130 lines
4.3 KiB
Mathematica
130 lines
4.3 KiB
Mathematica
:- module day18.
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:- interface.
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:- import_module basics.
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:- pred run(part::in, lines::in, answer::out) is cc_multi.
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:- implementation.
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:- import_module int.
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:- import_module char.
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:- import_module string.
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:- import_module list.
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:- import_module digraph.
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:- import_module ranges.
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:- import_module solutions.
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:- import_module set_tree234.
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:- type set(T) == set_tree234(T).
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:- type point3 ---> p(x :: int, y :: int, z :: int).
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:- type bounds ---> b(lo :: point3, hi :: point3).
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:- type dir ---> left; right; up; down; fore; back.
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:- type vertex ---> empty(point3) ; full(point3, dir).
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:- type points == set(point3).
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:- type graph == digraph(vertex).
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:- type key == digraph_key(vertex).
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:- pred lines(lines::in, list(point3)::out) is semidet.
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lines(Lines, Ps) :- map(line, Lines, Ps).
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:- pred line(string::in, point3::out) is semidet.
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line(Str, P) :- line(P, to_char_list(Str), []).
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:- pred line(point3::out, chars::in, chars::out) is semidet.
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line(p(X, Y, Z)) --> number(X), [','], number(Y), [','], number(Z).
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:- pred number(int::out, chars::in, chars::out) is semidet.
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number(N) --> digits(S), {to_int(from_char_list(S), N)}.
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:- pred digits(chars::out, chars::in, chars::out) is semidet.
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digits([C | Cs]) -->
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[C], {is_digit(C)},
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(if digits(Cs0) then {Cs = Cs0} else {Cs = []}).
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:- func pointwise(func(int) = int, point3) = point3.
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pointwise(F, p(X,Y,Z)) = p(F(X), F(Y), F(Z)).
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:- pred pointwise(pred(int, int, int), point3, point3, point3).
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:- mode pointwise(pred(in, in, out) is det, in, in, out) is det.
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pointwise(P, p(X1,Y1,Z1), p(X2,Y2,Z2), p(X,Y,Z)) :-
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P(X1, X2, X), P(Y1, Y2, Y), P(Z1, Z2, Z).
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:- pred bounds(list(point3), bounds).
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:- mode bounds(in, out) is semidet.
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:- mode bounds(in(non_empty_list), out) is det.
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bounds([P | Ps], b(Lo, Hi)) :-
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foldl(pointwise(min), Ps, P, Lo0), foldl(pointwise(max), Ps, P, Hi0),
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Lo = pointwise(func(I) = I - 1, Lo0),
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Hi = pointwise(func(I) = I + 1, Hi0).
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:- pred in_bounds(bounds::in, point3::in) is semidet.
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in_bounds(b(p(X1,Y1,Z1), p(X2,Y2,Z2)), p(X,Y,Z)) :-
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X1 =< X, X =< X2, Y1 =< Y, Y =< Y2, Z1 =< Z, Z =< Z2.
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:- pred nondet_in_bounds(bounds::in, point3::out) is nondet.
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nondet_in_bounds(b(p(X1,Y1,Z1), p(X2,Y2,Z2)), p(X,Y,Z)) :-
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Xs = range(X1, X2), Ys = range(Y1, Y2), Zs = range(Z1, Z2),
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nondet_member(X, Xs), nondet_member(Y, Ys), nondet_member(Z, Zs).
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:- pred adj0(point3::in, point3::out, dir::out) is multi.
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adj0(p(X,Y,Z), p(X1,Y,Z), D) :- X1 = X - 1, D = left ; X1 = X + 1, D = right.
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adj0(p(X,Y,Z), p(X,Y1,Z), D) :- Y1 = Y - 1, D = up ; Y1 = Y + 1, D = down.
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adj0(p(X,Y,Z), p(X,Y,Z1), D) :- Z1 = Z - 1, D = fore ; Z1 = Z + 1, D = back.
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:- pred adj(bounds::in, point3::in, {point3,dir}::out) is nondet.
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adj(Bounds, P, {Q, D}) :- adj0(P, Q, D), in_bounds(Bounds, Q).
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:- pred build_graph(list(point3)::in, graph::out, key::out) is cc_nondet.
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build_graph(PointList, Graph, StartKey) :-
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bounds(PointList, Bounds),
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list_to_set(PointList, Points),
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build_graph0(Bounds, Points, Graph),
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nondet_in_bounds(Bounds, Start),
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not member(Start, Points),
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search_key(Graph, empty(Start), StartKey).
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:- pred build_graph0(bounds::in, points::in, graph::out) is det.
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build_graph0(Bounds, Full, Graph) :-
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solutions(nondet_in_bounds(Bounds), AllPoints),
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foldl(add_adj_vertices(Bounds, Full), AllPoints, init, Graph).
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:- pred add_adj_vertices(bounds::in, points::in, point3::in,
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graph::in, graph::out) is det.
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add_adj_vertices(Bounds, Full, P, !G) :-
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if member(P, Full) then true else
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solutions(adj(Bounds, P), Adj),
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foldl(add_vertex(Full, P), Adj, !G).
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:- pred add_vertex(points::in, point3::in, {point3,dir}::in,
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graph::in, graph::out) is det.
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add_vertex(Full, From, {To, Dir}, !G) :-
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ToV = ite((pred) is semidet :- member(To, Full), full(To, Dir), empty(To)),
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add_vertices_and_edge(empty(From), ToV, !G).
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:- func count_faces(graph, key) = int.
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count_faces(Graph, Start) = Count :-
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dfs(Graph, Start, SeenKeys),
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foldl(pred(K::in, Acc0::in, Acc::out) is det :-
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(if lookup_vertex(Graph, K) = full(_, _) then Acc = Acc0 + 1
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else Acc = Acc0),
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SeenKeys, 0, Count).
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run(one, _, _) :- die("bqn").
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run(two, Lines, Out) :-
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if
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lines(Lines, PointList),
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build_graph(PointList, Graph, Start)
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then
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Out = int(count_faces(Graph, Start))
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else
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die("bad input").
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