/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_ADAPTORS_H

 #define LEMON_ADAPTORS_H

 /// \ingroup graph_adaptors

 /// \file

 /// \brief Several graph adaptors

 ///

 /// This file contains several useful adaptors for digraphs and graphs.

 #include <lemon/core.h>

 #include <lemon/maps.h>

 #include <lemon/bits/variant.h>

 #include <lemon/bits/graph_adaptor_extender.h>

 #include <lemon/tolerance.h>

 #include <algorithm>

 namespace lemon {

   template<typename _Digraph>

   class DigraphAdaptorBase {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorBase Adaptor;

     typedef Digraph ParentDigraph;

   protected:

     Digraph* _digraph;

     DigraphAdaptorBase() : _digraph(0) { }

     void setDigraph(Digraph& digraph) { _digraph = &digraph; }

   public:

     DigraphAdaptorBase(Digraph& digraph) : _digraph(&digraph) { }

     typedef typename Digraph::Node Node;

     typedef typename Digraph::Arc Arc;

     void first(Node& i) const { _digraph->first(i); }

     void first(Arc& i) const { _digraph->first(i); }

     void firstIn(Arc& i, const Node& n) const { _digraph->firstIn(i, n); }

     void firstOut(Arc& i, const Node& n ) const { _digraph->firstOut(i, n); }

     void next(Node& i) const { _digraph->next(i); }

     void next(Arc& i) const { _digraph->next(i); }

     void nextIn(Arc& i) const { _digraph->nextIn(i); }

     void nextOut(Arc& i) const { _digraph->nextOut(i); }

     Node source(const Arc& a) const { return _digraph->source(a); }

     Node target(const Arc& a) const { return _digraph->target(a); }

     typedef NodeNumTagIndicator<Digraph> NodeNumTag;

     int nodeNum() const { return _digraph->nodeNum(); }

     typedef ArcNumTagIndicator<Digraph> ArcNumTag;

     int arcNum() const { return _digraph->arcNum(); }

     typedef FindArcTagIndicator<Digraph> FindArcTag;

     Arc findArc(const Node& u, const Node& v, const Arc& prev = INVALID) const {

       return _digraph->findArc(u, v, prev);

     }

     Node addNode() { return _digraph->addNode(); }

     Arc addArc(const Node& u, const Node& v) { return _digraph->addArc(u, v); }

     void erase(const Node& n) { _digraph->erase(n); }

     void erase(const Arc& a) { _digraph->erase(a); }

     void clear() { _digraph->clear(); }

     int id(const Node& n) const { return _digraph->id(n); }

     int id(const Arc& a) const { return _digraph->id(a); }

     Node nodeFromId(int ix) const { return _digraph->nodeFromId(ix); }

     Arc arcFromId(int ix) const { return _digraph->arcFromId(ix); }

     int maxNodeId() const { return _digraph->maxNodeId(); }

     int maxArcId() const { return _digraph->maxArcId(); }

     typedef typename ItemSetTraits<Digraph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const { return _digraph->notifier(Node()); }

     typedef typename ItemSetTraits<Digraph, Arc>::ItemNotifier ArcNotifier;

     ArcNotifier& notifier(Arc) const { return _digraph->notifier(Arc()); }

     template <typename _Value>

     class NodeMap : public Digraph::template NodeMap<_Value> {

     public:

       typedef typename Digraph::template NodeMap<_Value> Parent;

       explicit NodeMap(const Adaptor& adaptor)

         : Parent(*adaptor._digraph) {}

       NodeMap(const Adaptor& adaptor, const _Value& value)

         : Parent(*adaptor._digraph, value) { }

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public Digraph::template ArcMap<_Value> {

     public:

       typedef typename Digraph::template ArcMap<_Value> Parent;

       explicit ArcMap(const Adaptor& adaptor)

         : Parent(*adaptor._digraph) {}

       ArcMap(const Adaptor& adaptor, const _Value& value)

         : Parent(*adaptor._digraph, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

   };

   template<typename _Graph>

   class GraphAdaptorBase {

   public:

     typedef _Graph Graph;

     typedef Graph ParentGraph;

   protected:

     Graph* _graph;

     GraphAdaptorBase() : _graph(0) {}

     void setGraph(Graph& graph) { _graph = &graph; }

   public:

     GraphAdaptorBase(Graph& graph) : _graph(&graph) {}

     typedef typename Graph::Node Node;

     typedef typename Graph::Arc Arc;

     typedef typename Graph::Edge Edge;

     void first(Node& i) const { _graph->first(i); }

     void first(Arc& i) const { _graph->first(i); }

     void first(Edge& i) const { _graph->first(i); }

     void firstIn(Arc& i, const Node& n) const { _graph->firstIn(i, n); }

     void firstOut(Arc& i, const Node& n ) const { _graph->firstOut(i, n); }

     void firstInc(Edge &i, bool &d, const Node &n) const {

       _graph->firstInc(i, d, n);

     }

     void next(Node& i) const { _graph->next(i); }

     void next(Arc& i) const { _graph->next(i); }

     void next(Edge& i) const { _graph->next(i); }

     void nextIn(Arc& i) const { _graph->nextIn(i); }

     void nextOut(Arc& i) const { _graph->nextOut(i); }

     void nextInc(Edge &i, bool &d) const { _graph->nextInc(i, d); }

     Node u(const Edge& e) const { return _graph->u(e); }

     Node v(const Edge& e) const { return _graph->v(e); }

     Node source(const Arc& a) const { return _graph->source(a); }

     Node target(const Arc& a) const { return _graph->target(a); }

     typedef NodeNumTagIndicator<Graph> NodeNumTag;

     int nodeNum() const { return _graph->nodeNum(); }

     typedef ArcNumTagIndicator<Graph> ArcNumTag;

     int arcNum() const { return _graph->arcNum(); }

     typedef EdgeNumTagIndicator<Graph> EdgeNumTag;

     int edgeNum() const { return _graph->edgeNum(); }

     typedef FindArcTagIndicator<Graph> FindArcTag;

     Arc findArc(const Node& u, const Node& v,

                 const Arc& prev = INVALID) const {

       return _graph->findArc(u, v, prev);

     }

     typedef FindEdgeTagIndicator<Graph> FindEdgeTag;

     Edge findEdge(const Node& u, const Node& v,

                   const Edge& prev = INVALID) const {

       return _graph->findEdge(u, v, prev);

     }

     Node addNode() { return _graph->addNode(); }

     Edge addEdge(const Node& u, const Node& v) { return _graph->addEdge(u, v); }

     void erase(const Node& i) { _graph->erase(i); }

     void erase(const Edge& i) { _graph->erase(i); }

     void clear() { _graph->clear(); }

     bool direction(const Arc& a) const { return _graph->direction(a); }

     Arc direct(const Edge& e, bool d) const { return _graph->direct(e, d); }

     int id(const Node& v) const { return _graph->id(v); }

     int id(const Arc& a) const { return _graph->id(a); }

     int id(const Edge& e) const { return _graph->id(e); }

     Node nodeFromId(int ix) const { return _graph->nodeFromId(ix); }

     Arc arcFromId(int ix) const { return _graph->arcFromId(ix); }

     Edge edgeFromId(int ix) const { return _graph->edgeFromId(ix); }

     int maxNodeId() const { return _graph->maxNodeId(); }

     int maxArcId() const { return _graph->maxArcId(); }

     int maxEdgeId() const { return _graph->maxEdgeId(); }

     typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const { return _graph->notifier(Node()); }

     typedef typename ItemSetTraits<Graph, Arc>::ItemNotifier ArcNotifier;

     ArcNotifier& notifier(Arc) const { return _graph->notifier(Arc()); }

     typedef typename ItemSetTraits<Graph, Edge>::ItemNotifier EdgeNotifier;

     EdgeNotifier& notifier(Edge) const { return _graph->notifier(Edge()); }

     template <typename _Value>

     class NodeMap : public Graph::template NodeMap<_Value> {

     public:

       typedef typename Graph::template NodeMap<_Value> Parent;

       explicit NodeMap(const GraphAdaptorBase<Graph>& adapter)

         : Parent(*adapter._graph) {}

       NodeMap(const GraphAdaptorBase<Graph>& adapter, const _Value& value)

         : Parent(*adapter._graph, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public Graph::template ArcMap<_Value> {

     public:

       typedef typename Graph::template ArcMap<_Value> Parent;

       explicit ArcMap(const GraphAdaptorBase<Graph>& adapter)

         : Parent(*adapter._graph) {}

       ArcMap(const GraphAdaptorBase<Graph>& adapter, const _Value& value)

         : Parent(*adapter._graph, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class EdgeMap : public Graph::template EdgeMap<_Value> {

     public:

       typedef typename Graph::template EdgeMap<_Value> Parent;

       explicit EdgeMap(const GraphAdaptorBase<Graph>& adapter)

         : Parent(*adapter._graph) {}

       EdgeMap(const GraphAdaptorBase<Graph>& adapter, const _Value& value)

         : Parent(*adapter._graph, value) {}

     private:

       EdgeMap& operator=(const EdgeMap& cmap) {

         return operator=<EdgeMap>(cmap);

       }

       template <typename CMap>

       EdgeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

   };

   template <typename _Digraph>

   class ReverseDigraphBase : public DigraphAdaptorBase<_Digraph> {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorBase<_Digraph> Parent;

   protected:

     ReverseDigraphBase() : Parent() { }

   public:

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     void firstIn(Arc& a, const Node& n) const { Parent::firstOut(a, n); }

     void firstOut(Arc& a, const Node& n ) const { Parent::firstIn(a, n); }

     void nextIn(Arc& a) const { Parent::nextOut(a); }

     void nextOut(Arc& a) const { Parent::nextIn(a); }

     Node source(const Arc& a) const { return Parent::target(a); }

     Node target(const Arc& a) const { return Parent::source(a); }

     Arc addArc(const Node& u, const Node& v) { return Parent::addArc(v, u); }

     typedef FindArcTagIndicator<Digraph> FindArcTag;

     Arc findArc(const Node& u, const Node& v,

                 const Arc& prev = INVALID) const {

       return Parent::findArc(v, u, prev);

     }

   };

   /// \ingroup graph_adaptors

   ///

   /// \brief A digraph adaptor which reverses the orientation of the arcs.

   ///

   /// ReverseDigraph reverses the arcs in the adapted digraph. The

   /// SubDigraph is conform to the \ref concepts::Digraph

   /// "Digraph concept".

   ///

   /// \tparam _Digraph It must be conform to the \ref concepts::Digraph

   /// "Digraph concept". The type can be specified to be const.

   template<typename _Digraph>

   class ReverseDigraph :

     public DigraphAdaptorExtender<ReverseDigraphBase<_Digraph> > {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorExtender<

       ReverseDigraphBase<_Digraph> > Parent;

   protected:

     ReverseDigraph() { }

   public:

     /// \brief Constructor

     ///

     /// Creates a reverse digraph adaptor for the given digraph

     explicit ReverseDigraph(Digraph& digraph) {

       Parent::setDigraph(digraph);

     }

   };

   /// \brief Just gives back a reverse digraph adaptor

   ///

   /// Just gives back a reverse digraph adaptor

   template<typename Digraph>

   ReverseDigraph<const Digraph> reverseDigraph(const Digraph& digraph) {

     return ReverseDigraph<const Digraph>(digraph);

   }

   template <typename _Digraph, typename _NodeFilterMap,

             typename _ArcFilterMap, bool _checked = true>

   class SubDigraphBase : public DigraphAdaptorBase<_Digraph> {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _ArcFilterMap ArcFilterMap;

     typedef SubDigraphBase Adaptor;

     typedef DigraphAdaptorBase<_Digraph> Parent;

   protected:

     NodeFilterMap* _node_filter;

     ArcFilterMap* _arc_filter;

     SubDigraphBase()

       : Parent(), _node_filter(0), _arc_filter(0) { }

     void setNodeFilterMap(NodeFilterMap& node_filter) {

       _node_filter = &node_filter;

     }

     void setArcFilterMap(ArcFilterMap& arc_filter) {

       _arc_filter = &arc_filter;

     }

   public:

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     void first(Node& i) const {

       Parent::first(i);

       while (i != INVALID && !(*_node_filter)[i]) Parent::next(i);

     }

     void first(Arc& i) const {

       Parent::first(i);

       while (i != INVALID && (!(*_arc_filter)[i]

                               || !(*_node_filter)[Parent::source(i)]

                               || !(*_node_filter)[Parent::target(i)]))

         Parent::next(i);

     }

     void firstIn(Arc& i, const Node& n) const {

       Parent::firstIn(i, n);

       while (i != INVALID && (!(*_arc_filter)[i]

                               || !(*_node_filter)[Parent::source(i)]))

         Parent::nextIn(i);

     }

     void firstOut(Arc& i, const Node& n) const {

       Parent::firstOut(i, n);

       while (i != INVALID && (!(*_arc_filter)[i]

                               || !(*_node_filter)[Parent::target(i)]))

         Parent::nextOut(i);

     }

     void next(Node& i) const {

       Parent::next(i);

       while (i != INVALID && !(*_node_filter)[i]) Parent::next(i);

     }

     void next(Arc& i) const {

       Parent::next(i);

       while (i != INVALID && (!(*_arc_filter)[i]

                               || !(*_node_filter)[Parent::source(i)]

                               || !(*_node_filter)[Parent::target(i)]))

         Parent::next(i);

     }

     void nextIn(Arc& i) const {

       Parent::nextIn(i);

       while (i != INVALID && (!(*_arc_filter)[i]

                               || !(*_node_filter)[Parent::source(i)]))

         Parent::nextIn(i);

     }

     void nextOut(Arc& i) const {

       Parent::nextOut(i);

       while (i != INVALID && (!(*_arc_filter)[i]

                               || !(*_node_filter)[Parent::target(i)]))

         Parent::nextOut(i);

     }

     void hide(const Node& n) const { _node_filter->set(n, false); }

     void hide(const Arc& a) const { _arc_filter->set(a, false); }

     void unHide(const Node& n) const { _node_filter->set(n, true); }

     void unHide(const Arc& a) const { _arc_filter->set(a, true); }

     bool hidden(const Node& n) const { return !(*_node_filter)[n]; }

     bool hidden(const Arc& a) const { return !(*_arc_filter)[a]; }

     typedef False NodeNumTag;

     typedef False ArcNumTag;

     typedef FindArcTagIndicator<Digraph> FindArcTag;

     Arc findArc(const Node& source, const Node& target,

                 const Arc& prev = INVALID) const {

       if (!(*_node_filter)[source] || !(*_node_filter)[target]) {

         return INVALID;

       }

       Arc arc = Parent::findArc(source, target, prev);

       while (arc != INVALID && !(*_arc_filter)[arc]) {

         arc = Parent::findArc(source, target, arc);

       }

       return arc;

     }

     template <typename _Value>

     class NodeMap : public SubMapExtender<Adaptor,

       typename Parent::template NodeMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template NodeMap<Value> > MapParent;

       NodeMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       NodeMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public SubMapExtender<Adaptor,

       typename Parent::template ArcMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template ArcMap<Value> > MapParent;

       ArcMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       ArcMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

   };

   template <typename _Digraph, typename _NodeFilterMap, typename _ArcFilterMap>

   class SubDigraphBase<_Digraph, _NodeFilterMap, _ArcFilterMap, false>

     : public DigraphAdaptorBase<_Digraph> {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _ArcFilterMap ArcFilterMap;

     typedef SubDigraphBase Adaptor;

     typedef DigraphAdaptorBase<Digraph> Parent;

   protected:

     NodeFilterMap* _node_filter;

     ArcFilterMap* _arc_filter;

     SubDigraphBase()

       : Parent(), _node_filter(0), _arc_filter(0) { }

     void setNodeFilterMap(NodeFilterMap& node_filter) {

       _node_filter = &node_filter;

     }

     void setArcFilterMap(ArcFilterMap& arc_filter) {

       _arc_filter = &arc_filter;

     }

   public:

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     void first(Node& i) const {

       Parent::first(i);

       while (i!=INVALID && !(*_node_filter)[i]) Parent::next(i);

     }

     void first(Arc& i) const {

       Parent::first(i);

       while (i!=INVALID && !(*_arc_filter)[i]) Parent::next(i);

     }

     void firstIn(Arc& i, const Node& n) const {

       Parent::firstIn(i, n);

       while (i!=INVALID && !(*_arc_filter)[i]) Parent::nextIn(i);

     }

     void firstOut(Arc& i, const Node& n) const {

       Parent::firstOut(i, n);

       while (i!=INVALID && !(*_arc_filter)[i]) Parent::nextOut(i);

     }

     void next(Node& i) const {

       Parent::next(i);

       while (i!=INVALID && !(*_node_filter)[i]) Parent::next(i);

     }

     void next(Arc& i) const {

       Parent::next(i);

       while (i!=INVALID && !(*_arc_filter)[i]) Parent::next(i);

     }

     void nextIn(Arc& i) const {

       Parent::nextIn(i);

       while (i!=INVALID && !(*_arc_filter)[i]) Parent::nextIn(i);

     }

     void nextOut(Arc& i) const {

       Parent::nextOut(i);

       while (i!=INVALID && !(*_arc_filter)[i]) Parent::nextOut(i);

     }

     void hide(const Node& n) const { _node_filter->set(n, false); }

     void hide(const Arc& e) const { _arc_filter->set(e, false); }

     void unHide(const Node& n) const { _node_filter->set(n, true); }

     void unHide(const Arc& e) const { _arc_filter->set(e, true); }

     bool hidden(const Node& n) const { return !(*_node_filter)[n]; }

     bool hidden(const Arc& e) const { return !(*_arc_filter)[e]; }

     typedef False NodeNumTag;

     typedef False ArcNumTag;

     typedef FindArcTagIndicator<Digraph> FindArcTag;

     Arc findArc(const Node& source, const Node& target,

                 const Arc& prev = INVALID) const {

       if (!(*_node_filter)[source] || !(*_node_filter)[target]) {

         return INVALID;

       }

       Arc arc = Parent::findArc(source, target, prev);

       while (arc != INVALID && !(*_arc_filter)[arc]) {

         arc = Parent::findArc(source, target, arc);

       }

       return arc;

     }

     template <typename _Value>

     class NodeMap : public SubMapExtender<Adaptor,

       typename Parent::template NodeMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template NodeMap<Value> > MapParent;

       NodeMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       NodeMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public SubMapExtender<Adaptor,

       typename Parent::template ArcMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template ArcMap<Value> > MapParent;

       ArcMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       ArcMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

   };

   /// \ingroup graph_adaptors

   ///

   /// \brief An adaptor for hiding nodes and arcs in a digraph

   ///

   /// SubDigraph hides nodes and arcs in a digraph. A bool node map

   /// and a bool arc map must be specified, which define the filters

   /// for nodes and arcs. Just the nodes and arcs with true value are

   /// shown in the subdigraph. The SubDigraph is conform to the \ref

   /// concepts::Digraph "Digraph concept". If the \c _checked parameter

   /// is true, then the arcs incident to filtered nodes are also

   /// filtered out.

   ///

   /// \tparam _Digraph It must be conform to the \ref

   /// concepts::Digraph "Digraph concept". The type can be specified

   /// to const.

   /// \tparam _NodeFilterMap A bool valued node map of the the adapted digraph.

   /// \tparam _ArcFilterMap A bool valued arc map of the the adapted digraph.

   /// \tparam _checked If the parameter is false then the arc filtering

   /// is not checked with respect to node filter. Otherwise, each arc

   /// is automatically filtered, which is incident to a filtered node.

   ///

   /// \see FilterNodes

   /// \see FilterArcs

   template<typename _Digraph,

            typename _NodeFilterMap = typename _Digraph::template NodeMap<bool>,

            typename _ArcFilterMap = typename _Digraph::template ArcMap<bool>,

            bool _checked = true>

   class SubDigraph

     : public DigraphAdaptorExtender<

       SubDigraphBase<_Digraph, _NodeFilterMap, _ArcFilterMap, _checked> > {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _ArcFilterMap ArcFilterMap;

     typedef DigraphAdaptorExtender<

       SubDigraphBase<Digraph, NodeFilterMap, ArcFilterMap, _checked> >

     Parent;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

   protected:

     SubDigraph() { }

   public:

     /// \brief Constructor

     ///

     /// Creates a subdigraph for the given digraph with

     /// given node and arc map filters.

     SubDigraph(Digraph& digraph, NodeFilterMap& node_filter,

                ArcFilterMap& arc_filter) {

       setDigraph(digraph);

       setNodeFilterMap(node_filter);

       setArcFilterMap(arc_filter);

     }

     /// \brief Hides the node of the graph

     ///

     /// This function hides \c n in the digraph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c n

     /// to be false in the corresponding node-map.

     void hide(const Node& n) const { Parent::hide(n); }

     /// \brief Hides the arc of the graph

     ///

     /// This function hides \c a in the digraph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c a

     /// to be false in the corresponding arc-map.

     void hide(const Arc& a) const { Parent::hide(a); }

     /// \brief Unhides the node of the graph

     ///

     /// The value of \c n is set to be true in the node-map which stores

     /// hide information. If \c n was hidden previuosly, then it is shown

     /// again

     void unHide(const Node& n) const { Parent::unHide(n); }

     /// \brief Unhides the arc of the graph

     ///

     /// The value of \c a is set to be true in the arc-map which stores

     /// hide information. If \c a was hidden previuosly, then it is shown

     /// again

     void unHide(const Arc& a) const { Parent::unHide(a); }

     /// \brief Returns true if \c n is hidden.

     ///

     /// Returns true if \c n is hidden.

     ///

     bool hidden(const Node& n) const { return Parent::hidden(n); }

     /// \brief Returns true if \c a is hidden.

     ///

     /// Returns true if \c a is hidden.

     ///

     bool hidden(const Arc& a) const { return Parent::hidden(a); }

   };

   /// \brief Just gives back a subdigraph

   ///

   /// Just gives back a subdigraph

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraph<const Digraph, NodeFilterMap, ArcFilterMap>

   subDigraph(const Digraph& digraph, NodeFilterMap& nfm, ArcFilterMap& afm) {

     return SubDigraph<const Digraph, NodeFilterMap, ArcFilterMap>

       (digraph, nfm, afm);

   }

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraph<const Digraph, const NodeFilterMap, ArcFilterMap>

   subDigraph(const Digraph& digraph,

              const NodeFilterMap& nfm, ArcFilterMap& afm) {

     return SubDigraph<const Digraph, const NodeFilterMap, ArcFilterMap>

       (digraph, nfm, afm);

   }

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraph<const Digraph, NodeFilterMap, const ArcFilterMap>

   subDigraph(const Digraph& digraph,

              NodeFilterMap& nfm, const ArcFilterMap& afm) {

     return SubDigraph<const Digraph, NodeFilterMap, const ArcFilterMap>

       (digraph, nfm, afm);

   }

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraph<const Digraph, const NodeFilterMap, const ArcFilterMap>

   subDigraph(const Digraph& digraph,

              const NodeFilterMap& nfm, const ArcFilterMap& afm) {

     return SubDigraph<const Digraph, const NodeFilterMap,

       const ArcFilterMap>(digraph, nfm, afm);

   }

   template <typename _Graph, typename _NodeFilterMap,

             typename _EdgeFilterMap, bool _checked = true>

   class SubGraphBase : public GraphAdaptorBase<_Graph> {

   public:

     typedef _Graph Graph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _EdgeFilterMap EdgeFilterMap;

     typedef SubGraphBase Adaptor;

     typedef GraphAdaptorBase<_Graph> Parent;

   protected:

     NodeFilterMap* _node_filter_map;

     EdgeFilterMap* _edge_filter_map;

     SubGraphBase()

       : Parent(), _node_filter_map(0), _edge_filter_map(0) { }

     void setNodeFilterMap(NodeFilterMap& node_filter_map) {

       _node_filter_map=&node_filter_map;

     }

     void setEdgeFilterMap(EdgeFilterMap& edge_filter_map) {

       _edge_filter_map=&edge_filter_map;

     }

   public:

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     typedef typename Parent::Edge Edge;

     void first(Node& i) const {

       Parent::first(i);

       while (i!=INVALID && !(*_node_filter_map)[i]) Parent::next(i);

     }

     void first(Arc& i) const {

       Parent::first(i);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::source(i)]

                             || !(*_node_filter_map)[Parent::target(i)]))

         Parent::next(i);

     }

     void first(Edge& i) const {

       Parent::first(i);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::u(i)]

                             || !(*_node_filter_map)[Parent::v(i)]))

         Parent::next(i);

     }

     void firstIn(Arc& i, const Node& n) const {

       Parent::firstIn(i, n);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::source(i)]))

         Parent::nextIn(i);

     }

     void firstOut(Arc& i, const Node& n) const {

       Parent::firstOut(i, n);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::target(i)]))

         Parent::nextOut(i);

     }

     void firstInc(Edge& i, bool& d, const Node& n) const {

       Parent::firstInc(i, d, n);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::u(i)]

                             || !(*_node_filter_map)[Parent::v(i)]))

         Parent::nextInc(i, d);

     }

     void next(Node& i) const {

       Parent::next(i);

       while (i!=INVALID && !(*_node_filter_map)[i]) Parent::next(i);

     }

     void next(Arc& i) const {

       Parent::next(i);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::source(i)]

                             || !(*_node_filter_map)[Parent::target(i)]))

         Parent::next(i);

     }

     void next(Edge& i) const {

       Parent::next(i);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::u(i)]

                             || !(*_node_filter_map)[Parent::v(i)]))

         Parent::next(i);

     }

     void nextIn(Arc& i) const {

       Parent::nextIn(i);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::source(i)]))

         Parent::nextIn(i);

     }

     void nextOut(Arc& i) const {

       Parent::nextOut(i);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::target(i)]))

         Parent::nextOut(i);

     }

     void nextInc(Edge& i, bool& d) const {

       Parent::nextInc(i, d);

       while (i!=INVALID && (!(*_edge_filter_map)[i]

                             || !(*_node_filter_map)[Parent::u(i)]

                             || !(*_node_filter_map)[Parent::v(i)]))

         Parent::nextInc(i, d);

     }

     void hide(const Node& n) const { _node_filter_map->set(n, false); }

     void hide(const Edge& e) const { _edge_filter_map->set(e, false); }

     void unHide(const Node& n) const { _node_filter_map->set(n, true); }

     void unHide(const Edge& e) const { _edge_filter_map->set(e, true); }

     bool hidden(const Node& n) const { return !(*_node_filter_map)[n]; }

     bool hidden(const Edge& e) const { return !(*_edge_filter_map)[e]; }

     typedef False NodeNumTag;

     typedef False ArcNumTag;

     typedef False EdgeNumTag;

     typedef FindArcTagIndicator<Graph> FindArcTag;

     Arc findArc(const Node& u, const Node& v,

                 const Arc& prev = INVALID) const {

       if (!(*_node_filter_map)[u] || !(*_node_filter_map)[v]) {

         return INVALID;

       }

       Arc arc = Parent::findArc(u, v, prev);

       while (arc != INVALID && !(*_edge_filter_map)[arc]) {

         arc = Parent::findArc(u, v, arc);

       }

       return arc;

     }

     typedef FindEdgeTagIndicator<Graph> FindEdgeTag;

     Edge findEdge(const Node& u, const Node& v,

                   const Edge& prev = INVALID) const {

       if (!(*_node_filter_map)[u] || !(*_node_filter_map)[v]) {

         return INVALID;

       }

       Edge edge = Parent::findEdge(u, v, prev);

       while (edge != INVALID && !(*_edge_filter_map)[edge]) {

         edge = Parent::findEdge(u, v, edge);

       }

       return edge;

     }

     template <typename _Value>

     class NodeMap : public SubMapExtender<Adaptor,

       typename Parent::template NodeMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template NodeMap<Value> > MapParent;

       NodeMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       NodeMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public SubMapExtender<Adaptor,

       typename Parent::template ArcMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template ArcMap<Value> > MapParent;

       ArcMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       ArcMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class EdgeMap : public SubMapExtender<Adaptor,

       typename Parent::template EdgeMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template EdgeMap<Value> > MapParent;

       EdgeMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       EdgeMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       EdgeMap& operator=(const EdgeMap& cmap) {

         return operator=<EdgeMap>(cmap);

       }

       template <typename CMap>

       EdgeMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

   };

   template <typename _Graph, typename _NodeFilterMap, typename _EdgeFilterMap>

   class SubGraphBase<_Graph, _NodeFilterMap, _EdgeFilterMap, false>

     : public GraphAdaptorBase<_Graph> {

   public:

     typedef _Graph Graph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _EdgeFilterMap EdgeFilterMap;

     typedef SubGraphBase Adaptor;

     typedef GraphAdaptorBase<_Graph> Parent;

   protected:

     NodeFilterMap* _node_filter_map;

     EdgeFilterMap* _edge_filter_map;

     SubGraphBase() : Parent(),

                      _node_filter_map(0), _edge_filter_map(0) { }

     void setNodeFilterMap(NodeFilterMap& node_filter_map) {

       _node_filter_map=&node_filter_map;

     }

     void setEdgeFilterMap(EdgeFilterMap& edge_filter_map) {

       _edge_filter_map=&edge_filter_map;

     }

   public:

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     typedef typename Parent::Edge Edge;

     void first(Node& i) const {

       Parent::first(i);

       while (i!=INVALID && !(*_node_filter_map)[i]) Parent::next(i);

     }

     void first(Arc& i) const {

       Parent::first(i);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::next(i);

     }

     void first(Edge& i) const {

       Parent::first(i);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::next(i);

     }

     void firstIn(Arc& i, const Node& n) const {

       Parent::firstIn(i, n);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::nextIn(i);

     }

     void firstOut(Arc& i, const Node& n) const {

       Parent::firstOut(i, n);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::nextOut(i);

     }

     void firstInc(Edge& i, bool& d, const Node& n) const {

       Parent::firstInc(i, d, n);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::nextInc(i, d);

     }

     void next(Node& i) const {

       Parent::next(i);

       while (i!=INVALID && !(*_node_filter_map)[i]) Parent::next(i);

     }

     void next(Arc& i) const {

       Parent::next(i);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::next(i);

     }

     void next(Edge& i) const {

       Parent::next(i);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::next(i);

     }

     void nextIn(Arc& i) const {

       Parent::nextIn(i);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::nextIn(i);

     }

     void nextOut(Arc& i) const {

       Parent::nextOut(i);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::nextOut(i);

     }

     void nextInc(Edge& i, bool& d) const {

       Parent::nextInc(i, d);

       while (i!=INVALID && !(*_edge_filter_map)[i]) Parent::nextInc(i, d);

     }

     void hide(const Node& n) const { _node_filter_map->set(n, false); }

     void hide(const Edge& e) const { _edge_filter_map->set(e, false); }

     void unHide(const Node& n) const { _node_filter_map->set(n, true); }

     void unHide(const Edge& e) const { _edge_filter_map->set(e, true); }

     bool hidden(const Node& n) const { return !(*_node_filter_map)[n]; }

     bool hidden(const Edge& e) const { return !(*_edge_filter_map)[e]; }

     typedef False NodeNumTag;

     typedef False ArcNumTag;

     typedef False EdgeNumTag;

     typedef FindArcTagIndicator<Graph> FindArcTag;

     Arc findArc(const Node& u, const Node& v,

                 const Arc& prev = INVALID) const {

       Arc arc = Parent::findArc(u, v, prev);

       while (arc != INVALID && !(*_edge_filter_map)[arc]) {

         arc = Parent::findArc(u, v, arc);

       }

       return arc;

     }

     typedef FindEdgeTagIndicator<Graph> FindEdgeTag;

     Edge findEdge(const Node& u, const Node& v,

                   const Edge& prev = INVALID) const {

       Edge edge = Parent::findEdge(u, v, prev);

       while (edge != INVALID && !(*_edge_filter_map)[edge]) {

         edge = Parent::findEdge(u, v, edge);

       }

       return edge;

     }

     template <typename _Value>

     class NodeMap : public SubMapExtender<Adaptor,

       typename Parent::template NodeMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template NodeMap<Value> > MapParent;

       NodeMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       NodeMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public SubMapExtender<Adaptor,

       typename Parent::template ArcMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template ArcMap<Value> > MapParent;

       ArcMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       ArcMap(const Adaptor& adaptor, const Value& value)

         : MapParent(adaptor, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class EdgeMap : public SubMapExtender<Adaptor,

       typename Parent::template EdgeMap<_Value> > {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, typename Parent::

                              template EdgeMap<Value> > MapParent;

       EdgeMap(const Adaptor& adaptor)

         : MapParent(adaptor) {}

       EdgeMap(const Adaptor& adaptor, const _Value& value)

         : MapParent(adaptor, value) {}

     private:

       EdgeMap& operator=(const EdgeMap& cmap) {

         return operator=<EdgeMap>(cmap);

       }

       template <typename CMap>

       EdgeMap& operator=(const CMap& cmap) {

         MapParent::operator=(cmap);

         return *this;

       }

     };

   };

   /// \ingroup graph_adaptors

   ///

   /// \brief A graph adaptor for hiding nodes and edges in an

   /// undirected graph.

   ///

   /// SubGraph hides nodes and edges in a graph. A bool node map and a

   /// bool edge map must be specified, which define the filters for

   /// nodes and edges. Just the nodes and edges with true value are

   /// shown in the subgraph. The SubGraph is conform to the \ref

   /// concepts::Graph "Graph concept". If the \c _checked parameter is

   /// true, then the edges incident to filtered nodes are also

   /// filtered out.

   ///

   /// \tparam _Graph It must be conform to the \ref

   /// concepts::Graph "Graph concept". The type can be specified

   /// to const.

   /// \tparam _NodeFilterMap A bool valued node map of the the adapted graph.

   /// \tparam _EdgeFilterMap A bool valued edge map of the the adapted graph.

   /// \tparam _checked If the parameter is false then the edge filtering

   /// is not checked with respect to node filter. Otherwise, each edge

   /// is automatically filtered, which is incident to a filtered node.

   ///

   /// \see FilterNodes

   /// \see FilterEdges

   template<typename _Graph, typename NodeFilterMap,

            typename EdgeFilterMap, bool _checked = true>

   class SubGraph

     : public GraphAdaptorExtender<

       SubGraphBase<_Graph, NodeFilterMap, EdgeFilterMap, _checked> > {

   public:

     typedef _Graph Graph;

     typedef GraphAdaptorExtender<

       SubGraphBase<_Graph, NodeFilterMap, EdgeFilterMap> > Parent;

     typedef typename Parent::Node Node;

     typedef typename Parent::Edge Edge;

   protected:

     SubGraph() { }

   public:

     /// \brief Constructor

     ///

     /// Creates a subgraph for the given graph with given node and

     /// edge map filters.

     SubGraph(Graph& _graph, NodeFilterMap& node_filter_map,

              EdgeFilterMap& edge_filter_map) {

       setGraph(_graph);

       setNodeFilterMap(node_filter_map);

       setEdgeFilterMap(edge_filter_map);

     }

     /// \brief Hides the node of the graph

     ///

     /// This function hides \c n in the graph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c n

     /// to be false in the corresponding node-map.

     void hide(const Node& n) const { Parent::hide(n); }

     /// \brief Hides the edge of the graph

     ///

     /// This function hides \c e in the graph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c e

     /// to be false in the corresponding edge-map.

     void hide(const Edge& e) const { Parent::hide(e); }

     /// \brief Unhides the node of the graph

     ///

     /// The value of \c n is set to be true in the node-map which stores

     /// hide information. If \c n was hidden previuosly, then it is shown

     /// again

     void unHide(const Node& n) const { Parent::unHide(n); }

     /// \brief Unhides the edge of the graph

     ///

     /// The value of \c e is set to be true in the edge-map which stores

     /// hide information. If \c e was hidden previuosly, then it is shown

     /// again

     void unHide(const Edge& e) const { Parent::unHide(e); }

     /// \brief Returns true if \c n is hidden.

     ///

     /// Returns true if \c n is hidden.

     ///

     bool hidden(const Node& n) const { return Parent::hidden(n); }

     /// \brief Returns true if \c e is hidden.

     ///

     /// Returns true if \c e is hidden.

     ///

     bool hidden(const Edge& e) const { return Parent::hidden(e); }

   };

   /// \brief Just gives back a subgraph

   ///

   /// Just gives back a subgraph

   template<typename Graph, typename NodeFilterMap, typename ArcFilterMap>

   SubGraph<const Graph, NodeFilterMap, ArcFilterMap>

   subGraph(const Graph& graph, NodeFilterMap& nfm, ArcFilterMap& efm) {

     return SubGraph<const Graph, NodeFilterMap, ArcFilterMap>(graph, nfm, efm);

   }

   template<typename Graph, typename NodeFilterMap, typename ArcFilterMap>

   SubGraph<const Graph, const NodeFilterMap, ArcFilterMap>

   subGraph(const Graph& graph,

            const NodeFilterMap& nfm, ArcFilterMap& efm) {

     return SubGraph<const Graph, const NodeFilterMap, ArcFilterMap>

       (graph, nfm, efm);

   }

   template<typename Graph, typename NodeFilterMap, typename ArcFilterMap>

   SubGraph<const Graph, NodeFilterMap, const ArcFilterMap>

   subGraph(const Graph& graph,

            NodeFilterMap& nfm, const ArcFilterMap& efm) {

     return SubGraph<const Graph, NodeFilterMap, const ArcFilterMap>

       (graph, nfm, efm);

   }

   template<typename Graph, typename NodeFilterMap, typename ArcFilterMap>

   SubGraph<const Graph, const NodeFilterMap, const ArcFilterMap>

   subGraph(const Graph& graph,

            const NodeFilterMap& nfm, const ArcFilterMap& efm) {

     return SubGraph<const Graph, const NodeFilterMap, const ArcFilterMap>

       (graph, nfm, efm);

   }

   /// \ingroup graph_adaptors

   ///

   /// \brief An adaptor for hiding nodes from a digraph or a graph.

   ///

   /// FilterNodes adaptor hides nodes in a graph or a digraph. A bool

   /// node map must be specified, which defines the filters for

   /// nodes. Just the unfiltered nodes and the arcs or edges incident

   /// to unfiltered nodes are shown in the subdigraph or subgraph. The

   /// FilterNodes is conform to the \ref concepts::Digraph

   /// "Digraph concept" or \ref concepts::Graph "Graph concept" depending

   /// on the \c _Digraph template parameter. If the \c _checked

   /// parameter is true, then the arc or edges incident to filtered nodes

   /// are also filtered out.

   ///

   /// \tparam _Digraph It must be conform to the \ref

   /// concepts::Digraph "Digraph concept" or \ref concepts::Graph

   /// "Graph concept". The type can be specified to be const.

   /// \tparam _NodeFilterMap A bool valued node map of the the adapted graph.

   /// \tparam _checked If the parameter is false then the arc or edge

   /// filtering is not checked with respect to node filter. In this

   /// case just isolated nodes can be filtered out from the

   /// graph.

 #ifdef DOXYGEN

   template<typename _Digraph,

            typename _NodeFilterMap = typename _Digraph::template NodeMap<bool>,

            bool _checked = true>

 #else

   template<typename _Digraph,

            typename _NodeFilterMap = typename _Digraph::template NodeMap<bool>,

            bool _checked = true,

            typename Enable = void>

 #endif

   class FilterNodes

     : public SubDigraph<_Digraph, _NodeFilterMap,

                         ConstMap<typename _Digraph::Arc, bool>, _checked> {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef SubDigraph<Digraph, NodeFilterMap,

                        ConstMap<typename Digraph::Arc, bool>, _checked>

     Parent;

     typedef typename Parent::Node Node;

   protected:

     ConstMap<typename Digraph::Arc, bool> const_true_map;

     FilterNodes() : const_true_map(true) {

       Parent::setArcFilterMap(const_true_map);

     }

   public:

     /// \brief Constructor

     ///

     /// Creates an adaptor for the given digraph or graph with

     /// given node filter map.

     FilterNodes(Digraph& _digraph, NodeFilterMap& node_filter) :

       Parent(), const_true_map(true) {

       Parent::setDigraph(_digraph);

       Parent::setNodeFilterMap(node_filter);

       Parent::setArcFilterMap(const_true_map);

     }

     /// \brief Hides the node of the graph

     ///

     /// This function hides \c n in the digraph or graph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c n

     /// to be false in the corresponding node map.

     void hide(const Node& n) const { Parent::hide(n); }

     /// \brief Unhides the node of the graph

     ///

     /// The value of \c n is set to be true in the node-map which stores

     /// hide information. If \c n was hidden previuosly, then it is shown

     /// again

     void unHide(const Node& n) const { Parent::unHide(n); }

     /// \brief Returns true if \c n is hidden.

     ///

     /// Returns true if \c n is hidden.

     ///

     bool hidden(const Node& n) const { return Parent::hidden(n); }

   };

   template<typename _Graph, typename _NodeFilterMap, bool _checked>

   class FilterNodes<_Graph, _NodeFilterMap, _checked,

                     typename enable_if<UndirectedTagIndicator<_Graph> >::type>

     : public SubGraph<_Graph, _NodeFilterMap,

                       ConstMap<typename _Graph::Edge, bool>, _checked> {

   public:

     typedef _Graph Graph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef SubGraph<Graph, NodeFilterMap,

                      ConstMap<typename Graph::Edge, bool> > Parent;

     typedef typename Parent::Node Node;

   protected:

     ConstMap<typename Graph::Edge, bool> const_true_map;

     FilterNodes() : const_true_map(true) {

       Parent::setEdgeFilterMap(const_true_map);

     }

   public:

     FilterNodes(Graph& _graph, NodeFilterMap& node_filter_map) :

       Parent(), const_true_map(true) {

       Parent::setGraph(_graph);

       Parent::setNodeFilterMap(node_filter_map);

       Parent::setEdgeFilterMap(const_true_map);

     }

     void hide(const Node& n) const { Parent::hide(n); }

     void unHide(const Node& n) const { Parent::unHide(n); }

     bool hidden(const Node& n) const { return Parent::hidden(n); }

   };

   /// \brief Just gives back a FilterNodes adaptor

   ///

   /// Just gives back a FilterNodes adaptor

   template<typename Digraph, typename NodeFilterMap>

   FilterNodes<const Digraph, NodeFilterMap>

   filterNodes(const Digraph& digraph, NodeFilterMap& nfm) {

     return FilterNodes<const Digraph, NodeFilterMap>(digraph, nfm);

   }

   template<typename Digraph, typename NodeFilterMap>

   FilterNodes<const Digraph, const NodeFilterMap>

   filterNodes(const Digraph& digraph, const NodeFilterMap& nfm) {

     return FilterNodes<const Digraph, const NodeFilterMap>(digraph, nfm);

   }

   /// \ingroup graph_adaptors

   ///

   /// \brief An adaptor for hiding arcs from a digraph.

   ///

   /// FilterArcs adaptor hides arcs in a digraph. A bool arc map must

   /// be specified, which defines the filters for arcs. Just the

   /// unfiltered arcs are shown in the subdigraph. The FilterArcs is

   /// conform to the \ref concepts::Digraph "Digraph concept".

   ///

   /// \tparam _Digraph It must be conform to the \ref concepts::Digraph

   /// "Digraph concept". The type can be specified to be const.

   /// \tparam _ArcFilterMap A bool valued arc map of the the adapted

   /// graph.

   template<typename _Digraph, typename _ArcFilterMap>

   class FilterArcs :

     public SubDigraph<_Digraph, ConstMap<typename _Digraph::Node, bool>,

                       _ArcFilterMap, false> {

   public:

     typedef _Digraph Digraph;

     typedef _ArcFilterMap ArcFilterMap;

     typedef SubDigraph<Digraph, ConstMap<typename Digraph::Node, bool>,

                        ArcFilterMap, false> Parent;

     typedef typename Parent::Arc Arc;

   protected:

     ConstMap<typename Digraph::Node, bool> const_true_map;

     FilterArcs() : const_true_map(true) {

       Parent::setNodeFilterMap(const_true_map);

     }

   public:

     /// \brief Constructor

     ///

     /// Creates a FilterArcs adaptor for the given graph with

     /// given arc map filter.

     FilterArcs(Digraph& digraph, ArcFilterMap& arc_filter)

       : Parent(), const_true_map(true) {

       Parent::setDigraph(digraph);

       Parent::setNodeFilterMap(const_true_map);

       Parent::setArcFilterMap(arc_filter);

     }

     /// \brief Hides the arc of the graph

     ///

     /// This function hides \c a in the graph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c a

     /// to be false in the corresponding arc map.

     void hide(const Arc& a) const { Parent::hide(a); }

     /// \brief Unhides the arc of the graph

     ///

     /// The value of \c a is set to be true in the arc-map which stores

     /// hide information. If \c a was hidden previuosly, then it is shown

     /// again

     void unHide(const Arc& a) const { Parent::unHide(a); }

     /// \brief Returns true if \c a is hidden.

     ///

     /// Returns true if \c a is hidden.

     ///

     bool hidden(const Arc& a) const { return Parent::hidden(a); }

   };

   /// \brief Just gives back an FilterArcs adaptor

   ///

   /// Just gives back an FilterArcs adaptor

   template<typename Digraph, typename ArcFilterMap>

   FilterArcs<const Digraph, ArcFilterMap>

   filterArcs(const Digraph& digraph, ArcFilterMap& afm) {

     return FilterArcs<const Digraph, ArcFilterMap>(digraph, afm);

   }

   template<typename Digraph, typename ArcFilterMap>

   FilterArcs<const Digraph, const ArcFilterMap>

   filterArcs(const Digraph& digraph, const ArcFilterMap& afm) {

     return FilterArcs<const Digraph, const ArcFilterMap>(digraph, afm);

   }

   /// \ingroup graph_adaptors

   ///

   /// \brief An adaptor for hiding edges from a graph.

   ///

   /// FilterEdges adaptor hides edges in a digraph. A bool edge map must

   /// be specified, which defines the filters for edges. Just the

   /// unfiltered edges are shown in the subdigraph. The FilterEdges is

   /// conform to the \ref concepts::Graph "Graph concept".

   ///

   /// \tparam _Graph It must be conform to the \ref concepts::Graph

   /// "Graph concept". The type can be specified to be const.

   /// \tparam _EdgeFilterMap A bool valued edge map of the the adapted

   /// graph.

   template<typename _Graph, typename _EdgeFilterMap>

   class FilterEdges :

     public SubGraph<_Graph, ConstMap<typename _Graph::Node,bool>,

                     _EdgeFilterMap, false> {

   public:

     typedef _Graph Graph;

     typedef _EdgeFilterMap EdgeFilterMap;

     typedef SubGraph<Graph, ConstMap<typename Graph::Node,bool>,

                      EdgeFilterMap, false> Parent;

     typedef typename Parent::Edge Edge;

   protected:

     ConstMap<typename Graph::Node, bool> const_true_map;

     FilterEdges() : const_true_map(true) {

       Parent::setNodeFilterMap(const_true_map);

     }

   public:

     /// \brief Constructor

     ///

     /// Creates a FilterEdges adaptor for the given graph with

     /// given edge map filters.

     FilterEdges(Graph& _graph, EdgeFilterMap& edge_filter_map) :

       Parent(), const_true_map(true) {

       Parent::setGraph(_graph);

       Parent::setNodeFilterMap(const_true_map);

       Parent::setEdgeFilterMap(edge_filter_map);

     }

     /// \brief Hides the edge of the graph

     ///

     /// This function hides \c e in the graph, i.e. the iteration

     /// jumps over it. This is done by simply setting the value of \c e

     /// to be false in the corresponding edge-map.

     void hide(const Edge& e) const { Parent::hide(e); }

     /// \brief Unhides the edge of the graph

     ///

     /// The value of \c e is set to be true in the edge-map which stores

     /// hide information. If \c e was hidden previuosly, then it is shown

     /// again

     void unHide(const Edge& e) const { Parent::unHide(e); }

     /// \brief Returns true if \c e is hidden.

     ///

     /// Returns true if \c e is hidden.

     ///

     bool hidden(const Edge& e) const { return Parent::hidden(e); }

   };

   /// \brief Just gives back a FilterEdges adaptor

   ///

   /// Just gives back a FilterEdges adaptor

   template<typename Graph, typename EdgeFilterMap>

   FilterEdges<const Graph, EdgeFilterMap>

   filterEdges(const Graph& graph, EdgeFilterMap& efm) {

     return FilterEdges<const Graph, EdgeFilterMap>(graph, efm);

   }

   template<typename Graph, typename EdgeFilterMap>

   FilterEdges<const Graph, const EdgeFilterMap>

   filterEdges(const Graph& graph, const EdgeFilterMap& efm) {

     return FilterEdges<const Graph, const EdgeFilterMap>(graph, efm);

   }

   template <typename _Digraph>

   class UndirectorBase {

   public:

     typedef _Digraph Digraph;

     typedef UndirectorBase Adaptor;

     typedef True UndirectedTag;

     typedef typename Digraph::Arc Edge;

     typedef typename Digraph::Node Node;

     class Arc : public Edge {

       friend class UndirectorBase;

     protected:

       bool _forward;

       Arc(const Edge& edge, bool forward) :

         Edge(edge), _forward(forward) {}

     public:

       Arc() {}

       Arc(Invalid) : Edge(INVALID), _forward(true) {}

       bool operator==(const Arc &other) const {

         return _forward == other._forward &&

           static_cast<const Edge&>(*this) == static_cast<const Edge&>(other);

       }

       bool operator!=(const Arc &other) const {

         return _forward != other._forward ||

           static_cast<const Edge&>(*this) != static_cast<const Edge&>(other);

       }

       bool operator<(const Arc &other) const {

         return _forward < other._forward ||

           (_forward == other._forward &&

            static_cast<const Edge&>(*this) < static_cast<const Edge&>(other));

       }

     };

     void first(Node& n) const {

       _digraph->first(n);

     }

     void next(Node& n) const {

       _digraph->next(n);

     }

     void first(Arc& a) const {

       _digraph->first(a);

       a._forward = true;

     }

     void next(Arc& a) const {

       if (a._forward) {

         a._forward = false;

       } else {

         _digraph->next(a);

         a._forward = true;

       }

     }

     void first(Edge& e) const {

       _digraph->first(e);

     }

     void next(Edge& e) const {

       _digraph->next(e);

     }

     void firstOut(Arc& a, const Node& n) const {

       _digraph->firstIn(a, n);

       if( static_cast<const Edge&>(a) != INVALID ) {

         a._forward = false;

       } else {

         _digraph->firstOut(a, n);

         a._forward = true;

       }

     }

     void nextOut(Arc &a) const {

       if (!a._forward) {

         Node n = _digraph->target(a);

         _digraph->nextIn(a);

         if (static_cast<const Edge&>(a) == INVALID ) {

           _digraph->firstOut(a, n);

           a._forward = true;

         }

       }

       else {

         _digraph->nextOut(a);

       }

     }

     void firstIn(Arc &a, const Node &n) const {

       _digraph->firstOut(a, n);

       if (static_cast<const Edge&>(a) != INVALID ) {

         a._forward = false;

       } else {

         _digraph->firstIn(a, n);

         a._forward = true;

       }

     }

     void nextIn(Arc &a) const {

       if (!a._forward) {

         Node n = _digraph->source(a);

         _digraph->nextOut(a);

         if( static_cast<const Edge&>(a) == INVALID ) {

           _digraph->firstIn(a, n);

           a._forward = true;

         }

       }

       else {

         _digraph->nextIn(a);

       }

     }

     void firstInc(Edge &e, bool &d, const Node &n) const {

       d = true;

       _digraph->firstOut(e, n);

       if (e != INVALID) return;

       d = false;

       _digraph->firstIn(e, n);

     }

     void nextInc(Edge &e, bool &d) const {

       if (d) {

         Node s = _digraph->source(e);

         _digraph->nextOut(e);

         if (e != INVALID) return;

         d = false;

         _digraph->firstIn(e, s);

       } else {

         _digraph->nextIn(e);

       }

     }

     Node u(const Edge& e) const {

       return _digraph->source(e);

     }

     Node v(const Edge& e) const {

       return _digraph->target(e);

     }

     Node source(const Arc &a) const {

       return a._forward ? _digraph->source(a) : _digraph->target(a);

     }

     Node target(const Arc &a) const {

       return a._forward ? _digraph->target(a) : _digraph->source(a);

     }

     static Arc direct(const Edge &e, bool d) {

       return Arc(e, d);

     }

     Arc direct(const Edge &e, const Node& n) const {

       return Arc(e, _digraph->source(e) == n);

     }

     static bool direction(const Arc &a) { return a._forward; }

     Node nodeFromId(int ix) const { return _digraph->nodeFromId(ix); }

     Arc arcFromId(int ix) const {

       return direct(_digraph->arcFromId(ix >> 1), bool(ix & 1));

     }

     Edge edgeFromId(int ix) const { return _digraph->arcFromId(ix); }

     int id(const Node &n) const { return _digraph->id(n); }

     int id(const Arc &a) const {

       return  (_digraph->id(a) << 1) | (a._forward ? 1 : 0);

     }

     int id(const Edge &e) const { return _digraph->id(e); }

     int maxNodeId() const { return _digraph->maxNodeId(); }

     int maxArcId() const { return (_digraph->maxArcId() << 1) | 1; }

     int maxEdgeId() const { return _digraph->maxArcId(); }

     Node addNode() { return _digraph->addNode(); }

     Edge addEdge(const Node& u, const Node& v) {

       return _digraph->addArc(u, v);

     }

     void erase(const Node& i) { _digraph->erase(i); }

     void erase(const Edge& i) { _digraph->erase(i); }

     void clear() { _digraph->clear(); }

     typedef NodeNumTagIndicator<Digraph> NodeNumTag;

     int nodeNum() const { return _digraph->nodeNum(); }

     typedef ArcNumTagIndicator<Digraph> ArcNumTag;

     int arcNum() const { return 2 * _digraph->arcNum(); }

     typedef ArcNumTag EdgeNumTag;

     int edgeNum() const { return _digraph->arcNum(); }

     typedef FindArcTagIndicator<Digraph> FindArcTag;

     Arc findArc(Node s, Node t, Arc p = INVALID) const {

       if (p == INVALID) {

         Edge arc = _digraph->findArc(s, t);

         if (arc != INVALID) return direct(arc, true);

         arc = _digraph->findArc(t, s);

         if (arc != INVALID) return direct(arc, false);

       } else if (direction(p)) {

         Edge arc = _digraph->findArc(s, t, p);

         if (arc != INVALID) return direct(arc, true);

         arc = _digraph->findArc(t, s);

         if (arc != INVALID) return direct(arc, false);

       } else {

         Edge arc = _digraph->findArc(t, s, p);

         if (arc != INVALID) return direct(arc, false);

       }

       return INVALID;

     }

     typedef FindArcTag FindEdgeTag;

     Edge findEdge(Node s, Node t, Edge p = INVALID) const {

       if (s != t) {

         if (p == INVALID) {

           Edge arc = _digraph->findArc(s, t);

           if (arc != INVALID) return arc;

           arc = _digraph->findArc(t, s);

           if (arc != INVALID) return arc;

         } else if (_digraph->source(p) == s) {

           Edge arc = _digraph->findArc(s, t, p);

           if (arc != INVALID) return arc;

           arc = _digraph->findArc(t, s);

           if (arc != INVALID) return arc;

         } else {

           Edge arc = _digraph->findArc(t, s, p);

           if (arc != INVALID) return arc;

         }

       } else {

         return _digraph->findArc(s, t, p);

       }

       return INVALID;

     }

   private:

     template <typename _Value>

     class ArcMapBase {

     private:

       typedef typename Digraph::template ArcMap<_Value> MapImpl;

     public:

       typedef typename MapTraits<MapImpl>::ReferenceMapTag ReferenceMapTag;

       typedef _Value Value;

       typedef Arc Key;

       typedef typename MapTraits<MapImpl>::ConstReturnValue ConstReturnValue;

       typedef typename MapTraits<MapImpl>::ReturnValue ReturnValue;

       typedef typename MapTraits<MapImpl>::ConstReturnValue ConstReference;

       typedef typename MapTraits<MapImpl>::ReturnValue Reference;

       ArcMapBase(const Adaptor& adaptor) :

         _forward(*adaptor._digraph), _backward(*adaptor._digraph) {}

       ArcMapBase(const Adaptor& adaptor, const Value& v)

         : _forward(*adaptor._digraph, v), _backward(*adaptor._digraph, v) {}

       void set(const Arc& a, const Value& v) {

         if (direction(a)) {

           _forward.set(a, v);

         } else {

           _backward.set(a, v);

         }

       }

       ConstReturnValue operator[](const Arc& a) const {

         if (direction(a)) {

           return _forward[a];

         } else {

           return _backward[a];

         }

       }

       ReturnValue operator[](const Arc& a) {

         if (direction(a)) {

           return _forward[a];

         } else {

           return _backward[a];

         }

       }

     protected:

       MapImpl _forward, _backward;

     };

   public:

     template <typename _Value>

     class NodeMap : public Digraph::template NodeMap<_Value> {

     public:

       typedef _Value Value;

       typedef typename Digraph::template NodeMap<Value> Parent;

       explicit NodeMap(const Adaptor& adaptor)

         : Parent(*adaptor._digraph) {}

       NodeMap(const Adaptor& adaptor, const _Value& value)

         : Parent(*adaptor._digraph, value) { }

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap

       : public SubMapExtender<Adaptor, ArcMapBase<_Value> >

     {

     public:

       typedef _Value Value;

       typedef SubMapExtender<Adaptor, ArcMapBase<Value> > Parent;

       explicit ArcMap(const Adaptor& adaptor)

         : Parent(adaptor) {}

       ArcMap(const Adaptor& adaptor, const Value& value)

         : Parent(adaptor, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class EdgeMap : public Digraph::template ArcMap<_Value> {

     public:

       typedef _Value Value;

       typedef typename Digraph::template ArcMap<Value> Parent;

       explicit EdgeMap(const Adaptor& adaptor)

         : Parent(*adaptor._digraph) {}

       EdgeMap(const Adaptor& adaptor, const Value& value)

         : Parent(*adaptor._digraph, value) {}

     private:

       EdgeMap& operator=(const EdgeMap& cmap) {

         return operator=<EdgeMap>(cmap);

       }

       template <typename CMap>

       EdgeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     typedef typename ItemSetTraits<Digraph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const { return _digraph->notifier(Node()); }

     typedef typename ItemSetTraits<Digraph, Edge>::ItemNotifier EdgeNotifier;

     EdgeNotifier& notifier(Edge) const { return _digraph->notifier(Edge()); }

   protected:

     UndirectorBase() : _digraph(0) {}

     Digraph* _digraph;

     void setDigraph(Digraph& digraph) {

       _digraph = &digraph;

     }

   };

   /// \ingroup graph_adaptors

   ///

   /// \brief Undirect the graph

   ///

   /// This adaptor makes an undirected graph from a directed

   /// graph. All arcs of the underlying digraph will be showed in the

   /// adaptor as an edge. The Orienter adaptor is conform to the \ref

   /// concepts::Graph "Graph concept".

   ///

   /// \tparam _Digraph It must be conform to the \ref

   /// concepts::Digraph "Digraph concept". The type can be specified

   /// to const.

   template<typename _Digraph>

   class Undirector

     : public GraphAdaptorExtender<UndirectorBase<_Digraph> > {

   public:

     typedef _Digraph Digraph;

     typedef GraphAdaptorExtender<UndirectorBase<Digraph> > Parent;

   protected:

     Undirector() { }

   public:

     /// \brief Constructor

     ///

     /// Creates a undirected graph from the given digraph

     Undirector(_Digraph& digraph) {

       setDigraph(digraph);

     }

     /// \brief ArcMap combined from two original ArcMap

     ///

     /// This class adapts two original digraph ArcMap to

     /// get an arc map on the undirected graph.

     template <typename _ForwardMap, typename _BackwardMap>

     class CombinedArcMap {

     public:

       typedef _ForwardMap ForwardMap;

       typedef _BackwardMap BackwardMap;

       typedef typename MapTraits<ForwardMap>::ReferenceMapTag ReferenceMapTag;

       typedef typename ForwardMap::Value Value;

       typedef typename Parent::Arc Key;

       typedef typename MapTraits<ForwardMap>::ReturnValue ReturnValue;

       typedef typename MapTraits<ForwardMap>::ConstReturnValue ConstReturnValue;

       typedef typename MapTraits<ForwardMap>::ReturnValue Reference;

       typedef typename MapTraits<ForwardMap>::ConstReturnValue ConstReference;

       /// \brief Constructor

       ///

       /// Constructor

       CombinedArcMap(ForwardMap& forward, BackwardMap& backward)

         : _forward(&forward), _backward(&backward) {}

       /// \brief Sets the value associated with a key.

       ///

       /// Sets the value associated with a key.

       void set(const Key& e, const Value& a) {

         if (Parent::direction(e)) {

           _forward->set(e, a);

         } else {

           _backward->set(e, a);

         }

       }

       /// \brief Returns the value associated with a key.

       ///

       /// Returns the value associated with a key.

       ConstReturnValue operator[](const Key& e) const {

         if (Parent::direction(e)) {

           return (*_forward)[e];

         } else {

           return (*_backward)[e];

         }

       }

       /// \brief Returns the value associated with a key.

       ///

       /// Returns the value associated with a key.

       ReturnValue operator[](const Key& e) {

         if (Parent::direction(e)) {

           return (*_forward)[e];

         } else {

           return (*_backward)[e];

         }

       }

     protected:

       ForwardMap* _forward;

       BackwardMap* _backward;

     };

     /// \brief Just gives back a combined arc map

     ///

     /// Just gives back a combined arc map

     template <typename ForwardMap, typename BackwardMap>

     static CombinedArcMap<ForwardMap, BackwardMap>

     combinedArcMap(ForwardMap& forward, BackwardMap& backward) {

       return CombinedArcMap<ForwardMap, BackwardMap>(forward, backward);

     }

     template <typename ForwardMap, typename BackwardMap>

     static CombinedArcMap<const ForwardMap, BackwardMap>

     combinedArcMap(const ForwardMap& forward, BackwardMap& backward) {

       return CombinedArcMap<const ForwardMap,

         BackwardMap>(forward, backward);

     }

     template <typename ForwardMap, typename BackwardMap>

     static CombinedArcMap<ForwardMap, const BackwardMap>

     combinedArcMap(ForwardMap& forward, const BackwardMap& backward) {

       return CombinedArcMap<ForwardMap,

         const BackwardMap>(forward, backward);

     }

     template <typename ForwardMap, typename BackwardMap>

     static CombinedArcMap<const ForwardMap, const BackwardMap>

     combinedArcMap(const ForwardMap& forward, const BackwardMap& backward) {

       return CombinedArcMap<const ForwardMap,

         const BackwardMap>(forward, backward);

     }

   };

   /// \brief Just gives back an undirected view of the given digraph

   ///

   /// Just gives back an undirected view of the given digraph

   template<typename Digraph>

   Undirector<const Digraph>

   undirector(const Digraph& digraph) {

     return Undirector<const Digraph>(digraph);

   }

   template <typename _Graph, typename _DirectionMap>

   class OrienterBase {

   public:

     typedef _Graph Graph;

     typedef _DirectionMap DirectionMap;

     typedef typename Graph::Node Node;

     typedef typename Graph::Edge Arc;

     void reverseArc(const Arc& arc) {

       _direction->set(arc, !(*_direction)[arc]);

     }

     void first(Node& i) const { _graph->first(i); }

     void first(Arc& i) const { _graph->first(i); }

     void firstIn(Arc& i, const Node& n) const {

       bool d = true;

       _graph->firstInc(i, d, n);

       while (i != INVALID && d == (*_direction)[i]) _graph->nextInc(i, d);

     }

     void firstOut(Arc& i, const Node& n ) const {

       bool d = true;

       _graph->firstInc(i, d, n);

       while (i != INVALID && d != (*_direction)[i]) _graph->nextInc(i, d);

     }

     void next(Node& i) const { _graph->next(i); }

     void next(Arc& i) const { _graph->next(i); }

     void nextIn(Arc& i) const {

       bool d = !(*_direction)[i];

       _graph->nextInc(i, d);

       while (i != INVALID && d == (*_direction)[i]) _graph->nextInc(i, d);

     }

     void nextOut(Arc& i) const {

       bool d = (*_direction)[i];

       _graph->nextInc(i, d);

       while (i != INVALID && d != (*_direction)[i]) _graph->nextInc(i, d);

     }

     Node source(const Arc& e) const {

       return (*_direction)[e] ? _graph->u(e) : _graph->v(e);

     }

     Node target(const Arc& e) const {

       return (*_direction)[e] ? _graph->v(e) : _graph->u(e);

     }

     typedef NodeNumTagIndicator<Graph> NodeNumTag;

     int nodeNum() const { return _graph->nodeNum(); }

     typedef EdgeNumTagIndicator<Graph> ArcNumTag;

     int arcNum() const { return _graph->edgeNum(); }

     typedef FindEdgeTagIndicator<Graph> FindArcTag;

     Arc findArc(const Node& u, const Node& v,

                 const Arc& prev = INVALID) const {

       Arc arc = _graph->findEdge(u, v, prev);

       while (arc != INVALID && source(arc) != u) {

         arc = _graph->findEdge(u, v, arc);

       }

       return arc;

     }

     Node addNode() {

       return Node(_graph->addNode());

     }

     Arc addArc(const Node& u, const Node& v) {

       Arc arc = _graph->addEdge(u, v);

       _direction->set(arc, _graph->u(arc) == u);

       return arc;

     }

     void erase(const Node& i) { _graph->erase(i); }

     void erase(const Arc& i) { _graph->erase(i); }

     void clear() { _graph->clear(); }

     int id(const Node& v) const { return _graph->id(v); }

     int id(const Arc& e) const { return _graph->id(e); }

     Node nodeFromId(int idx) const { return _graph->nodeFromId(idx); }

     Arc arcFromId(int idx) const { return _graph->edgeFromId(idx); }

     int maxNodeId() const { return _graph->maxNodeId(); }

     int maxArcId() const { return _graph->maxEdgeId(); }

     typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const { return _graph->notifier(Node()); }

     typedef typename ItemSetTraits<Graph, Arc>::ItemNotifier ArcNotifier;

     ArcNotifier& notifier(Arc) const { return _graph->notifier(Arc()); }

     template <typename _Value>

     class NodeMap : public _Graph::template NodeMap<_Value> {

     public:

       typedef typename _Graph::template NodeMap<_Value> Parent;

       explicit NodeMap(const OrienterBase& adapter)

         : Parent(*adapter._graph) {}

       NodeMap(const OrienterBase& adapter, const _Value& value)

         : Parent(*adapter._graph, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap : public _Graph::template EdgeMap<_Value> {

     public:

       typedef typename Graph::template EdgeMap<_Value> Parent;

       explicit ArcMap(const OrienterBase& adapter)

         : Parent(*adapter._graph) { }

       ArcMap(const OrienterBase& adapter, const _Value& value)

         : Parent(*adapter._graph, value) { }

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

   protected:

     Graph* _graph;

     DirectionMap* _direction;

     void setDirectionMap(DirectionMap& direction) {

       _direction = &direction;

     }

     void setGraph(Graph& graph) {

       _graph = &graph;

     }

   };

   /// \ingroup graph_adaptors

   ///

   /// \brief Orients the edges of the graph to get a digraph

   ///

   /// This adaptor orients each edge in the undirected graph. The

   /// direction of the arcs stored in an edge node map.  The arcs can

   /// be easily reverted by the \c reverseArc() member function in the

   /// adaptor. The Orienter adaptor is conform to the \ref

   /// concepts::Digraph "Digraph concept".

   ///

   /// \tparam _Graph It must be conform to the \ref concepts::Graph

   /// "Graph concept". The type can be specified to be const.

   /// \tparam _DirectionMap A bool valued edge map of the the adapted

   /// graph.

   ///

   /// \sa orienter

   template<typename _Graph,

            typename DirectionMap = typename _Graph::template EdgeMap<bool> >

   class Orienter :

     public DigraphAdaptorExtender<OrienterBase<_Graph, DirectionMap> > {

   public:

     typedef _Graph Graph;

     typedef DigraphAdaptorExtender<

       OrienterBase<_Graph, DirectionMap> > Parent;

     typedef typename Parent::Arc Arc;

   protected:

     Orienter() { }

   public:

     /// \brief Constructor of the adaptor

     ///

     /// Constructor of the adaptor

     Orienter(Graph& graph, DirectionMap& direction) {

       setGraph(graph);

       setDirectionMap(direction);

     }

     /// \brief Reverse arc

     ///

     /// It reverse the given arc. It simply negate the direction in the map.

     void reverseArc(const Arc& a) {

       Parent::reverseArc(a);

     }

   };

   /// \brief Just gives back a Orienter

   ///

   /// Just gives back a Orienter

   template<typename Graph, typename DirectionMap>

   Orienter<const Graph, DirectionMap>

   orienter(const Graph& graph, DirectionMap& dm) {

     return Orienter<const Graph, DirectionMap>(graph, dm);

   }

   template<typename Graph, typename DirectionMap>

   Orienter<const Graph, const DirectionMap>

   orienter(const Graph& graph, const DirectionMap& dm) {

     return Orienter<const Graph, const DirectionMap>(graph, dm);

   }

   namespace _adaptor_bits {

     template<typename _Digraph,

              typename _CapacityMap = typename _Digraph::template ArcMap<int>,

              typename _FlowMap = _CapacityMap,

              typename _Tolerance = Tolerance<typename _CapacityMap::Value> >

     class ResForwardFilter {

     public:

       typedef _Digraph Digraph;

       typedef _CapacityMap CapacityMap;

       typedef _FlowMap FlowMap;

       typedef _Tolerance Tolerance;

       typedef typename Digraph::Arc Key;

       typedef bool Value;

     private:

       const CapacityMap* _capacity;

       const FlowMap* _flow;

       Tolerance _tolerance;

     public:

       ResForwardFilter(const CapacityMap& capacity, const FlowMap& flow,

                        const Tolerance& tolerance = Tolerance())

         : _capacity(&capacity), _flow(&flow), _tolerance(tolerance) { }

       bool operator[](const typename Digraph::Arc& a) const {

         return _tolerance.positive((*_capacity)[a] - (*_flow)[a]);

       }

     };

     template<typename _Digraph,

              typename _CapacityMap = typename _Digraph::template ArcMap<int>,

              typename _FlowMap = _CapacityMap,

              typename _Tolerance = Tolerance<typename _CapacityMap::Value> >

     class ResBackwardFilter {

     public:

       typedef _Digraph Digraph;

       typedef _CapacityMap CapacityMap;

       typedef _FlowMap FlowMap;

       typedef _Tolerance Tolerance;

       typedef typename Digraph::Arc Key;

       typedef bool Value;

     private:

       const CapacityMap* _capacity;

       const FlowMap* _flow;

       Tolerance _tolerance;

     public:

       ResBackwardFilter(const CapacityMap& capacity, const FlowMap& flow,

                         const Tolerance& tolerance = Tolerance())

         : _capacity(&capacity), _flow(&flow), _tolerance(tolerance) { }

       bool operator[](const typename Digraph::Arc& a) const {

         return _tolerance.positive((*_flow)[a]);

       }

     };

   }

   /// \ingroup graph_adaptors

   ///

   /// \brief An adaptor for composing the residual graph for directed

   /// flow and circulation problems.

   ///

   /// An adaptor for composing the residual graph for directed flow and

   /// circulation problems.  Let \f$ G=(V, A) \f$ be a directed graph

   /// and let \f$ F \f$ be a number type. Let moreover \f$ f,c:A\to F \f$,

   /// be functions on the arc-set.

   ///

   /// Then Residual implements the digraph structure with

   /// node-set \f$ V \f$ and arc-set \f$ A_{forward}\cup A_{backward} \f$,

   /// where \f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$ and

   /// \f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$, i.e. the so

   /// called residual graph.  When we take the union

   /// \f$ A_{forward}\cup A_{backward} \f$, multiplicities are counted,

   /// i.e.  if an arc is in both \f$ A_{forward} \f$ and

   /// \f$ A_{backward} \f$, then in the adaptor it appears in both

   /// orientation.

   ///

   /// \tparam _Digraph It must be conform to the \ref concepts::Digraph

   /// "Digraph concept". The type is implicitly const.

   /// \tparam _CapacityMap An arc map of some numeric type, it defines

   /// the capacities in the flow problem. The map is implicitly const.

   /// \tparam _FlowMap An arc map of some numeric type, it defines

   /// the capacities in the flow problem.

   /// \tparam _Tolerance Handler for inexact computation.

   template<typename _Digraph,

            typename _CapacityMap = typename _Digraph::template ArcMap<int>,

            typename _FlowMap = _CapacityMap,

            typename _Tolerance = Tolerance<typename _CapacityMap::Value> >

   class Residual :

     public FilterArcs<

     Undirector<const _Digraph>,

     typename Undirector<const _Digraph>::template CombinedArcMap<

       _adaptor_bits::ResForwardFilter<const _Digraph, _CapacityMap,

                                       _FlowMap, _Tolerance>,

       _adaptor_bits::ResBackwardFilter<const _Digraph, _CapacityMap,

                                        _FlowMap, _Tolerance> > >

   {

   public:

     typedef _Digraph Digraph;

     typedef _CapacityMap CapacityMap;

     typedef _FlowMap FlowMap;

     typedef _Tolerance Tolerance;

     typedef typename CapacityMap::Value Value;

     typedef Residual Adaptor;

   protected:

     typedef Undirector<const Digraph> Undirected;

     typedef _adaptor_bits::ResForwardFilter<const Digraph, CapacityMap,

                                             FlowMap, Tolerance> ForwardFilter;

     typedef _adaptor_bits::ResBackwardFilter<const Digraph, CapacityMap,

                                              FlowMap, Tolerance> BackwardFilter;

     typedef typename Undirected::

     template CombinedArcMap<ForwardFilter, BackwardFilter> ArcFilter;

     typedef FilterArcs<Undirected, ArcFilter> Parent;

     const CapacityMap* _capacity;

     FlowMap* _flow;

     Undirected _graph;

     ForwardFilter _forward_filter;

     BackwardFilter _backward_filter;

     ArcFilter _arc_filter;

   public:

     /// \brief Constructor of the residual digraph.

     ///

     /// Constructor of the residual graph. The parameters are the digraph,

     /// the flow map, the capacity map and a tolerance object.

     Residual(const Digraph& digraph, const CapacityMap& capacity,

              FlowMap& flow, const Tolerance& tolerance = Tolerance())

       : Parent(), _capacity(&capacity), _flow(&flow), _graph(digraph),

         _forward_filter(capacity, flow, tolerance),

         _backward_filter(capacity, flow, tolerance),

         _arc_filter(_forward_filter, _backward_filter)

     {

       Parent::setDigraph(_graph);

       Parent::setArcFilterMap(_arc_filter);

     }

     typedef typename Parent::Arc Arc;

     /// \brief Gives back the residual capacity of the arc.

     ///

     /// Gives back the residual capacity of the arc.

     Value residualCapacity(const Arc& a) const {

       if (Undirected::direction(a)) {

         return (*_capacity)[a] - (*_flow)[a];

       } else {

         return (*_flow)[a];

       }

     }

     /// \brief Augment on the given arc in the residual graph.

     ///

     /// Augment on the given arc in the residual graph. It increase

     /// or decrease the flow on the original arc depend on the direction

     /// of the residual arc.

     void augment(const Arc& a, const Value& v) const {

       if (Undirected::direction(a)) {

         _flow->set(a, (*_flow)[a] + v);

       } else {

         _flow->set(a, (*_flow)[a] - v);

       }

     }

     /// \brief Returns the direction of the arc.

     ///

     /// Returns true when the arc is same oriented as the original arc.

     static bool forward(const Arc& a) {

       return Undirected::direction(a);

     }

     /// \brief Returns the direction of the arc.

     ///

     /// Returns true when the arc is opposite oriented as the original arc.

     static bool backward(const Arc& a) {

       return !Undirected::direction(a);

     }

     /// \brief Gives back the forward oriented residual arc.

     ///

     /// Gives back the forward oriented residual arc.

     static Arc forward(const typename Digraph::Arc& a) {

       return Undirected::direct(a, true);

     }

     /// \brief Gives back the backward oriented residual arc.

     ///

     /// Gives back the backward oriented residual arc.

     static Arc backward(const typename Digraph::Arc& a) {

       return Undirected::direct(a, false);

     }

     /// \brief Residual capacity map.

     ///

     /// In generic residual graph the residual capacity can be obtained

     /// as a map.

     class ResidualCapacity {

     protected:

       const Adaptor* _adaptor;

     public:

       /// The Key type

       typedef Arc Key;

       /// The Value type

       typedef typename _CapacityMap::Value Value;

       /// Constructor

       ResidualCapacity(const Adaptor& adaptor) : _adaptor(&adaptor) {}