d8p2 final optimized general solution

08/part2.pl

@@ -5,51 +5,32 @@ From r To :- From to _-To.
 
 answer(Answer) :-
     starts(Starts),
-    routes(Starts, Routes),
+    routes(Starts, [Route1 | RestOfRoutes]),
-    collapse_routes(Routes, _-(_-Answer-_)).
+    foldl(unify2, RestOfRoutes, Route1, _-(_-Answer-_)).
-
-collapse_routes([X], X).
-collapse_routes(Routes, Collapsed) :-
-    writef('Collapsing: %t\n', [Routes]),
-    sort(2, @=<, Routes, [Route1, Route2 | CdrRoutes]),
-    unify2(Route1, Route2, NewRoute),
-    collapse_routes([NewRoute | CdrRoutes], Collapsed).
 
 % unify2 combines 2 routes into one with its own stride-offsets-dests
-unify2(Route1, Route2, Route12) :- unify2(Route1, Route2, 0-0-0-0, [], Route12).
+unify2(Route1, Route2, NewRoute) :-
-unify2(Route1, Route2, N1-Dest1-N2-Dest2, Founds, NewRoute) :-
+    once(findnsols(2, S, converge(Route1, Route2, S), SolutionPair)),
+    SolutionPair = [NewA-LenA-NewZ, _-LenB-_],
+    NewStride is LenB - LenA,
+    NewRoute = NewA-(NewStride-LenA-[0-NewZ]).
+
+% Len = Stride1*X1 + Offset1 + Dest1 = Stride2*X2 + Offset2 + Dest2
+% For performance, Route1's Stride should =< Route2's Stride
+converge(Route1, Route2, NewA-Len-NewZ) :-
+    writef('Combining %t - %t\n', [Route1, Route2]),
     Route1 = A1-(Stride1-Offset1-Dests1),
     Route2 = A2-(Stride2-Offset2-Dests2),
-    nth0(Dest1, Dests1, C1-Z1),
+    natnum(X2),
-    nth0(Dest2, Dests2, C2-Z2),
+    pick([Dests1, Dests2], [Dest1-Z1, Dest2-Z2]),
-    Len1 is Offset1 + Stride1*N1 + C1,
+    0 is (Stride2*X2 + Offset2 + Dest2 - Offset1 - Dest1) mod Stride1,
-    Len2 is Offset2 + Stride2*N2 + C2,
+    Len is Stride2*X2 + Offset2 + Dest2,
-    next(Dests1, N1-Dest1, NextN1-NextDest1),
+    atom_concat(A1, A2, NewA), atom_concat(Z1, Z2, NewZ).
-    (   Len1 =:= Len2
-    ->  (   Founds = [OldLen]
-        ->  atom_concat(A1, A2, NewA), atom_concat(Z1, Z2, NewZ),
-            NewStride is Len1 - OldLen,
-            NewRoute = NewA-(NewStride-OldLen-[0-NewZ]),
-            !
-        ;   unify2(Route1, Route2, NextN1-NextDest1-N2-Dest2, [Len1], NewRoute)
-        )
-    ;   Len1 < Len2
-    ->  unify2(Route1, Route2, NextN1-NextDest1-N2-Dest2, Founds, NewRoute)
-    ;   next(Dests2, N2-Dest2, NextN2-NextDest2),
-        unify2(Route1, Route2, N1-Dest1-NextN2-NextDest2, Founds, NewRoute)
-    ).
-
-% next(Dests, NumberOfLoops-WhichInternalZ, NextNumberOfLoops-NextInternalZ)
-next(Dests, NLoops-Dest, NextNLoops-NextDest) :-
-    length(Dests, DestsLen),
-    (   Dest < DestsLen - 1
-    ->  NextNLoops is NLoops, NextDest is Dest + 1
-    ;   NextNLoops is NLoops + 1, NextDest is 0).
 
 routes(Starts, Routes) :-
     maplist([S, S-Route]>>(zloop(S, Route)), Starts, Routes).
 
-% zloop builds a route (Stride-Offset-Internals for a particular starting node.
+% zloop builds a route (Stride-Offset-Internals) for a particular starting node.
 zloop(Node, Route) :- zloop([], Node, 0, [], Route).
 zloop(_Direction, _Node, _Index, Zs, Stride-Offset-Dests) :-
     Zs = [FirstZIndex-Z | _], reverse(Zs, [LastZIndex-Z | ReversedZs]),
@@ -81,3 +62,10 @@ next_step([], Move, Remain) :- direction_list([Move | Remain]).
 
 direction_list(Dir) :- direction(Str), atom_chars(Str, Dir).
 direction_len(Len) :- direction_list(D), length(D, Len).
+
+% pick([[1,2,3], [4], [5,6]], X). X = [1,4,5]; X = [1,4,6]; X = [2,4,5]; ...
+pick(ListOfLists, Items) :-
+    maplist([SubList, X]>>(member(X, SubList)), ListOfLists, Items).
+
+natnum(0).
+natnum(N) :- natnum(N0), N is N0 + 1.

08/part2.unoptimized.pl

@@ -0,0 +1,83 @@
+:- op(700, xfx, l).
+:- op(700, xfx, r).
+From l To :- From to To-_.
+From r To :- From to _-To.
+
+answer(Answer) :-
+    starts(Starts),
+    routes(Starts, Routes),
+    collapse_routes(Routes, _-(_-Answer-_)).
+
+collapse_routes([X], X).
+collapse_routes(Routes, Collapsed) :-
+    writef('Collapsing: %t\n', [Routes]),
+    sort(2, @=<, Routes, [Route1, Route2 | CdrRoutes]),
+    unify2(Route1, Route2, NewRoute),
+    collapse_routes([NewRoute | CdrRoutes], Collapsed).
+
+% unify2 combines 2 routes into one with its own stride-offsets-dests
+unify2(Route1, Route2, Route12) :- unify2(Route1, Route2, 0-0-0-0, [], Route12).
+unify2(Route1, Route2, N1-Dest1-N2-Dest2, Founds, NewRoute) :-
+    Route1 = A1-(Stride1-Offset1-Dests1),
+    Route2 = A2-(Stride2-Offset2-Dests2),
+    nth0(Dest1, Dests1, C1-Z1),
+    nth0(Dest2, Dests2, C2-Z2),
+    Len1 is Offset1 + Stride1*N1 + C1,
+    Len2 is Offset2 + Stride2*N2 + C2,
+    next(Dests1, N1-Dest1, NextN1-NextDest1),
+    (   Len1 =:= Len2
+    ->  (   Founds = [OldLen]
+        ->  atom_concat(A1, A2, NewA), atom_concat(Z1, Z2, NewZ),
+            NewStride is Len1 - OldLen,
+            NewRoute = NewA-(NewStride-OldLen-[0-NewZ]),
+            !
+        ;   unify2(Route1, Route2, NextN1-NextDest1-N2-Dest2, [Len1], NewRoute)
+        )
+    ;   Len1 < Len2
+    ->  unify2(Route1, Route2, NextN1-NextDest1-N2-Dest2, Founds, NewRoute)
+    ;   next(Dests2, N2-Dest2, NextN2-NextDest2),
+        unify2(Route1, Route2, N1-Dest1-NextN2-NextDest2, Founds, NewRoute)
+    ).
+
+% next(Dests, NumberOfLoops-WhichInternalZ, NextNumberOfLoops-NextInternalZ)
+next(Dests, NLoops-Dest, NextNLoops-NextDest) :-
+    length(Dests, DestsLen),
+    (   Dest < DestsLen - 1
+    ->  NextNLoops is NLoops, NextDest is Dest + 1
+    ;   NextNLoops is NLoops + 1, NextDest is 0).
+
+routes(Starts, Routes) :-
+    maplist([S, S-Route]>>(zloop(S, Route)), Starts, Routes).
+
+% zloop builds a route (Stride-Offset-Internals for a particular starting node.
+zloop(Node, Route) :- zloop([], Node, 0, [], Route).
+zloop(_Direction, _Node, _Index, Zs, Stride-Offset-Dests) :-
+    Zs = [FirstZIndex-Z | _], reverse(Zs, [LastZIndex-Z | ReversedZs]),
+    DeltaZ is LastZIndex - FirstZIndex, DeltaZ =\= 0,
+    direction_len(Len),
+    divmod(DeltaZ, Len, _, 0),
+    Offset = FirstZIndex, Stride = DeltaZ,
+    foldl([Idx-Z, NewIdx-Z, Off, Off]>>(NewIdx is Idx - Off),
+          ReversedZs, ReversedDests, Offset, _),
+    reverse(ReversedDests, Dests),
+    !.
+zloop(Directions, Node, Index, Zs, Route) :-
+    (   is_end(Node)
+    ->  append(Zs, [Index-Node], NewZs)
+    ;   NewZs = Zs
+    ),
+    next_step(Directions, Move, Remain),
+    G =.. [Move, Node, To], G,
+    NewIndex is Index + 1,
+    zloop(Remain, To, NewIndex, NewZs, Route).
+
+starts(Starts) :- findall(X, X to _, Nodes), include(is_start, Nodes, Starts).
+
+is_start(Node) :- atom_chars(Node, [_, _, a]).
+is_end(Node) :- atom_chars(Node, [_, _, z]).
+
+next_step([Move | Remain], Move, Remain).
+next_step([], Move, Remain) :- direction_list([Move | Remain]).
+
+direction_list(Dir) :- direction(Str), atom_chars(Str, Dir).
+direction_len(Len) :- direction_list(D), length(D, Len).

08/test2.pl

@@ -8,4 +8,12 @@ nna to nnb-xxx.
 nnb to nnc-nnc.
 nnc to nnz-nnz.
 nnz to nnb-nnb.
+ooa to ooz-oob.
+oob to ood-ooc.
+ooc to ooa-oox.
+ood to ooz-ood.
+ooz to oob-ooz.
 xxx to xxx-xxx.
+
+% Routes = [mma-(2-2-[0-mmz]), nna-(6-3-[0-nnz, 3-nnz]), ooa-(8-1-[0-ooz, 1-ooz])].
+% X = mmannaooa-(24-18-[0-mmznnzooz]).