/*

  Global constraint alldifferent_modulo in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Calldifferent_modulo.html
  """
  Enforce all variables of the collection VARIABLES to have a distinct 
  rest when divided by M.
  
  Example
  (<25, 1, 14, 3>, 5)
  
  The equivalence classes associated with values 25, 1, 14 and 3 are 
  respectively equal to 
     25 mod 5 = 0, 1 mod 5 = 1, 14 mod 5 = 4 and 3 mod = 3. 
  Since they are distinct the alldifferent_modulo constraint holds.
  """

  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
   N = 4,
   X = new_list(N),
   X :: 1..25,
   % X = [25,1,14,3],

   % M :: 1..5,
   % indomain(M),
   M = 5,

   % L = findall([X,M], $test(X,M)),
   L = findall([X,M], (alldifferent_modulo(X, M), solve(X++[M]))),
   Len = length(L),

   % this give no solution since the local X and M conflicts with the global versions
   % foreach([X,M] in L) writeln([m=M2,x=X2]) end,

   % this works, though
   foreach([X2,M2] in L) writeln([m=M2,x=X2]) end,
   writeln(len=Len).


test(X,M) =>
   alldifferent_modulo(X,M), 
   solve(X).

alldifferent_modulo(Xs,M) =>
   all_different([T : X in Xs, T #= X mod M]).