% task 1

payment(Sum, Coins) :-
    payment_acc(0, Sum, Coins).

payment_acc(Acc, Sum, []) :-
    Acc #= Sum.

payment_acc(Acc, Sum, [coin(Count, Value, Available)|Tail]) :-
    Count in 0..Available,
    NewAcc #= Acc + Count * Value,
    payment_acc(NewAcc, Sum, Tail).

% task 2.1

distance(c1, c2, 10, 1). distance(c1, c3, 0, 0). distance(c1, c4, 7, 1).
distance(c1, c5, 5, 1). distance(c2, c3, 4, 1). distance(c2, c4, 12, 1).
distance(c2, c5, 20, 1). distance(c3, c4, 0, 0). distance(c3, c5, 0, 0).
distance(c4, c5, 0, 0). distance(c2, c1, 10, 1). distance(c3, c1, 0, 0).
distance(c4, c1, 7, 1). distance(c5, c1, 5, 1). distance(c3, c2, 4, 1).
distance(c4, c2, 12, 1). distance(c5, c2, 20, 1). distance(c4, c3, 0, 0).
distance(c5, c3, 0, 0). distance(c5, c4, 0, 0).

% arity 4 predicate
plan(Cabin1, Cabin2, Path, TotalDistance) :-
    plan(Cabin1, Cabin2, [Cabin1], Path, TotalDistance).

% base case
plan(Cabin1, Cabin2, Visited, Path, Distance) :-
    not(Cabin1 = Cabin2),
    distance(Cabin1, Cabin2, Distance, 1),
    append(Visited, [Cabin2], Path).

% recursive case
plan(Cabin1, Cabin2, Visited, Path, TotalDistance) :-
    not(Cabin1 = Cabin2),
    distance(Cabin1, CabinX, Distance, 1),
    \+ member(CabinX, Visited),
    append(Visited, [CabinX], NewVisited),
    plan(CabinX, Cabin2, NewVisited, Path, SubDistance),
    TotalDistance is Distance + SubDistance.

% task 2.2

bestplan(Cabin1, Cabin2, ShortestPath, ShortestDistance) :-
    findall([Path, Distance], (plan(Cabin1, Cabin2, Path, Distance)), Solutions),
    sort(2, @=<, Solutions, [ShortestSolution|_]),
    [ShortestPath, ShortestDistance] = ShortestSolution.