/* 

  Global constraint element_product in Picat.

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

      element_product(Y, TABLE, X, Z)
  
  Purpose

      Z is equal to the Yth item of TABLE multiplied by X.

  Example
      (3,<6, 9, 2, 9>, 5, 10)

      The element_product constraint holds since its fourth argument Z=10 
      is equal to the 3th (Y=3) item of the collection <6, 9, 2, 9> 
      multiplied by X=5.
  """


  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,
  ElementTable = new_list(N),
  ElementTable :: 1..9,
  X :: 0..10,
  Y :: 1..N,
  Z :: 0..100,

  ElementTable = [6,9,2,9],
  X #= 5,
  Y #= 3,
  element_product(Y,ElementTable,X,Z),

  Vars = ElementTable ++ [X,Y,Z],
  solve(Vars),

  println(elementTable=ElementTable),
  println([x=X,y=Y,z=Z]),
  nl,
  fail,
  
  nl.

go => true.


element_product(Y,ElementTable,X,Z) =>
    element(Y,ElementTable,T),
    Z #= T * X.