/*

% etat final du taquin 3x3 

final_state([ [a, b,  c],
              [h,vide,d],
              [g, f,  e] ]).




% etat final du taquin 4x4 

final_state([ [ 1,  2,  3,  4],
              [ 5,  6,  7,  8],
              [ 9, 10, 11, 12],			 
              [13, 14, 15,vide]]).  
*/

/*
% Etats initiaux du Taquin 3*3

initial_state([ [a,  b, c],
                [g,  h, d],
                [vide,f, e] ]). %f*=2

initial_state([ [b, h, c],
                [a, f, d],
                [g,vide,e] ]). %f*=5

initial_state([ [b, c, d],
                [a,vide,g],
                [f, h, e]  ]). %f*=10
			
initial_state([ [f, g, a],
                [h,vide,b],
                [d, c, e]  ]). %f*=20				

initial_state([ [e, f, g],
                [d,vide,h],
                [c, b, a]  ]). % f*=30

initial_state([ [a, b, c],
                [g,vide,d],
                [h, f, e]]). % etat non connexe avec l'etat final (PAS DE SOLUTION)
				

%Etats du Taquin 4*4
				
initial_state([ [  5,  1,  2,  3],
                [  9,  6,  7,  4],
                [ 13, 10, 11,  8],
                [ 14, 15, 12, vide] ]).  %f*=12
				
initial_state([ [  9,  5,  1,  2],
                [ 13,  6,  7,  3],
                [ 14, 10, 11,  4],
                [ 15, 12,  8, vide] ]).  %f*=24
				

initial_state([ [vide,  9,  1,  4],
                [ 14, 13,  2,  3],
                [ 15, 10,  5,  7],
                [ 11, 12,  6,  8] ]).  %f*=34				

initial_state([ [ 13,  9,  5,  1],
                [ 14,  6,  7,  2],
                [ 15, 10, 11,  3],
                [ 12,  8,  4, vide] ]).  %f*=36

initial_state([ [ 14, 13,  9,  5],
                [ 15,  6,  7,  1],
                [ 12, 10, 11,  2],
                [  8,  4,  3, vide] ]).  %f*=48 	

initial_state([ [ 15, 14, 13,  9],
                [ 12,  6,  7,  5],
                [  8, 10, 11,  1],
                [  4,  3,  2, vide] ]).  %f*=60

initial_state([ [ 15, 14, 13,  9],
                [ 12,  6,  7,vide],
                [  8, 10, 11,  5],
                [  4,  3,  2,  1] ]).   %f*=62		
				
initial_state([ [ 15, 14, 13,  9],
                [ 12,vide,  5, 11],
                [  8,  7,  6, 10],
                [  4,  3,  2,  1] ]).   %f*=88 (théorique) ERROR: Stack limit (1.0Gb) exceeded	
				
*/