/* 

  Global constraint global_cardinality_no_loop in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Cglobal_cardinality_no_loop.html
  """
  Constraint

      global_cardinality_no_loop(NLOOP,VARIABLES,VALUES)
  
  ...
  
  Purpose

      VALUES[i].noccurrence (1=<i=<|VALUES|) is equal to the number of 
      variables VARIABLES[j].var(j!=)i, 1=<j=<|VARIABLES|) that are 
      assigned value VALUES[i].val.

      The number of assignments of the form 
      VARIABLES[i].var=i(i∈[1,|VARIABLES|]) is equal to NLOOP.

  Example
      (
      1, <1, 1, 8,6>,
      〈val-1 noccurrence-1, val-5 noccurrence-0, val-6 noccurrence-1>
      )

      The global_cardinality_no_loop constraint holds since:
      *  Values 1, 5 and 6 are respectively assigned to the set 
         of variables {VARIABLES[2].var} (i.e., 1 occurrence 
         of value 1), {}(i.e., no occurrence of value 5) and 
         {VARIABLES[4].var} (i.e., 1 occurrence of value 6). Observe 
         that, due to the definition of the constraint, the fact that 
         VARIABLES[1].var is assigned to 1 is not counted.
      *  In addition the number of assignments of the form 
         VARIABLES[i].var=i(i∈[1, 4]) is equal to NLOOP=1.

  Usage

      Within the context of the tree constraint the 
      global_cardinality_no_loop constraint allows to model a minimum 
      and maximum degree constraint on each vertex of our trees.
  """

  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, % number of variables
  M = 3, % number of values
  
  Variables = new_list(N),
  Variables :: 1..8,

  Values = new_array(M,2),
  Values :: 0..8, 

  NLoop :: 0..N,

  Values = {
            {1,1},
            {5,0},
            {6,1}},
  Variables = [1,1,8,6],

  global_cardinality_no_loop(NLoop, Variables, Values),
  
  Vars = Variables ++ Values,
  println(vars=Vars),
  solve(Vars),

  println(variables=Variables),
  println(values=Values),
  println(nloop=NLoop),
  nl,
  fail,

  nl.

go => true.


global_cardinality_no_loop(NLoop,Variables,Values) =>
   M = Values[1].len,
   N = Variables.len,
   foreach(I in 1..M)
     Values[I,2] #= sum([Variables[J]#=Values[I,1] : J in 1..N, I!=J])
   end,
   NLoop #= sum([Variables[J] #= J : J in 1..N])