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findapath(X, Y, W, [X,Y], _) :- edge(X, Y, W). % findapath between X and Y has weight W if there is an edge between X and Y of weight W
findapath(X, Y, W, [X|P], V) :- % else findapath between X and Y
\+ member(X, V), % is true
edge(X, Z, W1), % if we can findapath between X and Z with weight W1
findapath(Z, Y, W2, P, [X|V]), % and there is findapat between Z and Y of weight W2
W is W1 + W2. % where W is W1 + W2
findminpath(X, Y, W, P) :-
\+ solution(_, _),
findapath(X, Y, W1, P1, []),
assertz(solution(W1, P1)),
!, findminpath(X,Y,W,P).
findminpath(X, Y, _, _) :-
findapath(X, Y, W1, P1, []),
solution(W2, P2),
W1 < W2,
retract(solution(W2, P2)),
asserta(solution(W1, P1)), fail.
findminpath(_, _, W, P) :- solution(W,P), retract(solution(W,P)).
main :-
write('the minimum cost that we must pay.'),
write('path that has the minimum cost.'),
nl, halt.
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