/*

All interval problem in Comet.

CSPLib problem number 7
http://www.csplib.org/Problems/prob007
"""
Given the twelve standard pitch-classes (c, c , d, ...), represented by
numbers 0,1,...,11, find a series in which each pitch-class occurs exactly
once and in which the musical intervals between neighbouring notes cover
the full set of intervals from the minor second (1 semitone) to the major
seventh (11 semitones). That is, for each of the intervals, there is a
pair of neigbhouring pitch-classes in the series, between which this
interval appears. The problem of finding such a series can be easily
formulated as an instance of a more general arithmetic problem on Z_n,
the set of integer residues modulo n. Given n in N, find a vector
s = (s_1, ..., s_n), such that (i) s is a permutation of
Z_n = {0,1,...,n-1}; and (ii) the interval vector
v = (|s_2-s_1|, |s_3-s_2|, ... |s_n-s_{n-1}|) is a permutation of
Z_n-{0} = {1,2,...,n-1}. A vector v satisfying these conditions is
called an all-interval series of size n; the problem of finding such
a series is the all-interval series problem of size n. We may also be
interested in finding all possible series of a given size.
"""

Compare with
* MiniZinc model: http://www.hakank.org/minizinc/all_interval.mzn
* Gecode/R model: http://www.hakank.org/gecode_r/all_interval.rb

This Comet model was created by Hakan Kjellerstrand (hakank@gmail.com)
Also, see my Comet page: http://www.hakank.org/comet

*/

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

/*

Note: For n = 12, all 1328 solution (no symmetry breaking) took about 16
seconds.
With symmetry breaking: 463 solutions in 5.5 seconds.

*/

import cotfd;

int t0 = System.getCPUTime();

int n = 12;
int sum_distinct = ((n+1)*n) / 2;

Solver<CP> m();

var<CP>{int} x[1..n](m, 1..n);
var<CP>{int} diffs[1..n-1](m, 1..n-1);

Integer num_solutions(0);

exploreall<m> {

forall(k in 1..n-1)
m.post(diffs[k] == abs(x[k+1] - x[k]), onValues);

m.post(alldifferent(x), onValues);
m.post(alldifferent(diffs), onValues);

// symmetry breaking
m.post(x[1] < x[n-1], onValues);
m.post(diffs[1] < diffs[2], onValues);

} using {

/*
forall(i in 1..n : !x[i].bound()) by (-x[i].getSize()) {
// tryall<m>(v in 1..n)
//  m.label(x[i], v);
label(x[i]);
}

forall(i in 1..n-1 : !diffs[i].bound()) by (diffs[i].getSize()) {
// tryall<m>(v in 1..n)
//   m.label(x[i], v);
label(diffs[i]);
}
*/

//label(m);

label(x);
// label(diffs);

num_solutions := num_solutions + 1;

cout << x << " " << sum_distinct << " " << diffs <<  endl;
cout << flush;

}

// cout << x << endl;
cout << "\nnum_solutions: " << num_solutions << endl;

int t1 = System.getCPUTime();
cout << "time:      " << (t1-t0) << endl;
cout << "#choices = " << m.getNChoice() << endl;
cout << "#fail    = " << m.getNFail() << endl;
cout << "#propag  = " << m.getNPropag() << endl;