/* 

  Global constraint distance_between in Picat.

  http://www.emn.fr/x-info/sdemasse/gccat/Cdistance_between.html
  """
  Let Ui and Vi be respectively the ith and jth variables (i!=j) of 
  the collection VARIABLES1. In a similar way, let Xi and Yi be 
  respectively the ith and jth variables (i!=j) of the collection 
  VARIABLES2. DIST is equal to the number of times one of the 
  following mutually incompatible conditions are true:
   *  Ui CTR Vi holds and Xi CTR Yi does not hold,
   *  Xi CTR Yi holds and Ui CTR Vi does not hold.
  Example
      (2, <3, 4, 6, 2, 4>, <2, 6, 9, 3, 6>, <)

  The distance_between constraint holds since the following DIST=2 conditions are verified:
  *  VARIABLES1[4].var=2 <  VARIABLES1[1].var=3 /\
     VARIABLES2[4].var=3 >= VARIABLES2[1].var=2
  *  VARIABLES2[1].var=2 <  VARIABLES2[4].var=3 /\
     VARIABLES1[1].var=3 >= VARIABLES1[4].var=2
  """

  TODO: I have problem negating the call/3 constraints. 


  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.


% Experiment:
% Picat> Op=$#<,[A,B]::1..4,call(Op,A,B), solve_all([A,B])=All
% Op = #<
% A = DV_0159a8_1..3
% B = DV_0159f8_2..4
% All = [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]
% yes

go ?=>
  N = 5,

  X = new_list(N),
  X :: 1..9,
  
  Y = new_list(N),
  Y :: 1..9,

  D :: 0..N*N, % the distance

  X = [3,4,6,2,4],
  Y = [2,6,9,3,6],
  
  distance_between(D, X, Y, #<),
  % distance_between(D, X, Y, -2),  
  % D #= 2,

  Vars = X++Y++[D],
  solve(Vars),

  println(x=X),
  println(y=Y),
  println(d=D),
  nl,
  fail,
  nl.

go => true.


distance_between(D, X, Y, Op) =>
  println(op=Op),
  N = X.len,
  
  S = 0,
  foreach (I in 1..N, J in 1..N, I != J)
    % As suggested by NFZ
    C1 = my_call(Op,X[I],X[J]),
    C2 = my_neg_call(Op,Y[I],Y[J]),

    % variant:
    % my_call(Op,X[I],X[J],C1),
    % my_neg_call(Op,Y[I],Y[J],C2),
    
    E1 = C1 #/\ C2,
    
    % C3 = my_call(Op,Y[I],Y[J]),
    % C4 = my_neg_call(Op,X[I],X[J]),    

    % E2 = C3 #/\ C4,
    % Sum := $(Sum + E1 +E2)
    
    Sum := $(Sum + E1)    
  end,
  D #= sum(S).
  
  

my_call(#<, X, Y)  = X #< Y.
% my_call(#<, X, Y, C)  => C = $(X #< Y).

my_neg_call(#<, X, Y)  = #~ X #< Y.
% my_neg_call(#<, X, Y)  = $(#~ X #< Y).
% my_neg_call(#<, X, Y, C)  => C = $(#~ X #< Y).