clpz:monotonic.
:- use_module(library(tabling)).
:- use_module(library(ugraphs)).

line(L-Outs)  --> seq(L), ": ", sequence(seq," ",Outs).
assert_nbs(G) :- vertices(G,Vs), abolish(nbs/2), maplist(G+\V^(neighbours(V,G,Ns), assertz(nbs(V,Ns))),Vs).
input :- phrase_from_file(sequence(line,"\n",G),"i/11.in"), assert_nbs(["out"-[]|G]).

:- table paths/3.
paths(V0,V0,1).
paths(V, V0,N) :- dif(V0,V), nbs(V0,Ns), maplist(paths(V),Ns,Ps), sum(Ps,N).

part2(P2) :-
	permutation(["fft","dac"],[A,B]), paths(B,A,N1), #N1 #> 0, paths(A,"svr",N0), paths("out",B,N2), #P2 #= #N0 * #N1 * #N2.

% do part 2 first, otherwise some weird backtracking stuff happens and it succeeds twice.
solve(P1,P2) :- input, part2(P2), paths("out","you",P1).
test         :- make_test(day(11),solve,788,316291887968000).

I was expecting something super difficult, was surprised to find that today was this easy.

~/aoc25pl/11