% 
% Global constraint all_different except 0 in MiniZinc.
%
% From Global constraint catalogue:
% http://www.emn.fr/x-info/sdemasse/gccat/sec4.6.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;
var int: z; % number of zeros

solve satisfy;
% solve minimize z;

predicate all_different_except_0(array[int] of var int: x) =
   let {
      int: n = length(x)
   }
   in
   forall(i,j in 1..n where i != j) (
        (x[i] > 0 /\ x[j] > 0) -> x[i] != x[j]
      
   )
;

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

;

%
% data
%
n = 6;