diff -r 0c5dd7ceda03 -r 05357da973ce lemon/digraph_adaptor.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/digraph_adaptor.h	Sun Nov 30 18:57:18 2008 +0100
@@ -0,0 +1,2530 @@
+/* -*- 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 {
+      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 An graph is made from a directed digraph by an adaptor
+  ///
+  /// This adaptor makes an undirected graph from a directed
+  /// digraph. All arc of the underlying 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);
+      }
+      
+    };
+
+  };
+
+  /// \brief Base class for split digraph adaptor
+  ///
+  /// Base class of split digraph adaptor. In most case you do not need to
+  /// use it directly but the documented member functions of this class can 
+  /// be used with the SplitDigraphAdaptor class.
+  /// \sa SplitDigraphAdaptor
+  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);
+    }
+
+    /// \brief Returns true when the node is in-node.
+    ///
+    /// Returns true when the node is in-node.
+    static bool inNode(const Node& n) {
+      return n._in;
+    }
+
+    /// \brief Returns true when the node is out-node.
+    ///
+    /// Returns true when the node is out-node.
+    static bool outNode(const Node& n) {
+      return !n._in;
+    }
+
+    /// \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& e) {
+      return e._item.firstState();
+    }
+
+    /// \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& e) {
+      return e._item.secondState();
+    }
+
+    /// \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 Node(n, true);
+    }
+
+    /// \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 Node(n, false);
+    }
+
+    /// \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 Arc(n);
+    }
+
+    /// \brief Gives back the arc of the original arc.
+    /// 
+    /// Gives back the arc of the original arc.
+    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.
+  /// 
+  /// By example a maximum flow algoritm 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 Parent::Node Node;
+    typedef typename Parent::Arc Arc;
+
+    /// \brief Constructor of the adaptor.
+    ///
+    /// Constructor of the adaptor.
+    SplitDigraphAdaptor(Digraph& g) {
+      Parent::setDigraph(g);
+    }
+
+    /// \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
+