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

row([1]) --> "B".
row([1|Ls]) --> "B", row(Ls).
row([0]) --> "F".
row([0|Ls]) --> "F", row(Ls).

col([1]) --> "R".
col([1|Ls]) --> "R", col(Ls).
col([0]) --> "L".
col([0|Ls]) --> "L", col(Ls).

position([Row,Col]) --> row(Row), col(Col).

seating([S]) --> position(S), blanks.
seating([S|Seats]) --> position(S), blanks, seating(Seats).

restrict(0, L-U0, L-U) :- U #= U0 - ((U0 - L) // 2) - 1.
restrict(1, L0-U, L-U) :- L #= L0 + ((U - L0) // 2) + 1.

seat([X, Y], Id) :-
    foldl(restrict, X, 0-127, Row-Row),
    foldl(restrict, Y, 0-7, Col-Col),
    Id #= Row * 8 + Col.

hole([A, B | _], Missing) :-
    2 #= B - A,
    Missing #= A + 1.
hole([_|Seats], Missing) :-
    hole(Seats, Missing).

main(Part1, Part2) :-
    phrase_from_file(seating(Seating), 'advent_5_inp.txt'),
    maplist(seat, Seating, Ids), !,
    max_list(Ids, Part1),
    sort(Ids, Sorted),
    hole(Sorted, Part2).