lights-out-all.lp

% This solves th lights out problem for the most common problem case
% where all the cells need to be inverted.
% Run this by modifying the input via the dim/2 literal and then simply calling:
% clingo lights-out-all.lp

% Input: Problem dimensions (width, height)
dim(5, 5). 

% Definitions of problem topology
coord(1..N, 1..M) :- dim(N, M).
adjacent(X, Y, A, B) :-
    |X-A| + |Y-B| <= 1,
    coord(X, Y),
    coord(A, B).

% Each cell needs to be selected at most once in the solution.
% This is represented by the choice of action/2 in model.
0 {action(X, Y)} 1 :- coord(X, Y).

% Penalize each action, i.e. minimize the total number of solution steps.
:~ action(X, Y). [1@1,(X,Y)]

% An action must be performed odd number of times in neighborhood of each cell in order
% to switch invert it. In other words it cannot be performed even number of times.
:- C = #count{ (A,B) : adjacent(A, B, X, Y), action(A, B)},
   C \ 2 = 0,
   coord(X, Y).

#show action/2.