From a3b2bd315d1202fdced423fa893834fa619fe6c4 Mon Sep 17 00:00:00 2001 From: pfaure Date: Fri, 19 Feb 2021 11:34:35 +0100 Subject: [PATCH] A* fini --- README.md | 2 + aetoile.pl | 181 ++++++++++++++++++++++++ avl.pl | 367 ++++++++++++++++++++++++++++++++++++++++++++++++ taquin.pl | 263 ++++++++++++++++++++++++++++++++++ tp_ia1_2021.pdf | Bin 0 -> 302801 bytes 5 files changed, 813 insertions(+) create mode 100644 README.md create mode 100644 aetoile.pl create mode 100644 avl.pl create mode 100644 taquin.pl create mode 100644 tp_ia1_2021.pdf diff --git a/README.md b/README.md new file mode 100644 index 0000000..521bf58 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Dépot du TP d'IA : 2020-2021 +Paul Faure 4IR - SI - A1 diff --git a/aetoile.pl b/aetoile.pl new file mode 100644 index 0000000..c6cc73c --- /dev/null +++ b/aetoile.pl @@ -0,0 +1,181 @@ +%******************************************************************************* +% AETOILE +%******************************************************************************* + +/* +Rappels sur l'algorithme + +- structures de donnees principales = 2 ensembles : P (etat pendants) et Q (etats clos) +- P est dedouble en 2 arbres binaires de recherche equilibres (AVL) : Pf et Pu + + Pf est l'ensemble des etats pendants (pending states), ordonnes selon + f croissante (h croissante en cas d'egalite de f). Il permet de trouver + rapidement le prochain etat a developper (celui qui a f(U) minimum). + + Pu est le meme ensemble mais ordonne lexicographiquement (selon la donnee de + l'etat). Il permet de retrouver facilement n'importe quel etat pendant + + On gere les 2 ensembles de façon synchronisee : chaque fois qu'on modifie + (ajout ou retrait d'un etat dans Pf) on fait la meme chose dans Pu. + + Q est l'ensemble des etats deja developpes. Comme Pu, il permet de retrouver + facilement un etat par la donnee de sa situation. + Q est modelise par un seul arbre binaire de recherche equilibre. + +Predicat principal de l'algorithme : + + aetoile(Pf,Pu,Q) + + - reussit si Pf est vide ou bien contient un etat minimum terminal + - sinon on prend un etat minimum U, on genere chaque successeur S et les valeurs g(S) et h(S) + et pour chacun + si S appartient a Q, on l'oublie + si S appartient a Ps (etat deja rencontre), on compare + g(S)+h(S) avec la valeur deja calculee pour f(S) + si g(S)+h(S) < f(S) on reclasse S dans Pf avec les nouvelles valeurs + g et f + sinon on ne touche pas a Pf + si S est entierement nouveau on l'insere dans Pf et dans Ps + - appelle recursivement etoile avec les nouvelles valeurs NewPF, NewPs, NewQs + +*/ + +%******************************************************************************* + +:- ['avl.pl']. % predicats pour gerer des arbres bin. de recherche +:- ['taquin.pl']. % predicats definissant le systeme a etudier + +%******************************************************************************* + +main :- + % initialisations Pf, Pu et Q + initial_state(S0), + heuristique(S0, H0), + empty(Pfi), + empty(Pui), + empty(Q), + insert([[H0, H0, 0], S0], Pfi, Pf), + insert([S0, [H0, H0, 0], nil, nil], Pui, Pu), + + % lancement de Aetoile + aetoile(Pf, Pu, Q). + + + + +%******************************************************************************* + +aetoile(Pf, _, _) :- + empty(Pf), + write("Pas de solution : l'état final n'est pas atteignable"), + nl. + +aetoile(Pf, Pu, Q) :- + initial_state(Ui), + suppress_min([_, U],Pf,_), + final_state(U), + suppress([U, _, Pere, A], Pu, _), + calculate_solution(Q, [U, Pere, A],Ui, [], L), + affiche_solution(L). + +aetoile(Pf, Pu, Q) :- + suppress_min([_, U],Pf, PfNext), + suppress([U, [F, H, G], Pere, A], Pu, PuNext), + expand(U, G, L), + loop_successors(L, PfNext, PuNext, Q, PfFinal, PuFinal), + insert([U, [F, H, G], Pere, A], Q, QFinal), + aetoile(PfFinal, PuFinal, QFinal). + +loop_successors([], Pf, Pu, _, Pf, Pu). + +loop_successors([[S, _, _, _] | Next], Pf, Pu, Q, PfFinal, PuFinal) :- + belongs([S, _, _, _], Q), + loop_successors(Next, Pf, Pu, Q, PfFinal, PuFinal). + +loop_successors([[S, [F, _, _], _, _] | Next], Pf, Pu, Q, PfFinal, PuFinal) :- + belongs([S, [F1, _, _], _, _], Pu), + F >= F1, + loop_successors(Next, Pf, Pu, Q, PfFinal, PuFinal). + +loop_successors([[S, [F, G, H], Pere, Act] | Next], Pf, Pu, Q, PfFinal, PuFinal) :- + belongs([S, [F1, H1, G1], Pere1, Act1], Pu), + F1 > F, + suppress([[F1, H1, G1], S], Pf, Pf1), + suppress([S, [F1, H1, G1], Pere1, Act1], Pu, Pu1), + insert([[F, H, G], S], Pf1, Pf2), + insert([S, [F, G, H], Pere, Act], Pu1, Pu2), + loop_successors(Next, Pf2, Pu2, Q, PfFinal, PuFinal). + +loop_successors([[S, [F, G, H], Pere, Act] | Next], Pf, Pu, Q, PfFinal, PuFinal) :- + insert([[F, H, G], S], Pf, Pf2), + insert([S, [F, G, H], Pere, Act], Pu, Pu2), + loop_successors(Next, Pf2, Pu2, Q, PfFinal, PuFinal). + +calculate_solution(_, [U, _, _],U, L, [[U, nil] | L]). + +calculate_solution(Q, [U, Pere, A],Ui, L, Lf) :- + write("1"), + suppress([Pere, _, NewPere, NewA], Q, NewQ), + calculate_solution(NewQ, [Pere, NewPere, NewA],Ui, [[U, A] | L], Lf). + +test_calculate_solution() :- + final_state(F), + Av = [[a,b,c], [h,f,d], [g, vide, e]], + empty(Qi), + insert([Av, [1, 1, 0], nil, nil], Qi, Q), + writeln(Q), + writeln(F), + writeln(Av), + calculate_solution(Q, [F, Av, up], Av, [], L), + nl, + writeln(L). + + +affiche_solution_aux([]). + +affiche_solution_aux([[U, A] | Next]) :- + writeln(" | "), + writeln(" | "), + write(" "), + writeln(A), + writeln(" | "), + writeln(" V "), + writeln(U), + affiche_solution_aux(Next). + + +affiche_solution([[U, _] | Next]) :- + writeln(U), + affiche_solution_aux(Next). + +test_affiche_solution() :- + final_state(F), + Av = [[a,b,c], [h,f,d], [g, vide, e]], + empty(Qi), + insert([Av, [1, 1, 0], nil, nil], Qi, Q), + calculate_solution(Q, [F, Av, up], Av, [], L), + affiche_solution(L). + + +valid([State, [Fs, Hs, Gs], U, Action], G) :- + rule(Action,_, U, State), + heuristique(State, Hs), + Gs is G + 1, + Fs is Gs + Hs. + + +expand(U, G, L) :- + Gs is G + 1, + findall([State, [Fs, Hs, Gs], U, Action], valid([State, [Fs, Hs, Gs], U, Action], G), L). + +test_expand() :- + initial_state(Ini), + expand(Ini, 0, LIni), + write(LIni), + nl. + + + + + + diff --git a/avl.pl b/avl.pl new file mode 100644 index 0000000..ddfdc28 --- /dev/null +++ b/avl.pl @@ -0,0 +1,367 @@ +%*************************** +% Gestion d'un AVL en Prolog +%*************************** + +%*************************** +% INSA TOULOUSE - P.ESQUIROL +% mars 2017 +%*************************** + +%************************* +% unit tests : OK +% integration aetoile : OK +%************************* + +% Les AVL sont des arbres BINAIRES DE RECHERCHE H-EQUILIBRES : +% La hauteur de l'avl A est définie par : +% -1, si A est vide (A=nil) +% 1 + max( hauteur(ss_arbre_gauche(A)), hauteur(ss_arbre_droitee(A)) ) sinon + +% Tout noeud de l'arbre est soit : +% - une feuille +% - un noeud interne tel que la différence de hauteur entre le sous-arbre droit +% et le sous-arbre gauche appartient à [-1,0,+1] + + +%*********************************************** +% PREDICATS EXPORTES ET COMPLEXITE ALGORITHMIQUE +%*********************************************** +% soit N = nombre de noeuds de l'arbre % UTILITE POUR A* +% % ---------------- +% empty(?Avl) O(1) %<<< initialisation de P et Q +% height(+Avl, ?Height) O(1) +% put_flat(+Avl) O(N) +% put_90(+Avl) O(N) +% belongs(+Elem, +Avl) O(log N) %<<< appartenance d'un noeud à Q +% subtree(+Elem, +Avl, Ss_Avl) O(log N) +%insert(+Elem, +Avant, ?Apres) O(log N) %<<< insertion d'un nouveau noeud dans P ou dans Q +% suppress(+Elem,+Avant,?Apres) O(log N) %<<< mise à jour <=> suppression puis insertion +% suppress_min(?Min,+Avant,?Apres) O(log N) %<<< supression du noeud minimal +% suppress_max(?Max,+Avant,?Apres) O(log N) + +%**************************** +% Prédicats internes (prives) +%**************************** + +% left_rotate(+Avant, ?Apres) O(1) +% right_rotate(+Avant, ?Apres) O(1) +% left_balance(+Avant, ?Apres) O(1) +% right_balance(+Avant, ?Apres) O(1) + + + + %------------------------------ + % Constructeur et test AVL vide + %------------------------------ + +empty(nil). + + %----------------- + % Hauteur d'un AVL + %----------------- + % par convention, un avl vide a une hauteur de -1 + % sinon la hauteur est enregistree au meme niveau que la racine de l'avl + % elle n'est pas calculee recursivement "from scratch" + % elle est mise à jour de façon incrémentale, apres chaque insertion ou suppression + % d'ou sa complexité en O(1) :-) + +height(nil, -1). +height(avl(_G,_R,_D, H), H). + + %------------------- + % Affichage d'un AVL + %------------------- + % dans l'ordre croissant (lexicographique) + +put_flat(nil). +put_flat(avl(G,R,D,_H)) :- + put_flat(G), + nl, write(R), + put_flat(D). + + %---------------------------- + % Affichage (couché) d'un AVL + %---------------------------- + +put_90(Avl) :- + nl, writeln('----------------------------------'), + put_90(Avl,""). + +put_90(nil,Str) :- + write(Str), write('.'). +put_90(avl(G,R,D,_H),Str) :- + append_strings(Str, " ", Str2), + put_90(D,Str2), + nl, write(Str), write(R),nl, + put_90(G,Str2). + + %----------------------------------------- + % Appartenance d'un element donne a un AVL + %----------------------------------------- + +belongs(Elem, avl(G,Racine,D,_Hauteur)) :- + (Elem = Racine -> + true + ; + (Elem @< Racine -> + belongs(Elem, G) + ; + belongs(Elem, D) %Racine @< Elem + ) + ). + + %------------------------------------------------------------ + % Recherche du sous-arbre qui a comme racine un element donne + %------------------------------------------------------------ + +subtree(Elem, avl(G,Racine,D,H), A) :- + (Elem = Racine -> + A = avl(G,Racine,D,H) + ; + (Elem @< Racine -> + subtree(Elem,G,A) + ; + subtree(Elem,D,A) %Racine @< Elem + ) + ). + + %---------------------- + % Rotations dans un avl + %---------------------- + % Les rotations ci-dessous décrivent uniquement les cas ou la rotation est possible. + % Dans les autres cas, ces relations échouent ; plus précisément : + % a/ si l'arbre est un avl vide, alors aucune rotation n'est possible ; + % b/ si l'arbre est un avl non vide mais si son ss-arbre gauche est un avl vide + % alors la rotation droite n'est pas possible ; + % c/ si l'arbre est un avl non vide mais si son ss-arbre droite est un avl vide + % alors la rotation gauche n'est pas possible. + +right_rotate(avl(G,R,D,_H), A_Apres) :- + height(D,HD), + G = avl(SG,RG,SD,_HG), + height(SD,HSD), + H_Inter is 1 + max(HSD, HD), + Inter = avl(SD,R,D,H_Inter), + height(SG,HSG), + H_Apres is 1 + max(HSG,H_Inter), + A_Apres = avl(SG,RG,Inter,H_Apres). + +left_rotate(avl(G,R,D,_), A_Apres) :- + height(G,HG), + D = avl(SG,RD,SD,_), + height(SG,HSG), + H_Inter is 1 + max(HSG, HG), + Inter = avl(G,R,SG,H_Inter), + height(SD,HSD), + H_Apres is 1 + max(H_Inter,HSD), + A_Apres = avl(Inter,RD,SD,H_Apres). + + %--------------------------------- + % Insertion equilibree dans un avl + %--------------------------------- + % On suppose que l'arbre avant insertion est equilibré (difference de hauteur + % entre les ss-arbres gauche et droite de 1 au maximum) + % L'insertion doit assurer qu'apres insertion l'arbre est toujours equilibre + % sinon les rotations necessaires sont effectuees. + + % On suppose que les noeuds contiennent des informations que l'on peut comparer + % a l'aide d'une relation d'ordre lexicographique (la cle c'est l'info elle-meme) + % En prolog, c'est la relation '@<' + % On peut comparer par exemple des integer, des string, des constantes, + % des listes d'entiers, des listes de constantes, etc ... bref, des termes clos + % T1 @< T2 est vrai si T1 est lexicographiquement inférieur a T2. + +insert(Elem, nil, avl(nil,Elem,nil,0)). +insert(Elem, AVL, NEW_AVL) :- + AVL = avl(Gauche,Racine,Droite,_Hauteur), + (Elem = Racine -> + % l'élément est déjà present, pas d'insertion possible + fail + ; + (Elem @< Racine -> + % insertion dans le ss-arbre gauche + insert(Elem, Gauche, New_Gauche), + height(New_Gauche, New_HG), + height(Droite, HD), + H_Int is 1+max(New_HG, HD), + AVL_INT = avl(New_Gauche, Racine, Droite, H_Int), + right_balance(AVL_INT, NEW_AVL) + ; + % Elem @> Racine + % insertion dans le ss-arbre droite + insert(Elem, Droite, New_Droite), + height(New_Droite, New_HD), + height(Gauche, HG), + H_Int is 1+max(New_HD, HG), + AVL_INT =avl(Gauche, Racine,New_Droite, H_Int), + left_balance(AVL_INT, NEW_AVL) + ) + ). + + %------------------------------------------------ + % Suppression d'un element quelconque dans un avl + %------------------------------------------------ + % On suppose que l'élément à supprimer appartient bien à l'AVL, + % sinon le predicat échoue (en particulier si l'AVL est vide). + +suppress(Elem, AVL, NEW_AVL) :- + AVL = avl(Gauche, Racine, Droite, _Hauteur), + (Elem = Racine -> + % cas de la suppression de la racine de l'avl + (Gauche = nil -> % cas simple d'une feuille ou d'un avl sans fils gauche + NEW_AVL = Droite + ; + (Droite = nil -> % cas simple d'un avl avec fils gauche mais sans fils droit + NEW_AVL = Gauche + ; + % cas d'un avl avec fils gauche ET fils droit + %Gauche \= nil + %Droite \= nil + suppress_max(Max, Gauche, New_Gauche), + AVL_INT = avl(New_Gauche,Max,Droite,_), + left_balance(AVL_INT, NEW_AVL) + ) + ) + ; + % cas des suppressions d'un element autre que la racine + (Elem @< Racine -> + % suppression dans le ss-arbre gauche + suppress(Elem, Gauche, New_Gauche), + AVL_INT = avl(New_Gauche, Racine, Droite,_), + left_balance(AVL_INT, NEW_AVL) + ; + %Racine @< Droite + % suppression dans le ss-arbre droite + suppress(Elem, Droite, New_Droite), + AVL_INT = avl(Gauche, Racine, New_Droite,_), + right_balance(AVL_INT, NEW_AVL) + ) + ). + + %------------------------------------------------------- + % Suppression du plus petit element dans un avl non vide + %------------------------------------------------------- + % Si l'avl est vide, le prédicat échoue + +suppress_min(Min, AVL, NEW_AVL) :- + AVL = avl(Gauche,Racine,Droite, _Hauteur), + (Gauche = nil -> + Min = Racine, + NEW_AVL = Droite + ; + % Gauche \= nil + suppress_min(Min, Gauche, New_Gauche), + AVL_INT = avl(New_Gauche, Racine, Droite,_), + left_balance(AVL_INT, NEW_AVL) + ). + + %------------------------------------------------------- + % Suppression du plus grand element dans un avl non vide + %------------------------------------------------------- + % Si l'avl est vide, le prédicat échoue + +suppress_max(Max, AVL, NEW_AVL) :- + AVL = avl(Gauche,Racine,Droite, _Hauteur), + (Droite = nil -> + Max = Racine, + NEW_AVL = Gauche + ; + % Droite \= nil + suppress_max(Max, Droite, New_Droite), + AVL_INT = avl(Gauche, Racine, New_Droite,_), + right_balance(AVL_INT, NEW_AVL) + ). + + %---------------------------------------- + % Re-equilibrages d'un avl vers la gauche + %---------------------------------------- + % - soit apres insertion d'un element dans le sous-arbre droite + % - soit apres suppression d'un élément dans le sous-arbre gauche + %---------------------------------------------------------------- + +left_balance(Avl, New_Avl) :- + Avl = avl(Gauche, Racine, Droite, _Hauteur), + height(Gauche, HG), + height(Droite, HD), + (HG is HD-2 -> + % le sous-arbre droite est trop haut + Droite = avl(G_Droite, _R_Droite, D_Droite, _HD), + height(G_Droite, HGD), + height(D_Droite, HDD), + (HDD > HGD -> + % une simple rotation gauche suffit + left_rotate(Avl, New_Avl) + ; + % il faut faire une rotation droite_gauche + right_rotate(Droite, New_Droite), + height(New_Droite, New_HD), + H_Int is 1+ max(HG, New_HD), + Avl_Int = avl(Gauche, Racine, New_Droite, H_Int), + left_rotate(Avl_Int, New_Avl) + ) + ; + % la suppression n'a pas desequilibre l'avl + New_Hauteur is 1+max(HG,HD), + New_Avl = avl(Gauche, Racine, Droite, New_Hauteur) + ). + + %---------------------------------------- + % Re-equilibrages d'un avl vers la droite + %---------------------------------------- + % - soit apres insertion d'un element dans le sous-arbre gauche + % - soit apres suppression d'un élément dans le sous-arbre droite + %---------------------------------------------------------------- + +right_balance(Avl, New_Avl) :- + Avl = avl(Gauche, Racine, Droite, _Hauteur), + height(Gauche, HG), + height(Droite, HD), + (HD is HG-2 -> + % le sous-arbre gauche est trop haut + Gauche = avl(G_Gauche, _R_Gauche, D_Gauche, _HG), + height(G_Gauche, HGG), + height(D_Gauche, HDG), + (HGG > HDG -> + % une simple rotation droite suffit + right_rotate(Avl, New_Avl) + ; + % il faut faire une rotation gauche_droite + left_rotate(Gauche, New_Gauche), + height(New_Gauche, New_HG), + H_Int is 1+ max(New_HG, HD), + Avl_Int = avl(New_Gauche, Racine, Droite, H_Int), + right_rotate(Avl_Int, New_Avl) + ) + ; + % la suppression n'a pas desequilibre l'avl + New_Hauteur is 1+max(HG,HD), + New_Avl = avl(Gauche, Racine, Droite, New_Hauteur) + ). + +%----------------------------------------- +% Arbres utilises pour les tests unitaires +%----------------------------------------- +avl_test(1, nil). +avl_test(2, avl(nil, 1, nil, 0)). +avl_test(3, avl(nil, 1, avl(nil,2,nil,0), 1)). +avl_test(4, avl(avl(nil,1,nil,0),2, nil, 1)). +avl_test(5, avl(avl(nil,1,nil,0), 2, avl(nil,3,nil,0),1) ). +avl_test(6, avl(avl(nil,5,nil,0), 6, avl(nil,7,nil,0),1) ). +avl_test(7, avl(G,4,D,2)) :- + avl_test(5,G), + avl_test(6,D). +avl_test(8, avl(G,5,D,2)) :- + D = avl(nil,6,nil,0), + avl_test(3,G). +avl_test(9, avl(G,3,D,2)) :- + G = avl(nil,1,nil,0), + avl_test(4,D). + +/* Test uniquement valable avec ECLiPSe + +avl_test(10, Final) :- + empty(Init), + (for(I,1,20), fromto(Init,In,Out,Final) do + insert(I,In,Out) + ). +*/ diff --git a/taquin.pl b/taquin.pl new file mode 100644 index 0000000..8dd412a --- /dev/null +++ b/taquin.pl @@ -0,0 +1,263 @@ +/* Fichier du probleme. + +Doit contenir au moins 4 predicats qui seront utilises par A* + + etat_initial(I) % definit l'etat initial + + etat_final(F) % definit l'etat final + + rule(Rule_Name, Rule_Cost, Before_State, After_State) % règles applicables + + heuristique(Current_State, Hval) % calcul de l'heuristique + + +Les autres prédicats sont spécifiques au Taquin. +*/ + + +%:- lib(listut). % Laisser cette directive en commentaire si vous utilisez Swi-Prolog + + % Sinon décommentez la ligne si vous utilisez ECLiPSe Prolog : + % -> permet de disposer du predicat nth1(N, List, E) + % -> permet de disposer du predicat sumlist(List, S) + % (qui sont predefinis en Swi-Prolog) + + +%*************************** +%DESCRIPTION DU JEU DU TAKIN +%*************************** + + %******************** + % ETAT INITIAL DU JEU + %******************** + % format : initial_state(+State) ou State est une matrice (liste de listes) + + +initial_state([ [b, h, c], % C'EST L'EXEMPLE PRIS EN COURS + [a, f, d], % + [g,vide,e] ]). % h1=4, h2=5, f*=5 + + + +% AUTRES EXEMPLES POUR LES TESTS DE A* + +/* +initial_state([ [ a, b, c], + [ g, h, d], + [vide,f, e] ]). % h2=2, f*=2 + +initial_state([ [b, c, d], + [a,vide,g], + [f, h, e] ]). % h2=10 f*=10 + +initial_state([ [f, g, a], + [h,vide,b], + [d, c, e] ]). % h2=16, f*=20 + +initial_state([ [e, f, g], + [d,vide,h], + [c, b, a] ]). % h2=24, f*=30 + +initial_state([ [a, b, c], + [g,vide,d], + [h, f, e]]). % etat non connexe avec l'etat final (PAS DE SOLUTION) +*/ + + + %****************** + % ETAT FINAL DU JEU + %****************** + % format : final_state(+State) ou State est une matrice (liste de listes) + +final_state([[a, b, c], + [h,vide, d], + [g, f, e]]). + + + %******************** + % AFFICHAGE D UN ETAT + %******************** + % format : write_state(?State) ou State est une liste de lignes a afficher + +write_state([]). +write_state([Line|Rest]) :- + writeln(Line), + write_state(Rest). + + +%********************************************** +% REGLES DE DEPLACEMENT (up, down, left, right) +%********************************************** + % format : rule(+Rule_Name, ?Rule_Cost, +Current_State, ?Next_State) + +rule(up, 1, S1, S2) :- + vertical_permutation(_X,vide,S1,S2). + +rule(down, 1, S1, S2) :- + vertical_permutation(vide,_X,S1,S2). + +rule(left, 1, S1, S2) :- + horizontal_permutation(_X,vide,S1,S2). + +rule(right,1, S1, S2) :- + horizontal_permutation(vide,_X,S1,S2). + +find_all_next_state_from_U0(NextState) :- + initial_state(Ini), + rule(_, _, Ini, NextState). + +find_all_action_next_state_from_U0(Action, NextState) :- + initial_state(Ini), + rule(Action, _, Ini, NextState). + +find_all_next_state_from_U0_list(L) :- + findall(NextState, find_all_next_state_from_U0(NextState), L). + +find_all_action_next_state_from_U0_list(L) :- + findall([Action, NextState], find_all_action_next_state_from_U0(Action, NextState), L). + + + +find_all_action_next_state(U, Action, NextState) :- + rule(Action, _, U, NextState). + +find_all_action_next_state_list(U, L) :- + findall([Action, NextState], find_all_action_next_state(Action, NextState), L). + + %*********************** + % Deplacement horizontal + %*********************** + % format : horizontal_permutation(?Piece1,?Piece2,+Current_State, ?Next_State) + +horizontal_permutation(X,Y,S1,S2) :- + append(Above,[Line1|Rest], S1), + exchange(X,Y,Line1,Line2), + append(Above,[Line2|Rest], S2). + + %*********************************************** + % Echange de 2 objets consecutifs dans une liste + %*********************************************** + +exchange(X,Y,[X,Y|List], [Y,X|List]). +exchange(X,Y,[Z|List1], [Z|List2] ):- + exchange(X,Y,List1,List2). + + %********************* + % Deplacement vertical + %********************* + +vertical_permutation(X,Y,S1,S2) :- + append(Above, [Line1,Line2|Below], S1), % decompose S1 + delete(N,X,Line1,Rest1), % enleve X en position N a Line1, donne Rest1 + delete(N,Y,Line2,Rest2), % enleve Y en position N a Line2, donne Rest2 + delete(N,Y,Line3,Rest1), % insere Y en position N dans Rest1 donne Line3 + delete(N,X,Line4,Rest2), % insere X en position N dans Rest2 donne Line4 + append(Above, [Line3,Line4|Below], S2). % recompose S2 + + %*********************************************************************** + % Retrait d une occurrence X en position N dans une liste L (resultat R) + %*********************************************************************** + % use case 1 : delete(?N,?X,+L,?R) + % use case 2 : delete(?N,?X,?L,+R) + +delete(1,X,[X|L], L). +delete(N,X,[Y|L], [Y|R]) :- + delete(N1,X,L,R), + N is N1 + 1. + + + + %******************* + % PARTIE A COMPLETER + %******************* + + %******************************************************************* + % Coordonnees X(colonne),Y(Ligne) d une piece P dans une situation U + %******************************************************************* + % format : coordonnees(?Coord, +Matrice, ?Element) + % Définit la relation entre des coordonnees [Ligne, Colonne] et un element de la matrice + /* + Exemples + + ?- coordonnees(Coord, [[a,b,c],[d,e,f]], e). % quelles sont les coordonnees de e ? + Coord = [2,2] + yes + + ?- coordonnees([2,3], [[a,b,c],[d,e,f]], P). % qui a les coordonnees [2,3] ? + P=f + yes + */ + + wellplaced(U, Lettre) :- + nth1(L, U, Ligne), + nth1(C, Ligne, Lettre), + final_state(Uf), + nth1(L, Uf, Lign2), + nth1(C, Lign2, Lettre). + + + coordonnees([L,C], Mat, Elt) :- + nth1(L, Mat, Ligne), + nth1(C, Ligne, Elt). + + + %************* + % HEURISTIQUES + %************* + +heuristique(U,H) :- +% heuristique1(U, H). % au debut on utilise l'heuristique 1 + heuristique2(U, H). % ensuite utilisez plutot l'heuristique 2 + + + %**************** + %HEURISTIQUE no 1 + %**************** + % Nombre de pieces mal placees dans l'etat courant U + % par rapport a l'etat final F + + + % Suggestions : définir d'abord le prédicat coordonnees(Piece,Etat,Lig,Col) qui associe à une pièce présente dans Etat + % ses coordonnees (Lig= numero de ligne, Col= numero de Colonne) + + % Definir ensuite le predicat malplace(P,U,F) qui est vrai si les coordonnes de P dans U et dans F sont differentes. + % On peut également comparer les pieces qui se trouvent aux mêmes coordonnees dans U et dans H et voir s'il sagit de la + % même piece. + + % Definir enfin l'heuristique qui détermine toutes les pièces mal placées (voir prédicat findall) + % et les compte (voir prédicat length) + badplaced(U, Lettre) :- + coordonnees(Coor, U, Lettre), + Lettre \= vide, + final_state(Uf), + coordonnees(Coor, Uf, Lettre2), + Lettre \= Lettre2. + + heuristique1(U, H) :- + findall(Lettre, badplaced(U, Lettre), L), + length(L, H). %******** + % A FAIRE + %******** + + + %**************** + %HEURISTIQUE no 2 + %**************** + + % Somme des distances de Manhattan à parcourir par chaque piece + % entre sa position courante et sa positon dans l'etat final + get_manhattan_cost(U, Lettre, Cost) :- + final_state(Uf), + coordonnees([L, C], U, Lettre), + coordonnees([L2, C2], Uf, Lettre), + Lettre \= vide, + Cost is abs(L - L2) + abs(C - C2). + + heuristique2(U, H) :- + findall(Cost, get_manhattan_cost(U, _Lettre, Cost), L), + sumlist(L, H). + %******** + % A FAIRE + %******** + + diff --git a/tp_ia1_2021.pdf b/tp_ia1_2021.pdf new file mode 100644 index 0000000000000000000000000000000000000000..23799139b737cce9041a958f95eb5ed22ffd6b51 GIT binary patch literal 302801 zcmbTe1za3U(>J=fJHg$3VOcb|lVCxDySux4f+i3M?iM7tL-61pAOv@};1J+0NzOTW zzVF=kdGDS5%}(`nb@jixt8HewXq6s5_L!nK<#mz&( z3Fg%m5<)YzGkFw6@#g`_g9r3a9ulU;_9muEhEBH5kQ~MBZCq{boFO8WoJ>tDja}@W zC^$euLO>}?8y8b2pp=cFi|MZNk!qdVTY+rL0EbT1Ak2}rw1K>)ImoAU;O~p@4rV6V&?#{Zv^%b5+IOX zX9iN9@reXL0YYtvTG5ap74#e7@2YZkF?4eAa56PRLuN-qrlplsltM%Pv-%!sNEPz& z{ZobF6d+!%f2|=%dGY>Lh9E9Zi0Od1`G6`E9NfJBQ8Wey2GBXTs5Ypm$h`z11ehYP 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