/* Copyright (c) 1997-2009
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Darmstadt, Germany)
   http://www.polymake.de

   This program is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by the
   Free Software Foundation; either version 2, or (at your option) any
   later version: http://www.gnu.org/licenses/gpl.txt.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
--------------------------------------------------------------------------------
   $Project: polymake $$Id: invert_bases.cc 9298 2009-09-02 23:10:56Z gawrilow $
*/

#include <polymake.h>
#include <Array.h>
#include <Integer.h>
#include <PowerSet.h>

namespace polymake { namespace matroid {


Array<Set <int> >invert_bases(const Array< Set<int> >& bases, int n_elements)
{
  const int rank=bases[0].size();
  Set< Set<int> > bases_set;
  for (Entire< Array <Set <int> > >::const_iterator i = entire(bases); !i.at_end(); ++i)
    bases_set.insert(*i);
    

  Array< Set <int> > inverted(Integer::binom(n_elements,rank)-bases.size());
  int j=0;
  for (Entire< Subsets_of_k <sequence> >::const_iterator i=entire(all_subsets_of_k(sequence(0,n_elements),rank)); !i.at_end(); ++i)
    {
      const Set<int> base = *i;
      if (!bases_set.contains(base)) inverted[j++]=base;
    }

  return inverted;
}

Function4perl(&invert_bases, "invert_bases");

} }

