DAG Traversal + Cost in Prolog - prolog

Question

I'm trying to implement a DAG traversal algorithm that also gets the costs between the edges. I think I'm pretty close but queries always return paths that aren't valid. Can anyone take a look and see what I'm missing here?
edge(b, a, 5).
edge(a, u, 10).
edge(u, o, 140).
edge(u, r, 130).
edge(r, o, 20).
edge(r, v, 50).
edge(o, v, 45).
edge(b, v, 20).
path(Start, Start, [], 0).
path(Start, Finish, [Start, Finish], C) :-
edge(Start, Finish, Cost),
C is Cost.
path(Start, Finish, [Start|Path], C) :-
edge(Start, X, Cost),
path(X, Finish, Path, RCost),
C is Cost + RCost.
I'm trying to run path(b, v, S, C).. It is generating all the valid paths, but it's also generating a few invalid paths.
C = 20,
S = [b, v]
C = 200,
S = [b, a, u, o, v]
C = 200,
S = [b, a, u, o]
C = 195,
S = [b, a, u, r, v]
C = 210,
S = [b, a, u, r, o, v]
C = 210,
S = [b, a, u, r, o]
C = 195,
S = [b, a, u, r]
C = 20,
S = [b]
Thanks.

Answer 1

The best graph traversal code I have seen is in this question:
Definition of a path/trail/walk
We can adapt that for your case to be:
edge(b, a, 5).
edge(a, u, 10).
edge(u, o, 140).
edge(u, r, 130).
edge(r, o, 20).
edge(r, v, 50).
edge(o, v, 45).
edge(b, v, 20).
:- meta_predicate path(3,?,?,?).
:- meta_predicate path(3,?,?,?,+).
path(R_3, [X0|Ys], X0,X) :-
path(R_3, Ys, X0,X, [X0]).
path(_R_3, [], X-0,X-0, _).
path(R_3, [X1-Cost2|Ys], X0-Cost,X, Xs) :-
call(R_3, X0,X1,Cost),
non_member(X1, Xs),
path(R_3, Ys, X1-Cost2,X, [X1-Cost2|Xs]).
non_member(_E, []).
non_member(E, [X-_Cost|Xs]) :-
dif(E,X),
non_member(E, Xs).
Then we can query :
?- path(edge,Path,From,To).
Path = [_22918-0],
From = To, To = _22918-0 ;
Path = [b-5, a-0],
From = b-5,
To = a-0 ;
Path = [b-5, a-10, u-0],
From = b-5,
To = u-0 ;
Path = [b-5, a-10, u-140, o-0],
From = b-5,
To = o-0 ;
Path = [b-5, a-10, u-140, o-45, v-0],
From = b-5,
To = v-0 ;
etc
So we get a list of nodes with the cost to get to the next node.
You can then simply sum them like this:
?- path(edge,Path,From,To), pairs_values(Path,Values), sumlist(Values,Sum).
Path = [_24478-0],
From = To, To = _24478-0,
Values = [0],
Sum = 0 ;
Path = [b-5, a-0],
From = b-5,
To = a-0,
Values = [5, 0],
Sum = 5 ;
Path = [b-5, a-10, u-0],
From = b-5,
To = u-0,
Values = [5, 10, 0],
Sum = 15 ;
Path = [b-5, a-10, u-140, o-0],
From = b-5,
To = o-0,
Values = [5, 10, 140, 0],
Sum = 155
etc
or you could adapt the code to count the sum as you go saving sum computation.
In this I think we are assuming that there is only one edge from any one node to another.

Answer 2

You have one error in your code. This:
path(Start, Start, [], 0).
should have been
path(Start, Start, [Start], 0).
otherwise Path in
path(Start, Finish, [Start|Path], C) :-
edge(Start, X, Cost),
path(X, Finish, Path, RCost),
C is Cost + RCost.
comes back empty from that (first) clause, but what you really intended here is for it to contain Finish as the last element.
Indeed this follows from the logical reading of your predicate as well. If path(Start, Start, Path, Cost) is to succeed, it means there's a Path from Start to Start, which is the non-empty [Start]. An empty path is no path at all.
Now all reported paths are valid. Some are reported multiple times, but that's another issue.