% 
% Global constraint max_index (and the extension max_index_val) in MiniZinc.
% 
% From Global Constraint Catalogue
% http://www.emn.fr/x-info/sdemasse/gccat/sec4.179.html
% """
% max_index​(MAX_INDEX,​VARIABLES)
% 
% Purpose
%
% MAX_INDEX is the index of the variables corresponding to the maximum value of the collection 
% of variables VARIABLES.
% 
% Example
%     (
%     3, <
%     index-1  var-3,
%     index-2  var-2,
%     index-3  var-7,
%     index-4  var-2,
%     index-5  var-6
%     >
%     )
%
% The attribute var=7 of the third item of the collection VARIABLES is the maximum value over 
% values 3,​2,​7,​2,​6. Consequently, the max_index constraint holds since its first argument 
% MAX_INDEX is set to 3.
% """

% 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 1..7: variables;
var 1..n: max_ind;
var 1..7: max_val;

% I assume that the indices are ordered and unique
predicate max_index(var int: mi, array[int] of var int: x) =
  exists(i in index_set(x)) (
     maximum(x[i], x)
     /\
     mi = i 
  )
;

%
% An extension of max_index: also returns the maximum value
%
predicate max_index_val(var int: mi, array[int] of var int: x, var int: val) =
  exists(i in index_set(x)) (
     maximum(x[i], x)
     /\
     mi = i 
     /\
     val = x[i]
  )
;


% solve satisfy;
solve :: int_search(variables ++ [max_ind, max_val], "first_fail", "indomain", "complete") satisfy;

constraint
  variables = [3,2,7,2,6]
  /\
  % max_index(max_ind, variables)
  max_index_val(max_ind, variables, max_val)
  
;

output [
  "variables: ", show(variables), "\n",
  "max_ind: ", show(max_ind), "\n",
  "max_val: ", show(max_val), "\n",
];