/* 

  Global constraint among_interval in Picat.

  From Global Constraint Catalogue
  http://www.emn.fr/x-info/sdemasse/gccat/Camong_interval.html
  """
  NVAR is the number of variables of the collection VARIABLES taking a 
  value that is located within interval [LOW, UP].
  
  Example
      (3,〈4,5,8,4,1〉,3,5)
  
  The among_interval constraint holds since we have 3 values, 
  namely 4, 5 and 4 that are situated within interval [3, 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 = 5,
  X = new_list(N),
  X :: 1..8,

  NVar :: 0..N,
  Low :: 1..N,
  Up :: 1..N,

  X = [4,5,8,4,1],
  % Low #= 3,
  % Up #= 5,
  NVar #= 3,

  among_interval(NVar, X, Low, Up),

  Vars = X ++ [NVar,Low,Up],

  solve(Vars),
  
  println(x=X),
  println(nvar=NVar),
  println(low=Low),
  println(up=Up),
  nl,

  fail,
  
  nl.


go => true.


among_interval(NVar, X, Low, Upper) =>
  Low #<= Upper,
  NVar #= sum([X[I] #>= Low #/\ X[I] #<= Upper : I in 1..X.len]).