% :- table valid/1.
:- table path/3.

answer(Answer) :-
    pipe_at(From, ess),
    once(path(From, Via, From)),
    length(Via, ViaLen),
    writef('%t -> %t\n', [From, Via]),
    Answer is (ViaLen + 1) div 2 .

% path(From, Next, To, Dist) :-
%     pipe_at(From, FromPipe),
%     FromG =.. [FromPipe, From, Next

path(From, [Via], To) :-
    pipe_at(Via, ViaPipe),
    ViaG =.. [ViaPipe, Via, From, To], ViaG.

path(From, [Via1, Via2 | Vias], To) :-
    path(From, [Via1], Via2), 
    path(Via1, [Via2 | Vias], To).

dot(_, _, _) :- fail.
    
vert(X-Y, X1-Y, X2-Y) :-
    pipe_at(X-Y, vert),
    (   X1 is X+1, X2 is X-1
    ;   X1 is X-1, X2 is X+1),
    valid(X1-Y), valid(X2-Y).

horz(X-Y, X-Y1, X-Y2) :-
    pipe_at(X-Y, horz),
    (   Y1 is Y+1, Y2 is Y-1
    ;   Y1 is Y-1, Y2 is Y+1),
    valid(X-Y1), valid(X-Y2).

el(X-Y, X1-Y1, X2-Y2) :-
    pipe_at(X-Y, el),
    (   Y1 = Y, X1 is X-1, Y2 is Y+1, X2 = X
    ;   X1 = X, Y1 is Y+1, X2 is X-1, Y2 = Y),
    valid(X1-Y1), valid(X2-Y2).

jay(X-Y, X1-Y1, X2-Y2) :-
    pipe_at(X-Y, jay),
    (   Y1 = Y, X1 is X-1, Y2 is Y-1, X2 = X
    ;   X1 = X, Y1 is Y-1, X2 is X-1, Y2 = Y),
    valid(X1-Y1), valid(X2-Y2).

seven(X-Y, X1-Y1, X2-Y2) :-
    pipe_at(X-Y, seven),
    (   Y1 = Y, X1 is X+1, Y2 is Y-1, X2 = X
    ;   X1 = X, Y1 is Y-1, X2 is X+1, Y2 = Y),
    valid(X1-Y1), valid(X2-Y2).

eff(X-Y, X1-Y1, X2-Y2) :-
    pipe_at(X-Y, eff),
    (   Y1 = Y, X1 is X+1, Y2 is Y+1, X2 = X
    ;   X1 = X, Y1 is Y+1, X2 is X+1, Y2 = Y),
    valid(X1-Y1), valid(X2-Y2).

ess(X-Y, X1-Y1, X2-Y2) :-
    pipe_at(X-Y, ess),
    findall(Coord, ess_adjacent(Coord), [X1-Y1, X2-Y2]).

ess_adjacent(X1-Y1) :-
    pipe_at(X-Y, ess),
    (   X1 is X-1, Y1 = Y, pipe_at(X1-Y1, El), points_down(El)
    ;   X1 = X, Y1 is Y+1, pipe_at(X1-Y1, El), points_left(El)
    ;   X1 is X+1, Y1 = Y, pipe_at(X1-Y1, El), points_up(El)
    ;   X1 = X, Y1 is Y-1, pipe_at(X1-Y1, El), points_right(El)),
    valid(X1-Y1).

points_down(El) :- (El=ess; El=vert; El=seven; El=eff).
points_left(El) :- (El=ess; El=horz; El=jay; El=seven).
points_up(El) :- (El=ess; El=vert; El=el; El=jay).
points_right(El) :- (El=ess; El=horz; El=el; El=eff).

valid(X-Y) :-
    input(Map), length(Map, NRows),
    Map = [Row0 | _], length(Row0, NCols),
    X >= 0, Y >= 0,
    X < NRows, Y < NCols.

% Element is at (Row, Column) in the map.
pipe_at(Row-Column, Element) :-
    input(Map),
    nth0(Row, Map, SubList),
    nth0(Column, SubList, Symbol),
    symbol_predicate(Symbol, Element).

symbol_predicate("|", vert).
symbol_predicate("-", horz).
symbol_predicate("L", el).
symbol_predicate("J", jay).
symbol_predicate("7", seven).
symbol_predicate("F", eff).
symbol_predicate(".", dot).
symbol_predicate("S", ess).