aoc23/08/part2.pl

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:- op(700, xfx, l).
:- op(700, xfx, r).
From l To :- From to To-_.
From r To :- From to _-To.
answer(Answer) :-
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findall(Node, (Node to _, atom_chars(Node, [_, _, a])), Starts),
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routes(Starts, [Route1 | RestOfRoutes]),
foldl(unify2, RestOfRoutes, Route1, _-(_-Answer-_)).
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% unify2 combines 2 routes into one with its own stride-offsets-dests
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unify2(Route1, Route2, NewRoute) :-
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writef('Combining %t + %t', [Route1, Route2]),
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once(findnsols(2, S, converge(Route1, Route2, S), SolutionPair)),
SolutionPair = [NewA-LenA-NewZ, _-LenB-_],
NewStride is LenB - LenA,
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NewRoute = NewA-(NewStride-LenA-[0-NewZ]),
writef(' --> %t\n', [NewRoute]).
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% Len = Stride1*X1 + Offset1 + Dest1 = Stride2*X2 + Offset2 + Dest2
% For performance, Route1's Stride should =< Route2's Stride
converge(Route1, Route2, NewA-Len-NewZ) :-
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Route1 = A1-(Stride1-Offset1-Dests1),
Route2 = A2-(Stride2-Offset2-Dests2),
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natnum(X2),
pick([Dests1, Dests2], [Dest1-Z1, Dest2-Z2]),
0 is (Stride2*X2 + Offset2 + Dest2 - Offset1 - Dest1) mod Stride1,
Len is Stride2*X2 + Offset2 + Dest2,
atom_concat(A1, A2, NewA), atom_concat(Z1, Z2, NewZ).
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routes(Starts, Routes) :-
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maplist([S, S-Route]>>(route_at(S, Route)), Starts, Routes).
% route_at(N, Node, Dests, AllDests) means going N steps will arrive at Node
% passing through Dests.
route_at(Start, Route) :- route_at(0, Start, [], Route).
route_at(N, FirstZ, [FirstZN-FirstZ | Zs], Stride-Offset-AllZs) :-
Stride is N - FirstZN, direction_looped(Stride),
Offset is FirstZN,
maplist({Offset}/[N-X, M-X]>>(M is N-Offset), [FirstZN-FirstZ | Zs], AllZs),
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!.
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route_at(N, Node, Dests, AllDests) :-
( atom_chars(Node, [_, _, z])
-> append(Dests, [N-Node], NextDests)
; NextDests = Dests),
Nplus1 is N + 1, step_at(N, Step), call(Step, Node, NextNode),
route_at(Nplus1, NextNode, NextDests, AllDests).
% Step is the N-th step (counting starts from 0).
step_at(N, Step) :-
direction_list(Dir), length(Dir, DirLen), Remainder is N mod DirLen,
nth0(Remainder, Dir, Step).
direction_looped(Len) :- direction_list(D), length(D, DLen), 0 is Len mod DLen.
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direction_list(Dir) :- direction(Str), atom_chars(Str, Dir).
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% pick one item from each sublist of ListOfLists & put them into Items in order.
% [[1,2,3], [4], [5,6]] -> [1,4,5]; [1,4,6]; [2,4,5]; [2,4,6]; [3,4,5]; [3,4,6].
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pick(ListOfLists, Items) :-
maplist([SubList, X]>>(member(X, SubList)), ListOfLists, Items).
natnum(0).
natnum(N) :- natnum(N0), N is N0 + 1.