%Program for Farmer-Lion-Goat-Cabbage Puzzle

% f=0, c=1, g=2, l=3
achievable(s([0,1,2,3],[]),L).

achievable(s(L1,L2),Visited) :- chooseFarmerSide(L1,L2,L3,FS),chooseOtherSide(L1,L2,L4,OS), getPassenger(X,L3),
	myDelete(0,L3,L5),myDelete(X,L5,L6),noDestruction(L6),orderlyInsert(0,L4,L7),orderlyInsert(X,L7,L8),
	leftSide(L6,FS,L8,OS,L9), rightSide(L6,FS,L8,OS,L10), nott(inList(s(L9,L10),Visited)), write(s(L1,L2)),nl,
	achievable(s(L9,L10),[s(L1,L2)|Visited]).


chooseFarmerSide(L1,L2,L1,left):- inList(0,L1).
chooseFarmerSide(L1,L2,L2,right):- inList(0,L2).
chooseOtherSide(L1,L2,L1,left):- inList(0,L2).
chooseOtherSide(L1,L2,L2,right):- inList(0,L1).

getPassenger(X,L) :- inList(X,L), X =\= 0.
getPassenger(4,L).

noDestruction(L):- nott(goatAndCabbage(L)), nott(goatAndLion(L)).
goatAndCabbage(L):- inList(2,L),inList(1,L).
goatAndLion(L):- inList(2,L),inList(3,L).

leftSide(L1,left,L2,X,L1).
leftSide(L1,X,L2,left,L2).
rightSide(L1,right,L2,X,L1).
rightSide(L1,X,L2,right,L2).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%utility relations
size([],0).
size([X|L],Y) :- size(L,Y2), Y is Y2 + 1.

%List Membership
inList(X,[X|Tail]).
inList(X,[Head|Tail]) :- inList(X,Tail).

% concatenation of two lists
concat([],L,L).
concat([X|L], L2, [X|L3]):- concat(L,L2,L3).

%defining negation
nott(P) :- P,!,fail;true.

%when one list is a prefix of another
prefix([],L).
prefix([X | L1], [X | L2]) :- prefix(L1,L2).

% deleting from a list
myDelete(4,L,L).
myDelete(X,[X | L],L):- X < 4.
myDelete(X, [Y|L1],[Y|L2]):- X < 4, myDelete(X,L1,L2).

% adding to the end of a list
addListEnd(X,[],[X]).
addListEnd(X,[Y|L1],[Y|L2]):- addListEnd(X,L1,L2).

%inserting an integer in numerical order
orderlyInsert(4,L,L).
orderlyInsert(X,[],[X]):- X < 4.
orderlyInsert(X,[Y|L1],[X,Y|L1]):- X < 4,X =< Y.
orderlyInsert(X,[Y|L1],[Y|L2]):- X < 4,X >Y, orderlyInsert(X,L1,L2).

prefSize(L1,L2,N):- prefix(L1,L2),size(L1,N).
prefSize(L1,L2,0).

myMax(N1,N2,N1) :- N1 >= N2.
myMax(N1,N2,N2) :- N2 >= N1.

maxPref(L1,[],0).
maxPref([],L,0).
maxPref(L1,[X|L2],N):- prefSize(X,L1,S1), maxPref(L1,L2,S2), myMax(S1,S2,N).