/*Jacob Besse
Prolog*/

/*This is the data set.*/

edge(a,b,2).  edge(a,c,3).  edge(a,d,1).
edge(b,d,2).  edge(b,e,2).  edge(b,f,4).
edge(c,a,3).  edge(c,d,2).  edge(c,e,2).
edge(d,a,1).  edge(d,b,2).
edge(e,c,2).  edge(e,d,2).  edge(e,f,1).
edge(f,b,4).  edge(f,c,3).  edge(f,e,1).

len([], 0).
len([_|T], N):- len(T, X), N is X+1 .

best_path(Visited, Total):- path(a, a, Visited, Total).

path(Start, Fin, Visited, Total) :- path(Start, Fin, [Start], Visited, 0, Total).

path(Start, Fin, CurrentLoc, Visited, Costn, Total) :-
    edge(Start, StopLoc, Distance), NewCostn is Costn + Distance, \+ member(StopLoc, CurrentLoc),
    path(StopLoc, Fin, [StopLoc|CurrentLoc], Visited, NewCostn, Total).

path(Start, Fin, CurrentLoc, Visited, Costn, Total) :-
    edge(Start, Fin, Distance), reverse([Fin|CurrentLoc], Visited), len(Visited, Q),
    (Q\=7 -> Total is 100000; Total is Costn + Distance).

shortest_path(Path):-setof(Cost-Path, best_path(Path,Cost), Holder),pick(Holder,Path).

best(Cost-Holder,Bcost-_,Cost-Holder):- Cost<Bcost,!.
best(_,X,X).

pick([Cost-Holder|R],X):- pick(R,Bcost-Bholder),best(Cost-Holder,Bcost-Bholder,X),!.
pick([X],X).