%
% 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;
set of int: differ = 1..n-1;

% Search space: The set of permutations of integer range [0..n-1]
array[classes] of var classes: series;
array[0..n-2] of var differ: differences;

solve ::int_search(series, first_fail, indomain_max, 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
% AUX: Addition of auxiliary predicates
% Auxiliary predicate stores the interval between pairs of neighbouring notes
forall(i in 0..n-2) (
differences[i] = abs(series[i+1] - series[i])
)
/\
% GCAD: Exploitation of alldifferent() global constraint
all_different(differences)
/\
% SBSO: Symmetry-breaking by selective ordering
% The first note is less than last one
series[0] < series[n-1]
;

output [
"series: " ++ show(series) ++ "\n" ++
"differences: " ++ show(differences)
];