/* 

  Global constraint cardinality_atleast in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Ccardinality_atleast.html
  """
  ATLEAST is the minimum number of time that a value of VALUES is taken by the 
  variables of the collection VARIABLES.
  
  Example
  (1, <3, 3, 8>, <3, 8>)
  
  In this example, values 3 and 8 are respectively used 2, and 1 times. 
  The cardinality_atleast constraint holds since its first argument ATLEAST = 1 
  is assigned to the minimum number of time that values 3 and 8 occur in the 
  collection <3, 3, 8>.
  """

  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 = 3,
  M = 2,

  Variables = new_list(N),
  Variables :: 1..8,

  Values = new_list(M),
  Values :: 1..8,

  NVar :: 0..8,

  Variables = [3,3,8],
  Values = [3,8],
  % NVar #= 1,

  cardinality_atleast(NVar, Variables, Values),

  Vars = Variables ++ Values ++ [NVar],
  solve(Vars),

  println(variables=Variables),
  println(values=Values),
  println(nvar=NVar),
  nl,
  fail,

  
  nl.

go => true.


cardinality_atleast(NVar, Variables, Values) =>
   foreach(I in 1..Values.len) 
     sum([Values[I] #= Variables[J] : J in 1..Variables.len])  #>= NVar
   end.