import cp.

% CP approach
queens_cp(N, Q) =>
   Q = new_list(N),
   Q :: 1..N,

   all_different(Q),
   all_different([$Q[I]-I : I in 1..N]),
   all_different([$Q[I]+I : I in 1..N]),
   solve([ff],Q).

% SAT approach (using a N x N matrix)
queens_sat(N,Q) =>
  Q = new_array(N,N),
  Q :: 0..1,

  foreach (K in 1-N..N-1)
    sum([Q[I,J] : I in 1..N, J in 1..N, I-J==K]) #=< 1
  end,

  foreach (K in 2..2*N)
    sum([Q[I,J] :  I in 1..N, J in 1..N, I+J==K]) #=< 1
  end,

  foreach (I in 1..N)
    sum([Q[I,J] : J in 1..N]) #= 1
  end,

  foreach (J in 1..N)
    sum([Q[I,J] : I in 1..N]) #= 1
  end,
  solve([inout],Q).