% 
% Global constraint ith pos different from 0 in MiniZinc.
% 
% From Global Constraint Catalogue
% http://www.emn.fr/x-info/sdemasse/gccat/sec4.151.html
% """
% ith_pos_different_from_0​(ITH,​POS,​VARIABLES)
%
% Purpose
% POS is the position of the ITHth non-zero item of the sequence of variables 
% VARIABLES.
% 
% Example
%    ​(2,​4,​〈3,​0,​0,​8,​6〉)​
%
% The ith_pos_different_from_0 constraint holds since 4 corresponds to the 
% position of the 2th non-zero item of the sequence 3 0 0 8 6.
% 
% """


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

% include "globals.mzn"; 

int: n = 5;
array[1..n] of var 0..8: x;
var 1..n: ith;
var 1..n: pos;

predicate ith_pos_different_from_0(var int: ith, 
                                   var int: pos, 
                                   array[int] of var int: x) =
   exists(i in 1..length(x)) (
     pos = i 
     /\
     ith = sum(j in 1..i) (bool2int(x[j] != 0))
     /\
     x[i] != 0
   )
;

solve satisfy;

constraint
   x = [3,0,0,8,6]
   /\
   pos = 4
   /\
   ith = 2
   /\
   ith_pos_different_from_0(ith, pos, x)
;