% 
% Global constraint all_different except 0 in MiniZinc.
%
% From Global constraint catalogue:
% http://www.emn.fr/x-info/sdemasse/gccat/Calldifferent_except_0.html
% """ 
% Enforce all variables of the collection VARIABLES to take distinct 
% values, except those variables that are assigned to 0.
% 
% Example
%    (<5, 0, 1, 9, 0, 3>)
% 
% The alldifferent_except_0 constraint holds since all the values 
% (that are different from 0) 5, 1, 9 and 3 are distinct.
% 

% 
% Model created by Hakan Kjellerstrand, hakank@bonetmail.com
% See also my MiniZinc page: http://www.hakank.org/minizinc

include "globals.mzn"; 

int: n;

array[1..n] of var 0..9: x :: is_output;
var int: z :: is_output; % number of zeros

solve satisfy;
% solve minimize z;

predicate all_different_except_0(array[int] of var int: x) =

   forall(i,j in index_set(x) where i != j) (
        (x[i] > 0 /\ x[j] > 0) -> x[i] != x[j]      
   )
;

% copy 
predicate cp1d(array[int] of int: x, array[int] of var int: y) =
  assert(index_set(x) = index_set(y),
           "cp1d: x and y have different sizes",
    forall(i in index_set(x)) (
        x[i] = y[i]
    )
  )
; 


constraint
  cp1d([5,0,1,9,0,3], x)
  /\
  all_different_except_0(x)
  /\
  z = sum(i in index_set(x)) (bool2int(x[i] = 0))

;

%
% data
%
n = 6;