#include <Rcpp.h>
// Copyright (c) 2019 CNRS and LIRIS' Establishments (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Surface_mesh_topology/include/CGAL/Face_graph_wrapper.h $
// $Id: include/CGAL/Face_graph_wrapper.h 50cfbde3b84 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
//
#ifndef CGAL_FACE_GRAPH_WRAPPER_H
#define CGAL_FACE_GRAPH_WRAPPER_H 1

#include <CGAL/license/Surface_mesh_topology.h>
#include <CGAL/assertions.h>

#include <CGAL/Surface_mesh_topology/internal/Functors_for_face_graph_wrapper.h>
#include <CGAL/Surface_mesh_topology/internal/Iterators_for_face_graph_wrapper.h>
#include <CGAL/Combinatorial_map/internal/Combinatorial_map_internal_functors.h>
#include <CGAL/Polyhedron_3_fwd.h>
#include <CGAL/Surface_mesh/Surface_mesh_fwd.h>
#include <CGAL/Combinatorial_map_fwd.h>
#include <CGAL/Generalized_map_fwd.h>
#include <CGAL/Linear_cell_complex_fwd.h>
#include <CGAL/Polygonal_schema_fwd.h>

#include <bitset>

namespace CGAL
{
////////////////////////////////////////////////////////////////////////////////
/** Class Face_graph_wrapper: to wrap any model of FaceGraph into a
 *  Combinatorial map. For now, only for const models, i.e. does not support
 *  modification operators.
 */
template<typename HEG_>
class Face_graph_wrapper
{
public:
  typedef HEG_                    HEG;
  typedef Face_graph_wrapper<HEG> Self;
  typedef std::uint32_t /*std::size_t*/ size_type;
  typedef Self                    Refs;

  struct Dart_container
  {
    typedef typename boost::graph_traits<HEG>::halfedge_iterator iterator;
    typedef typename boost::graph_traits<HEG>::halfedge_iterator const_iterator; // TODO ?
    // typedef My_halfedge_iterator<HEG> iterator;
    // typedef My_halfedge_iterator<HEG> const_iterator; // TODO ?
  };

  typedef typename boost::graph_traits<HEG>::halfedge_descriptor Dart_descriptor;
  typedef typename boost::graph_traits<HEG>::halfedge_descriptor Dart_const_descriptor;

   typedef Dart_descriptor Null_descriptor_type;
  // typedef CGAL::Void* Null_descriptor_type;
   static const Null_descriptor_type null_descriptor; //=Dart_descriptor();
   static const Null_descriptor_type null_dart_descriptor; //=Dart_descriptor();

  /// Number of marks
  static const size_type NB_MARKS = 32;
  static const size_type INVALID_MARK = NB_MARKS;

  /// The dimension of the combinatorial map.
  static const unsigned int dimension=2;
  static const unsigned int ambient_dimension=3;

  typedef typename boost::graph_traits<HEG>::vertex_descriptor vertex_descriptor;
  typedef typename boost::graph_traits<HEG>::edge_descriptor   edge_descriptor;
  typedef typename boost::graph_traits<HEG>::face_descriptor   face_descriptor;
  typedef boost::undirected_tag                                directed_category;
  typedef boost::disallow_parallel_edge_tag                    edge_parallel_category;

  struct SM_graph_traversal_category : public virtual boost::bidirectional_graph_tag,
                                       public virtual boost::vertex_list_graph_tag,
                                       public virtual boost::edge_list_graph_tag
  {};
  typedef SM_graph_traversal_category traversal_category;


  Face_graph_wrapper(const HEG& f) : m_fg(f),
                                     mdarts(*this),
                                     m_nb_darts(0),
                                     m_marks_initialized(false),
                                     mnb_used_marks(0)

  {
    // Store locally the number of darts: the HEG must not be modified
    m_nb_darts=darts().size();
  }

  void initialize_marks() const
  {
    if (m_marks_initialized) return;

    mmask_marks.reset();

    for (size_type i=0; i<NB_MARKS; ++i)
    {
      mfree_marks_stack[i]       =i;
      mindex_marks[i]            =i;
      mnb_marked_darts[i]        =0;
      mnb_times_reserved_marks[i]=0;
    }

    m_all_marks=get(CGAL::dynamic_halfedge_property_t<std::bitset<NB_MARKS> >(), m_fg);
    for (typename Dart_range::const_iterator it(darts().begin()),
           itend(darts().end()); it!=itend; ++it)
    { put(m_all_marks, it, std::bitset<NB_MARKS>()); }

    m_marks_initialized=true;
  }

  const HEG& get_fg() const
  { return m_fg; }

  template<unsigned int i>
  bool is_free(Dart_const_descriptor /* dh */) const
  { return false; } // Not possible to have a free dart with an HEG.
  bool is_free(Dart_const_descriptor /*dh*/, unsigned int /*i*/) const
  { return false; } // Not possible to have a free dart with an HEG.

  bool is_perforated(Dart_const_descriptor dh) const
  { return is_border(dh, m_fg); }

  Dart_const_descriptor get_beta(Dart_const_descriptor ADart, int B1) const
  {
    CGAL_assertion(B1>=0 && B1<=static_cast<int>(dimension));
    if (B1==1) return internal::Get_beta<HEG, 1>::value(m_fg, ADart);
    if (B1==2) return internal::Get_beta<HEG, 2>::value(m_fg, ADart);
    return internal::Get_beta<HEG, 0>::value(m_fg, ADart);
  }
  template<int B1>
  Dart_const_descriptor get_beta(Dart_const_descriptor ADart) const
  {
    CGAL_assertion(B1>=0 && B1<=static_cast<int>(dimension));
    return internal::Get_beta<HEG, B1>::value(m_fg, ADart);
  }

  bool is_empty() const
  { return number_of_darts()==0; }

  /* ??  bool is_dart_used(Dart_const_descriptor dh) const
      { return true; ?? } */

  int highest_nonfree_dimension(Dart_const_descriptor /* dh */) const
  { return 2; }

  Dart_const_descriptor previous(Dart_const_descriptor ADart) const
  { return get_beta<0>(ADart); }
  Dart_const_descriptor next(Dart_const_descriptor ADart) const
  { return get_beta<1>(ADart); }
  Dart_const_descriptor opposite(Dart_const_descriptor dh) const
  { return get_beta<2>(dh); }
  Dart_const_descriptor opposite2(Dart_const_descriptor dh) const
  { return get_beta<2>(dh); }
  Dart_const_descriptor other_extremity(Dart_const_descriptor dh) const
  { return get_beta<1>(dh); }

  template<unsigned int dim>
  Dart_const_descriptor opposite(Dart_const_descriptor ADart) const
  { return this->template get_beta<dim>(ADart); }
  Dart_const_descriptor other_orientation(Dart_const_descriptor ADart) const
  { return ADart; }

  bool is_previous_exist(Dart_const_descriptor) const
  { return true; }
  bool is_next_exist(Dart_const_descriptor) const
  { return true; }
  template<unsigned int dim>
  bool is_opposite_exist(Dart_const_descriptor /* ADart */) const
  { return true; }

  template<typename ...Betas>
  Dart_descriptor beta(Dart_descriptor ADart, Betas... betas)
  { return CGAL::internal::Beta_functor<Self, Dart_descriptor, Betas...>::
      run(*this, ADart, betas...); }
  template<typename ...Betas>
  Dart_const_descriptor beta(Dart_const_descriptor ADart, Betas... betas) const
  { return CGAL::internal::Beta_functor<const Self, Dart_const_descriptor, Betas...>::
      run(*this, ADart, betas...); }
  template<int... Betas>
  Dart_descriptor beta(Dart_descriptor ADart)
  { return CGAL::internal::Beta_functor_static<Self, Dart_descriptor, Betas...>::
      run(*this, ADart); }
  template<int... Betas>
  Dart_const_descriptor beta(Dart_const_descriptor ADart) const
  { return CGAL::internal::Beta_functor_static<const Self, Dart_const_descriptor, Betas...>::
      run(*this, ADart); }

  size_type number_of_darts() const
  { return m_nb_darts; }

  size_type number_of_halfedges() const
  { return number_of_darts(); }

  size_type number_of_used_marks() const
  { return mnb_used_marks; }

  bool is_reserved(size_type amark) const
  {
    CGAL_assertion(amark<NB_MARKS);
    return (m_marks_initialized && mnb_times_reserved_marks[amark]!=0);
  }

  size_type number_of_marked_darts(size_type amark) const
  {
    CGAL_assertion( is_reserved(amark) );
    return mnb_marked_darts[amark];
  }

  size_type number_of_unmarked_darts(size_type amark) const
  {
    return number_of_darts() - number_of_marked_darts(amark);
  }

  bool is_whole_map_unmarked(size_type amark) const
  { return number_of_marked_darts(amark)==0; }

  bool is_whole_map_marked(size_type amark) const
  {  return number_of_marked_darts(amark)==number_of_darts(); }

  class Exception_no_more_available_mark {};

  size_type get_new_mark() const
  {
    initialize_marks();
    if (mnb_used_marks==NB_MARKS)
    {
      Rcpp::Rcerr << "Not enough Boolean marks: "
        "increase NB_MARKS in item class." << std::endl;
      Rcpp::Rcerr << "  (exception launched)" << std::endl;
      throw Exception_no_more_available_mark();
    }

    size_type m=mfree_marks_stack[mnb_used_marks];
    mused_marks_stack[mnb_used_marks]=m;

    mindex_marks[m]=mnb_used_marks;
    mnb_times_reserved_marks[m]=1;

    ++mnb_used_marks;
    CGAL_assertion(is_whole_map_unmarked(m));

    return m;
  }

  void share_a_mark(size_type amark) const
  {
    CGAL_assertion( is_reserved(amark) );
    ++mnb_times_reserved_marks[amark];
  }

  size_type get_number_of_times_mark_reserved(size_type amark) const
  {
    CGAL_assertion( is_reserved(amark) );
    return mnb_times_reserved_marks[amark];
  }

  void negate_mark(size_type amark) const
  {
    CGAL_assertion(is_reserved(amark));

    mnb_marked_darts[amark]=number_of_darts()-mnb_marked_darts[amark];
    mmask_marks.flip(amark);
  }

  void mark_null_dart( size_type /*amark*/) const
  {}

  bool get_dart_mark(Dart_const_descriptor ADart, size_type amark) const
  {
    CGAL_assertion(is_reserved(amark));
    return get(m_all_marks, ADart)[amark];
  }
  void set_dart_mark(Dart_const_descriptor ADart, size_type amark, bool avalue) const
  {
    CGAL_assertion(is_reserved(amark));
    const_cast<std::bitset<NB_MARKS>& >(get(m_all_marks, ADart)).set(amark, avalue);
  }

  void flip_dart_mark(Dart_const_descriptor ADart, size_type amark) const
  { set_dart_mark(ADart, amark, !get_dart_mark(ADart, amark)); }

  bool is_marked(Dart_const_descriptor adart, size_type amark) const
  {
    CGAL_assertion(is_reserved(amark));
    return get_dart_mark(adart, amark)!=mmask_marks[amark];
  }

  void set_mark_to(Dart_const_descriptor adart, size_type amark,
                   bool astate) const
  {
    CGAL_assertion(is_reserved(amark));

    if (is_marked(adart, amark)!=astate)
    {
      if (astate) ++mnb_marked_darts[amark];
      else --mnb_marked_darts[amark];

      flip_dart_mark(adart, amark);
    }
  }

  void mark(Dart_const_descriptor adart, size_type amark) const
  {
    CGAL_assertion(is_reserved(amark));

    if (is_marked(adart, amark)) return;

    ++mnb_marked_darts[amark];
    flip_dart_mark(adart, amark);
  }

  void unmark(Dart_const_descriptor adart, size_type amark) const
  {
    CGAL_assertion( adart!=this->null_dart_descriptor );
    CGAL_assertion( is_reserved(amark) );

    if (!is_marked(adart, amark)) return;

    --mnb_marked_darts[amark];
    flip_dart_mark(adart, amark);
  }

  void unmark_all(size_type amark) const
  {
    CGAL_assertion( is_reserved(amark) );

    if ( is_whole_map_marked(amark) )
    {
      negate_mark(amark);
    }
    else if ( !is_whole_map_unmarked(amark) )
    {
      for (typename Dart_range::const_iterator it(darts().begin()),
           itend(darts().end()); it!=itend; ++it)
        unmark(*it, amark);
    }
    CGAL_assertion(is_whole_map_unmarked(amark));
  }

  void free_mark(size_type amark) const
  {
    CGAL_assertion( is_reserved(amark) );

    if ( mnb_times_reserved_marks[amark]>1 )
    {
      --mnb_times_reserved_marks[amark];
      return;
    }

    unmark_all(amark);

    // 1) We remove amark from the array mused_marks_stack by
    //    replacing it with the last mark in this array.
    mused_marks_stack[mindex_marks[amark]] =
      mused_marks_stack[--mnb_used_marks];
    mindex_marks[mused_marks_stack[mnb_used_marks]] =
      mindex_marks[amark];

    // 2) We add amark in the array mfree_marks_stack and update its index.
    mfree_marks_stack[ mnb_used_marks ]=amark;
    mindex_marks[amark] = mnb_used_marks;

    mnb_times_reserved_marks[amark]=0;
  }

  bool is_without_boundary(unsigned int i) const
  {
    CGAL_assertion(1<=i && i<=dimension);
    if (i==1) return true;

    for ( typename Dart_range::const_iterator it(darts().begin()),
            itend(darts().end()); it!=itend; ++it)
    { if (is_perforated(it)) return false; }
    return true;
  }

  bool is_without_boundary() const
  { return is_without_boundary(2); }

  //**************************************************************************
  // Dart_of_cell_range
  template<unsigned int i>
  struct Dart_of_cell_range
  {
    typedef CGAL::internal::FGW_cell_iterator<Self, i> iterator;
    typedef CGAL::internal::FGW_cell_iterator<Self, i> const_iterator;
    Dart_of_cell_range(const Self &amap, Dart_descriptor adart) : mmap(amap),
                                                              m_initdart(adart),
                                                              msize(0)
    {}
    const_iterator begin() const { return const_iterator(mmap, m_initdart); }
    const_iterator end() const   { return const_iterator(mmap, m_initdart, mmap.null_descriptor); }
    size_type size() const
    {
      if (msize==0)
      {
        for (const_iterator it=begin(), itend=end(); it!=itend; ++it)
        { ++msize; }
      }
      return msize;
    }

    bool empty() const
    { return mmap.is_empty(); }
  private:
    const Self & mmap;
    Dart_descriptor m_initdart;
    mutable typename Self::size_type msize;
  };
  //**************************************************************************
  // Dart_of_cell_const_range
  /*  template<unsigned int i,int dim=Self::dimension>
  struct Dart_of_cell_const_range // TODO REMOVE ??
  {}; */
  //--------------------------------------------------------------------------
  template<unsigned int i>
  Dart_of_cell_range<i> darts_of_cell(Dart_descriptor adart)
  { return Dart_of_cell_range<i>(*this,adart); }
  //--------------------------------------------------------------------------
  template<unsigned int i>
  Dart_of_cell_range<i> darts_of_cell(Dart_const_descriptor adart) const
  { return Dart_of_cell_range<i>(*this,adart); } // Before it was Dart_of_cell_const_range<i>
  //**************************************************************************
  // Dart_range
  struct Dart_range {
    typedef CGAL::internal::FGW_dart_iterator_basic_of_all<Self> iterator;
    typedef CGAL::internal::FGW_dart_iterator_basic_of_all<Self> const_iterator;
    Dart_range(const Self &amap) : mmap(amap), msize(0)
    {}
    iterator begin() { return iterator(mmap); }
    iterator end()   { return iterator(mmap,mmap.null_descriptor); }
    const_iterator begin() const { return const_iterator(mmap); }
    const_iterator end() const   { return const_iterator(mmap,mmap.null_descriptor); }
    size_type size() const
    {
      if (msize==0)
      { msize=static_cast<size_type>(halfedges(mmap.get_fg()).size()); }
      return msize;
    }
    bool empty() const
    { return mmap.is_empty(); }

    size_type capacity() const
    { return static_cast<size_type>(num_halfedges(mmap.get_fg())); }

    bool is_used(size_type i) const
    { return internal::Is_index_used<HEG>::run(mmap.get_fg(), i); }

    size_type index(const_iterator it) const
    {
      return internal::Index_from_halfedge_descriptor<HEG>::
        run(mmap.get_fg(), *it);
    }

    size_type index(Dart_const_descriptor it) const
    {
      return internal::Index_from_halfedge_descriptor<HEG>::
        run(mmap.get_fg(), it);
    }

  private:
    const Self & mmap;
    mutable typename Self::size_type msize;
  };
  //**************************************************************************
  // Dart_const_range // TODO REMOVE ?
  /*  struct Dart_const_range {
    typedef CGAL::FGW_dart_iterator_basic_of_all<Self, true> const_iterator;
    Dart_const_range(const Self &amap) : mmap(amap), msize(0)
    {}
    const_iterator begin() const { return const_iterator(mmap); }
    const_iterator end() const   { return const_iterator(mmap,mmap.null_descriptor); }
    size_type size() const
    {
      if (msize==0)
      {
        for (const_iterator it=begin(), itend=end(); it!=itend; ++it)
        { ++msize; }
      }
      return msize;
    }

    bool empty() const
    { return mmap.is_empty(); }
  private:
    const Self & mmap;
    mutable typename Self::size_type msize;
    };*/
  //**************************************************************************
  Dart_range& darts()
  { return mdarts; }
  //--------------------------------------------------------------------------
  const Dart_range& darts() const
  { return mdarts; } // Before it was Dart_const_range(*this)
  //**************************************************************************
  Dart_descriptor dart_descriptor(size_type i)
  {
    CGAL_assertion(darts().is_used(i));
    return internal::Halfedge_descriptor_from_index<HEG>::run(get_fg(), i);
  }
  Dart_const_descriptor dart_descriptor(size_type i) const
  {
    CGAL_assertion(darts().is_used(i));
    return internal::Halfedge_descriptor_from_index<HEG>::run(get_fg(), i);
  }

  template <unsigned int i>
  bool belong_to_same_cell(Dart_const_descriptor adart1,
                           Dart_const_descriptor adart2) const
  {
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart1).begin(),
           itend=darts_of_cell<i>(adart1).end(); it!=itend; ++it)
    { if (*it==adart2) { return true; } }
    return false;
  }

  template <unsigned int i>
  bool is_whole_cell_unmarked(Dart_const_descriptor adart, size_type amark) const
  {
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart).begin(),
           itend=darts_of_cell<i>(adart).end(); it!=itend; ++it)
    { if (is_marked(*it, amark)) { return false; } }
    return true;
  }

  template <unsigned int i>
  bool is_whole_cell_marked(Dart_const_descriptor adart, size_type amark) const
  {
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart).begin(),
           itend=darts_of_cell<i>(adart).end(); it!=itend; ++it)
    { if (!is_marked(*it, amark)) { return false; } }
    return true;
  }

  template <unsigned int i>
  size_type mark_cell(Dart_const_descriptor adart, size_type amark) const
  {
    size_type res=0;
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart).begin(),
           itend=darts_of_cell<i>(adart).end(); it!=itend; ++it)
    { mark(*it, amark); ++res; }
    return res;
}

  size_type mark_cell(Dart_const_descriptor adart, unsigned int i, size_type amark) const
  {
    if (i==0) { return mark_cell<0>(adart, amark); }
    else if (i==1) { return mark_cell<1>(adart, amark); }
    else if (i==2) { return mark_cell<2>(adart, amark); }
    return mark_cell<3>(adart, amark);
  }

  template <unsigned int i>
  size_type unmark_cell(Dart_const_descriptor adart, size_type amark) const
  {
    size_type res=0;
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart).begin(),
           itend=darts_of_cell<i>(adart).end(); it!=itend; ++it)
    { unmark(*it, amark); ++res; }
    return res;
  }

  template <unsigned int i>
  size_type mark_oriented_cell(Dart_const_descriptor adart, size_type amark,
                               size_type amark2=INVALID_MARK) const
  {
    size_type res=0;
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart).begin(),
           itend=darts_of_cell<i>(adart).end(); it!=itend; ++it)
    {
      mark(*it, amark); ++res;
      if (amark2!=INVALID_MARK) { mark(*it, amark2); }
    }
    return res;
  }

  template <unsigned int i>
  size_type unmark_oriented_cell(Dart_const_descriptor adart, size_type amark,
                                 size_type amark2=INVALID_MARK) const
  {
    size_type res=0;
    for (typename Dart_of_cell_range<i>::iterator it=darts_of_cell<i>(adart).begin(),
           itend=darts_of_cell<i>(adart).end(); it!=itend; ++it)
    {
      unmark(*it, amark); ++res;
      if (amark2!=INVALID_MARK) { unmark(*it, amark2); }
    }
    return res;
  }

  std::size_t orient(size_type amark) const
  { negate_mark(amark); return number_of_darts(); }

  std::vector<unsigned int>
  count_marked_cells(size_type amark, const std::vector<unsigned int>& acells) const
  {
    std::vector<unsigned int> res(dimension+2);
    std::vector<size_type> marks(dimension+2);

    // Initialization of the result
    for (unsigned int i=0; i<dimension+2; ++i)
    {
      res[i]=0;
      marks[i]=INVALID_MARK;
    }

    // Mark reservation
    for (unsigned int i=0; i<acells.size(); ++i)
    {
      CGAL_assertion(acells[i]<=dimension+1);
      if (marks[acells[i]]==INVALID_MARK )
      {
        marks[acells[i]]=get_new_mark();
        CGAL_assertion(is_whole_map_unmarked(marks[acells[i]]));
      }
    }

    // Counting and marking cells
    for (typename Dart_range::const_iterator it(darts().begin()),
           itend(darts().end()); it!=itend; ++it)
    {
      if (is_marked(*it, amark))
      {
        for (unsigned int i=0; i<acells.size(); ++i)
        {
          if (!is_marked(*it, marks[acells[i]]))
          {
            mark_cell(*it, acells[i], marks[acells[i]]);
            ++res[acells[i]];
          }
        }
      }
    }

    // Unmarking darts
    std::vector<size_type> tounmark;
    for (unsigned int i=0; i<acells.size(); ++i)
    {
      if (is_whole_map_marked(marks[acells[i]]) ||
          is_whole_map_unmarked(marks[acells[i]]))
      { free_mark(marks[acells[i]]); }
      else
      { tounmark.push_back(marks[acells[i]]); }
    }

    if (tounmark.size()>0)
    {
      for (typename Dart_range::const_iterator it(darts().begin()),
             itend(darts().end()); it!=itend; ++it)
      {
        for (unsigned int i=0; i<tounmark.size(); ++i)
        { unmark(*it, tounmark[i]); }
      }
      for (unsigned int i=0; i<tounmark.size(); ++i)
      {
        CGAL_assertion(is_whole_map_unmarked(tounmark[i]));
        free_mark(tounmark[i]);
      }
    }

    return res;
  }

  std::vector<unsigned int>
  count_cells(const std::vector<unsigned int>& acells) const
  {
    std::vector<unsigned int> res;
    size_type m=get_new_mark();
    negate_mark(m); // We mark all the cells.

    res=count_marked_cells(m, acells);

    negate_mark(m); // We unmark the cells
    free_mark(m);

    return res;
  }

  std::vector<unsigned int> count_all_cells() const
  {
    std::vector<unsigned int> dim(dimension+2);

    for ( unsigned int i=0; i<=dimension+1; ++i)
    { dim[i]=i; }

    return count_cells(dim);
  }

  std::ostream& display_characteristics(std::ostream & os) const
  {
    std::vector<unsigned int> cells(dimension+2);
    for ( unsigned int i=0; i<=dimension+1; ++i)
    { cells[i]=i; }

    std::vector<unsigned int> res=count_cells(cells);

    os<<"#Darts="<<number_of_darts();
    for (unsigned int i=0; i<=dimension; ++i)
      os<<", #"<<i<<"-cells="<<res[i];
    os<<", #ccs="<<res[dimension+1];

    return os;
  }

protected:
  const HEG& m_fg;
  Dart_range mdarts;
  size_type m_nb_darts;
  mutable bool m_marks_initialized; /// True iff marks are initialized (we use lazy initialization)

  /// Number of times each mark is reserved. 0 if the mark is free.
  mutable size_type mnb_times_reserved_marks[NB_MARKS];

  /// Mask marks to know the value of unmark dart, for each index i.
  mutable std::bitset<NB_MARKS> mmask_marks;

  /// Number of used marks.
  mutable size_type mnb_used_marks;

  /// Index of each mark, in mfree_marks_stack or in mfree_marks_stack.
  mutable size_type mindex_marks[NB_MARKS];

  /// "Stack" of free marks.
  mutable size_type mfree_marks_stack[NB_MARKS];

  /// "Stack" of used marks.
  mutable size_type mused_marks_stack[NB_MARKS];

  /// Number of marked darts for each used marks.
  mutable size_type mnb_marked_darts[NB_MARKS];

  /// Array of property maps; one for each reserved mark.
  typedef typename boost::property_map
  <HEG, CGAL::dynamic_halfedge_property_t<std::bitset<NB_MARKS> > >::const_type MarkPMap;
  mutable MarkPMap m_all_marks;
};

  /// null_descriptor
  // template <typename HEG>
  // const typename Face_graph_wrapper<HEG>::Null_descriptor_type
  // Face_graph_wrapper<HEG>::null_descriptor=nullptr;
  template <typename HEG>
  const typename Face_graph_wrapper<HEG>::Null_descriptor_type
  Face_graph_wrapper<HEG>::null_descriptor=typename Face_graph_wrapper<HEG>::Dart_descriptor();

  /// null_dart_descriptor
  // template <typename HEG>
  // const typename Face_graph_wrapper<HEG>::Null_descriptor_type
  // Face_graph_wrapper<HEG>::null_dart_descriptor=nullptr;
  template <typename HEG>
  const typename Face_graph_wrapper<HEG>::Null_descriptor_type
  Face_graph_wrapper<HEG>::null_dart_descriptor=typename Face_graph_wrapper<HEG>::Dart_descriptor();

  template<class Base, class HEG>
  struct Get_map
  {
    typedef Face_graph_wrapper<HEG>       type;
    typedef const Face_graph_wrapper<HEG> storage_type;
    Get_map(const HEG& heg): m_map(heg) {}
    static const HEG& get_mesh(const storage_type& amap)
    { return amap.get_fg(); }

    storage_type m_map;
  };

  template <unsigned int d, typename Refs, typename Items, typename Alloc,
            typename Storage, class Map>
  struct Get_map<CGAL::Combinatorial_map_base<d, Refs, Items, Alloc, Storage>, Map>
  {
    typedef Map        type;
    typedef const Map& storage_type;
    Get_map(const Map& heg): m_map(heg) {}
    static const Map& get_mesh(storage_type& amap)
    { return amap; }
   storage_type m_map;
  };

  template <unsigned int d, typename Refs, typename Items, typename Alloc,
            typename Storage, class Map>
  struct Get_map<CGAL::Generalized_map_base<d, Refs, Items, Alloc, Storage>, Map>
  {
    typedef Map        type;
    typedef const Map& storage_type;
    Get_map(const Map& heg): m_map(heg) {}
    static const Map& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template <unsigned int d, unsigned int d2, typename Traits, typename Items,
            typename Alloc,
            template<unsigned int,class,class,class,class>
            class Map, typename Refs, typename Storage, class LCC>
  struct Get_map<CGAL::Linear_cell_complex_base<d, d2, Traits, Items, Alloc,
      Map, Refs, Storage>, LCC>
  {
    typedef LCC        type;
    typedef const LCC& storage_type;
    Get_map(const LCC& heg): m_map(heg) {}
     static const LCC& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template <unsigned int d, typename Items, typename Alloc,
            typename Storage, class Map>
  struct Get_map<CGAL::Combinatorial_map<d, Items, Alloc, Storage>, Map>
  {
    typedef Map        type;
    typedef const Map& storage_type;
    Get_map(const Map& heg): m_map(heg) {}
     static const Map& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template <typename Items, typename Alloc, typename Storage, class Map>
  struct Get_map<CGAL::Surface_mesh_topology::
                 Polygonal_schema_with_combinatorial_map<Items, Alloc, Storage>, Map>
  {
    typedef Map        type;
    typedef const Map& storage_type;
    Get_map(const Map& heg): m_map(heg) {}
     static const Map& get_mesh(storage_type& amap)
    { return amap; }
   storage_type m_map;
  };

  template <unsigned int d, typename Items, typename Alloc,
            typename Storage, class Map>
  struct Get_map<CGAL::Generalized_map<d, Items, Alloc, Storage>, Map>
  {
    typedef Map        type;
    typedef const Map& storage_type;
    Get_map(const Map& heg): m_map(heg) {}
    static const Map& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template <typename Items, typename Alloc, typename Storage, class Map>
  struct Get_map<CGAL::Surface_mesh_topology::
                 Polygonal_schema_with_generalized_map<Items, Alloc, Storage>, Map>
  {
    typedef Map        type;
    typedef const Map& storage_type;
    Get_map(const Map& heg): m_map(heg) {}
    static const Map& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template <unsigned int d, unsigned int d2, typename Traits, typename Items,
            typename Alloc,
            template<unsigned int,class,class,class,class>
            class Map, typename Storage, class LCC>
  struct Get_map<CGAL::Linear_cell_complex_for_combinatorial_map
      <d, d2, Traits, Items, Alloc, Map, Storage>, LCC>
  {
    typedef LCC        type;
    typedef const LCC& storage_type;
    Get_map(const LCC& heg): m_map(heg) {}
    static const LCC& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template <unsigned int d, unsigned int d2, typename Traits, typename Items,
            typename Alloc,
            template<unsigned int,class,class,class,class>
            class Map, typename Storage, class LCC>
  struct Get_map<CGAL::Linear_cell_complex_for_generalized_map
      <d, d2, Traits, Items, Alloc, Map, Storage>, LCC>
  {
    typedef LCC        type;
    typedef const LCC& storage_type;
    Get_map(const LCC& heg): m_map(heg) {}
    static const LCC& get_mesh(storage_type& amap)
    { return amap; }
    storage_type m_map;
  };

  template<class Mesh_>
  struct Get_traits
  {
    typedef Mesh_                 Mesh;
    typedef typename Mesh::Traits Kernel;
    typedef typename Mesh::Point  Point;
    typedef typename Mesh::Vector Vector;

    template<class Dart_descriptor>
    static const Point& get_point(const Mesh& m, Dart_descriptor dh)
    { return m.point(dh); }
  };

  template<class P>
  struct Get_traits<CGAL::Surface_mesh<P> >
  {
    typedef CGAL::Surface_mesh<P>                   Mesh;
    typedef typename CGAL::Kernel_traits<P>::Kernel Kernel;
    typedef typename Kernel::Point_3                Point;
    typedef typename Kernel::Vector_3               Vector;

    template<class Dart_descriptor>
    static const Point& get_point(const Mesh& m, Dart_descriptor dh)
    { return m.point(m.source(dh)); }
  };

  template<class PolyhedronTraits_3,
      class PolyhedronItems_3,
      template<class T, class I, class A> class T_HDS,
      class Alloc>
  struct Get_traits<CGAL::Polyhedron_3<PolyhedronTraits_3,
      PolyhedronItems_3, T_HDS, Alloc> >
  {
    typedef CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3,
    T_HDS, Alloc>                    Mesh;
    typedef PolyhedronTraits_3        Kernel;
    typedef typename Kernel::Point_3  Point;
    typedef typename Kernel::Vector_3 Vector;

    template<class Dart_descriptor>
    static const Point& get_point(const Mesh& /*m*/, Dart_descriptor dh)
    { return dh->opposite()->vertex()->point(); }
  };

} // Namespace CGAL

#endif // CGAL_FACE_GRAPH_WRAPPER_H //
// EOF //

