/* Copyright (c) 1997-2015
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
   http://www.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/Array.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/Set.h"
#include "polymake/Graph.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;

   //Checks whether a matroid is nested, i.e. its lattice of cyclic flats is a chain.
   bool is_nested(perl::Object matroid) {
      perl::Object cgraph_obj = matroid.give("LATTICE_OF_CYCLIC_FLATS");
      const Lattice<BasicDecoration, Sequential> cgraph(cgraph_obj);
      int current_node = cgraph.bottom_node();
      int top_node = cgraph.top_node();

      while(current_node != top_node) {
         Set<int> neighbours = cgraph.out_adjacent_nodes(current_node);
         if(neighbours.size() > 1) return false;
         current_node = *(neighbours.begin());
      }

      return true;
   }

   //For a nested matroid, computes the maximal transversal presentation
   Array<Set<int> > nested_presentation(perl::Object matroid) {
      int n = matroid.give("N_ELEMENTS");
      perl::Object cyclic_flats_obj = matroid.give("LATTICE_OF_CYCLIC_FLATS");
      Lattice<BasicDecoration, Sequential> cyclic_flats(cyclic_flats_obj);
      Array<Set<int> > ordered_faces(cyclic_flats.nodes());
      Array<int> ordered_ranks(cyclic_flats.nodes());

      //Convert faces into ordered list
      ordered_faces[0] = cyclic_flats.face(cyclic_flats.bottom_node());
      ordered_ranks[0] = 0;
      int current_index = 1;
      for(int i = 0; i <= cyclic_flats.rank()-1; i++) {
         const auto& n_of_dim = cyclic_flats.nodes_of_rank(i+1);
         if(n_of_dim.size() != 0) {
            ordered_faces[current_index] = cyclic_flats.face(*(n_of_dim.begin()));
            ordered_ranks[current_index] = i+1;
            current_index++;
         }
      }

      //First set in presentation: Coloops as complements of largest cyclic flat
      Set<int> coloops = sequence(0,n) - cyclic_flats.face(cyclic_flats.top_node());
      int total_rank = coloops.size() + ordered_ranks[ ordered_ranks.size()-1];
      Array<Set<int> > result(total_rank);
      int presentation_index = 0;
      for(int c = 0; c < coloops.size(); c++, presentation_index++) {
         result[c] = coloops;
      }

      //Now move backwards in the list of flats and take complements
      for(int j = ordered_faces.size()-2; j>= 0; j--) {
         Set<int> complement = sequence(0,n) - ordered_faces[j];
         int occ = ordered_ranks[j+1] - ordered_ranks[j];
         for(int k = 0; k < occ; k++, presentation_index++) {
            result[presentation_index] = complement;
         }
      }

      return result;
   }

   UserFunction4perl("# @category Advanced properties"
                     "# Checks whether a matroid is nested, i.e. its lattice of cyclic flats is a chain."
                     "# @param Matroid M"
                     "# @return Bool Whether M is nested.",
                     &is_nested, "is_nested_matroid(Matroid)");

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

}}
