:- use_module(library(clpfd)).
:- use_module(library(dcg/basics)).

line(Line) -->
    string_without("\n", L),
    { Line =.. [line | L] }.

lines([Line]) --> line(Line), blanks.
lines([L|Lines]) -->
    line(L),
    blanks,
    lines(Lines).

traverse(_, _, [], []).
traverse(R-D, Rd-Dd, Lines, Tiles) :-
    R #> 31,
    R1 #= R - 31,
    traverse(R1-D, Rd-Dd, Lines, Tiles).
traverse(_, _-Dd, Lines, []) :-
    length(Lines, L),
    Dd #> L.
traverse(R-D, Rd-Dd, [Line | Lines], [T|Tiles]) :-
    arg(R, Line, T),
    R1 #= R + Rd,
    D1 #= D + Dd,
    length(Head, Dd),
    append(Head, Lines1, [Line | Lines]),
    traverse(R1-D1, Rd-Dd, Lines1, Tiles).

path(Lines, D, Count) :-
    traverse(1-1, D, Lines, Path),
    aggregate_all(count, member(35, Path), Count).

step_1(Trees) :-
    phrase_from_file(lines(Lines), 'advent_3_inp.txt'),
    path(3-1, Lines, Path),
    aggregate_all(count, member(35, Path), Trees), !.

product_(N, M, P) :- P #= N * M.

step_2([C|Counts], Product) :-
    phrase_from_file(lines(Lines), 'advent_3_inp.txt'),
    maplist(path(Lines), [1-1, 3-1, 5-1, 7-1, 1-2], [C|Counts]),
    foldl(product_, Counts, C, Product), !.