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Les graphes

Les graphes. Représentation: g([Noeud, ...],[arc(Noeud1,Noeud2,Valeur), ...]). arc(g(Ns,Arcs),N1,N2,Valeur):- member(arc(N1,N2,Valeur),Arcs). % pour un graphe non-dirigé arc(g(Ns,Arcs),N1,N2,Valeur):- member(arc(N1,N2,Valeur),Arcs);

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Les graphes

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  1. Les graphes Représentation: g([Noeud, ...],[arc(Noeud1,Noeud2,Valeur), ...]). arc(g(Ns,Arcs),N1,N2,Valeur):- member(arc(N1,N2,Valeur),Arcs). % pour un graphe non-dirigé arc(g(Ns,Arcs),N1,N2,Valeur):- member(arc(N1,N2,Valeur),Arcs); member(arc(N2,N1,Valeur),Arcs).

  2. Voisins dans un graphe voisins(Graphe,Noeud,Voisins):- setof((N,Arc),arc(Graphe,Noeud,N,Arc),Voisins). ?- voisins(g([a,b,c,d,e,f], [arc(a,b,3),arc(a,c,5),arc(a,d,7),arc(e,f,1),arc(d,f,6)]),c,V). V = [ (a, 5)]. ?- voisins(g([a,b,c,d,e,f], [arc(a,b,3),arc(a,c,5),arc(a,d,7),arc(e,f,1),arc(d,f,6)]),a,V). V = [ (b, 3), (c, 5), (d, 7)].

  3. Coloriage de graphe coloriage(g(Ns,Arcs),Couleurs,Coloriage):- genere(Ns,Couleurs,Coloriage), test(Arcs,Coloriage). genere([],_,[]). genere([N|Ns],Couleurs,[(N,C)|Q]):- member(C,Couleurs), genere(Ns,Couleurs,Q). test([],_). test([arc(N1,N2,_)|Ns],Coloriage):- member((N1,C1),Coloriage), member((N2,C2),Coloriage), C1\=C2, test(Ns,Coloriage).

  4. Coloriage de graphe ?- coloriage(g([a,b,c,d,e,f], [arc(a,b,3),arc(a,c,5),arc(a,d,7),arc(e,f,1),arc(d,f,6)]), [rouge,bleu,blanc,vert],V). V = [ (a, rouge), (b, bleu), (c, bleu), (d, bleu), (e, rouge), (f, blanc)] ; V = [ (a, rouge), (b, bleu), (c, bleu), (d, bleu), (e, rouge), (f, vert)] ; V = [ (a, rouge), (b, bleu), (c, bleu), (d, bleu), (e, bleu), (f, rouge)]; …

  5. Labyrinthe connecte(0,1). % depart = 0 connecte(1,2). connecte(2,6). connecte(6,5). connecte(6,7). connecte(5,4). connecte(5,9). connecte(9,8). connecte(8,12). connecte(9,10). connecte(10,11). connecte(9,13). connecte(13,14). connecte(14,15). %fin = 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  6. Labyrinthe successeur(A,B):-connecte(A,B). successeur(A,B):-connecte(B,A). but(15). resoudre([Fin|Chemin],[Fin|Chemin]):-but(Fin). resoudre([Courant|Chemin],Solution):- successeur(Courant,Suivant), \+member(Suivant,Chemin),write(Suivant),nl, resoudre([Suivant,Courant|Chemin],Solution).

  7. Labyrinthe ?- resoudre([0],S). 1 2 6 5 9 8 12 10 11 13 14 15 S = [15, 14, 13, 9, 5, 6, 2, 1, 0] ; 7 4 false.

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