/* 

  Global constraint lex2 in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Clex2.html
  """
  lex2 (MATRIX)
  
  Purpose

  Given a matrix of domain variables, enforces that both adjacent rows, 
  and adjacent columns are lexicographically ordered (adjacent rows and 
  adjacent columns can be equal).

  Example
      (
      <
      vec-<2, 2, 3>,
      vec-<2, 3, 1>
      >
      )

  The lex2 constraint holds since:

  * The first row <2, 2, 3> is lexicographically less than or equal to the 
    second row <2, 3, 1>.
  * The first column <2, 2> is lexicographically less than or equal to the 
    second column <2, 3>.
  * The second column <2, 3> is lexicographically less than or equal to the 
    third column <3, 1>.
  """

  Note: Picat has built-in lex_lt/2 and lex_le/2 for comparing two lists, 
  but not lex2/1, i.e. for a matrix.

  Here we implement lex2/1 as lex2eq. In lex_alldifferent.pi is
  the lex2/1 constraint.

  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 ?=>
  R = 2,
  C = 3,

  X = new_array(R,C),
  X :: 1..4,

  % X = {
  %      {2,2,3},
  %      {2,3,1}
  %     },

  lex2eq(X),

  solve(X),
  foreach(Row in X) println(Row) end,
  nl,
  fail,

  nl.

go => true.


lex2(X) =>
  Len = X[1].length,
  foreach(I in 2..X.length) 
     lex_lt(X[I-1], X[I])
   end.

% This use lex_lesseq/1
lex2eq(X) =>
   Len = X[1].length,
   foreach(I in 2..X.length) 
     lex_le(X[I-1], X[I])
   end.