/* 

  Global constraint element_matrix in Picat.

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

      element_matrix(MAX_I,MAX_J,INDEX_I,INDEX_J,MATRIX,VALUE)

  Purpose

      The MATRIX collection corresponds to the two-dimensional matrix 
      MATRIX[1..MAX_I,1..MAX_J]. VALUE is equal to the entry MATRIX[INDEX_I,INDEX_J] of the p
revious matrix.

  Example
      (
      4,3,1,3,<
      i-1 j-1 v-4,
      i-1 j-2 v-1,
      i-1 j-3 v-7,
      i-2 j-1 v-1,
      i-2 j-2 v-0,
      i-2 j-3 v-8,
      i-3 j-1 v-3,
      i-3 j-2 v-2,
      i-3 j-3 v-1,
      i-4 j-1 v-0,
      i-4 j-2 v-0,
      i-4 j-3 v-6
      >,7
      )

      The element_matrix constraint holds since its last argument 
      VALUE=7 is equal to the v attribute of the kth item of the MATRIX 
      collection such that MATRIX[k].i=INDEX_I=1 and MATRIX[k].j=INDEX_J=3.
  """

  Note that Picat has the built-in matrix_element(Matrix,I,J,Value) which is used here.

  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 ?=>
  MaxI = 4,
  MaxJ= 3,
  IndexI :: 1..MaxI,
  IndexJ :: 1..MaxJ,
  
  Matrix = new_array(MaxI,MaxJ),
  Matrix :: 0..9, 
  Value :: 0..8,

  Matrix = {{4,1,7},
            {1,0,8},
            {3,2,1},
            {0,0,6}},

  % IndexI #= 1,
  % IndexJ #= 3,
  % Value #= 7,
  element_matrix(IndexI,IndexJ, Matrix, Value),

  Vars = Matrix.vars ++ [IndexI,IndexJ],
  solve(Vars),
  println(matrix=Matrix),
  println([indexI=IndexI,indexJ=IndexJ,value=Value]),
  nl,
  fail,
  nl.


go => true.

element_matrix(IndexI, IndexJ, Matrix,Value) =>
   % Matrix[IndexI,IndexJ] #= Value.
   matrix_element(Matrix,IndexI,IndexJ,Value).