/* 

  Global constraint open_alldifferent in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Copen_alldifferent.html
  """
  open_alldifferent(S, VARIABLES)
  
  Purpose

  Let V be the variables of the collection VARIABLES for which the 
  corresponding position belongs to the set S. Enforce all variables of 
  V to take distinct values.

  Example
   ({2, 3, 4}, <9,1,9,3>)

  The open_alldifferent constraint holds since the last three (i.e., 
  S = {2, 3, 4}) values of the collection 9,1,9,3 are distinct. 
  """

  Note: This model yield these three solutions to open_alldifferent(X, [9,1,9,3]):

    x = [9,1,9,3]
    s = [0,1,0,1]
    s = [2,4]

    x = [9,1,9,3]
    s = [0,1,1,1]
    s = [2,3,4]

    x = [9,1,9,3]
    s = [1,1,0,1]
    s = [1,2,4]

  I'm not sure if the last solution is correct...

  This Picat model was 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..9,
  
  % var set of 1..n: s;
  S = new_list(N),
  S :: 0..1,

  X = [9,1,9,3],

  % S = [0,1,1,1], % {2,3,4}

  open_alldifferent(X, S),

  Vars = X ++ S,
  % solve($[max(sum(S))],Vars),
  solve([],Vars),  

  println(x=X),
  println(s=S),
  println(s=[I : I in 1..N, S[I] == 1]),
  nl,
  fail,
  
  nl.

go => true.


open_alldifferent(X, S) =>
  Len = X.len,
  all_different_except_0($[X[I]*S[I] : I in 1..Len ]),
  foreach(I in 1..Len)
    sum([X[J] #= X[I] : J in 1..Len]) #= 1 #=> S[I] #= 1
  end.