/* Copyright (c) 1997-2020
   Ewgenij Gawrilow, Michael Joswig, and the polymake team
   Technische Universität Berlin, Germany
   https://polymake.org

   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.
--------------------------------------------------------------------------------
*/

#include "polymake/client.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/Set.h"
#include "polymake/graph/Lattice.h"
#include "polymake/graph/Decoration.h"

namespace polymake { namespace matroid {

using graph::Lattice;
using graph::lattice::Sequential;
using graph::lattice::BasicDecoration;

// Assumes that c1.size() <= c2.size()
bool check_circuit_compatibility(const Set<Int>& c1, const Set<Int>& c2, const Lattice<BasicDecoration, Sequential>& hd)
{
  const auto relevant_faces = hd.nodes_of_rank(c2.size()-1);
  Set<Int> closure;
  for (const auto& rf : relevant_faces) {
    const auto& rf_face = hd.face(rf);
    // Check if the flat contains c2
    if (incl(c2, rf_face) <= 0) {
      if (closure.empty())
        closure = rf_face;
      else
        closure *= rf_face;
    }
  }
  return incl(c1, closure) <= 0; // Check that the closure of c2 contains c1.
}

// Checks whether a matroid is laminar
bool is_laminar_matroid(BigObject matroid)
{
  BigObject lattice_of_flats_obj = matroid.give("LATTICE_OF_FLATS");
  Lattice<BasicDecoration, Sequential> lattice_of_flats(lattice_of_flats_obj);
  IncidenceMatrix<> circuits = matroid.give("CIRCUITS");

  for (auto c1 = entire(rows(circuits)); !c1.at_end(); ++c1) {
    for (auto c2 = c1; !(++c2).at_end();) {
      if (!((*c1) * (*c2)).empty()) {
        const bool flip = (*c2).size() < (*c1).size();
        if (!check_circuit_compatibility( flip? (*c2) : (*c1), flip? (*c1) : (*c2),
                                          lattice_of_flats ))
          return false;
      }
    }
  }
  return true;
}

Function4perl(&is_laminar_matroid, "is_laminar_matroid(Matroid)");

} }

// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
