/*

All interval problem  in Gecode.

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 the following models:
* MiniZinc: http://www.hakank.org/minizinc/all_interval.mzn
* Comet   : http://www.hakank.org/comet/all_interval.co
* Gecode/R: http://www.hakank.org/gecode_r/all_interval.rb
* ECLiPSe: http://www.hakank.org/eclipse/all_interval.ecl
* SICStus Prolog: http://www.hakank.org/sicstus/all_interval.pl

Note: This is a fairly true port from the MiniZinc model.
A faster implementation is in the Gecode distribution:
http://www.gecode.org/doc-latest/reference/all-interval_8cpp_source.html

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

*/

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

#include <gecode/driver.hh>
#include <gecode/int.hh>
#include <gecode/minimodel.hh>

using namespace Gecode;

using std::cout;
using std::endl;
using std::setw;
using std::string;

class AllInterval : public Script {
protected:

int n;

IntVarArray x;
IntVarArray diffs;

public:

AllInterval(const SizeOptions& opt)
:
n(opt.size()),
x(*this, n, 1, n),
diffs(*this, n-1, 0, n-1)
{

cout << "Size: " << n << endl;

distinct(*this, x, opt.icl());
distinct(*this, diffs, opt.icl());

for(int k = 0; k < n-1; k++) {
rel(*this, diffs[k] == abs(x[k+1] - x[k]), opt.icl());
}

// symmetry breaking
rel(*this, x[0] < x[n-1], opt.icl());
rel(*this, diffs[0] < diffs[1], opt.icl());

// branching
branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_MIN());

}

// Print solution
virtual void
print(std::ostream& os) const {
os << "x    : " << x << endl;
os << "diffs: " << diffs << endl;
os << endl;
}

// Constructor for cloning s
AllInterval(bool share, AllInterval& s) : Script(share,s) {
x.update(*this, share, s.x);
diffs.update(*this, share, s.diffs);
}

// Copy during cloning
virtual Space*
copy(bool share) {
return new AllInterval(share,*this);
}
};

int
main(int argc, char* argv[]) {

SizeOptions opt("AllInterval");

opt.icl(ICL_DOM);
opt.solutions(0);
opt.size(12);

opt.parse(argc,argv);

Script::run<AllInterval,DFS,SizeOptions>(opt);

return 0;
}