/B/C/D/0/F/H/I/J , A/B/C/D/I/F/H/0/J ).

down( A/B/C/D/E/0/H/I/J , A/B/C/D/E/J/H/I/0 ).

down( 0/B/C/D/E/F/H/I/J , D/B/C/0/E/F/H/I/J ).

down( A/0/C/D/E/F/H/I/J , A/E/C/D/0/F/H/I/J ).

down( A/B/0/D/E/F/H/I/J , A/B/F/D/E/0/H/I/J ).

%%% the heuristic function

h_function(Puzz,H) :- p_fcn(Puzz,P),

s_fcn(Puzz,S),

H is P + 3*S.

%%% the move

move(P,C,left) :-  left(P,C).

move(P,C,up) :-  up(P,C).

move(P,C,right) :-  right(P,C).

move(P,C,down) :-  down(P,C).

%%% the Manhattan distance function

p_fcn(A/B/C/D/E/F/G/H/I, P) :-

a(A,Pa), b(B,Pb), c(C,Pc),

d(D,Pd), e(E,Pe), f(F,Pf),

g(G,Pg), h(H,Ph), i(I,Pi),

P is Pa+Pb+Pc+Pd+Pe+Pf+Pg+Ph+Pg+Pi.

a(0,0). a(1,0). a(2,1). a(3,2). a(4,3). a(5,4). a(6,3). a(7,2). a(8,1).

b(0,0). b(1,1). b(2,0). b(3,1). b(4,2). b(5,3). b(6,2). b(7,3). b(8,2).

c(0,0). c(1,2). c(2,1). c(3,0). c(4,1). c(5,2). c(6,3). c(7,4). c(8,3).

d(0,0). d(1,1). d(2,2). d(3,3). d(4,2). d(5,3). d(6,2). d(7,2). d(8,0).

e(0,0). e(1,2). e(2,1). e(3,2). e(4,1). e(5,2). e(6,1). e(7,2). e(8,1).

f(0,0). f(1,3). f(2,2). f(3,1). f(4,0). f(5,1). f(6,2). f(7,3). f(8,2).

g(0,0). g(1,2). g(2,3). g(3,4). g(4,3). g(5,2). g(6,2). g(7,0). g(8,1).

h(0,0). h(1,3). h(2,3). h(3,3). h(4,2). h(5,1). h(6,0). h(7,1). h(8,2).

i(0,0). i(1,4). i(2,3). i(3,2). i(4,1). i(5,0). i(6,1). i(7,2). i(8,3).

%%% the out-of-cycle function

s_fcn(A/B/C/D/E/F/G/H/I, S) :-

s_aux(A,B,S1), s_aux(B,C,S2), s_aux(C,F,S3),

s_aux(F,I,S4), s_aux(I,H,S5), s_aux(H,G,S6),

s_aux(G,D,S7), s_aux(D,A,S8), s_aux(E,S9),

S is S1+S2+S3+S4+S5+S6+S7+S8+S9.

s_aux(0,0) :- !.

s_aux(_,1).

s_aux(X,Y,0) :- Y is X+1, !.

s_aux(8,1,0) :- !.

s_aux(_,_,2).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%

%%%     8-puzzle animation -- using VT100 character graphics

%%%

%%%

%%%

puzzle(P) :- solve(P,S),

animate(P,S),

message.

animate(P,S) :- initialize(P),

cursor(1,2), write(S),

cursor(1,22), write('Hit ENTER to step solver.'),

get0(_X),

play_back(S).

:- dynamic location/3.   %%% So that location of a tile

%%%  can be retracted/asserted.

%%% Location(s) asserted and retracted

%%%  by puzzle animator below

initialize(A/B/C/D/E/F/H/I/J) :-

cls,

retractall(location(_,_,_)),

assert(location(A,20,5)),

assert(location(B,30,5)),

assert(location(C,40,5)),

assert(location(F,40,10)),

assert(location(J,40,15)),

assert(location(I,30,15)),

assert(location(H,20,15)),

assert(location(D,20,10)),

assert(location(E,30,10)), draw_all.

draw_all :- draw(1), draw(2), draw(3), draw(4),

draw(5), draw(6), draw(7), draw(8).

%%% play_back([left,right,up,...]).

play_back([M|R]) :- call(M), get0(_X), play_back(R).

play_back([]) :- cursor(1,24).  %%% Put cursor out of the way

message :- nl,nl,

write('    ********************************************'), nl,

write('    *  Enter 8-puzzle goals in the form ...    *'), nl,

write('    *     ?-  puzzle(0/8/1/2/4/3/7/6/5).       *'), nl,

write('    *   Enter goal ''message'' to reread this.   *'), nl,

write('    ********************************************'), nl, nl.

cursor(X,Y) :- put(27), put(91), %%% ESC [

write(Y),

put(59),           %%%   ;

write(X),

put(72).           %%%   M

%%% clear the screen, quickly

cls :-  put(27), put("["), put("2"), put("J").

%%% video attributes -- bold and blink not working

plain         :- put(27), put("["), put("0"), put("m").

reverse_video :- put(27), put("["), put("7"), put("m").

%%% Tile objects, character map(s)

%%% Each tile should be drawn using the character map,

%%%   drawn at 'location', which is asserted and retracted

%%%   by 'playback'.

character_map(N, [ [' ',' ',' ',' ',' ',' ',' '],

[' ',' ',' ', N ,' ',' ',' '],

[' ',' ',' ',' ',' ',' ',' '] ]).

%%% move empty tile (spot) to the left

left :- retract(location(0,X0,Y0)),

Xnew is X0 - 10,

location(Tile,Xnew,Y0),

assert(location(0,Xnew,Y0)),

right(Tile),right(Tile),right(Tile),

right(Tile),right(Tile),

right(Tile),right(Tile),right(Tile),

right(Tile),right(Tile).

up :- retract(location(0,X0,Y0)),

Ynew is Y0 - 5,

location(Tile,X0,Ynew),

assert(location(0,X0,Ynew)),

down(Tile),down(Tile),down(Tile),down(Tile),down(Tile).

right :- retract(location(0,X0,Y0)),

Xnew is X0 + 10,

location(Tile,Xnew,Y0),

assert(location(0,Xnew,Y0)),

left(Tile),left(Tile),left(Tile),left(Tile),left(Tile),

left(Tile),left(Tile),left(Tile),left(Tile),left(Tile).

down :- retract(location(0,X0,Y0)),

Ynew is Y0 + 5,

location(Tile,X0,Ynew),

assert(location(0,X0,Ynew)),

up(Tile),up(Tile),up(Tile),up(Tile),up(Tile).

draw(Obj) :- reverse_video, character_map(Obj,M),

location(Obj,X,Y),

draw(X,Y,M), plain.

%%% hide tile

hide(Obj) :- character_map(Obj,M),

location(Obj,X,Y),

hide(X,Y,M).

hide(_,_,[]).

hide(X,Y,[R|G]) :- hide_row(X,Y,R),

Y1 is Y + 1,

hide(X,Y1,G).

hide_row(_,_,[]).

hide_row(X,Y,[_|R]) :- cursor(X,Y),

write(' '),

X1 is X + 1,

hide_row(X1,Y,R).

%%% draw tile

draw(_,_,[]).

draw(X,Y,[R|G]) :- draw_row(X,Y,R),

Y1 is Y + 1,

draw(X,Y1,G).

draw_row(_,_,[]).

draw_row(X,Y,[P|R]) :- cursor(X,Y),

write(P),

X1 is X + 1,

draw_row(X1,Y,R).

%%% Move an Object up

up(Obj)    :- hide(Obj),

retract(location(Obj,X,Y)),

Y1 is Y - 1,

assert(location(Obj,X,Y1)),

draw(Obj).

down(Obj)  :- hide(Obj),

retract(location(Obj,X,Y)),

Y1 is Y + 1,

assert(location(Obj,X,Y1)),

draw(Obj).

left(Obj)  :- hide(Obj),

retract(location(Obj,X,Y)),

X1 is X - 1,

assert(location(Obj,X1,Y)),

draw(Obj).

right(Obj) :- hide(Obj),

retract(location(Obj,X,Y)),

X1 is X + 1,

assert(location(Obj,X1,Y)),

draw(Obj).

:- message.

% ?- solve(0/8/1/2/4/3/7/6/5, S).```