d8

2023-12-08 17:10:35 -08:00
parent d5ee7282e9
commit d9980e3b33
10 changed files with 1844 additions and 0 deletions
--- a/08/part2.cheese.pl
+++ b/08/part2.cheese.pl
@@ -0,0 +1,85 @@
+:- table direction_loop/1.
+
+:- op(700, xfx, l).
+:- op(700, xfx, r).
+From l To :- From to To-_.
+From r To :- From to _-To.
+
+% We want to satisfy {Offset_i + Stride_i*Loops_i + Sub_ij = Z}
+answer() :-
+    starts(Starts),
+    maplist([S, S-Off-Stride-Loop]>>(zloop([], S, 0, [], Off, Stride, Loop)),
+            Starts, Events),
+    maplist(split, Events, EquationSets),
+    pick(EquationSets, Eqs),
+    index1(Eqs, IEqs),
+    write('Find N_i such that: '),
+    foldl(write_eq, IEqs, _, _),
+    write('Z\n'),
+    % foldl(satisfy, EquationsN, _, Answer),
+    true.
+
+write_eq(I-(A-B-C), _, _) :-
+    writef('%t + %t*N%t ', [A, B, I]),
+    (C =\= 0 -> writef('+ %t ', [C]); true),
+    write('= ').
+
+% satisfy((A-B-C), N, Z, Z) :- natnum(N), Z is A + B*N + C.
+
+% [mma-2-2-[0-mmz], nna-3-6-[0-nnz, 3-nnz]] -> [2-2-0, 3-6-0, 3-6-3]
+split(_-_-_-[], []).
+split(A-Offset-Stride-[Sub-_ | Loop], [Offset-Stride-Sub | Cdr]) :-
+    split(A-Offset-Stride-Loop, Cdr).
+
+% Everything above this is not needed to get the input answer
+% starts(Starts),
+% maplist([S, S-Off-Stride-Loop]>>(zloop([], S, 0, [], Off, Stride, Loop)),
+%         Starts, Loops).
+% then find the LCD of the strides (which are equal to offsets).
+
+zloop(_, _, _, Zs, Offset, Stride, Loop) :-
+    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, ReversedLoop, Offset, _),
+    reverse(ReversedLoop, Loop),
+    !.
+
+zloop(Directions, Node, Index, Zs, Offset, Stride, Loop) :-
+    (   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, Offset, Stride, Loop).
+
+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).
+
+% 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).
+
+index1(L, IL) :- reverse(L, RL), index1r(RL, IRL), reverse(IRL, IL).
+index1r([X], [1-X]).
+index1r([X, Y | Cdr], [NextI-X, I-Y | ICdr]) :-
+    index1r([Y | Cdr], [I-Y | ICdr]), NextI is I + 1.
+
+same_elements([_]).
+same_elements([X-_, Y-Z2 | Cdr]) :- X =:= Y, same_elements([Y-Z2 | Cdr]).
+
+natnum(0).
+natnum(N) :- natnum(N0), N is N0 + 1.