/* 

  Global constraint among_modulo in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Camong_modulo.html
  """
  NVAR is the number of variables of the collection VARIABLES taking a value 
  that is congruent to REMAINDER modulo QUOTIENT.
  
  Example
  (3, <4, 5, 8, 4, 1>, 0, 2)
  
  In this example REMAINDER = 0 and QUOTIENT = 2 specifies that we count the 
  number of even values taken by the different variables. As a consequence 
  the among_modulo constraint holds since exactly 3 values of the 
  collection <4, 5, 8, 4, 1> are even.

  """


  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 ?=>
  X = new_list(5),
  X :: 1..8,

  NVar :: 0..10,
  Remainder :: 0..10,
  Quotient :: 1..10,


  X = [4,5,8,4,1],
  Quotient #= 2,  
  Remainder #= 0,
  % NVar #= 3,

  among_modulo(NVar, X, Remainder, Quotient),

  Vars = X ++ [NVar,Remainder,Quotient],
  solve(Vars),

  println(x=X),
  println(nvar=NVar),
  println(quotient=Quotient),  
  println(remainder=Remainder),
  nl,
  fail,

  nl.

go => true.


%
% among_modulo
% 
among_modulo(NVar, X, Remainder, Quotient) =>
  NVar #= sum([X[I] mod Quotient #= Remainder : I in 1..X.len]).