/* exercice 2*/

engendre(0,[]).
engendre(N,[1|L]):-N>0, P is N-1, engendre(P,L).
engendre(N,[0|L]):-N>0, P is N-1, engendre(P,L).

est_dense_aux([],_).
est_dense_aux([0|L],M):-M>0, P is M-1, est_dense_aux(L,P).
est_dense_aux([1|L],M):-S is M+1, est_dense_aux(L,S).
est_dense(L):-est_dense_aux(L,0).

denses(N,L):-engendre(N,L),est_dense(L).

denses_bis(N,L):-aux(N,0,L).
aux(0,_,[]).
aux(N,K,[1|L]):-N>0, S is K+1, P is N-1, aux(P,S,L).
aux(N,K,[0|L]):-N>0, K>0, S is K-1, P is N-1, aux(P,S,L).

card_dense1(N,R):-setof(L,denses(N,L),H),length(H,R).
/*card_dense2(N,R):-setof(L,denses_bis(N,L),H),length(H,R).*/

/* exercice 3*/

map2_somme([],[],[]):-!.
map2_somme([],_,_):-write("Arguments non valides"), fail.
map2_somme(_,[],_):-write("Arguments non valides"), fail.
    map2_somme([X|L],[Y|G],[Z|R]):-(integer(X),integer(Y)) -> (Z is X+Y, map2_somme(L,G,R)); (write("Arguments non valides"), fail).

map2(_,[],[],[]):-!.
map2(_,[],_,_):-write("Arguments non valides"), fail.
map2(_,_,[],_):-write("Arguments non valides"), fail.

map2(P,[X|L],[Y|G],[Z|H]):-(integer(X),integer(Y)) -> (Q=..[P,X,Y,Z],Q,map2(P,L,G,H));  (write("Arguments non valides"), fail).

produit(X,Y,Z):- Z is X*Y.

map3(_,[],[],[],[]):-!.
map3(_,[],_,_,_):-write("Arguments non valides"), fail.
map3(_,_,[],_,_):-write("Arguments non valides"), fail.
map3(_,_,_,[],_):-write("Arguments non valides"), fail.

map3(P,[X|L],[Y|G],[W|K],[Z|H]):-(integer(X),integer(Y),integer(W)) -> (Q=..[P,X,Y,W,Z],Q,map3(P,L,G,K,H));  (write("Arguments non valides"), fail).


somme_3(A,B,C,D):-D is A+B+C.
/* exercice 4*/



est_formule(X):-atomic(X),!.
est_formule(neg(X)):-est_formule(X).
est_formule(et(X,Y)):-est_formule(X),est_formule(Y).
est_formule(ou(X,Y)):-est_formule(X),est_formule(Y).


symboles(X,1,0,0,0):-atomic(X).
symboles(neg(P),A,N,E,O):-symboles(P,A,M,E,O), N is M+1.
symboles(et(P,Q),A,N,E,O):-symboles(P,Aa,Na,Ea,Oa),
    symboles(Q,Ab,Nb,Eb,Ob), A is Aa+Ab, N is Na+Nb, E is Ea+Eb+1,O is Oa+Ob.
symboles(ou(P,Q),A,N,E,O):-symboles(P,Aa,Na,Ea,Oa),
    symboles(Q,Ab,Nb,Eb,Ob), A is Aa+Ab, N is Na+Nb, E is Ea+Eb,O is Oa+Ob+1.


variables(X,[X]):-atomic(X),!.
variables(neg(X),L):-variables(X,L).
variables(et(X,Y), L):-variables(X,L1),variables(Y,L2),union(L1,L2,L).
variables(ou(X,Y), L):-variables(X,L1),variables(Y,L2),union(L1,L2,L).

combine([],[],[]).
combine([X|L],[Y|G],[(X,Y)|H]) :- combine(L,G,H).

assoc(X,[(X,Y)|_],Y):-!.
assoc(X,[_|L],Y):-assoc(X,L,Y).

combiner([],[]).
    combiner([X|L],[(X,Y)|R]):-combiner(L,R),(Y=1;Y=0).

evaluer(X,A):-atomic(X),  assoc(X,A,1).
evaluer(neg(X),A):-not(evaluer(X,A)).
evaluer(et(X,Y),A):-evaluer(X,A),evaluer(Y,A).
evaluer(ou(X,Y),A):-(evaluer(X,A), !); evaluer(Y,A).


/* sat(F,A):-variables(F,L), length(L,N), engendre(N,H), combine(L,H,A),
evaluer(F,A,1).*/

satisfait(F,A):-variables(F,L), combiner(L,A),
evaluer(F,A).