%
% 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

% 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)
];