/* 

  Global constraint k_same in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Ck_same.html
  """
  k_same<U+200B>(SETS)
  
  Purpose

  Given |SETS| sets, each containing the same number of domain variables, 
  the k_same constraint enforces that the multisets of values assigned to each set are all i
dentical.

  Example
      (
      <
      set-<1, 9, 1, 5, 2, 1>,
      set-<9, 1, 1, 1, 2, 5>,
      set-<5, 2, 1, 1, 9, 1>
      >
      )

  The k_same constraint holds since:

   * The first and second collections of variables are assigned to the 
      same multiset.

   * The second and third collections of variables are also assigned to 
     the same multiset.
  """


  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 = 6,
  X = new_array(N,M),
  X :: 1..9,

  X = {{1,9,1,5,2,1},
       {_,9,_,_,_,1}, % test
       % {9,1,1,1,2,5},
       {5,2,1,1,9,1}},

  k_same(X),

  solve(X),
  
  println(X),
  fail,
  
  nl.

go => true.


k_same(X) =>
  N = X.len,
  M = X[1].len,
  foreach(I in 2..N)
    Max = fd_max_array(X[I]),   
    IGcc = $[J-C : J in 0..Max],
    JGcc = $[J-C : J in 0..Max],
    
    global_cardinality([X[I,K] : K in 1..M], IGcc),
    global_cardinality([X[I-1,K] : K in 1..M], JGcc),
     
    foreach(K in 1..Max)
      IGcc[K] #= JGcc[K]
    end
   end.


fd_max_array(A) = max(Maxes) =>
    Maxes = [fd_max(A[I]) : I in 1..A.len].