/*

  (Decomposition of) global constraint nvalue  Picat.

  From MiniZinc:
  """
  Requires that the number of distinct values in 'x' is 'n'.
  """

  Note: Picat has a built-in nvalue/2. 
  Here we define nvalue_me/2 instead.

  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go ?=>

   Len = 5,
   X = new_list(Len),
   X :: 1..Len,
   N :: 1..Len,      

   % nvalue(N,X), % built-in
   nvalue_me(N,X), % decomposition

   Vars = X ++ [N],

   solve(Vars),

   writeln([n=N, x=X]),
   fail.

go => true.

%
% nvalue(?N,?X)
%
% Requires that the number of distinct values in X is N.
%
nvalue_me(N, X) =>
   Len = length(X),
   LB = min([fd_min(X[I]) : I in 1..Len]),
   UB = max([fd_max(X[I]) : I in 1..Len]),
   N #= sum([ (sum([ (X[J] #= I) : J in 1..Len]) #> 0) : I in LB..UB]).