/* -*- C++ -*-

  *

  * 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_DIGRAPH_ADAPTOR_H

 #define LEMON_DIGRAPH_ADAPTOR_H

 ///\ingroup graph_adaptors

 ///\file

 ///\brief Several digraph adaptors.

 ///

 ///This file contains several useful digraph adaptor classes.

 #include <lemon/core.h>

 #include <lemon/maps.h>

 #include <lemon/bits/variant.h>

 #include <lemon/bits/base_extender.h>

 #include <lemon/bits/graph_adaptor_extender.h>

 #include <lemon/bits/graph_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 EdgeNumTagIndicator<Digraph> EdgeNumTag;

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

     typedef FindEdgeTagIndicator<Digraph> FindEdgeTag;

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

       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) const { _digraph->erase(n); }

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

     void clear() const { _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 _Digraph>

   class RevDigraphAdaptorBase : public DigraphAdaptorBase<_Digraph> {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorBase<_Digraph> Parent;

   protected:

     RevDigraphAdaptorBase() : 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); }

     typedef FindEdgeTagIndicator<Digraph> FindEdgeTag;

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

 		const Arc& prev = INVALID) {

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

     }

   };

   ///\ingroup graph_adaptors

   ///

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

   ///

   /// If \c g is defined as

   ///\code

   /// ListDigraph dg;

   ///\endcode

   /// then

   ///\code

   /// RevDigraphAdaptor<ListDigraph> dga(dg);

   ///\endcode

   /// implements the digraph obtained from \c dg by 

   /// reversing the orientation of its arcs.

   ///

   /// A good example of using RevDigraphAdaptor is to decide whether

   /// the directed graph is strongly connected or not. The digraph is

   /// strongly connected iff each node is reachable from one node and

   /// this node is reachable from the others. Instead of this

   /// condition we use a slightly different, from one node each node

   /// is reachable both in the digraph and the reversed digraph. Now

   /// this condition can be checked with the Dfs algorithm and the

   /// RevDigraphAdaptor class.

   ///

   /// The implementation:

   ///\code

   /// bool stronglyConnected(const Digraph& digraph) {

   ///   if (NodeIt(digraph) == INVALID) return true;

   ///   Dfs<Digraph> dfs(digraph);

   ///   dfs.run(NodeIt(digraph));

   ///   for (NodeIt it(digraph); it != INVALID; ++it) {

   ///     if (!dfs.reached(it)) {

   ///       return false;

   ///     }

   ///   }

   ///   typedef RevDigraphAdaptor<const Digraph> RDigraph;

   ///   RDigraph rdigraph(digraph);

   ///   DfsVisit<RDigraph> rdfs(rdigraph);

   ///   rdfs.run(NodeIt(digraph));

   ///   for (NodeIt it(digraph); it != INVALID; ++it) {

   ///     if (!rdfs.reached(it)) {

   ///       return false;

   ///     }

   ///   }

   ///   return true;

   /// }

   ///\endcode

   template<typename _Digraph>

   class RevDigraphAdaptor : 

     public DigraphAdaptorExtender<RevDigraphAdaptorBase<_Digraph> > {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorExtender<

       RevDigraphAdaptorBase<_Digraph> > Parent;

   protected:

     RevDigraphAdaptor() { }

   public:

     /// \brief Constructor

     ///

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

     explicit RevDigraphAdaptor(Digraph& digraph) { 

       Parent::setDigraph(digraph); 

     }

   };

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

   ///

   /// Just gives back a reverse digraph adaptor

   template<typename Digraph>

   RevDigraphAdaptor<const Digraph>

   revDigraphAdaptor(const Digraph& digraph) {

     return RevDigraphAdaptor<const Digraph>(digraph);

   }

   template <typename _Digraph, typename _NodeFilterMap, 

 	    typename _ArcFilterMap, bool checked = true>

   class SubDigraphAdaptorBase : public DigraphAdaptorBase<_Digraph> {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _ArcFilterMap ArcFilterMap;

     typedef SubDigraphAdaptorBase Adaptor;

     typedef DigraphAdaptorBase<_Digraph> Parent;

   protected:

     NodeFilterMap* _node_filter;

     ArcFilterMap* _arc_filter;

     SubDigraphAdaptorBase() 

       : 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 EdgeNumTag;

     typedef FindEdgeTagIndicator<Digraph> FindEdgeTag;

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

 		const Arc& prev = INVALID) {

       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 SubDigraphAdaptorBase<_Digraph, _NodeFilterMap, _ArcFilterMap, false> 

     : public DigraphAdaptorBase<_Digraph> {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _ArcFilterMap ArcFilterMap;

     typedef SubDigraphAdaptorBase Adaptor;

     typedef DigraphAdaptorBase<Digraph> Parent;

   protected:

     NodeFilterMap* _node_filter;

     ArcFilterMap* _arc_filter;

     SubDigraphAdaptorBase() 

       : 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 EdgeNumTag;

     typedef FindEdgeTagIndicator<Digraph> FindEdgeTag;

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

 		  const Arc& prev = INVALID) {

       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 A digraph adaptor for hiding nodes and arcs from a digraph.

   /// 

   /// SubDigraphAdaptor shows the digraph with filtered node-set and 

   /// arc-set. If the \c checked parameter is true then it filters the arc-set

   /// respect to the source and target.

   /// 

   /// If the \c checked template parameter is false then the

   /// node-iterator cares only the filter on the node-set, and the

   /// arc-iterator cares only the filter on the arc-set.  Therefore

   /// the arc-map have to filter all arcs which's source or target is

   /// filtered by the node-filter.

   ///\code

   /// typedef ListDigraph Digraph;

   /// DIGRAPH_TYPEDEFS(Digraph);

   /// Digraph g;

   /// Node u=g.addNode(); //node of id 0

   /// Node v=g.addNode(); //node of id 1

   /// Arc a=g.addArc(u, v); //arc of id 0

   /// Arc f=g.addArc(v, u); //arc of id 1

   /// BoolNodeMap nm(g, true);

   /// nm.set(u, false);

   /// BoolArcMap am(g, true);

   /// am.set(a, false);

   /// typedef SubDigraphAdaptor<Digraph, BoolNodeMap, BoolArcMap> SubDGA;

   /// SubDGA ga(g, nm, am);

   /// for (SubDGA::NodeIt n(ga); n!=INVALID; ++n)

   ///   std::cout << g.id(n) << std::endl;

   /// for (SubDGA::ArcIt a(ga); a!=INVALID; ++a) 

   ///   std::cout << g.id(a) << std::endl;

   ///\endcode

   /// The output of the above code is the following.

   ///\code

   /// 1

   /// 1

   ///\endcode

   /// Note that \c n is of type \c SubDGA::NodeIt, but it can be converted to

   /// \c Digraph::Node that is why \c g.id(n) can be applied.

   /// 

   /// For other examples see also the documentation of

   /// NodeSubDigraphAdaptor and ArcSubDigraphAdaptor.

   template<typename _Digraph, 

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

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

 	   bool checked = true>

   class SubDigraphAdaptor : 

     public DigraphAdaptorExtender<

     SubDigraphAdaptorBase<_Digraph, _NodeFilterMap, _ArcFilterMap, checked> > {

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef _ArcFilterMap ArcFilterMap;

     typedef DigraphAdaptorExtender<

       SubDigraphAdaptorBase<Digraph, NodeFilterMap, ArcFilterMap, checked> >

     Parent;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

   protected:

     SubDigraphAdaptor() { }

   public:

     /// \brief Constructor

     ///

     /// Creates a sub-digraph-adaptor for the given digraph with

     /// given node and arc map filters.

     SubDigraphAdaptor(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 sub-digraph-adaptor

   ///

   /// Just gives back a sub-digraph-adaptor

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraphAdaptor<const Digraph, NodeFilterMap, ArcFilterMap>

   subDigraphAdaptor(const Digraph& digraph, 

 		    NodeFilterMap& nfm, ArcFilterMap& afm) {

     return SubDigraphAdaptor<const Digraph, NodeFilterMap, ArcFilterMap>

       (digraph, nfm, afm);

   }

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraphAdaptor<const Digraph, const NodeFilterMap, ArcFilterMap>

   subDigraphAdaptor(const Digraph& digraph, 

                    NodeFilterMap& nfm, ArcFilterMap& afm) {

     return SubDigraphAdaptor<const Digraph, const NodeFilterMap, ArcFilterMap>

       (digraph, nfm, afm);

   }

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraphAdaptor<const Digraph, NodeFilterMap, const ArcFilterMap>

   subDigraphAdaptor(const Digraph& digraph, 

                    NodeFilterMap& nfm, ArcFilterMap& afm) {

     return SubDigraphAdaptor<const Digraph, NodeFilterMap, const ArcFilterMap>

       (digraph, nfm, afm);

   }

   template<typename Digraph, typename NodeFilterMap, typename ArcFilterMap>

   SubDigraphAdaptor<const Digraph, const NodeFilterMap, const ArcFilterMap>

   subDigraphAdaptor(const Digraph& digraph, 

                    NodeFilterMap& nfm, ArcFilterMap& afm) {

     return SubDigraphAdaptor<const Digraph, const NodeFilterMap, 

       const ArcFilterMap>(digraph, nfm, afm);

   }

   ///\ingroup graph_adaptors

   ///

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

   ///

   ///An adaptor for hiding nodes from a digraph.  This adaptor

   ///specializes SubDigraphAdaptor in the way that only the node-set

   ///can be filtered. In usual case the checked parameter is true, we

   ///get the induced subgraph. But if the checked parameter is false

   ///then we can filter only isolated nodes.

   template<typename _Digraph, 

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

 	   bool checked = true>

   class NodeSubDigraphAdaptor : 

     public SubDigraphAdaptor<_Digraph, _NodeFilterMap, 

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

   public:

     typedef _Digraph Digraph;

     typedef _NodeFilterMap NodeFilterMap;

     typedef SubDigraphAdaptor<Digraph, NodeFilterMap, 

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

     Parent;

     typedef typename Parent::Node Node;

   protected:

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

     NodeSubDigraphAdaptor() : const_true_map(true) {

       Parent::setArcFilterMap(const_true_map);

     }

   public:

     /// \brief Constructor

     ///

     /// Creates a node-sub-digraph-adaptor for the given digraph with

     /// given node map filter.

     NodeSubDigraphAdaptor(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, 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); }

   };

   /// \brief Just gives back a  node-sub-digraph adaptor

   ///

   /// Just gives back a node-sub-digraph adaptor

   template<typename Digraph, typename NodeFilterMap>

   NodeSubDigraphAdaptor<const Digraph, NodeFilterMap>

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

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

   }

   template<typename Digraph, typename NodeFilterMap>

   NodeSubDigraphAdaptor<const Digraph, const NodeFilterMap>

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

     return NodeSubDigraphAdaptor<const Digraph, const NodeFilterMap>

       (digraph, nfm);

   }

   ///\ingroup graph_adaptors

   ///

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

   ///

   ///An adaptor for hiding arcs from a digraph. This adaptor

   ///specializes SubDigraphAdaptor in the way that only the arc-set

   ///can be filtered. The usefulness of this adaptor is demonstrated

   ///in the problem of searching a maximum number of arc-disjoint

   ///shortest paths between two nodes \c s and \c t. Shortest here

   ///means being shortest with respect to non-negative

   ///arc-lengths. Note that the comprehension of the presented

   ///solution need's some elementary knowledge from combinatorial

   ///optimization.

   ///

   ///If a single shortest path is to be searched between \c s and \c

   ///t, then this can be done easily by applying the Dijkstra

   ///algorithm. What happens, if a maximum number of arc-disjoint

   ///shortest paths is to be computed. It can be proved that an arc

   ///can be in a shortest path if and only if it is tight with respect

   ///to the potential function computed by Dijkstra.  Moreover, any

   ///path containing only such arcs is a shortest one.  Thus we have

   ///to compute a maximum number of arc-disjoint paths between \c s

   ///and \c t in the digraph which has arc-set all the tight arcs. The

   ///computation will be demonstrated on the following digraph, which

   ///is read from the dimacs file \c sub_digraph_adaptor_demo.dim.

   ///The full source code is available in \ref

   ///sub_digraph_adaptor_demo.cc.  If you are interested in more demo

   ///programs, you can use \ref dim_to_dot.cc to generate .dot files

   ///from dimacs files.  The .dot file of the following figure was

   ///generated by the demo program \ref dim_to_dot.cc.

   ///

   ///\dot

   ///digraph lemon_dot_example {

   ///node [ shape=ellipse, fontname=Helvetica, fontsize=10 ];

   ///n0 [ label="0 (s)" ];

   ///n1 [ label="1" ];

   ///n2 [ label="2" ];

   ///n3 [ label="3" ];

   ///n4 [ label="4" ];

   ///n5 [ label="5" ];

   ///n6 [ label="6 (t)" ];

   ///arc [ shape=ellipse, fontname=Helvetica, fontsize=10 ];

   ///n5 ->  n6 [ label="9, length:4" ];

   ///n4 ->  n6 [ label="8, length:2" ];

   ///n3 ->  n5 [ label="7, length:1" ];

   ///n2 ->  n5 [ label="6, length:3" ];

   ///n2 ->  n6 [ label="5, length:5" ];

   ///n2 ->  n4 [ label="4, length:2" ];

   ///n1 ->  n4 [ label="3, length:3" ];

   ///n0 ->  n3 [ label="2, length:1" ];

   ///n0 ->  n2 [ label="1, length:2" ];

   ///n0 ->  n1 [ label="0, length:3" ];

   ///}

   ///\enddot

   ///

   ///\code

   ///Digraph g;

   ///Node s, t;

   ///LengthMap length(g);

   ///

   ///readDimacs(std::cin, g, length, s, t);

   ///

   ///cout << "arcs with lengths (of form id, source--length->target): " << endl;

   ///for(ArcIt e(g); e!=INVALID; ++e) 

   ///  cout << g.id(e) << ", " << g.id(g.source(e)) << "--" 

   ///       << length[e] << "->" << g.id(g.target(e)) << endl;

   ///

   ///cout << "s: " << g.id(s) << " t: " << g.id(t) << endl;

   ///\endcode

   ///Next, the potential function is computed with Dijkstra.

   ///\code

   ///typedef Dijkstra<Digraph, LengthMap> Dijkstra;

   ///Dijkstra dijkstra(g, length);

   ///dijkstra.run(s);

   ///\endcode

   ///Next, we consrtruct a map which filters the arc-set to the tight arcs.

   ///\code

   ///typedef TightArcFilterMap<Digraph, const Dijkstra::DistMap, LengthMap> 

   ///  TightArcFilter;

   ///TightArcFilter tight_arc_filter(g, dijkstra.distMap(), length);

   ///

   ///typedef ArcSubDigraphAdaptor<Digraph, TightArcFilter> SubGA;

   ///SubGA ga(g, tight_arc_filter);

   ///\endcode

   ///Then, the maximum nimber of arc-disjoint \c s-\c t paths are computed 

   ///with a max flow algorithm Preflow.

   ///\code

   ///ConstMap<Arc, int> const_1_map(1);

   ///Digraph::ArcMap<int> flow(g, 0);

   ///

   ///Preflow<SubGA, ConstMap<Arc, int>, Digraph::ArcMap<int> > 

   ///  preflow(ga, const_1_map, s, t);

   ///preflow.run();

   ///\endcode

   ///Last, the output is:

   ///\code  

   ///cout << "maximum number of arc-disjoint shortest path: " 

   ///     << preflow.flowValue() << endl;

   ///cout << "arcs of the maximum number of arc-disjoint shortest s-t paths: " 

   ///     << endl;

   ///for(ArcIt e(g); e!=INVALID; ++e) 

   ///  if (preflow.flow(e))

   ///    cout << " " << g.id(g.source(e)) << "--"

   ///         << length[e] << "->" << g.id(g.target(e)) << endl;

   ///\endcode

   ///The program has the following (expected :-)) output:

   ///\code

   ///arcs with lengths (of form id, source--length->target):

   /// 9, 5--4->6

   /// 8, 4--2->6

   /// 7, 3--1->5

   /// 6, 2--3->5

   /// 5, 2--5->6

   /// 4, 2--2->4

   /// 3, 1--3->4

   /// 2, 0--1->3

   /// 1, 0--2->2

   /// 0, 0--3->1

   ///s: 0 t: 6

   ///maximum number of arc-disjoint shortest path: 2

   ///arcs of the maximum number of arc-disjoint shortest s-t paths:

   /// 9, 5--4->6

   /// 8, 4--2->6

   /// 7, 3--1->5

   /// 4, 2--2->4

   /// 2, 0--1->3

   /// 1, 0--2->2

   ///\endcode

   template<typename _Digraph, typename _ArcFilterMap>

   class ArcSubDigraphAdaptor : 

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

 			     _ArcFilterMap, false> {

   public:

     typedef _Digraph Digraph;

     typedef _ArcFilterMap ArcFilterMap;

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

 			      ArcFilterMap, false> Parent;

     typedef typename Parent::Arc Arc;

   protected:

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

     ArcSubDigraphAdaptor() : const_true_map(true) {

       Parent::setNodeFilterMap(const_true_map);

     }

   public:

     /// \brief Constructor

     ///

     /// Creates a arc-sub-digraph-adaptor for the given digraph with

     /// given arc map filter.

     ArcSubDigraphAdaptor(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 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 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 arc-sub-digraph adaptor

   ///

   /// Just gives back an arc-sub-digraph adaptor

   template<typename Digraph, typename ArcFilterMap>

   ArcSubDigraphAdaptor<const Digraph, ArcFilterMap>

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

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

   }

   template<typename Digraph, typename ArcFilterMap>

   ArcSubDigraphAdaptor<const Digraph, const ArcFilterMap>

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

     return ArcSubDigraphAdaptor<const Digraph, const ArcFilterMap>

       (digraph, afm);

   }

   template <typename _Digraph>

   class UndirDigraphAdaptorBase { 

   public:

     typedef _Digraph Digraph;

     typedef UndirDigraphAdaptorBase Adaptor;

     typedef True UndirectedTag;

     typedef typename Digraph::Arc Edge;

     typedef typename Digraph::Node Node;

     class Arc : public Edge {

       friend class UndirDigraphAdaptorBase;

     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 2 * _digraph->arcNum(); }

     typedef EdgeNumTagIndicator<Digraph> EdgeNumTag;

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

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

     typedef FindEdgeTagIndicator<Digraph> FindEdgeTag;

     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;

     }

     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->s(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;

       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);

         } 

       }

       typename MapTraits<MapImpl>::ConstReturnValue 

       operator[](const Arc& a) const { 

 	if (direction(a)) {

 	  return _forward[a]; 

 	} else { 

 	  return _backward[a]; 

         }

       }

       typename MapTraits<MapImpl>::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;

       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()); } 

   protected:

     UndirDigraphAdaptorBase() : _digraph(0) {}

     Digraph* _digraph;

     void setDigraph(Digraph& digraph) {

       _digraph = &digraph;

     }

   };

   ///\ingroup graph_adaptors

   ///

   /// \brief A graph is made from a directed digraph by an adaptor

   ///

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

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

   /// adaptor as an edge. Let's see an informal example about using

   /// this adaptor.

   ///

   /// There is a network of the streets of a town. Of course there are

   /// some one-way street in the town hence the network is a directed

   /// one. There is a crazy driver who go oppositely in the one-way

   /// street without moral sense. Of course he can pass this streets

   /// slower than the regular way, in fact his speed is half of the

   /// normal speed. How long should he drive to get from a source

   /// point to the target? Let see the example code which calculate it:

   ///

   /// \todo BadCode, SimpleMap does no exists

   ///\code

   /// typedef UndirDigraphAdaptor<Digraph> Graph;

   /// Graph graph(digraph);

   ///

   /// typedef SimpleMap<LengthMap> FLengthMap;

   /// FLengthMap flength(length);

   ///

   /// typedef ScaleMap<LengthMap> RLengthMap;

   /// RLengthMap rlength(length, 2.0);

   ///

   /// typedef Graph::CombinedArcMap<FLengthMap, RLengthMap > ULengthMap;

   /// ULengthMap ulength(flength, rlength);

   /// 

   /// Dijkstra<Graph, ULengthMap> dijkstra(graph, ulength);

   /// std::cout << "Driving time : " << dijkstra.run(src, trg) << std::endl;

   ///\endcode

   ///

   /// The combined arc map makes the length map for the undirected

   /// graph. It is created from a forward and reverse map. The forward

   /// map is created from the original length map with a SimpleMap

   /// adaptor which just makes a read-write map from the reference map

   /// i.e. it forgets that it can be return reference to values. The

   /// reverse map is just the scaled original map with the ScaleMap

   /// adaptor. The combination solves that passing the reverse way

   /// takes double time than the original. To get the driving time we

   /// run the dijkstra algorithm on the graph.

   template<typename _Digraph>

   class UndirDigraphAdaptor 

     : public GraphAdaptorExtender<UndirDigraphAdaptorBase<_Digraph> > {

   public:

     typedef _Digraph Digraph;

     typedef GraphAdaptorExtender<UndirDigraphAdaptorBase<Digraph> > Parent;

   protected:

     UndirDigraphAdaptor() { }

   public:

     /// \brief Constructor

     ///

     /// Constructor

     UndirDigraphAdaptor(_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 adaptor.

     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;

       /// \brief Constructor      

       ///

       /// Constructor      

       CombinedArcMap() : _forward(0), _backward(0) {}

       /// \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.

       typename MapTraits<ForwardMap>::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.

       typename MapTraits<ForwardMap>::ReturnValue 

       operator[](const Key& e) { 

 	if (Parent::direction(e)) {

 	  return (*_forward)[e]; 

 	} else { 

 	  return (*_backward)[e]; 

         }

       }

       /// \brief Sets the forward map

       ///

       /// Sets the forward map

       void setForwardMap(ForwardMap& forward) {

         _forward = &forward;

       }

       /// \brief Sets the backward map

       ///

       /// Sets the backward map

       void setBackwardMap(BackwardMap& backward) {

         _backward = &backward;

       }

     protected:

       ForwardMap* _forward;

       BackwardMap* _backward; 

     };

   };

   /// \brief Just gives back an undir digraph adaptor

   ///

   /// Just gives back an undir digraph adaptor

   template<typename Digraph>

   UndirDigraphAdaptor<const Digraph>

   undirDigraphAdaptor(const Digraph& digraph) {

     return UndirDigraphAdaptor<const Digraph>(digraph);

   }

   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) { }

     ResForwardFilter(const Tolerance& tolerance = Tolerance()) 

       : _capacity(0), _flow(0), _tolerance(tolerance)  { }

     void setCapacity(const CapacityMap& capacity) { _capacity = &capacity; }

     void setFlow(const FlowMap& flow) { _flow = &flow; }

     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) { }

     ResBackwardFilter(const Tolerance& tolerance = Tolerance())

       : _capacity(0), _flow(0), _tolerance(tolerance) { }

     void setCapacity(const CapacityMap& capacity) { _capacity = &capacity; }

     void setFlow(const FlowMap& flow) { _flow = &flow; }

     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 digraph

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

   ///\f$, be functions on the arc-set.

   ///

   ///In the appications of ResDigraphAdaptor, \f$ f \f$ usually stands

   ///for a flow and \f$ c \f$ for a capacity function.  Suppose that a

   ///graph instance \c g of type \c ListDigraph implements \f$ G \f$.

   ///

   ///\code 

   ///  ListDigraph g;

   ///\endcode 

   ///

   ///Then ResDigraphAdaptor 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$, multilicities 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 twice. The

   /// following code shows how such an instance can be constructed.

   ///

   ///\code 

   ///  typedef ListDigraph Digraph; 

   ///  IntArcMap f(g), c(g);

   ///  ResDigraphAdaptor<Digraph, int, IntArcMap, IntArcMap> ga(g); 

   ///\endcode

   template<typename _Digraph, 

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

 	   typename _FlowMap = _CapacityMap,

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

   class ResDigraphAdaptor : 

     public ArcSubDigraphAdaptor< 

     UndirDigraphAdaptor<const _Digraph>, 

     typename UndirDigraphAdaptor<const _Digraph>::template CombinedArcMap<

       ResForwardFilter<const _Digraph, _CapacityMap, _FlowMap>,  

       ResBackwardFilter<const _Digraph, _CapacityMap, _FlowMap> > > {

   public:

     typedef _Digraph Digraph;

     typedef _CapacityMap CapacityMap;

     typedef _FlowMap FlowMap;

     typedef _Tolerance Tolerance;

     typedef typename CapacityMap::Value Value;

     typedef ResDigraphAdaptor Adaptor;

   protected:

     typedef UndirDigraphAdaptor<const Digraph> UndirDigraph;

     typedef ResForwardFilter<const Digraph, CapacityMap, FlowMap> 

     ForwardFilter;

     typedef ResBackwardFilter<const Digraph, CapacityMap, FlowMap> 

     BackwardFilter;

     typedef typename UndirDigraph::

     template CombinedArcMap<ForwardFilter, BackwardFilter> ArcFilter;

     typedef ArcSubDigraphAdaptor<UndirDigraph, ArcFilter> Parent;

     const CapacityMap* _capacity;

     FlowMap* _flow;

     UndirDigraph _graph;

     ForwardFilter _forward_filter;

     BackwardFilter _backward_filter;

     ArcFilter _arc_filter;

     void setCapacityMap(const CapacityMap& capacity) {

       _capacity = &capacity;

       _forward_filter.setCapacity(capacity);

       _backward_filter.setCapacity(capacity);

     }

     void setFlowMap(FlowMap& flow) {

       _flow = &flow;

       _forward_filter.setFlow(flow);

       _backward_filter.setFlow(flow);

     }

   public:

     /// \brief Constructor of the residual digraph.

     ///

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

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

     ResDigraphAdaptor(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 rescap(const Arc& arc) const {

       if (UndirDigraph::direction(arc)) {

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

       } else {

         return (*_flow)[arc];

       }

     } 

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

     ///

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

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

     /// of the residual arc.

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

       if (UndirDigraph::direction(e)) {

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

       } else {  

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

       }

     }

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

     ///

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

     static bool forward(const Arc& e) {

       return UndirDigraph::direction(e);

     }

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

     ///

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

     static bool backward(const Arc& e) {

       return !UndirDigraph::direction(e);

     }

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

     ///

     /// Gives back the forward oriented residual arc.

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

       return UndirDigraph::direct(e, true);

     }

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

     ///

     /// Gives back the backward oriented residual arc.

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

       return UndirDigraph::direct(e, false);

     }

     /// \brief Residual capacity map.

     ///

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

     /// as a map. 

     class ResCap {

     protected:

       const Adaptor* _adaptor;

     public:

       typedef Arc Key;

       typedef typename _CapacityMap::Value Value;

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

       Value operator[](const Arc& e) const {

         return _adaptor->rescap(e);

       }

     };

   };

   template <typename _Digraph>

   class SplitDigraphAdaptorBase {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorBase<const _Digraph> Parent;

     typedef SplitDigraphAdaptorBase Adaptor;

     typedef typename Digraph::Node DigraphNode;

     typedef typename Digraph::Arc DigraphArc;

     class Node;

     class Arc;

   private:

     template <typename T> class NodeMapBase;

     template <typename T> class ArcMapBase;

   public:

     class Node : public DigraphNode {

       friend class SplitDigraphAdaptorBase;

       template <typename T> friend class NodeMapBase;

     private:

       bool _in;

       Node(DigraphNode node, bool in)

 	: DigraphNode(node), _in(in) {}

     public:

       Node() {}

       Node(Invalid) : DigraphNode(INVALID), _in(true) {}

       bool operator==(const Node& node) const {

 	return DigraphNode::operator==(node) && _in == node._in;

       }

       bool operator!=(const Node& node) const {

 	return !(*this == node);

       }

       bool operator<(const Node& node) const {

 	return DigraphNode::operator<(node) || 

 	  (DigraphNode::operator==(node) && _in < node._in);

       }

     };

     class Arc {

       friend class SplitDigraphAdaptorBase;

       template <typename T> friend class ArcMapBase;

     private:

       typedef BiVariant<DigraphArc, DigraphNode> ArcImpl;

       explicit Arc(const DigraphArc& arc) : _item(arc) {}

       explicit Arc(const DigraphNode& node) : _item(node) {}

       ArcImpl _item;

     public:

       Arc() {}

       Arc(Invalid) : _item(DigraphArc(INVALID)) {}

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

         if (_item.firstState()) {

           if (arc._item.firstState()) {

             return _item.first() == arc._item.first();

           }

         } else {

           if (arc._item.secondState()) {

             return _item.second() == arc._item.second();

           }

         }

         return false;

       }

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

 	return !(*this == arc);

       }

       bool operator<(const Arc& arc) const {

         if (_item.firstState()) {

           if (arc._item.firstState()) {

             return _item.first() < arc._item.first();

           }

           return false;

         } else {

           if (arc._item.secondState()) {

             return _item.second() < arc._item.second();

           }

           return true;

         }

       }

       operator DigraphArc() const { return _item.first(); }

       operator DigraphNode() const { return _item.second(); }

     };

     void first(Node& n) const {

       _digraph->first(n);

       n._in = true;

     }

     void next(Node& n) const {

       if (n._in) {

 	n._in = false;

       } else {

 	n._in = true;

 	_digraph->next(n);

       }

     }

     void first(Arc& e) const {

       e._item.setSecond();

       _digraph->first(e._item.second());

       if (e._item.second() == INVALID) {

         e._item.setFirst();

 	_digraph->first(e._item.first());

       }

     }

     void next(Arc& e) const {

       if (e._item.secondState()) {

 	_digraph->next(e._item.second());

         if (e._item.second() == INVALID) {

           e._item.setFirst();

           _digraph->first(e._item.first());

         }

       } else {

 	_digraph->next(e._item.first());

       }      

     }

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

       if (n._in) {

         e._item.setSecond(n);

       } else {

         e._item.setFirst();

 	_digraph->firstOut(e._item.first(), n);

       }

     }

     void nextOut(Arc& e) const {

       if (!e._item.firstState()) {

 	e._item.setFirst(INVALID);

       } else {

 	_digraph->nextOut(e._item.first());

       }      

     }

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

       if (!n._in) {

         e._item.setSecond(n);        

       } else {

         e._item.setFirst();

 	_digraph->firstIn(e._item.first(), n);

       }

     }

     void nextIn(Arc& e) const {

       if (!e._item.firstState()) {

 	e._item.setFirst(INVALID);

       } else {

 	_digraph->nextIn(e._item.first());

       }

     }

     Node source(const Arc& e) const {

       if (e._item.firstState()) {

 	return Node(_digraph->source(e._item.first()), false);

       } else {

 	return Node(e._item.second(), true);

       }

     }

     Node target(const Arc& e) const {

       if (e._item.firstState()) {

 	return Node(_digraph->target(e._item.first()), true);

       } else {

 	return Node(e._item.second(), false);

       }

     }

     int id(const Node& n) const {

       return (_digraph->id(n) << 1) | (n._in ? 0 : 1);

     }

     Node nodeFromId(int ix) const {

       return Node(_digraph->nodeFromId(ix >> 1), (ix & 1) == 0);

     }

     int maxNodeId() const {

       return 2 * _digraph->maxNodeId() + 1;

     }

     int id(const Arc& e) const {

       if (e._item.firstState()) {

         return _digraph->id(e._item.first()) << 1;

       } else {

         return (_digraph->id(e._item.second()) << 1) | 1;

       }

     }

     Arc arcFromId(int ix) const {

       if ((ix & 1) == 0) {

         return Arc(_digraph->arcFromId(ix >> 1));

       } else {

         return Arc(_digraph->nodeFromId(ix >> 1));

       }

     }

     int maxArcId() const {

       return std::max(_digraph->maxNodeId() << 1, 

                       (_digraph->maxArcId() << 1) | 1);

     }

     static bool inNode(const Node& n) {

       return n._in;

     }

     static bool outNode(const Node& n) {

       return !n._in;

     }

     static bool origArc(const Arc& e) {

       return e._item.firstState();

     }

     static bool bindArc(const Arc& e) {

       return e._item.secondState();

     }

     static Node inNode(const DigraphNode& n) {

       return Node(n, true);

     }

     static Node outNode(const DigraphNode& n) {

       return Node(n, false);

     }

     static Arc arc(const DigraphNode& n) {

       return Arc(n);

     }

     static Arc arc(const DigraphArc& e) {

       return Arc(e);

     }

     typedef True NodeNumTag;

     int nodeNum() const {

       return  2 * countNodes(*_digraph);

     }

     typedef True EdgeNumTag;

     int arcNum() const {

       return countArcs(*_digraph) + countNodes(*_digraph);

     }

     typedef True FindEdgeTag;

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

 		const Arc& prev = INVALID) const {

       if (inNode(u)) {

         if (outNode(v)) {

           if (static_cast<const DigraphNode&>(u) == 

               static_cast<const DigraphNode&>(v) && prev == INVALID) {

             return Arc(u);

           }

         }

       } else {

         if (inNode(v)) {

           return Arc(::lemon::findArc(*_digraph, u, v, prev));

         }

       }

       return INVALID;

     }

   private:

     template <typename _Value>

     class NodeMapBase 

       : public MapTraits<typename Parent::template NodeMap<_Value> > {

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

     public:

       typedef Node Key;

       typedef _Value Value;

       NodeMapBase(const Adaptor& adaptor) 

 	: _in_map(*adaptor._digraph), _out_map(*adaptor._digraph) {}

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

 	: _in_map(*adaptor._digraph, value), 

 	  _out_map(*adaptor._digraph, value) {}

       void set(const Node& key, const Value& val) {

 	if (Adaptor::inNode(key)) { _in_map.set(key, val); }

 	else {_out_map.set(key, val); }

       }

       typename MapTraits<NodeImpl>::ReturnValue 

       operator[](const Node& key) {

 	if (Adaptor::inNode(key)) { return _in_map[key]; }

 	else { return _out_map[key]; }

       }

       typename MapTraits<NodeImpl>::ConstReturnValue

       operator[](const Node& key) const {

 	if (Adaptor::inNode(key)) { return _in_map[key]; }

 	else { return _out_map[key]; }

       }

     private:

       NodeImpl _in_map, _out_map;

     };

     template <typename _Value>

     class ArcMapBase 

       : public MapTraits<typename Parent::template ArcMap<_Value> > {

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

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

     public:

       typedef Arc Key;

       typedef _Value Value;

       ArcMapBase(const Adaptor& adaptor) 

 	: _arc_map(*adaptor._digraph), _node_map(*adaptor._digraph) {}

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

 	: _arc_map(*adaptor._digraph, value), 

 	  _node_map(*adaptor._digraph, value) {}

       void set(const Arc& key, const Value& val) {

 	if (Adaptor::origArc(key)) { 

           _arc_map.set(key._item.first(), val); 

         } else {

           _node_map.set(key._item.second(), val); 

         }

       }

       typename MapTraits<ArcImpl>::ReturnValue

       operator[](const Arc& key) {

 	if (Adaptor::origArc(key)) { 

           return _arc_map[key._item.first()];

         } else {

           return _node_map[key._item.second()];

         }

       }

       typename MapTraits<ArcImpl>::ConstReturnValue

       operator[](const Arc& key) const {

 	if (Adaptor::origArc(key)) { 

           return _arc_map[key._item.first()];

         } else {

           return _node_map[key._item.second()];

         }

       }

     private:

       ArcImpl _arc_map;

       NodeImpl _node_map;

     };

   public:

     template <typename _Value>

     class NodeMap 

       : public SubMapExtender<Adaptor, NodeMapBase<_Value> > 

     {

     public:

       typedef _Value Value;

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

       NodeMap(const Adaptor& adaptor) 

 	: Parent(adaptor) {}

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

 	: Parent(adaptor, 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;

       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;

       }

     };

   protected:

     SplitDigraphAdaptorBase() : _digraph(0) {}

     Digraph* _digraph;

     void setDigraph(Digraph& digraph) {

       _digraph = &digraph;

     }

   };

   /// \ingroup graph_adaptors

   ///

   /// \brief Split digraph adaptor class

   /// 

   /// This is an digraph adaptor which splits all node into an in-node

   /// and an out-node. Formaly, the adaptor replaces each \f$ u \f$

   /// node in the digraph with two node, \f$ u_{in} \f$ node and 

   /// \f$ u_{out} \f$ node. If there is an \f$ (v, u) \f$ arc in the 

   /// original digraph the new target of the arc will be \f$ u_{in} \f$ and

   /// similarly the source of the original \f$ (u, v) \f$ arc will be

   /// \f$ u_{out} \f$.  The adaptor will add for each node in the 

   /// original digraph an additional arc which will connect 

   /// \f$ (u_{in}, u_{out}) \f$.

   ///

   /// The aim of this class is to run algorithm with node costs if the 

   /// algorithm can use directly just arc costs. In this case we should use

   /// a \c SplitDigraphAdaptor and set the node cost of the digraph to the

   /// bind arc in the adapted digraph.

   /// 

   /// For example a maximum flow algorithm can compute how many arc

   /// disjoint paths are in the digraph. But we would like to know how

   /// many node disjoint paths are in the digraph. First we have to

   /// adapt the digraph with the \c SplitDigraphAdaptor. Then run the flow

   /// algorithm on the adapted digraph. The bottleneck of the flow will

   /// be the bind arcs which bounds the flow with the count of the

   /// node disjoint paths.

   ///

   ///\code

   ///

   /// typedef SplitDigraphAdaptor<SmartDigraph> SDigraph;

   ///

   /// SDigraph sdigraph(digraph);

   ///

   /// typedef ConstMap<SDigraph::Arc, int> SCapacity;

   /// SCapacity scapacity(1);

   ///

   /// SDigraph::ArcMap<int> sflow(sdigraph);

   ///

   /// Preflow<SDigraph, SCapacity> 

   ///   spreflow(sdigraph, scapacity, 

   ///            SDigraph::outNode(source), SDigraph::inNode(target));

   ///                                            

   /// spreflow.run();

   ///

   ///\endcode

   ///

   /// The result of the mamixum flow on the original digraph

   /// shows the next figure:

   ///

   /// \image html arc_disjoint.png

   /// \image latex arc_disjoint.eps "Arc disjoint paths" width=\textwidth

   /// 

   /// And the maximum flow on the adapted digraph:

   ///

   /// \image html node_disjoint.png

   /// \image latex node_disjoint.eps "Node disjoint paths" width=\textwidth

   ///

   /// The second solution contains just 3 disjoint paths while the first 4.

   /// The full code can be found in the \ref disjoint_paths_demo.cc demo file.

   ///

   /// This digraph adaptor is fully conform to the 

   /// \ref concepts::Digraph "Digraph" concept and

   /// contains some additional member functions and types. The 

   /// documentation of some member functions may be found just in the

   /// SplitDigraphAdaptorBase class.

   ///

   /// \sa SplitDigraphAdaptorBase

   template <typename _Digraph>

   class SplitDigraphAdaptor 

     : public DigraphAdaptorExtender<SplitDigraphAdaptorBase<_Digraph> > {

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorExtender<SplitDigraphAdaptorBase<Digraph> > Parent;

     typedef typename Digraph::Node DigraphNode;

     typedef typename Digraph::Arc DigraphArc;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     /// \brief Constructor of the adaptor.

     ///

     /// Constructor of the adaptor.

     SplitDigraphAdaptor(Digraph& g) {

       Parent::setDigraph(g);

     }

     /// \brief Returns true when the node is in-node.

     ///

     /// Returns true when the node is in-node.

     static bool inNode(const Node& n) {

       return Parent::inNode(n);

     }

     /// \brief Returns true when the node is out-node.

     ///

     /// Returns true when the node is out-node.

     static bool outNode(const Node& n) {

       return Parent::outNode(n);

     }

     /// \brief Returns true when the arc is arc in the original digraph.

     ///

     /// Returns true when the arc is arc in the original digraph.

     static bool origArc(const Arc& a) {

       return Parent::origArc(a);

     }

     /// \brief Returns true when the arc binds an in-node and an out-node.

     ///

     /// Returns true when the arc binds an in-node and an out-node.

     static bool bindArc(const Arc& a) {

       return Parent::bindArc(a);

     }

     /// \brief Gives back the in-node created from the \c node.

     ///

     /// Gives back the in-node created from the \c node.

     static Node inNode(const DigraphNode& n) {

       return Parent::inNode(n);

     }

     /// \brief Gives back the out-node created from the \c node.

     ///

     /// Gives back the out-node created from the \c node.

     static Node outNode(const DigraphNode& n) {

       return Parent::outNode(n);

     }

     /// \brief Gives back the arc binds the two part of the node.

     /// 

     /// Gives back the arc binds the two part of the node.

     static Arc arc(const DigraphNode& n) {

       return Parent::arc(n);

     }

     /// \brief Gives back the arc of the original arc.

     /// 

     /// Gives back the arc of the original arc.

     static Arc arc(const DigraphArc& a) {

       return Parent::arc(a);

     }

     /// \brief NodeMap combined from two original NodeMap

     ///

     /// This class adapt two of the original digraph NodeMap to

     /// get a node map on the adapted digraph.

     template <typename InNodeMap, typename OutNodeMap>

     class CombinedNodeMap {

     public:

       typedef Node Key;

       typedef typename InNodeMap::Value Value;

       /// \brief Constructor

       ///

       /// Constructor.

       CombinedNodeMap(InNodeMap& in_map, OutNodeMap& out_map) 

 	: _in_map(in_map), _out_map(out_map) {}

       /// \brief The subscript operator.

       ///

       /// The subscript operator.

       Value& operator[](const Key& key) {

 	if (Parent::inNode(key)) {

 	  return _in_map[key];

 	} else {

 	  return _out_map[key];

 	}

       }

       /// \brief The const subscript operator.

       ///

       /// The const subscript operator.

       Value operator[](const Key& key) const {

 	if (Parent::inNode(key)) {

 	  return _in_map[key];

 	} else {

 	  return _out_map[key];

 	}

       }

       /// \brief The setter function of the map.

       /// 

       /// The setter function of the map.

       void set(const Key& key, const Value& value) {

 	if (Parent::inNode(key)) {

 	  _in_map.set(key, value);

 	} else {

 	  _out_map.set(key, value);

 	}

       }

     private:

       InNodeMap& _in_map;

       OutNodeMap& _out_map;

     };

     /// \brief Just gives back a combined node map.

     /// 

     /// Just gives back a combined node map.

     template <typename InNodeMap, typename OutNodeMap>

     static CombinedNodeMap<InNodeMap, OutNodeMap> 

     combinedNodeMap(InNodeMap& in_map, OutNodeMap& out_map) {

       return CombinedNodeMap<InNodeMap, OutNodeMap>(in_map, out_map);

     }

     template <typename InNodeMap, typename OutNodeMap>

     static CombinedNodeMap<const InNodeMap, OutNodeMap> 

     combinedNodeMap(const InNodeMap& in_map, OutNodeMap& out_map) {

       return CombinedNodeMap<const InNodeMap, OutNodeMap>(in_map, out_map);

     }

     template <typename InNodeMap, typename OutNodeMap>

     static CombinedNodeMap<InNodeMap, const OutNodeMap> 

     combinedNodeMap(InNodeMap& in_map, const OutNodeMap& out_map) {

       return CombinedNodeMap<InNodeMap, const OutNodeMap>(in_map, out_map);

     }

     template <typename InNodeMap, typename OutNodeMap>

     static CombinedNodeMap<const InNodeMap, const OutNodeMap> 

     combinedNodeMap(const InNodeMap& in_map, const OutNodeMap& out_map) {

       return CombinedNodeMap<const InNodeMap, 

         const OutNodeMap>(in_map, out_map);

     }

     /// \brief ArcMap combined from an original ArcMap and NodeMap

     ///

     /// This class adapt an original digraph ArcMap and NodeMap to

     /// get an arc map on the adapted digraph.

     template <typename DigraphArcMap, typename DigraphNodeMap>

     class CombinedArcMap {

     public:

       typedef Arc Key;

       typedef typename DigraphArcMap::Value Value;

       /// \brief Constructor

       ///

       /// Constructor.

       CombinedArcMap(DigraphArcMap& arc_map, DigraphNodeMap& node_map) 

 	: _arc_map(arc_map), _node_map(node_map) {}

       /// \brief The subscript operator.

       ///

       /// The subscript operator.

       void set(const Arc& arc, const Value& val) {

 	if (Parent::origArc(arc)) {

 	  _arc_map.set(arc, val);

 	} else {

 	  _node_map.set(arc, val);

 	}

       }

       /// \brief The const subscript operator.

       ///

       /// The const subscript operator.

       Value operator[](const Key& arc) const {

 	if (Parent::origArc(arc)) {

 	  return _arc_map[arc];

 	} else {

 	  return _node_map[arc];

 	}

       }      

       /// \brief The const subscript operator.

       ///

       /// The const subscript operator.

       Value& operator[](const Key& arc) {

 	if (Parent::origArc(arc)) {

 	  return _arc_map[arc];

 	} else {

 	  return _node_map[arc];

 	}

       }      

     private:

       DigraphArcMap& _arc_map;

       DigraphNodeMap& _node_map;

     };

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

     /// 

     /// Just gives back a combined arc map.

     template <typename DigraphArcMap, typename DigraphNodeMap>

     static CombinedArcMap<DigraphArcMap, DigraphNodeMap> 

     combinedArcMap(DigraphArcMap& arc_map, DigraphNodeMap& node_map) {

       return CombinedArcMap<DigraphArcMap, DigraphNodeMap>(arc_map, node_map);

     }

     template <typename DigraphArcMap, typename DigraphNodeMap>

     static CombinedArcMap<const DigraphArcMap, DigraphNodeMap> 

     combinedArcMap(const DigraphArcMap& arc_map, DigraphNodeMap& node_map) {

       return CombinedArcMap<const DigraphArcMap, 

         DigraphNodeMap>(arc_map, node_map);

     }

     template <typename DigraphArcMap, typename DigraphNodeMap>

     static CombinedArcMap<DigraphArcMap, const DigraphNodeMap> 

     combinedArcMap(DigraphArcMap& arc_map, const DigraphNodeMap& node_map) {

       return CombinedArcMap<DigraphArcMap, 

         const DigraphNodeMap>(arc_map, node_map);

     }

     template <typename DigraphArcMap, typename DigraphNodeMap>

     static CombinedArcMap<const DigraphArcMap, const DigraphNodeMap> 

     combinedArcMap(const DigraphArcMap& arc_map, 

                     const DigraphNodeMap& node_map) {

       return CombinedArcMap<const DigraphArcMap, 

         const DigraphNodeMap>(arc_map, node_map);

     }

   };

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

   ///

   /// Just gives back a split digraph adaptor

   template<typename Digraph>

   SplitDigraphAdaptor<Digraph>

   splitDigraphAdaptor(const Digraph& digraph) {

     return SplitDigraphAdaptor<Digraph>(digraph);

   }

 } //namespace lemon

 #endif //LEMON_DIGRAPH_ADAPTOR_H