007: All-Interval Series

%
% All interval problem in MiniZinc.
% 
% Different approaches inspired by
% http://www.dis.uniroma1.it/~tmancini/index.php?currItem=research.publications.webappendices.csplib2x.problemDetails&problemid=007
%
% Also see
%   http://www.hakank.org/minizinc/all_interval1.mzn
%   http://www.hakank.org/minizinc/all_interval2.mzn
%   http://www.hakank.org/minizinc/all_interval3.mzn
%   http://www.hakank.org/minizinc/all_interval4.mzn
%   http://www.hakank.org/minizinc/all_interval5.mzn
%   http://www.hakank.org/minizinc/all_interval6.mzn
%

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

% Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

include "globals.mzn";

int: n = 12;
set of int: classes = 0..n-1;

% Search space: The set of permutations of integer range [0..n-1]
array[classes] of var classes: series;

solve :: int_search(series, first_fail, indomain_median, complete) satisfy;

constraint
  % C1: Each pitch class occurs exactly once
  % GCAD: Exploitation of alldifferent() global constraint
  all_different(series)
  /\

  % C2: Differences between neighbouring notes are all different
  % GCAD: Exploitation of alldifferent() global constraint
  % alldifferent(all (i in classes: i <> n-1) abs(series[i+1] - series[i]));
  all_different( 
         [ abs(series[i+1] - series[i]) | i in classes where i != n-1]
  )
  
;

output [
  show(series)
];