/* 

  Inter-distance constraint in Picat.

  From 
  Claude-Guy Quimper: "Efficient Propagators for Global Constraints"
  page 3:
  """
  The Inter-Distance constraint ensures that all variables, among a set 
  of variables x1,...,xn, are pairwise distant from p,
  i.e. |xi-xj| >= p for all i != j. 
  """

  Note: when p = 1 then inter_distance is the same as alldifferent.

  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,
  X = new_list(N),
  X :: 0..N*4,
  P :: 0..10,

  inter_distance(X, P),
  P #= 3,

  Vars = X ++ [P],
  solve($[],Vars),

  println(x=X),
  println(p=P),
  nl,
  fail,

  nl.

go => true.


inter_distance(X, P) =>
  N = X.len,
  foreach(I in 1..N, J in I+1..N) 
    abs(X[I]-X[J]) #>= P
  end.