/* -*- 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 functions.

 #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 {

   ///\brief Base type for the Digraph Adaptors

   ///

   ///Base type for the Digraph Adaptors

   ///

   ///This is the base type for most of LEMON digraph adaptors. This

   ///class implements a trivial digraph adaptor i.e. it only wraps the

   ///functions and types of the digraph. The purpose of this class is

   ///to make easier implementing digraph adaptors. E.g. if an adaptor

   ///is considered which differs from the wrapped digraph only in some

   ///of its functions or types, then it can be derived from

   ///DigraphAdaptor, and only the differences should be implemented.

   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;

       }

     };

   };

   ///\ingroup graph_adaptors

   ///

   ///\brief Trivial Digraph Adaptor

   /// 

   /// This class is an adaptor which does not change the adapted

   /// digraph.  It can be used only to test the digraph adaptors.

   template <typename _Digraph>

   class DigraphAdaptor :

     public DigraphAdaptorExtender<DigraphAdaptorBase<_Digraph> > { 

   public:

     typedef _Digraph Digraph;

     typedef DigraphAdaptorExtender<DigraphAdaptorBase<_Digraph> > Parent;

   protected:

     DigraphAdaptor() : Parent() { }

   public:

     explicit DigraphAdaptor(Digraph& digraph) { setDigraph(digraph); }

   };

   /// \brief Just gives back a digraph adaptor

   ///

   /// Just gives back a digraph adaptor which 

   /// should be provide original digraph

   template<typename Digraph>

   DigraphAdaptor<const Digraph>

   digraphAdaptor(const Digraph& digraph) {

     return DigraphAdaptor<const Digraph>(digraph);

   }

   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 g;

   ///\endcode

   /// then

   ///\code

   /// RevDigraphAdaptor<ListDigraph> ga(g);

   ///\endcode

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

   /// reversing the orientation of its arcs.

   ///

   /// A good example of using RevDigraphAdaptor is to decide that the

   /// directed graph is wheter strongly connected or not. If from one

   /// node each node is reachable and from each node is reachable this

   /// node then and just then the digraph is strongly

   /// connected. Instead of this condition we use a little bit

   /// different. From one node each node ahould be reachable in the

   /// digraph and in the reversed digraph. Now this condition can be

   /// checked with the Dfs algorithm class and the RevDigraphAdaptor

   /// algorithm class.

   ///

   /// And look at the code:

   ///

   ///\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:

     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); 

     }

     ///\e

     /// 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 { _node_filter->set(n, false); }

     ///\e

     /// 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 { _arc_filter->set(a, false); }

     ///\e

     /// 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 { _node_filter->set(n, true); }

     ///\e

     /// 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 { _arc_filter->set(a, true); }

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

     ///\e

     ///

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

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

     ///\e

     ///

     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); 

     }

     ///\e

     /// 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 { _node_filter->set(n, false); }

     ///\e

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

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

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

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

     ///\e

     /// 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 { _node_filter->set(n, true); }

     ///\e

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

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

     /// again

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

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

     ///\e

     ///

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

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

     ///\e

     ///

     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 arcset

   /// to do not get invalid arcs without source or target.

   /// Let \f$ G=(V, A) \f$ be a directed digraph

   /// and suppose that the digraph instance \c g of type ListDigraph

   /// implements \f$ G \f$.

   /// Let moreover \f$ b_V \f$ and \f$ b_A \f$ be bool-valued functions resp.

   /// on the node-set and arc-set.

   /// SubDigraphAdaptor<...>::NodeIt iterates 

   /// on the node-set \f$ \{v\in V : b_V(v)=true\} \f$ and 

   /// SubDigraphAdaptor<...>::ArcIt iterates 

   /// on the arc-set \f$ \{e\in A : b_A(e)=true\} \f$. Similarly, 

   /// SubDigraphAdaptor<...>::OutArcIt and

   /// SubDigraphAdaptor<...>::InArcIt iterates 

   /// only on arcs leaving and entering a specific node which have true value.

   /// 

   /// If the \c checked template parameter is false then we have to

   /// note that the node-iterator cares only the filter on the

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

   /// arc-set.  This way the arc-map should 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> SubGA;

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

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

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

   /// std::cout << ":-)" << std::endl;

   /// for (SubGA::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 SubGA::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;

   protected:

     SubDigraphAdaptor() { }

   public:

     SubDigraphAdaptor(Digraph& digraph, NodeFilterMap& node_filter, 

 		      ArcFilterMap& arc_filter) { 

       setDigraph(digraph);

       setNodeFilterMap(node_filter);

       setArcFilterMap(arc_filter);

     }

   };

   /// \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;

   protected:

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

     NodeSubDigraphAdaptor() : const_true_map(true) {

       Parent::setArcFilterMap(const_true_map);

     }

   public:

     NodeSubDigraphAdaptor(Digraph& _digraph, NodeFilterMap& node_filter) : 

       Parent(), const_true_map(true) { 

       Parent::setDigraph(_digraph);

       Parent::setNodeFilterMap(node_filter);

       Parent::setArcFilterMap(const_true_map);

     }

   };

   /// \brief Just gives back a \c NodeSubDigraphAdaptor

   ///

   /// Just gives back a \c NodeSubDigraphAdaptor

   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 w.r.t.  non-negative arc-lengths. Note that

   ///the comprehension of the presented solution need's some

   ///elementary knowlarc 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

   ///didigraph 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;

   protected:

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

     ArcSubDigraphAdaptor() : const_true_map(true) {

       Parent::setNodeFilterMap(const_true_map);

     }

   public:

     ArcSubDigraphAdaptor(Digraph& digraph, ArcFilterMap& arc_filter) 

       : Parent(), const_true_map(true) { 

       Parent::setDigraph(digraph);

       Parent::setNodeFilterMap(const_true_map);

       Parent::setArcFilterMap(arc_filter);

     }

   };

   /// \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 {