# HG changeset patch
# User Alpar Juttner <alpar@cs.elte.hu>
# Date 1206015144 0
# Node ID 70f3967ca6eb8c62d5194a2ad078dd36d9a36374
# Parent  cc7e6b8b59bf2085f0c9584e5c4190096858c5e5# Parent  4f754b4cf82b87c14835ac0a1a4d2b9ffd8e8c11
Merge

diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/Makefile.am
--- a/lemon/Makefile.am	Tue Mar 18 16:45:21 2008 +0100
+++ b/lemon/Makefile.am	Thu Mar 20 12:12:24 2008 +0000
@@ -17,12 +17,17 @@
 
 lemon_HEADERS += \
         lemon/arg_parser.h \
-        lemon/concept_check.h \
+        lemon/bfs.h \
+        lemon/bin_heap.h \
+        lemon/dfs.h \
+        lemon/dijkstra.h \
         lemon/dim2.h \
 	lemon/error.h \
+        lemon/graph_utils.h \
 	lemon/list_graph.h \
 	lemon/maps.h \
 	lemon/math.h \
+	lemon/path.h \
         lemon/random.h \
         lemon/tolerance.h
 
@@ -34,6 +39,7 @@
 	lemon/bits/graph_extender.h \
         lemon/bits/invalid.h \
 	lemon/bits/map_extender.h \
+	lemon/bits/path_dump.h \
 	lemon/bits/traits.h \
         lemon/bits/utility.h \
 	lemon/bits/vector_map.h
@@ -42,5 +48,7 @@
 	lemon/concept_check.h \
 	lemon/concepts/digraph.h \
 	lemon/concepts/graph.h \
+	lemon/concepts/heap.h \
 	lemon/concepts/maps.h \
+	lemon/concepts/path.h \
 	lemon/concepts/graph_components.h
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/bfs.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/bfs.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,1597 @@
+/* -*- 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_BFS_H
+#define LEMON_BFS_H
+
+///\ingroup search
+///\file
+///\brief Bfs algorithm.
+
+#include <lemon/list_graph.h>
+#include <lemon/graph_utils.h>
+#include <lemon/bits/path_dump.h>
+#include <lemon/bits/invalid.h>
+#include <lemon/error.h>
+#include <lemon/maps.h>
+
+namespace lemon {
+
+
+  
+  ///Default traits class of Bfs class.
+
+  ///Default traits class of Bfs class.
+  ///\param GR Digraph type.
+  template<class GR>
+  struct BfsDefaultTraits
+  {
+    ///The digraph type the algorithm runs on. 
+    typedef GR Digraph;
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the shortest paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \ref PredMap. 
+    ///\param G is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient to initialize
+    static PredMap *createPredMap(const GR &G) 
+    {
+      return new PredMap(G);
+    }
+    ///The type of the map that indicates which nodes are processed.
+ 
+    ///The type of the map that indicates which nodes are processed.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \ref ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \ref ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that indicates which nodes are reached.
+ 
+    ///The type of the map that indicates which nodes are reached.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef typename Digraph::template NodeMap<bool> ReachedMap;
+    ///Instantiates a ReachedMap.
+ 
+    ///This function instantiates a \ref ReachedMap. 
+    ///\param G is the digraph, to which
+    ///we would like to define the \ref ReachedMap.
+    static ReachedMap *createReachedMap(const GR &G)
+    {
+      return new ReachedMap(G);
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<int> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param G is the digraph, to which we would like to define the \ref DistMap
+    static DistMap *createDistMap(const GR &G)
+    {
+      return new DistMap(G);
+    }
+  };
+  
+  ///%BFS algorithm class.
+  
+  ///\ingroup search
+  ///This class provides an efficient implementation of the %BFS algorithm.
+  ///
+  ///\param GR The digraph type the algorithm runs on. The default value is
+  ///\ref ListDigraph. The value of GR is not used directly by Bfs, it
+  ///is only passed to \ref BfsDefaultTraits.
+  ///\param TR Traits class to set various data types used by the algorithm.
+  ///The default traits class is
+  ///\ref BfsDefaultTraits "BfsDefaultTraits<GR>".
+  ///See \ref BfsDefaultTraits for the documentation of
+  ///a Bfs traits class.
+  ///
+  ///\author Alpar Juttner
+
+#ifdef DOXYGEN
+  template <typename GR,
+	    typename TR>
+#else
+  template <typename GR=ListDigraph,
+	    typename TR=BfsDefaultTraits<GR> >
+#endif
+  class Bfs {
+  public:
+    /**
+     * \brief \ref Exception for uninitialized parameters.
+     *
+     * This error represents problems in the initialization
+     * of the parameters of the algorithms.
+     */
+    class UninitializedParameter : public lemon::UninitializedParameter {
+    public:
+      virtual const char* what() const throw() {
+	return "lemon::Bfs::UninitializedParameter";
+      }
+    };
+
+    typedef TR Traits;
+    ///The type of the underlying digraph.
+    typedef typename TR::Digraph Digraph;
+    
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    typedef typename TR::PredMap PredMap;
+    ///The type of the map indicating which nodes are reached.
+    typedef typename TR::ReachedMap ReachedMap;
+    ///The type of the map indicating which nodes are processed.
+    typedef typename TR::ProcessedMap ProcessedMap;
+    ///The type of the map that stores the dists of the nodes.
+    typedef typename TR::DistMap DistMap;
+  private:
+
+    typedef typename Digraph::Node Node;
+    typedef typename Digraph::NodeIt NodeIt;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::OutArcIt OutArcIt;
+
+    /// Pointer to the underlying digraph.
+    const Digraph *G;
+    ///Pointer to the map of predecessors arcs.
+    PredMap *_pred;
+    ///Indicates if \ref _pred is locally allocated (\c true) or not.
+    bool local_pred;
+    ///Pointer to the map of distances.
+    DistMap *_dist;
+    ///Indicates if \ref _dist is locally allocated (\c true) or not.
+    bool local_dist;
+    ///Pointer to the map of reached status of the nodes.
+    ReachedMap *_reached;
+    ///Indicates if \ref _reached is locally allocated (\c true) or not.
+    bool local_reached;
+    ///Pointer to the map of processed status of the nodes.
+    ProcessedMap *_processed;
+    ///Indicates if \ref _processed is locally allocated (\c true) or not.
+    bool local_processed;
+
+    std::vector<typename Digraph::Node> _queue;
+    int _queue_head,_queue_tail,_queue_next_dist;
+    int _curr_dist;
+
+    ///Creates the maps if necessary.
+    
+    ///\todo Better memory allocation (instead of new).
+    void create_maps() 
+    {
+      if(!_pred) {
+	local_pred = true;
+	_pred = Traits::createPredMap(*G);
+      }
+      if(!_dist) {
+	local_dist = true;
+	_dist = Traits::createDistMap(*G);
+      }
+      if(!_reached) {
+	local_reached = true;
+	_reached = Traits::createReachedMap(*G);
+      }
+      if(!_processed) {
+	local_processed = true;
+	_processed = Traits::createProcessedMap(*G);
+      }
+    }
+
+  protected:
+    
+    Bfs() {}
+    
+  public:
+ 
+    typedef Bfs Create;
+
+    ///\name Named template parameters
+
+    ///@{
+
+    template <class T>
+    struct DefPredMapTraits : public Traits {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///PredMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting PredMap type
+    ///
+    template <class T>
+    struct DefPredMap : public Bfs< Digraph, DefPredMapTraits<T> > { 
+      typedef Bfs< Digraph, DefPredMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefDistMapTraits : public Traits {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///DistMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting DistMap type
+    ///
+    template <class T>
+    struct DefDistMap : public Bfs< Digraph, DefDistMapTraits<T> > { 
+      typedef Bfs< Digraph, DefDistMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefReachedMapTraits : public Traits {
+      typedef T ReachedMap;
+      static ReachedMap *createReachedMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///ReachedMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting ReachedMap type
+    ///
+    template <class T>
+    struct DefReachedMap : public Bfs< Digraph, DefReachedMapTraits<T> > { 
+      typedef Bfs< Digraph, DefReachedMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefProcessedMapTraits : public Traits {
+      typedef T ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///ProcessedMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
+    ///
+    template <class T>
+    struct DefProcessedMap : public Bfs< Digraph, DefProcessedMapTraits<T> > {
+      typedef Bfs< Digraph, DefProcessedMapTraits<T> > Create;
+    };
+    
+    struct DefDigraphProcessedMapTraits : public Traits {
+      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &G) 
+      {
+	return new ProcessedMap(G);
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///
+    ///\ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///If you don't set it explicitly, it will be automatically allocated.
+    template <class T>
+    struct DefProcessedMapToBeDefaultMap :
+      public Bfs< Digraph, DefDigraphProcessedMapTraits> { 
+      typedef Bfs< Digraph, DefDigraphProcessedMapTraits> Create;
+    };
+    
+    ///@}
+
+  public:      
+    
+    ///Constructor.
+    
+    ///\param _G the digraph the algorithm will run on.
+    ///
+    Bfs(const Digraph& _G) :
+      G(&_G),
+      _pred(NULL), local_pred(false),
+      _dist(NULL), local_dist(false),
+      _reached(NULL), local_reached(false),
+      _processed(NULL), local_processed(false)
+    { }
+    
+    ///Destructor.
+    ~Bfs() 
+    {
+      if(local_pred) delete _pred;
+      if(local_dist) delete _dist;
+      if(local_reached) delete _reached;
+      if(local_processed) delete _processed;
+    }
+
+    ///Sets the map storing the predecessor arcs.
+
+    ///Sets the map storing the predecessor arcs.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destructor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Bfs &predMap(PredMap &m) 
+    {
+      if(local_pred) {
+	delete _pred;
+	local_pred=false;
+      }
+      _pred = &m;
+      return *this;
+    }
+
+    ///Sets the map indicating the reached nodes.
+
+    ///Sets the map indicating the reached nodes.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destructor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Bfs &reachedMap(ReachedMap &m) 
+    {
+      if(local_reached) {
+	delete _reached;
+	local_reached=false;
+      }
+      _reached = &m;
+      return *this;
+    }
+
+    ///Sets the map indicating the processed nodes.
+
+    ///Sets the map indicating the processed nodes.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destructor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Bfs &processedMap(ProcessedMap &m) 
+    {
+      if(local_processed) {
+	delete _processed;
+	local_processed=false;
+      }
+      _processed = &m;
+      return *this;
+    }
+
+    ///Sets the map storing the distances calculated by the algorithm.
+
+    ///Sets the map storing the distances calculated by the algorithm.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destructor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Bfs &distMap(DistMap &m) 
+    {
+      if(local_dist) {
+	delete _dist;
+	local_dist=false;
+      }
+      _dist = &m;
+      return *this;
+    }
+
+  public:
+    ///\name Execution control
+    ///The simplest way to execute the algorithm is to use
+    ///one of the member functions called \c run(...).
+    ///\n
+    ///If you need more control on the execution,
+    ///first you must call \ref init(), then you can add several source nodes
+    ///with \ref addSource().
+    ///Finally \ref start() will perform the actual path
+    ///computation.
+
+    ///@{
+
+    ///\brief Initializes the internal data structures.
+    ///
+    ///Initializes the internal data structures.
+    ///
+    void init()
+    {
+      create_maps();
+      _queue.resize(countNodes(*G));
+      _queue_head=_queue_tail=0;
+      _curr_dist=1;
+      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
+	_pred->set(u,INVALID);
+	_reached->set(u,false);
+	_processed->set(u,false);
+      }
+    }
+    
+    ///Adds a new source node.
+
+    ///Adds a new source node to the set of nodes to be processed.
+    ///
+    void addSource(Node s)
+    {
+      if(!(*_reached)[s])
+	{
+	  _reached->set(s,true);
+	  _pred->set(s,INVALID);
+	  _dist->set(s,0);
+	  _queue[_queue_head++]=s;
+	  _queue_next_dist=_queue_head;
+	}
+    }
+    
+    ///Processes the next node.
+
+    ///Processes the next node.
+    ///
+    ///\return The processed node.
+    ///
+    ///\warning The queue must not be empty!
+    Node processNextNode()
+    {
+      if(_queue_tail==_queue_next_dist) {
+	_curr_dist++;
+	_queue_next_dist=_queue_head;
+      }
+      Node n=_queue[_queue_tail++];
+      _processed->set(n,true);
+      Node m;
+      for(OutArcIt e(*G,n);e!=INVALID;++e)
+	if(!(*_reached)[m=G->target(e)]) {
+	  _queue[_queue_head++]=m;
+	  _reached->set(m,true);
+	  _pred->set(m,e);
+	  _dist->set(m,_curr_dist);
+	}
+      return n;
+    }
+
+    ///Processes the next node.
+
+    ///Processes the next node. And checks that the given target node
+    ///is reached. If the target node is reachable from the processed
+    ///node then the reached parameter will be set true. The reached
+    ///parameter should be initially false.
+    ///
+    ///\param target The target node.
+    ///\retval reach Indicates that the target node is reached.
+    ///\return The processed node.
+    ///
+    ///\warning The queue must not be empty!
+    Node processNextNode(Node target, bool& reach)
+    {
+      if(_queue_tail==_queue_next_dist) {
+	_curr_dist++;
+	_queue_next_dist=_queue_head;
+      }
+      Node n=_queue[_queue_tail++];
+      _processed->set(n,true);
+      Node m;
+      for(OutArcIt e(*G,n);e!=INVALID;++e)
+	if(!(*_reached)[m=G->target(e)]) {
+	  _queue[_queue_head++]=m;
+	  _reached->set(m,true);
+	  _pred->set(m,e);
+	  _dist->set(m,_curr_dist);
+          reach = reach || (target == m);
+	}
+      return n;
+    }
+
+    ///Processes the next node.
+
+    ///Processes the next node. And checks that at least one of
+    ///reached node has true value in the \c nm node map. If one node
+    ///with true value is reachable from the processed node then the
+    ///rnode parameter will be set to the first of such nodes.
+    ///
+    ///\param nm The node map of possible targets.
+    ///\retval rnode The reached target node.
+    ///\return The processed node.
+    ///
+    ///\warning The queue must not be empty!
+    template<class NM>
+    Node processNextNode(const NM& nm, Node& rnode)
+    {
+      if(_queue_tail==_queue_next_dist) {
+	_curr_dist++;
+	_queue_next_dist=_queue_head;
+      }
+      Node n=_queue[_queue_tail++];
+      _processed->set(n,true);
+      Node m;
+      for(OutArcIt e(*G,n);e!=INVALID;++e)
+	if(!(*_reached)[m=G->target(e)]) {
+	  _queue[_queue_head++]=m;
+	  _reached->set(m,true);
+	  _pred->set(m,e);
+	  _dist->set(m,_curr_dist);
+	  if (nm[m] && rnode == INVALID) rnode = m;
+	}
+      return n;
+    }
+      
+    ///Next node to be processed.
+
+    ///Next node to be processed.
+    ///
+    ///\return The next node to be processed or INVALID if the queue is
+    /// empty.
+    Node nextNode()
+    { 
+      return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
+    }
+ 
+    ///\brief Returns \c false if there are nodes
+    ///to be processed in the queue
+    ///
+    ///Returns \c false if there are nodes
+    ///to be processed in the queue
+    bool emptyQueue() { return _queue_tail==_queue_head; }
+    ///Returns the number of the nodes to be processed.
+    
+    ///Returns the number of the nodes to be processed in the queue.
+    int queueSize() { return _queue_head-_queue_tail; }
+    
+    ///Executes the algorithm.
+
+    ///Executes the algorithm.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///This method runs the %BFS algorithm from the root node(s)
+    ///in order to
+    ///compute the
+    ///shortest path to each node. The algorithm computes
+    ///- The shortest path tree.
+    ///- The distance of each node from the root(s).
+    void start()
+    {
+      while ( !emptyQueue() ) processNextNode();
+    }
+    
+    ///Executes the algorithm until \c dest is reached.
+
+    ///Executes the algorithm until \c dest is reached.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///This method runs the %BFS algorithm from the root node(s)
+    ///in order to compute the shortest path to \c dest.
+    ///The algorithm computes
+    ///- The shortest path to \c  dest.
+    ///- The distance of \c dest from the root(s).
+    void start(Node dest)
+    {
+      bool reach = false;
+      while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
+    }
+    
+    ///Executes the algorithm until a condition is met.
+
+    ///Executes the algorithm until a condition is met.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///\param nm must be a bool (or convertible) node map. The
+    ///algorithm will stop when it reaches a node \c v with
+    /// <tt>nm[v]</tt> true.
+    ///
+    ///\return The reached node \c v with <tt>nm[v]</tt> true or
+    ///\c INVALID if no such node was found.
+    template<class NM>
+    Node start(const NM &nm)
+    {
+      Node rnode = INVALID;
+      while ( !emptyQueue() && rnode == INVALID ) {
+	processNextNode(nm, rnode);
+      }
+      return rnode;
+    }
+    
+    ///Runs %BFS algorithm from node \c s.
+    
+    ///This method runs the %BFS algorithm from a root node \c s
+    ///in order to
+    ///compute the
+    ///shortest path to each node. The algorithm computes
+    ///- The shortest path tree.
+    ///- The distance of each node from the root.
+    ///
+    ///\note b.run(s) is just a shortcut of the following code.
+    ///\code
+    ///  b.init();
+    ///  b.addSource(s);
+    ///  b.start();
+    ///\endcode
+    void run(Node s) {
+      init();
+      addSource(s);
+      start();
+    }
+    
+    ///Finds the shortest path between \c s and \c t.
+    
+    ///Finds the shortest path between \c s and \c t.
+    ///
+    ///\return The length of the shortest s---t path if there exists one,
+    ///0 otherwise.
+    ///\note Apart from the return value, b.run(s) is
+    ///just a shortcut of the following code.
+    ///\code
+    ///  b.init();
+    ///  b.addSource(s);
+    ///  b.start(t);
+    ///\endcode
+    int run(Node s,Node t) {
+      init();
+      addSource(s);
+      start(t);
+      return reached(t) ? _curr_dist : 0;
+    }
+    
+    ///@}
+
+    ///\name Query Functions
+    ///The result of the %BFS algorithm can be obtained using these
+    ///functions.\n
+    ///Before the use of these functions,
+    ///either run() or start() must be calleb.
+    
+    ///@{
+
+    typedef PredMapPath<Digraph, PredMap> Path;
+
+    ///Gives back the shortest path.
+    
+    ///Gives back the shortest path.
+    ///\pre The \c t should be reachable from the source.
+    Path path(Node t) 
+    {
+      return Path(*G, *_pred, t);
+    }
+
+    ///The distance of a node from the root(s).
+
+    ///Returns the distance of a node from the root(s).
+    ///\pre \ref run() must be called before using this function.
+    ///\warning If node \c v in unreachable from the root(s) the return value
+    ///of this function is undefined.
+    int dist(Node v) const { return (*_dist)[v]; }
+
+    ///Returns the 'previous arc' of the shortest path tree.
+
+    ///For a node \c v it returns the 'previous arc'
+    ///of the shortest path tree,
+    ///i.e. it returns the last arc of a shortest path from the root(s) to \c
+    ///v. It is \ref INVALID
+    ///if \c v is unreachable from the root(s) or \c v is a root. The
+    ///shortest path tree used here is equal to the shortest path tree used in
+    ///\ref predNode().
+    ///\pre Either \ref run() or \ref start() must be called before using
+    ///this function.
+    Arc predArc(Node v) const { return (*_pred)[v];}
+
+    ///Returns the 'previous node' of the shortest path tree.
+
+    ///For a node \c v it returns the 'previous node'
+    ///of the shortest path tree,
+    ///i.e. it returns the last but one node from a shortest path from the
+    ///root(a) to \c /v.
+    ///It is INVALID if \c v is unreachable from the root(s) or
+    ///if \c v itself a root.
+    ///The shortest path tree used here is equal to the shortest path
+    ///tree used in \ref predArc().
+    ///\pre Either \ref run() or \ref start() must be called before
+    ///using this function.
+    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
+				  G->source((*_pred)[v]); }
+    
+    ///Returns a reference to the NodeMap of distances.
+
+    ///Returns a reference to the NodeMap of distances.
+    ///\pre Either \ref run() or \ref init() must
+    ///be called before using this function.
+    const DistMap &distMap() const { return *_dist;}
+ 
+    ///Returns a reference to the shortest path tree map.
+
+    ///Returns a reference to the NodeMap of the arcs of the
+    ///shortest path tree.
+    ///\pre Either \ref run() or \ref init()
+    ///must be called before using this function.
+    const PredMap &predMap() const { return *_pred;}
+ 
+    ///Checks if a node is reachable from the root.
+
+    ///Returns \c true if \c v is reachable from the root.
+    ///\warning The source nodes are indicated as unreached.
+    ///\pre Either \ref run() or \ref start()
+    ///must be called before using this function.
+    ///
+    bool reached(Node v) { return (*_reached)[v]; }
+    
+    ///@}
+  };
+
+  ///Default traits class of Bfs function.
+
+  ///Default traits class of Bfs function.
+  ///\param GR Digraph type.
+  template<class GR>
+  struct BfsWizardDefaultTraits
+  {
+    ///The digraph type the algorithm runs on. 
+    typedef GR Digraph;
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the shortest paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap<typename Digraph::Node,typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \ref PredMap. 
+    ///\param g is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient to initialize
+#ifdef DOXYGEN
+    static PredMap *createPredMap(const GR &g) 
+#else
+    static PredMap *createPredMap(const GR &) 
+#endif
+    {
+      return new PredMap();
+    }
+
+    ///The type of the map that indicates which nodes are processed.
+ 
+    ///The type of the map that indicates which nodes are processed.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \ref ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \ref ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that indicates which nodes are reached.
+ 
+    ///The type of the map that indicates which nodes are reached.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef typename Digraph::template NodeMap<bool> ReachedMap;
+    ///Instantiates a ReachedMap.
+ 
+    ///This function instantiates a \ref ReachedMap. 
+    ///\param G is the digraph, to which
+    ///we would like to define the \ref ReachedMap.
+    static ReachedMap *createReachedMap(const GR &G)
+    {
+      return new ReachedMap(G);
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap<typename Digraph::Node,int> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param g is the digraph, to which we would like to define the \ref DistMap
+#ifdef DOXYGEN
+    static DistMap *createDistMap(const GR &g)
+#else
+    static DistMap *createDistMap(const GR &)
+#endif
+    {
+      return new DistMap();
+    }
+  };
+  
+  /// Default traits used by \ref BfsWizard
+
+  /// To make it easier to use Bfs algorithm
+  ///we have created a wizard class.
+  /// This \ref BfsWizard class needs default traits,
+  ///as well as the \ref Bfs class.
+  /// The \ref BfsWizardBase is a class to be the default traits of the
+  /// \ref BfsWizard class.
+  template<class GR>
+  class BfsWizardBase : public BfsWizardDefaultTraits<GR>
+  {
+
+    typedef BfsWizardDefaultTraits<GR> Base;
+  protected:
+    /// Type of the nodes in the digraph.
+    typedef typename Base::Digraph::Node Node;
+
+    /// Pointer to the underlying digraph.
+    void *_g;
+    ///Pointer to the map of reached nodes.
+    void *_reached;
+    ///Pointer to the map of processed nodes.
+    void *_processed;
+    ///Pointer to the map of predecessors arcs.
+    void *_pred;
+    ///Pointer to the map of distances.
+    void *_dist;
+    ///Pointer to the source node.
+    Node _source;
+    
+    public:
+    /// Constructor.
+    
+    /// This constructor does not require parameters, therefore it initiates
+    /// all of the attributes to default values (0, INVALID).
+    BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
+			   _dist(0), _source(INVALID) {}
+
+    /// Constructor.
+    
+    /// This constructor requires some parameters,
+    /// listed in the parameters list.
+    /// Others are initiated to 0.
+    /// \param g is the initial value of  \ref _g
+    /// \param s is the initial value of  \ref _source
+    BfsWizardBase(const GR &g, Node s=INVALID) :
+      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))), 
+      _reached(0), _processed(0), _pred(0), _dist(0), _source(s) {}
+
+  };
+  
+  /// A class to make the usage of Bfs algorithm easier
+
+  /// This class is created to make it easier to use Bfs algorithm.
+  /// It uses the functions and features of the plain \ref Bfs,
+  /// but it is much simpler to use it.
+  ///
+  /// Simplicity means that the way to change the types defined
+  /// in the traits class is based on functions that returns the new class
+  /// and not on templatable built-in classes.
+  /// When using the plain \ref Bfs
+  /// the new class with the modified type comes from
+  /// the original class by using the ::
+  /// operator. In the case of \ref BfsWizard only
+  /// a function have to be called and it will
+  /// return the needed class.
+  ///
+  /// It does not have own \ref run method. When its \ref run method is called
+  /// it initiates a plain \ref Bfs class, and calls the \ref Bfs::run
+  /// method of it.
+  template<class TR>
+  class BfsWizard : public TR
+  {
+    typedef TR Base;
+
+    ///The type of the underlying digraph.
+    typedef typename TR::Digraph Digraph;
+    //\e
+    typedef typename Digraph::Node Node;
+    //\e
+    typedef typename Digraph::NodeIt NodeIt;
+    //\e
+    typedef typename Digraph::Arc Arc;
+    //\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///\brief The type of the map that stores
+    ///the reached nodes
+    typedef typename TR::ReachedMap ReachedMap;
+    ///\brief The type of the map that stores
+    ///the processed nodes
+    typedef typename TR::ProcessedMap ProcessedMap;
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    typedef typename TR::PredMap PredMap;
+    ///The type of the map that stores the dists of the nodes.
+    typedef typename TR::DistMap DistMap;
+
+  public:
+    /// Constructor.
+    BfsWizard() : TR() {}
+
+    /// Constructor that requires parameters.
+
+    /// Constructor that requires parameters.
+    /// These parameters will be the default values for the traits class.
+    BfsWizard(const Digraph &g, Node s=INVALID) :
+      TR(g,s) {}
+
+    ///Copy constructor
+    BfsWizard(const TR &b) : TR(b) {}
+
+    ~BfsWizard() {}
+
+    ///Runs Bfs algorithm from a given node.
+    
+    ///Runs Bfs algorithm from a given node.
+    ///The node can be given by the \ref source function.
+    void run()
+    {
+      if(Base::_source==INVALID) throw UninitializedParameter();
+      Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
+      if(Base::_reached)
+	alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
+      if(Base::_processed) 
+        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
+      if(Base::_pred) 
+        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
+      if(Base::_dist) 
+        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
+      alg.run(Base::_source);
+    }
+
+    ///Runs Bfs algorithm from the given node.
+
+    ///Runs Bfs algorithm from the given node.
+    ///\param s is the given source.
+    void run(Node s)
+    {
+      Base::_source=s;
+      run();
+    }
+
+    template<class T>
+    struct DefPredMapBase : public Base {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &) { return 0; };
+      DefPredMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting PredMap
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting PredMap
+    ///
+    template<class T>
+    BfsWizard<DefPredMapBase<T> > predMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return BfsWizard<DefPredMapBase<T> >(*this);
+    }
+    
+ 
+    template<class T>
+    struct DefReachedMapBase : public Base {
+      typedef T ReachedMap;
+      static ReachedMap *createReachedMap(const Digraph &) { return 0; };
+      DefReachedMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting ReachedMap
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting ReachedMap
+    ///
+    template<class T>
+    BfsWizard<DefReachedMapBase<T> > reachedMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return BfsWizard<DefReachedMapBase<T> >(*this);
+    }
+    
+
+    template<class T>
+    struct DefProcessedMapBase : public Base {
+      typedef T ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
+      DefProcessedMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting ProcessedMap
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting ProcessedMap
+    ///
+    template<class T>
+    BfsWizard<DefProcessedMapBase<T> > processedMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return BfsWizard<DefProcessedMapBase<T> >(*this);
+    }
+    
+   
+    template<class T>
+    struct DefDistMapBase : public Base {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) { return 0; };
+      DefDistMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    template<class T>
+    BfsWizard<DefDistMapBase<T> > distMap(const T &t) 
+    {
+      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return BfsWizard<DefDistMapBase<T> >(*this);
+    }
+    
+    /// Sets the source node, from which the Bfs algorithm runs.
+
+    /// Sets the source node, from which the Bfs algorithm runs.
+    /// \param s is the source node.
+    BfsWizard<TR> &source(Node s) 
+    {
+      Base::_source=s;
+      return *this;
+    }
+    
+  };
+  
+  ///Function type interface for Bfs algorithm.
+
+  /// \ingroup search
+  ///Function type interface for Bfs algorithm.
+  ///
+  ///This function also has several
+  ///\ref named-templ-func-param "named parameters",
+  ///they are declared as the members of class \ref BfsWizard.
+  ///The following
+  ///example shows how to use these parameters.
+  ///\code
+  ///  bfs(g,source).predMap(preds).run();
+  ///\endcode
+  ///\warning Don't forget to put the \ref BfsWizard::run() "run()"
+  ///to the end of the parameter list.
+  ///\sa BfsWizard
+  ///\sa Bfs
+  template<class GR>
+  BfsWizard<BfsWizardBase<GR> >
+  bfs(const GR &g,typename GR::Node s=INVALID)
+  {
+    return BfsWizard<BfsWizardBase<GR> >(g,s);
+  }
+
+#ifdef DOXYGEN
+  /// \brief Visitor class for bfs.
+  ///  
+  /// This class defines the interface of the BfsVisit events, and
+  /// it could be the base of a real Visitor class.
+  template <typename _Digraph>
+  struct BfsVisitor {
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::Node Node;
+    /// \brief Called when the arc reach a node.
+    /// 
+    /// It is called when the bfs find an arc which target is not
+    /// reached yet.
+    void discover(const Arc& arc) {}
+    /// \brief Called when the node reached first time.
+    /// 
+    /// It is Called when the node reached first time.
+    void reach(const Node& node) {}
+    /// \brief Called when the arc examined but target of the arc 
+    /// already discovered.
+    /// 
+    /// It called when the arc examined but the target of the arc 
+    /// already discovered.
+    void examine(const Arc& arc) {}
+    /// \brief Called for the source node of the bfs.
+    /// 
+    /// It is called for the source node of the bfs.
+    void start(const Node& node) {}
+    /// \brief Called when the node processed.
+    /// 
+    /// It is Called when the node processed.
+    void process(const Node& node) {}
+  };
+#else
+  template <typename _Digraph>
+  struct BfsVisitor {
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::Node Node;
+    void discover(const Arc&) {}
+    void reach(const Node&) {}
+    void examine(const Arc&) {}
+    void start(const Node&) {}
+    void process(const Node&) {}
+
+    template <typename _Visitor>
+    struct Constraints {
+      void constraints() {
+	Arc arc;
+	Node node;
+	visitor.discover(arc);
+	visitor.reach(node);
+	visitor.examine(arc);
+	visitor.start(node);
+        visitor.process(node);
+      }
+      _Visitor& visitor;
+    };
+  };
+#endif
+
+  /// \brief Default traits class of BfsVisit class.
+  ///
+  /// Default traits class of BfsVisit class.
+  /// \param _Digraph Digraph type.
+  template<class _Digraph>
+  struct BfsVisitDefaultTraits {
+
+    /// \brief The digraph type the algorithm runs on. 
+    typedef _Digraph Digraph;
+
+    /// \brief The type of the map that indicates which nodes are reached.
+    /// 
+    /// The type of the map that indicates which nodes are reached.
+    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    /// \todo named parameter to set this type, function to read and write.
+    typedef typename Digraph::template NodeMap<bool> ReachedMap;
+
+    /// \brief Instantiates a ReachedMap.
+    ///
+    /// This function instantiates a \ref ReachedMap. 
+    /// \param digraph is the digraph, to which
+    /// we would like to define the \ref ReachedMap.
+    static ReachedMap *createReachedMap(const Digraph &digraph) {
+      return new ReachedMap(digraph);
+    }
+
+  };
+
+  /// \ingroup search
+  ///  
+  /// \brief %BFS Visit algorithm class.
+  ///  
+  /// This class provides an efficient implementation of the %BFS algorithm
+  /// with visitor interface.
+  ///
+  /// The %BfsVisit class provides an alternative interface to the Bfs
+  /// class. It works with callback mechanism, the BfsVisit object calls
+  /// on every bfs event the \c Visitor class member functions. 
+  ///
+  /// \param _Digraph The digraph type the algorithm runs on. The default value is
+  /// \ref ListDigraph. The value of _Digraph is not used directly by Bfs, it
+  /// is only passed to \ref BfsDefaultTraits.
+  /// \param _Visitor The Visitor object for the algorithm. The 
+  /// \ref BfsVisitor "BfsVisitor<_Digraph>" is an empty Visitor which
+  /// does not observe the Bfs events. If you want to observe the bfs
+  /// events you should implement your own Visitor class.
+  /// \param _Traits Traits class to set various data types used by the 
+  /// algorithm. The default traits class is
+  /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Digraph>".
+  /// See \ref BfsVisitDefaultTraits for the documentation of
+  /// a Bfs visit traits class.
+  ///
+  /// \author Jacint Szabo, Alpar Juttner and Balazs Dezso
+#ifdef DOXYGEN
+  template <typename _Digraph, typename _Visitor, typename _Traits>
+#else
+  template <typename _Digraph = ListDigraph,
+	    typename _Visitor = BfsVisitor<_Digraph>,
+	    typename _Traits = BfsDefaultTraits<_Digraph> >
+#endif
+  class BfsVisit {
+  public:
+    
+    /// \brief \ref Exception for uninitialized parameters.
+    ///
+    /// This error represents problems in the initialization
+    /// of the parameters of the algorithms.
+    class UninitializedParameter : public lemon::UninitializedParameter {
+    public:
+      virtual const char* what() const throw() 
+      {
+	return "lemon::BfsVisit::UninitializedParameter";
+      }
+    };
+
+    typedef _Traits Traits;
+
+    typedef typename Traits::Digraph Digraph;
+
+    typedef _Visitor Visitor;
+
+    ///The type of the map indicating which nodes are reached.
+    typedef typename Traits::ReachedMap ReachedMap;
+
+  private:
+
+    typedef typename Digraph::Node Node;
+    typedef typename Digraph::NodeIt NodeIt;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::OutArcIt OutArcIt;
+
+    /// Pointer to the underlying digraph.
+    const Digraph *_digraph;
+    /// Pointer to the visitor object.
+    Visitor *_visitor;
+    ///Pointer to the map of reached status of the nodes.
+    ReachedMap *_reached;
+    ///Indicates if \ref _reached is locally allocated (\c true) or not.
+    bool local_reached;
+
+    std::vector<typename Digraph::Node> _list;
+    int _list_front, _list_back;
+
+    /// \brief Creates the maps if necessary.
+    ///
+    /// Creates the maps if necessary.
+    void create_maps() {
+      if(!_reached) {
+	local_reached = true;
+	_reached = Traits::createReachedMap(*_digraph);
+      }
+    }
+
+  protected:
+
+    BfsVisit() {}
+    
+  public:
+
+    typedef BfsVisit Create;
+
+    /// \name Named template parameters
+
+    ///@{
+    template <class T>
+    struct DefReachedMapTraits : public Traits {
+      typedef T ReachedMap;
+      static ReachedMap *createReachedMap(const Digraph &digraph) {
+	throw UninitializedParameter();
+      }
+    };
+    /// \brief \ref named-templ-param "Named parameter" for setting 
+    /// ReachedMap type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting ReachedMap type
+    template <class T>
+    struct DefReachedMap : public BfsVisit< Digraph, Visitor,
+					    DefReachedMapTraits<T> > {
+      typedef BfsVisit< Digraph, Visitor, DefReachedMapTraits<T> > Create;
+    };
+    ///@}
+
+  public:      
+    
+    /// \brief Constructor.
+    ///
+    /// Constructor.
+    ///
+    /// \param digraph the digraph the algorithm will run on.
+    /// \param visitor The visitor of the algorithm.
+    ///
+    BfsVisit(const Digraph& digraph, Visitor& visitor) 
+      : _digraph(&digraph), _visitor(&visitor),
+	_reached(0), local_reached(false) {}
+    
+    /// \brief Destructor.
+    ///
+    /// Destructor.
+    ~BfsVisit() {
+      if(local_reached) delete _reached;
+    }
+
+    /// \brief Sets the map indicating if a node is reached.
+    ///
+    /// Sets the map indicating if a node is reached.
+    /// If you don't use this function before calling \ref run(),
+    /// it will allocate one. The destuctor deallocates this
+    /// automatically allocated map, of course.
+    /// \return <tt> (*this) </tt>
+    BfsVisit &reachedMap(ReachedMap &m) {
+      if(local_reached) {
+	delete _reached;
+	local_reached = false;
+      }
+      _reached = &m;
+      return *this;
+    }
+
+  public:
+    /// \name Execution control
+    /// The simplest way to execute the algorithm is to use
+    /// one of the member functions called \c run(...).
+    /// \n
+    /// If you need more control on the execution,
+    /// first you must call \ref init(), then you can adda source node
+    /// with \ref addSource().
+    /// Finally \ref start() will perform the actual path
+    /// computation.
+
+    /// @{
+    /// \brief Initializes the internal data structures.
+    ///
+    /// Initializes the internal data structures.
+    ///
+    void init() {
+      create_maps();
+      _list.resize(countNodes(*_digraph));
+      _list_front = _list_back = -1;
+      for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
+	_reached->set(u, false);
+      }
+    }
+    
+    /// \brief Adds a new source node.
+    ///
+    /// Adds a new source node to the set of nodes to be processed.
+    void addSource(Node s) {
+      if(!(*_reached)[s]) {
+	  _reached->set(s,true);
+	  _visitor->start(s);
+	  _visitor->reach(s);
+          _list[++_list_back] = s;
+	}
+    }
+    
+    /// \brief Processes the next node.
+    ///
+    /// Processes the next node.
+    ///
+    /// \return The processed node.
+    ///
+    /// \pre The queue must not be empty!
+    Node processNextNode() { 
+      Node n = _list[++_list_front];
+      _visitor->process(n);
+      Arc e;
+      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
+        Node m = _digraph->target(e);
+        if (!(*_reached)[m]) {
+          _visitor->discover(e);
+          _visitor->reach(m);
+          _reached->set(m, true);
+          _list[++_list_back] = m;
+        } else {
+          _visitor->examine(e);
+        }
+      }
+      return n;
+    }
+
+    /// \brief Processes the next node.
+    ///
+    /// Processes the next node. And checks that the given target node
+    /// is reached. If the target node is reachable from the processed
+    /// node then the reached parameter will be set true. The reached
+    /// parameter should be initially false.
+    ///
+    /// \param target The target node.
+    /// \retval reach Indicates that the target node is reached.
+    /// \return The processed node.
+    ///
+    /// \warning The queue must not be empty!
+    Node processNextNode(Node target, bool& reach) {
+      Node n = _list[++_list_front];
+      _visitor->process(n);
+      Arc e;
+      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
+        Node m = _digraph->target(e);
+        if (!(*_reached)[m]) {
+          _visitor->discover(e);
+          _visitor->reach(m);
+          _reached->set(m, true);
+          _list[++_list_back] = m;
+          reach = reach || (target == m);
+        } else {
+          _visitor->examine(e);
+        }
+      }
+      return n;
+    }
+
+    /// \brief Processes the next node.
+    ///
+    /// Processes the next node. And checks that at least one of
+    /// reached node has true value in the \c nm node map. If one node
+    /// with true value is reachable from the processed node then the
+    /// rnode parameter will be set to the first of such nodes.
+    ///
+    /// \param nm The node map of possible targets.
+    /// \retval rnode The reached target node.
+    /// \return The processed node.
+    ///
+    /// \warning The queue must not be empty!
+    template <typename NM>
+    Node processNextNode(const NM& nm, Node& rnode) {
+      Node n = _list[++_list_front];
+      _visitor->process(n);
+      Arc e;
+      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
+        Node m = _digraph->target(e);
+        if (!(*_reached)[m]) {
+          _visitor->discover(e);
+          _visitor->reach(m);
+          _reached->set(m, true);
+          _list[++_list_back] = m;
+          if (nm[m] && rnode == INVALID) rnode = m;
+        } else {
+          _visitor->examine(e);
+        }
+      }
+      return n;
+    }
+
+    /// \brief Next node to be processed.
+    ///
+    /// Next node to be processed.
+    ///
+    /// \return The next node to be processed or INVALID if the stack is
+    /// empty.
+    Node nextNode() { 
+      return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
+    }
+
+    /// \brief Returns \c false if there are nodes
+    /// to be processed in the queue
+    ///
+    /// Returns \c false if there are nodes
+    /// to be processed in the queue
+    bool emptyQueue() { return _list_front == _list_back; }
+
+    /// \brief Returns the number of the nodes to be processed.
+    ///
+    /// Returns the number of the nodes to be processed in the queue.
+    int queueSize() { return _list_back - _list_front; }
+    
+    /// \brief Executes the algorithm.
+    ///
+    /// Executes the algorithm.
+    ///
+    /// \pre init() must be called and at least one node should be added
+    /// with addSource() before using this function.
+    void start() {
+      while ( !emptyQueue() ) processNextNode();
+    }
+    
+    /// \brief Executes the algorithm until \c dest is reached.
+    ///
+    /// Executes the algorithm until \c dest is reached.
+    ///
+    /// \pre init() must be called and at least one node should be added
+    /// with addSource() before using this function.
+    void start(Node dest) {
+      bool reach = false;
+      while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
+    }
+    
+    /// \brief Executes the algorithm until a condition is met.
+    ///
+    /// Executes the algorithm until a condition is met.
+    ///
+    /// \pre init() must be called and at least one node should be added
+    /// with addSource() before using this function.
+    ///
+    ///\param nm must be a bool (or convertible) node map. The
+    ///algorithm will stop when it reaches a node \c v with
+    /// <tt>nm[v]</tt> true.
+    ///
+    ///\return The reached node \c v with <tt>nm[v]</tt> true or
+    ///\c INVALID if no such node was found.
+    template <typename NM>
+    Node start(const NM &nm) {
+      Node rnode = INVALID;
+      while ( !emptyQueue() && rnode == INVALID ) {
+	processNextNode(nm, rnode);
+      }
+      return rnode;
+    }
+
+    /// \brief Runs %BFSVisit algorithm from node \c s.
+    ///
+    /// This method runs the %BFS algorithm from a root node \c s.
+    /// \note b.run(s) is just a shortcut of the following code.
+    ///\code
+    ///   b.init();
+    ///   b.addSource(s);
+    ///   b.start();
+    ///\endcode
+    void run(Node s) {
+      init();
+      addSource(s);
+      start();
+    }
+
+    /// \brief Runs %BFSVisit algorithm to visit all nodes in the digraph.
+    ///    
+    /// This method runs the %BFS algorithm in order to
+    /// compute the %BFS path to each node. The algorithm computes
+    /// - The %BFS tree.
+    /// - The distance of each node from the root in the %BFS tree.
+    ///
+    ///\note b.run() is just a shortcut of the following code.
+    ///\code
+    ///  b.init();
+    ///  for (NodeIt it(digraph); it != INVALID; ++it) {
+    ///    if (!b.reached(it)) {
+    ///      b.addSource(it);
+    ///      b.start();
+    ///    }
+    ///  }
+    ///\endcode
+    void run() {
+      init();
+      for (NodeIt it(*_digraph); it != INVALID; ++it) {
+        if (!reached(it)) {
+          addSource(it);
+          start();
+        }
+      }
+    }
+    ///@}
+
+    /// \name Query Functions
+    /// The result of the %BFS algorithm can be obtained using these
+    /// functions.\n
+    /// Before the use of these functions,
+    /// either run() or start() must be called.
+    ///@{
+
+    /// \brief Checks if a node is reachable from the root.
+    ///
+    /// Returns \c true if \c v is reachable from the root(s).
+    /// \warning The source nodes are inditated as unreachable.
+    /// \pre Either \ref run() or \ref start()
+    /// must be called before using this function.
+    ///
+    bool reached(Node v) { return (*_reached)[v]; }
+    ///@}
+  };
+
+} //END OF NAMESPACE LEMON
+
+#endif
+
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/bin_heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/bin_heap.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,346 @@
+/* -*- 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_BIN_HEAP_H
+#define LEMON_BIN_HEAP_H
+
+///\ingroup auxdat
+///\file
+///\brief Binary Heap implementation.
+
+#include <vector>
+#include <utility>
+#include <functional>
+
+namespace lemon {
+
+  ///\ingroup auxdat
+  ///
+  ///\brief A Binary Heap implementation.
+  ///
+  ///This class implements the \e binary \e heap data structure. A \e heap
+  ///is a data structure for storing items with specified values called \e
+  ///priorities in such a way that finding the item with minimum priority is
+  ///efficient. \c Compare specifies the ordering of the priorities. In a heap
+  ///one can change the priority of an item, add or erase an item, etc.
+  ///
+  ///\param _Prio Type of the priority of the items.
+  ///\param _ItemIntMap A read and writable Item int map, used internally
+  ///to handle the cross references.
+  ///\param _Compare A class for the ordering of the priorities. The
+  ///default is \c std::less<_Prio>.
+  ///
+  ///\sa FibHeap
+  ///\sa Dijkstra
+  template <typename _Prio, typename _ItemIntMap,
+	    typename _Compare = std::less<_Prio> >
+  class BinHeap {
+
+  public:
+    ///\e
+    typedef _ItemIntMap ItemIntMap;
+    ///\e
+    typedef _Prio Prio;
+    ///\e
+    typedef typename ItemIntMap::Key Item;
+    ///\e
+    typedef std::pair<Item,Prio> Pair;
+    ///\e
+    typedef _Compare Compare;
+
+    /// \brief Type to represent the items states.
+    ///
+    /// Each Item element have a state associated to it. It may be "in heap",
+    /// "pre heap" or "post heap". The latter two are indifferent from the
+    /// heap's point of view, but may be useful to the user.
+    ///
+    /// The ItemIntMap \e should be initialized in such way that it maps
+    /// PRE_HEAP (-1) to any element to be put in the heap...
+    enum State {
+      IN_HEAP = 0,
+      PRE_HEAP = -1,
+      POST_HEAP = -2
+    };
+
+  private:
+    std::vector<Pair> data;
+    Compare comp;
+    ItemIntMap &iim;
+
+  public:
+    /// \brief The constructor.
+    ///
+    /// The constructor.
+    /// \param _iim should be given to the constructor, since it is used
+    /// internally to handle the cross references. The value of the map
+    /// should be PRE_HEAP (-1) for each element.
+    explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
+    
+    /// \brief The constructor.
+    ///
+    /// The constructor.
+    /// \param _iim should be given to the constructor, since it is used
+    /// internally to handle the cross references. The value of the map
+    /// should be PRE_HEAP (-1) for each element.
+    ///
+    /// \param _comp The comparator function object.
+    BinHeap(ItemIntMap &_iim, const Compare &_comp) 
+      : iim(_iim), comp(_comp) {}
+
+
+    /// The number of items stored in the heap.
+    ///
+    /// \brief Returns the number of items stored in the heap.
+    int size() const { return data.size(); }
+    
+    /// \brief Checks if the heap stores no items.
+    ///
+    /// Returns \c true if and only if the heap stores no items.
+    bool empty() const { return data.empty(); }
+
+    /// \brief Make empty this heap.
+    /// 
+    /// Make empty this heap. It does not change the cross reference map.
+    /// If you want to reuse what is not surely empty you should first clear
+    /// the heap and after that you should set the cross reference map for
+    /// each item to \c PRE_HEAP.
+    void clear() { 
+      data.clear(); 
+    }
+
+  private:
+    static int parent(int i) { return (i-1)/2; }
+
+    static int second_child(int i) { return 2*i+2; }
+    bool less(const Pair &p1, const Pair &p2) const {
+      return comp(p1.second, p2.second);
+    }
+
+    int bubble_up(int hole, Pair p) {
+      int par = parent(hole);
+      while( hole>0 && less(p,data[par]) ) {
+	move(data[par],hole);
+	hole = par;
+	par = parent(hole);
+      }
+      move(p, hole);
+      return hole;
+    }
+
+    int bubble_down(int hole, Pair p, int length) {
+      int child = second_child(hole);
+      while(child < length) {
+	if( less(data[child-1], data[child]) ) {
+	  --child;
+	}
+	if( !less(data[child], p) )
+	  goto ok;
+	move(data[child], hole);
+	hole = child;
+	child = second_child(hole);
+      }
+      child--;
+      if( child<length && less(data[child], p) ) {
+	move(data[child], hole);
+	hole=child;
+      }
+    ok:
+      move(p, hole);
+      return hole;
+    }
+
+    void move(const Pair &p, int i) {
+      data[i] = p;
+      iim.set(p.first, i);
+    }
+
+  public:
+    /// \brief Insert a pair of item and priority into the heap.
+    ///
+    /// Adds \c p.first to the heap with priority \c p.second.
+    /// \param p The pair to insert.
+    void push(const Pair &p) {
+      int n = data.size();
+      data.resize(n+1);
+      bubble_up(n, p);
+    }
+
+    /// \brief Insert an item into the heap with the given heap.
+    ///    
+    /// Adds \c i to the heap with priority \c p. 
+    /// \param i The item to insert.
+    /// \param p The priority of the item.
+    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
+
+    /// \brief Returns the item with minimum priority relative to \c Compare.
+    ///
+    /// This method returns the item with minimum priority relative to \c
+    /// Compare.  
+    /// \pre The heap must be nonempty.  
+    Item top() const {
+      return data[0].first;
+    }
+
+    /// \brief Returns the minimum priority relative to \c Compare.
+    ///
+    /// It returns the minimum priority relative to \c Compare.
+    /// \pre The heap must be nonempty.
+    Prio prio() const {
+      return data[0].second;
+    }
+
+    /// \brief Deletes the item with minimum priority relative to \c Compare.
+    ///
+    /// This method deletes the item with minimum priority relative to \c
+    /// Compare from the heap.  
+    /// \pre The heap must be non-empty.  
+    void pop() {
+      int n = data.size()-1;
+      iim.set(data[0].first, POST_HEAP);
+      if (n > 0) {
+	bubble_down(0, data[n], n);
+      }
+      data.pop_back();
+    }
+
+    /// \brief Deletes \c i from the heap.
+    ///
+    /// This method deletes item \c i from the heap.
+    /// \param i The item to erase.
+    /// \pre The item should be in the heap.
+    void erase(const Item &i) {
+      int h = iim[i];
+      int n = data.size()-1;
+      iim.set(data[h].first, POST_HEAP);
+      if( h < n ) {
+	if ( bubble_up(h, data[n]) == h) {
+	  bubble_down(h, data[n], n);
+	}
+      }
+      data.pop_back();
+    }
+
+    
+    /// \brief Returns the priority of \c i.
+    ///
+    /// This function returns the priority of item \c i.  
+    /// \pre \c i must be in the heap.
+    /// \param i The item.
+    Prio operator[](const Item &i) const {
+      int idx = iim[i];
+      return data[idx].second;
+    }
+
+    /// \brief \c i gets to the heap with priority \c p independently 
+    /// if \c i was already there.
+    ///
+    /// This method calls \ref push(\c i, \c p) if \c i is not stored
+    /// in the heap and sets the priority of \c i to \c p otherwise.
+    /// \param i The item.
+    /// \param p The priority.
+    void set(const Item &i, const Prio &p) {
+      int idx = iim[i];
+      if( idx < 0 ) {
+	push(i,p);
+      }
+      else if( comp(p, data[idx].second) ) {
+	bubble_up(idx, Pair(i,p));
+      }
+      else {
+	bubble_down(idx, Pair(i,p), data.size());
+      }
+    }
+
+    /// \brief Decreases the priority of \c i to \c p.
+    ///
+    /// This method decreases the priority of item \c i to \c p.
+    /// \pre \c i must be stored in the heap with priority at least \c
+    /// p relative to \c Compare.
+    /// \param i The item.
+    /// \param p The priority.
+    void decrease(const Item &i, const Prio &p) {
+      int idx = iim[i];
+      bubble_up(idx, Pair(i,p));
+    }
+    
+    /// \brief Increases the priority of \c i to \c p.
+    ///
+    /// This method sets the priority of item \c i to \c p. 
+    /// \pre \c i must be stored in the heap with priority at most \c
+    /// p relative to \c Compare.
+    /// \param i The item.
+    /// \param p The priority.
+    void increase(const Item &i, const Prio &p) {
+      int idx = iim[i];
+      bubble_down(idx, Pair(i,p), data.size());
+    }
+
+    /// \brief Returns if \c item is in, has already been in, or has 
+    /// never been in the heap.
+    ///
+    /// This method returns PRE_HEAP if \c item has never been in the
+    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
+    /// otherwise. In the latter case it is possible that \c item will
+    /// get back to the heap again.
+    /// \param i The item.
+    State state(const Item &i) const {
+      int s = iim[i];
+      if( s>=0 )
+	s=0;
+      return State(s);
+    }
+
+    /// \brief Sets the state of the \c item in the heap.
+    ///
+    /// Sets the state of the \c item in the heap. It can be used to
+    /// manually clear the heap when it is important to achive the
+    /// better time complexity.
+    /// \param i The item.
+    /// \param st The state. It should not be \c IN_HEAP. 
+    void state(const Item& i, State st) {
+      switch (st) {
+      case POST_HEAP:
+      case PRE_HEAP:
+        if (state(i) == IN_HEAP) {
+          erase(i);
+        }
+        iim[i] = st;
+        break;
+      case IN_HEAP:
+        break;
+      }
+    }
+
+    /// \brief Replaces an item in the heap.
+    ///
+    /// The \c i item is replaced with \c j item. The \c i item should
+    /// be in the heap, while the \c j should be out of the heap. The
+    /// \c i item will out of the heap and \c j will be in the heap
+    /// with the same prioriority as prevoiusly the \c i item.
+    void replace(const Item& i, const Item& j) {
+      int idx = iim[i];
+      iim.set(i, iim[j]);
+      iim.set(j, idx);
+      data[idx].first = j;
+    }
+
+  }; // class BinHeap
+  
+} // namespace lemon
+
+#endif // LEMON_BIN_HEAP_H
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/bits/path_dump.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/bits/path_dump.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,174 @@
+/* -*- 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_BITS_PRED_MAP_PATH_H
+#define LEMON_BITS_PRED_MAP_PATH_H
+
+namespace lemon {
+
+  template <typename _Digraph, typename _PredMap>
+  class PredMapPath {
+  public:
+    typedef True RevPathTag;
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+    typedef _PredMap PredMap;
+
+    PredMapPath(const Digraph& _digraph, const PredMap& _predMap,
+                typename Digraph::Node _target)
+      : digraph(_digraph), predMap(_predMap), target(_target) {}
+
+    int length() const {
+      int len = 0;
+      typename Digraph::Node node = target;
+      typename Digraph::Arc arc;
+      while ((arc = predMap[node]) != INVALID) {
+        node = digraph.source(arc);
+        ++len;
+      }
+      return len;
+    }
+
+    bool empty() const {
+      return predMap[target] != INVALID;
+    }
+
+    class RevArcIt {
+    public:
+      RevArcIt() {}
+      RevArcIt(Invalid) : path(0), current(INVALID) {}
+      RevArcIt(const PredMapPath& _path) 
+        : path(&_path), current(_path.target) {
+        if (path->predMap[current] == INVALID) current = INVALID;
+      }
+
+      operator const typename Digraph::Arc() const {
+        return path->predMap[current];
+      }
+
+      RevArcIt& operator++() {
+        current = path->digraph.source(path->predMap[current]);
+        if (path->predMap[current] == INVALID) current = INVALID;
+        return *this;
+      }
+
+      bool operator==(const RevArcIt& e) const { 
+        return current == e.current; 
+      }
+
+      bool operator!=(const RevArcIt& e) const {
+        return current != e.current; 
+      }
+
+      bool operator<(const RevArcIt& e) const { 
+        return current < e.current; 
+      }
+      
+    private:
+      const PredMapPath* path;
+      typename Digraph::Node current;
+    };
+
+  private:
+    const Digraph& digraph;
+    const PredMap& predMap;
+    typename Digraph::Node target;
+  };
+
+
+  template <typename _Digraph, typename _PredMatrixMap>
+  class PredMatrixMapPath {
+  public:
+    typedef True RevPathTag;
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+    typedef _PredMatrixMap PredMatrixMap;
+
+    PredMatrixMapPath(const Digraph& _digraph, 
+                      const PredMatrixMap& _predMatrixMap,
+                      typename Digraph::Node _source, 
+                      typename Digraph::Node _target)
+      : digraph(_digraph), predMatrixMap(_predMatrixMap), 
+        source(_source), target(_target) {}
+
+    int length() const {
+      int len = 0;
+      typename Digraph::Node node = target;
+      typename Digraph::Arc arc;
+      while ((arc = predMatrixMap(source, node)) != INVALID) {
+        node = digraph.source(arc);
+        ++len;
+      }
+      return len;
+    }
+
+    bool empty() const {
+      return source != target;
+    }
+
+    class RevArcIt {
+    public:
+      RevArcIt() {}
+      RevArcIt(Invalid) : path(0), current(INVALID) {}
+      RevArcIt(const PredMatrixMapPath& _path) 
+        : path(&_path), current(_path.target) {
+        if (path->predMatrixMap(path->source, current) == INVALID) 
+          current = INVALID;
+      }
+
+      operator const typename Digraph::Arc() const {
+        return path->predMatrixMap(path->source, current);
+      }
+
+      RevArcIt& operator++() {
+        current = 
+          path->digraph.source(path->predMatrixMap(path->source, current));
+        if (path->predMatrixMap(path->source, current) == INVALID) 
+          current = INVALID;
+        return *this;
+      }
+
+      bool operator==(const RevArcIt& e) const { 
+        return current == e.current; 
+      }
+
+      bool operator!=(const RevArcIt& e) const {
+        return current != e.current; 
+      }
+
+      bool operator<(const RevArcIt& e) const { 
+        return current < e.current; 
+      }
+      
+    private:
+      const PredMatrixMapPath* path;
+      typename Digraph::Node current;
+    };
+
+  private:
+    const Digraph& digraph;
+    const PredMatrixMap& predMatrixMap;
+    typename Digraph::Node source;
+    typename Digraph::Node target;
+  };
+
+}
+
+#endif
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/concepts/heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/concepts/heap.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,226 @@
+/* -*- 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.
+ *
+ */
+
+///\ingroup concept
+///\file
+///\brief Classes for representing heaps.
+///
+
+#ifndef LEMON_CONCEPT_HEAP_H
+#define LEMON_CONCEPT_HEAP_H
+
+#include <lemon/bits/invalid.h>
+
+namespace lemon {
+  namespace concepts {
+    /// \addtogroup concept
+    /// @{
+
+
+    /// \brief A concept structure describes the main interface of heaps.
+    ///
+    /// A concept structure describes the main interface of heaps.
+    ///
+    template <typename Prio, typename ItemIntMap>
+    class Heap {
+    public:
+
+      ///\brief Type of the items stored in the heap.
+      typedef typename ItemIntMap::Key  Item;
+  
+
+      /// \brief Type to represent the items states.
+      ///
+      /// Each Item element have a state associated to it. It may be "in heap",
+      /// "pre heap" or "post heap". The later two are indifferent from the
+      /// heap's point of view, but may be useful to the user.
+      ///
+      /// The ItemIntMap _should_ be initialized in such way, that it maps
+      /// PRE_HEAP (-1) to any element to be put in the heap...
+      enum State {
+	IN_HEAP = 0,
+	PRE_HEAP = -1,
+	POST_HEAP = -2
+      };
+      
+      /// \brief The constructor.
+      ///
+      /// The constructor.
+      /// \param _iim should be given to the constructor, since it is used
+      /// internally to handle the cross references. The value of the map
+      /// should be PRE_HEAP (-1) for each element.
+      explicit Heap(ItemIntMap &_iim) {}
+
+      /// \brief The number of items stored in the heap.
+      ///
+      /// Returns the number of items stored in the heap.
+      int size() const { return 0; }
+
+      /// \brief Checks if the heap stores no items.
+      ///
+      /// Returns \c true if and only if the heap stores no items.
+      bool empty() const { return false; }
+
+      /// \brief Makes empty this heap.
+      ///
+      /// Makes this heap empty.
+      void clear();
+
+      /// \brief Insert an item into the heap with the given heap.
+      ///    
+      /// Adds \c i to the heap with priority \c p. 
+      /// \param i The item to insert.
+      /// \param p The priority of the item.
+      void push(const Item &i, const Prio &p) {}
+
+      /// \brief Returns the item with minimum priority.
+      ///
+      /// This method returns the item with minimum priority.  
+      /// \pre The heap must be nonempty.  
+      Item top() const {}
+
+      /// \brief Returns the minimum priority.
+      ///
+      /// It returns the minimum priority.
+      /// \pre The heap must be nonempty.
+      Prio prio() const {}
+
+      /// \brief Deletes the item with minimum priority.
+      ///
+      /// This method deletes the item with minimum priority.
+      /// \pre The heap must be non-empty.  
+      void pop() {}
+
+      /// \brief Deletes \c i from the heap.
+      ///
+      /// This method deletes item \c i from the heap, if \c i was
+      /// already stored in the heap.
+      /// \param i The item to erase. 
+      void erase(const Item &i) {}
+
+      /// \brief Returns the priority of \c i.
+      ///
+      /// This function returns the priority of item \c i.  
+      /// \pre \c i must be in the heap.
+      /// \param i The item.
+      Prio operator[](const Item &i) const {}
+
+      /// \brief \c i gets to the heap with priority \c p independently 
+      /// if \c i was already there.
+      ///
+      /// This method calls \ref push(\c i, \c p) if \c i is not stored
+      /// in the heap and sets the priority of \c i to \c p otherwise.
+      /// It may throw an \e UnderFlowPriorityException. 
+      /// \param i The item.
+      /// \param p The priority.
+      void set(const Item &i, const Prio &p) {}
+      
+      /// \brief Decreases the priority of \c i to \c p.
+      ///
+      /// This method decreases the priority of item \c i to \c p.
+      /// \pre \c i must be stored in the heap with priority at least \c p.
+      /// \param i The item.
+      /// \param p The priority.
+      void decrease(const Item &i, const Prio &p) {}
+
+      /// \brief Increases the priority of \c i to \c p.
+      ///
+      /// This method sets the priority of item \c i to \c p. 
+      /// \pre \c i must be stored in the heap with priority at most \c
+      /// p relative to \c Compare.
+      /// \param i The item.
+      /// \param p The priority.
+      void increase(const Item &i, const Prio &p) {}
+
+      /// \brief Returns if \c item is in, has already been in, or has 
+      /// never been in the heap.
+      ///
+      /// This method returns PRE_HEAP if \c item has never been in the
+      /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
+      /// otherwise. In the latter case it is possible that \c item will
+      /// get back to the heap again.
+      /// \param i The item.
+      State state(const Item &i) const {}
+
+      /// \brief Sets the state of the \c item in the heap.
+      ///
+      /// Sets the state of the \c item in the heap. It can be used to
+      /// manually clear the heap when it is important to achive the
+      /// better time complexity.
+      /// \param i The item.
+      /// \param st The state. It should not be \c IN_HEAP. 
+      void state(const Item& i, State st) {}
+
+
+      template <typename _Heap>
+      struct Constraints {
+      public:
+    
+	void constraints() {
+	  Item item;
+	  Prio prio;
+
+	  item=Item();
+	  prio=Prio();
+
+	  ignore_unused_variable_warning(item);
+	  ignore_unused_variable_warning(prio);
+
+	  typedef typename _Heap::State State;
+	  State state;
+
+	  ignore_unused_variable_warning(state);
+      
+	  _Heap heap1 = _Heap(map);
+
+	  ignore_unused_variable_warning(heap1);
+      
+	  heap.push(item, prio);
+
+	  prio = heap.prio();
+	  item = heap.top();
+
+	  heap.pop();
+
+	  heap.set(item, prio);
+	  heap.decrease(item, prio);
+	  heap.increase(item, prio);
+	  prio = heap[item];
+
+	  heap.erase(item);
+
+	  state = heap.state(item);
+
+	  state = _Heap::PRE_HEAP;
+	  state = _Heap::IN_HEAP;
+	  state = _Heap::POST_HEAP;
+
+	  heap.clear();
+	}
+    
+	_Heap& heap;
+	ItemIntMap& map;
+
+	Constraints() : heap(0), map(0) {}
+      };
+    };
+
+    /// @}
+  } // namespace lemon
+}
+#endif // LEMON_CONCEPT_PATH_H
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/concepts/path.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/concepts/path.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,307 @@
+/* -*- 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.
+ *
+ */
+
+///\ingroup concept
+///\file
+///\brief Classes for representing paths in digraphs.
+///
+///\todo Iterators have obsolete style
+
+#ifndef LEMON_CONCEPT_PATH_H
+#define LEMON_CONCEPT_PATH_H
+
+#include <lemon/bits/invalid.h>
+#include <lemon/bits/utility.h>
+#include <lemon/concept_check.h>
+
+namespace lemon {
+  namespace concepts {
+
+    /// \addtogroup concept
+    /// @{
+
+    /// \brief A skeleton structure for representing directed paths in
+    /// a digraph.
+    ///
+    /// A skeleton structure for representing directed paths in a
+    /// digraph.  
+    /// \param _Digraph The digraph type in which the path is.
+    ///
+    /// In a sense, the path can be treated as a list of arcs. The
+    /// lemon path type stores just this list. As a consequence it
+    /// cannot enumerate the nodes in the path and the zero length
+    /// paths cannot store the source.
+    ///
+    template <typename _Digraph>
+    class Path {
+    public:
+
+      /// Type of the underlying digraph.
+      typedef _Digraph Digraph;
+      /// Arc type of the underlying digraph.
+      typedef typename Digraph::Arc Arc;
+
+      class ArcIt;
+
+      /// \brief Default constructor
+      Path() {}
+
+      /// \brief Template constructor
+      template <typename CPath>
+      Path(const CPath& cpath) {}
+
+      /// \brief Template assigment
+      template <typename CPath>
+      Path& operator=(const CPath& cpath) {}
+
+      /// Length of the path ie. the number of arcs in the path.
+      int length() const { return 0;}
+
+      /// Returns whether the path is empty.
+      bool empty() const { return true;}
+
+      /// Resets the path to an empty path.
+      void clear() {}
+
+      /// \brief Lemon style iterator for path arcs
+      ///
+      /// This class is used to iterate on the arcs of the paths.
+      class ArcIt {
+      public:
+	/// Default constructor
+	ArcIt() {}
+	/// Invalid constructor
+	ArcIt(Invalid) {}
+	/// Constructor for first arc
+	ArcIt(const Path &) {}
+
+        /// Conversion to Arc
+	operator Arc() const { return INVALID; }
+
+	/// Next arc
+	ArcIt& operator++() {return *this;}
+
+	/// Comparison operator
+	bool operator==(const ArcIt&) const {return true;}
+	/// Comparison operator
+	bool operator!=(const ArcIt&) const {return true;}
+ 	/// Comparison operator
+ 	bool operator<(const ArcIt&) const {return false;}
+
+      };
+
+      template <typename _Path>
+      struct Constraints {
+        void constraints() {
+          Path<Digraph> pc;
+          _Path p, pp(pc);
+          int l = p.length();
+          int e = p.empty();
+          p.clear();
+
+          p = pc;
+
+          typename _Path::ArcIt id, ii(INVALID), i(p);
+
+          ++i;
+          typename Digraph::Arc ed = i;
+
+          e = (i == ii);
+          e = (i != ii);
+          e = (i < ii);
+
+          ignore_unused_variable_warning(l);
+          ignore_unused_variable_warning(pp);
+          ignore_unused_variable_warning(e);
+          ignore_unused_variable_warning(id);
+          ignore_unused_variable_warning(ii);
+          ignore_unused_variable_warning(ed);
+        }
+      };
+
+    };
+
+    namespace _path_bits {
+      
+      template <typename _Digraph, typename _Path, typename RevPathTag = void>
+      struct PathDumperConstraints {
+        void constraints() {
+          int l = p.length();
+          int e = p.empty();
+
+          typename _Path::ArcIt id, i(p);
+
+          ++i;
+          typename _Digraph::Arc ed = i;
+
+          e = (i == INVALID);
+          e = (i != INVALID);
+
+          ignore_unused_variable_warning(l);
+          ignore_unused_variable_warning(e);
+          ignore_unused_variable_warning(id);
+          ignore_unused_variable_warning(ed);
+        }
+        _Path& p;
+      };
+
+      template <typename _Digraph, typename _Path>
+      struct PathDumperConstraints<
+        _Digraph, _Path, 
+        typename enable_if<typename _Path::RevPathTag, void>::type
+      > {
+        void constraints() {
+          int l = p.length();
+          int e = p.empty();
+
+          typename _Path::RevArcIt id, i(p);
+
+          ++i;
+          typename _Digraph::Arc ed = i;
+
+          e = (i == INVALID);
+          e = (i != INVALID);
+
+          ignore_unused_variable_warning(l);
+          ignore_unused_variable_warning(e);
+          ignore_unused_variable_warning(id);
+          ignore_unused_variable_warning(ed);
+        }
+        _Path& p;
+      };
+    
+    }
+
+
+    /// \brief A skeleton structure for path dumpers.
+    ///
+    /// A skeleton structure for path dumpers. The path dumpers are
+    /// the generalization of the paths. The path dumpers can
+    /// enumerate the arcs of the path wheter in forward or in
+    /// backward order.  In most time these classes are not used
+    /// directly rather it used to assign a dumped class to a real
+    /// path type.
+    ///
+    /// The main purpose of this concept is that the shortest path
+    /// algorithms can enumerate easily the arcs in reverse order.
+    /// If we would like to give back a real path from these
+    /// algorithms then we should create a temporarly path object. In
+    /// Lemon such algorithms gives back a path dumper what can
+    /// assigned to a real path and the dumpers can be implemented as
+    /// an adaptor class to the predecessor map.
+
+    /// \param _Digraph  The digraph type in which the path is.
+    ///
+    /// The paths can be constructed from any path type by a
+    /// template constructor or a template assignment operator.
+    /// 
+    template <typename _Digraph>
+    class PathDumper {
+    public:
+
+      /// Type of the underlying digraph.
+      typedef _Digraph Digraph;
+      /// Arc type of the underlying digraph.
+      typedef typename Digraph::Arc Arc;
+
+      /// Length of the path ie. the number of arcs in the path.
+      int length() const { return 0;}
+
+      /// Returns whether the path is empty.
+      bool empty() const { return true;}
+
+      /// \brief Forward or reverse dumping
+      ///
+      /// If the RevPathTag is defined and true then reverse dumping
+      /// is provided in the path dumper. In this case instead of the
+      /// ArcIt the RevArcIt iterator should be implemented in the
+      /// dumper.
+      typedef False RevPathTag;
+
+      /// \brief Lemon style iterator for path arcs
+      ///
+      /// This class is used to iterate on the arcs of the paths.
+      class ArcIt {
+      public:
+	/// Default constructor
+	ArcIt() {}
+	/// Invalid constructor
+	ArcIt(Invalid) {}
+	/// Constructor for first arc
+	ArcIt(const PathDumper&) {}
+
+        /// Conversion to Arc
+	operator Arc() const { return INVALID; }
+
+	/// Next arc
+	ArcIt& operator++() {return *this;}
+
+	/// Comparison operator
+	bool operator==(const ArcIt&) const {return true;}
+	/// Comparison operator
+	bool operator!=(const ArcIt&) const {return true;}
+ 	/// Comparison operator
+ 	bool operator<(const ArcIt&) const {return false;}
+
+      };
+
+      /// \brief Lemon style iterator for path arcs
+      ///
+      /// This class is used to iterate on the arcs of the paths in
+      /// reverse direction.
+      class RevArcIt {
+      public:
+	/// Default constructor
+	RevArcIt() {}
+	/// Invalid constructor
+	RevArcIt(Invalid) {}
+	/// Constructor for first arc
+	RevArcIt(const PathDumper &) {}
+
+        /// Conversion to Arc
+	operator Arc() const { return INVALID; }
+
+	/// Next arc
+	RevArcIt& operator++() {return *this;}
+
+	/// Comparison operator
+	bool operator==(const RevArcIt&) const {return true;}
+	/// Comparison operator
+	bool operator!=(const RevArcIt&) const {return true;}
+ 	/// Comparison operator
+ 	bool operator<(const RevArcIt&) const {return false;}
+
+      };
+
+      template <typename _Path>
+      struct Constraints {
+        void constraints() {
+          function_requires<_path_bits::
+            PathDumperConstraints<Digraph, _Path> >();
+        }
+      };
+
+    };
+
+
+    ///@}
+  }
+
+} // namespace lemon
+
+#endif // LEMON_CONCEPT_PATH_H
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/dfs.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/dfs.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,1543 @@
+/* -*- 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_DFS_H
+#define LEMON_DFS_H
+
+///\ingroup search
+///\file
+///\brief Dfs algorithm.
+
+#include <lemon/list_graph.h>
+#include <lemon/graph_utils.h>
+#include <lemon/bits/path_dump.h>
+#include <lemon/bits/invalid.h>
+#include <lemon/error.h>
+#include <lemon/maps.h>
+
+#include <lemon/concept_check.h>
+
+namespace lemon {
+
+  
+  ///Default traits class of Dfs class.
+
+  ///Default traits class of Dfs class.
+  ///\param GR Digraph type.
+  template<class GR>
+  struct DfsDefaultTraits
+  {
+    ///The digraph type the algorithm runs on. 
+    typedef GR Digraph;
+    ///\brief The type of the map that stores the last
+    ///arcs of the %DFS paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the %DFS paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \ref PredMap. 
+    ///\param G is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient to initialize
+    static PredMap *createPredMap(const GR &G) 
+    {
+      return new PredMap(G);
+    }
+
+    ///The type of the map that indicates which nodes are processed.
+ 
+    ///The type of the map that indicates which nodes are processed.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \ref ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \ref ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that indicates which nodes are reached.
+ 
+    ///The type of the map that indicates which nodes are reached.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef typename Digraph::template NodeMap<bool> ReachedMap;
+    ///Instantiates a ReachedMap.
+ 
+    ///This function instantiates a \ref ReachedMap. 
+    ///\param G is the digraph, to which
+    ///we would like to define the \ref ReachedMap.
+    static ReachedMap *createReachedMap(const GR &G)
+    {
+      return new ReachedMap(G);
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<int> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param G is the digraph, to which we would like to define the \ref DistMap
+    static DistMap *createDistMap(const GR &G)
+    {
+      return new DistMap(G);
+    }
+  };
+  
+  ///%DFS algorithm class.
+  
+  ///\ingroup search
+  ///This class provides an efficient implementation of the %DFS algorithm.
+  ///
+  ///\param GR The digraph type the algorithm runs on. The default value is
+  ///\ref ListDigraph. The value of GR is not used directly by Dfs, it
+  ///is only passed to \ref DfsDefaultTraits.
+  ///\param TR Traits class to set various data types used by the algorithm.
+  ///The default traits class is
+  ///\ref DfsDefaultTraits "DfsDefaultTraits<GR>".
+  ///See \ref DfsDefaultTraits for the documentation of
+  ///a Dfs traits class.
+  ///
+  ///\author Jacint Szabo and Alpar Juttner
+#ifdef DOXYGEN
+  template <typename GR,
+	    typename TR>
+#else
+  template <typename GR=ListDigraph,
+	    typename TR=DfsDefaultTraits<GR> >
+#endif
+  class Dfs {
+  public:
+    /**
+     * \brief \ref Exception for uninitialized parameters.
+     *
+     * This error represents problems in the initialization
+     * of the parameters of the algorithms.
+     */
+    class UninitializedParameter : public lemon::UninitializedParameter {
+    public:
+      virtual const char* what() const throw() {
+	return "lemon::Dfs::UninitializedParameter";
+      }
+    };
+
+    typedef TR Traits;
+    ///The type of the underlying digraph.
+    typedef typename TR::Digraph Digraph;
+    ///\e
+    typedef typename Digraph::Node Node;
+    ///\e
+    typedef typename Digraph::NodeIt NodeIt;
+    ///\e
+    typedef typename Digraph::Arc Arc;
+    ///\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///\brief The type of the map that stores the last
+    ///arcs of the %DFS paths.
+    typedef typename TR::PredMap PredMap;
+    ///The type of the map indicating which nodes are reached.
+    typedef typename TR::ReachedMap ReachedMap;
+    ///The type of the map indicating which nodes are processed.
+    typedef typename TR::ProcessedMap ProcessedMap;
+    ///The type of the map that stores the dists of the nodes.
+    typedef typename TR::DistMap DistMap;
+  private:
+    /// Pointer to the underlying digraph.
+    const Digraph *G;
+    ///Pointer to the map of predecessors arcs.
+    PredMap *_pred;
+    ///Indicates if \ref _pred is locally allocated (\c true) or not.
+    bool local_pred;
+    ///Pointer to the map of distances.
+    DistMap *_dist;
+    ///Indicates if \ref _dist is locally allocated (\c true) or not.
+    bool local_dist;
+    ///Pointer to the map of reached status of the nodes.
+    ReachedMap *_reached;
+    ///Indicates if \ref _reached is locally allocated (\c true) or not.
+    bool local_reached;
+    ///Pointer to the map of processed status of the nodes.
+    ProcessedMap *_processed;
+    ///Indicates if \ref _processed is locally allocated (\c true) or not.
+    bool local_processed;
+
+    std::vector<typename Digraph::OutArcIt> _stack;
+    int _stack_head;
+
+    ///Creates the maps if necessary.
+    
+    ///\todo Better memory allocation (instead of new).
+    void create_maps() 
+    {
+      if(!_pred) {
+	local_pred = true;
+	_pred = Traits::createPredMap(*G);
+      }
+      if(!_dist) {
+	local_dist = true;
+	_dist = Traits::createDistMap(*G);
+      }
+      if(!_reached) {
+	local_reached = true;
+	_reached = Traits::createReachedMap(*G);
+      }
+      if(!_processed) {
+	local_processed = true;
+	_processed = Traits::createProcessedMap(*G);
+      }
+    }
+
+  protected:
+
+    Dfs() {}
+    
+  public:
+
+    typedef Dfs Create;
+
+    ///\name Named template parameters
+
+    ///@{
+
+    template <class T>
+    struct DefPredMapTraits : public Traits {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &G) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///PredMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting PredMap type
+    ///
+    template <class T>
+    struct DefPredMap : public Dfs<Digraph, DefPredMapTraits<T> > {
+      typedef Dfs<Digraph, DefPredMapTraits<T> > Create;
+    };
+    
+    
+    template <class T>
+    struct DefDistMapTraits : public Traits {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///DistMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting DistMap
+    ///type
+    template <class T>
+    struct DefDistMap {
+      typedef Dfs<Digraph, DefDistMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefReachedMapTraits : public Traits {
+      typedef T ReachedMap;
+      static ReachedMap *createReachedMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///ReachedMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting ReachedMap type
+    ///
+    template <class T>
+    struct DefReachedMap : public Dfs< Digraph, DefReachedMapTraits<T> > {
+      typedef Dfs< Digraph, DefReachedMapTraits<T> > Create;
+    };
+
+    template <class T>
+    struct DefProcessedMapTraits : public Traits {
+      typedef T ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///ProcessedMap type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
+    ///
+    template <class T>
+    struct DefProcessedMap : public Dfs< Digraph, DefProcessedMapTraits<T> > { 
+      typedef Dfs< Digraph, DefProcessedMapTraits<T> > Create;
+    };
+    
+    struct DefDigraphProcessedMapTraits : public Traits {
+      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &G) 
+      {
+	return new ProcessedMap(G);
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///
+    ///\ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///If you don't set it explicitely, it will be automatically allocated.
+    template <class T>
+    class DefProcessedMapToBeDefaultMap :
+      public Dfs< Digraph, DefDigraphProcessedMapTraits> { 
+      typedef Dfs< Digraph, DefDigraphProcessedMapTraits> Create;
+    };
+    
+    ///@}
+
+  public:      
+    
+    ///Constructor.
+    
+    ///\param _G the digraph the algorithm will run on.
+    ///
+    Dfs(const Digraph& _G) :
+      G(&_G),
+      _pred(NULL), local_pred(false),
+      _dist(NULL), local_dist(false),
+      _reached(NULL), local_reached(false),
+      _processed(NULL), local_processed(false)
+    { }
+    
+    ///Destructor.
+    ~Dfs() 
+    {
+      if(local_pred) delete _pred;
+      if(local_dist) delete _dist;
+      if(local_reached) delete _reached;
+      if(local_processed) delete _processed;
+    }
+
+    ///Sets the map storing the predecessor arcs.
+
+    ///Sets the map storing the predecessor arcs.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Dfs &predMap(PredMap &m) 
+    {
+      if(local_pred) {
+	delete _pred;
+	local_pred=false;
+      }
+      _pred = &m;
+      return *this;
+    }
+
+    ///Sets the map storing the distances calculated by the algorithm.
+
+    ///Sets the map storing the distances calculated by the algorithm.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Dfs &distMap(DistMap &m) 
+    {
+      if(local_dist) {
+	delete _dist;
+	local_dist=false;
+      }
+      _dist = &m;
+      return *this;
+    }
+
+    ///Sets the map indicating if a node is reached.
+
+    ///Sets the map indicating if a node is reached.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Dfs &reachedMap(ReachedMap &m) 
+    {
+      if(local_reached) {
+	delete _reached;
+	local_reached=false;
+      }
+      _reached = &m;
+      return *this;
+    }
+
+    ///Sets the map indicating if a node is processed.
+
+    ///Sets the map indicating if a node is processed.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Dfs &processedMap(ProcessedMap &m) 
+    {
+      if(local_processed) {
+	delete _processed;
+	local_processed=false;
+      }
+      _processed = &m;
+      return *this;
+    }
+
+  public:
+    ///\name Execution control
+    ///The simplest way to execute the algorithm is to use
+    ///one of the member functions called \c run(...).
+    ///\n
+    ///If you need more control on the execution,
+    ///first you must call \ref init(), then you can add a source node
+    ///with \ref addSource().
+    ///Finally \ref start() will perform the actual path
+    ///computation.
+
+    ///@{
+
+    ///Initializes the internal data structures.
+
+    ///Initializes the internal data structures.
+    ///
+    void init()
+    {
+      create_maps();
+      _stack.resize(countNodes(*G));
+      _stack_head=-1;
+      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
+	_pred->set(u,INVALID);
+	// _predNode->set(u,INVALID);
+	_reached->set(u,false);
+	_processed->set(u,false);
+      }
+    }
+    
+    ///Adds a new source node.
+
+    ///Adds a new source node to the set of nodes to be processed.
+    ///
+    ///\warning dists are wrong (or at least strange)
+    ///in case of multiple sources.
+    void addSource(Node s)
+    {
+      if(!(*_reached)[s])
+	{
+	  _reached->set(s,true);
+	  _pred->set(s,INVALID);
+	  OutArcIt e(*G,s);
+	  if(e!=INVALID) {
+	    _stack[++_stack_head]=e;
+	    _dist->set(s,_stack_head);
+	  }
+	  else {
+	    _processed->set(s,true);
+	    _dist->set(s,0);
+	  }
+	}
+    }
+    
+    ///Processes the next arc.
+
+    ///Processes the next arc.
+    ///
+    ///\return The processed arc.
+    ///
+    ///\pre The stack must not be empty!
+    Arc processNextArc()
+    { 
+      Node m;
+      Arc e=_stack[_stack_head];
+      if(!(*_reached)[m=G->target(e)]) {
+	_pred->set(m,e);
+	_reached->set(m,true);
+	++_stack_head;
+	_stack[_stack_head] = OutArcIt(*G, m);
+	_dist->set(m,_stack_head);
+      }
+      else {
+	m=G->source(e);
+	++_stack[_stack_head];
+      }
+      while(_stack_head>=0 && _stack[_stack_head]==INVALID) {
+	_processed->set(m,true);
+	--_stack_head;
+	if(_stack_head>=0) {
+	  m=G->source(_stack[_stack_head]);
+	  ++_stack[_stack_head];
+	}
+      }
+      return e;
+    }
+    ///Next arc to be processed.
+
+    ///Next arc to be processed.
+    ///
+    ///\return The next arc to be processed or INVALID if the stack is
+    /// empty.
+    OutArcIt nextArc()
+    { 
+      return _stack_head>=0?_stack[_stack_head]:INVALID;
+    }
+
+    ///\brief Returns \c false if there are nodes
+    ///to be processed in the queue
+    ///
+    ///Returns \c false if there are nodes
+    ///to be processed in the queue
+    bool emptyQueue() { return _stack_head<0; }
+    ///Returns the number of the nodes to be processed.
+    
+    ///Returns the number of the nodes to be processed in the queue.
+    int queueSize() { return _stack_head+1; }
+    
+    ///Executes the algorithm.
+
+    ///Executes the algorithm.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///This method runs the %DFS algorithm from the root node(s)
+    ///in order to
+    ///compute the
+    ///%DFS path to each node. The algorithm computes
+    ///- The %DFS tree.
+    ///- The distance of each node from the root(s) in the %DFS tree.
+    ///
+    void start()
+    {
+      while ( !emptyQueue() ) processNextArc();
+    }
+    
+    ///Executes the algorithm until \c dest is reached.
+
+    ///Executes the algorithm until \c dest is reached.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///This method runs the %DFS algorithm from the root node(s)
+    ///in order to
+    ///compute the
+    ///%DFS path to \c dest. The algorithm computes
+    ///- The %DFS path to \c  dest.
+    ///- The distance of \c dest from the root(s) in the %DFS tree.
+    ///
+    void start(Node dest)
+    {
+      while ( !emptyQueue() && G->target(_stack[_stack_head])!=dest ) 
+	processNextArc();
+    }
+    
+    ///Executes the algorithm until a condition is met.
+
+    ///Executes the algorithm until a condition is met.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///\param em must be a bool (or convertible) arc map. The algorithm
+    ///will stop when it reaches an arc \c e with <tt>em[e]</tt> true.
+    ///
+    ///\return The reached arc \c e with <tt>em[e]</tt> true or
+    ///\c INVALID if no such arc was found.
+    ///
+    ///\warning Contrary to \ref Bfs and \ref Dijkstra, \c em is an arc map,
+    ///not a node map.
+    template<class EM>
+    Arc start(const EM &em)
+    {
+      while ( !emptyQueue() && !em[_stack[_stack_head]] )
+        processNextArc();
+      return emptyQueue() ? INVALID : _stack[_stack_head];
+    }
+
+    ///Runs %DFS algorithm to visit all nodes in the digraph.
+    
+    ///This method runs the %DFS algorithm in order to
+    ///compute the
+    ///%DFS path to each node. The algorithm computes
+    ///- The %DFS tree.
+    ///- The distance of each node from the root in the %DFS tree.
+    ///
+    ///\note d.run() is just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  for (NodeIt it(digraph); it != INVALID; ++it) {
+    ///    if (!d.reached(it)) {
+    ///      d.addSource(it);
+    ///      d.start();
+    ///    }
+    ///  }
+    ///\endcode
+    void run() {
+      init();
+      for (NodeIt it(*G); it != INVALID; ++it) {
+        if (!reached(it)) {
+          addSource(it);
+          start();
+        }
+      }
+    }
+
+    ///Runs %DFS algorithm from node \c s.
+    
+    ///This method runs the %DFS algorithm from a root node \c s
+    ///in order to
+    ///compute the
+    ///%DFS path to each node. The algorithm computes
+    ///- The %DFS tree.
+    ///- The distance of each node from the root in the %DFS tree.
+    ///
+    ///\note d.run(s) is just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  d.addSource(s);
+    ///  d.start();
+    ///\endcode
+    void run(Node s) {
+      init();
+      addSource(s);
+      start();
+    }
+    
+    ///Finds the %DFS path between \c s and \c t.
+    
+    ///Finds the %DFS path between \c s and \c t.
+    ///
+    ///\return The length of the %DFS s---t path if there exists one,
+    ///0 otherwise.
+    ///\note Apart from the return value, d.run(s,t) is
+    ///just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  d.addSource(s);
+    ///  d.start(t);
+    ///\endcode
+    int run(Node s,Node t) {
+      init();
+      addSource(s);
+      start(t);
+      return reached(t)?_stack_head+1:0;
+    }
+    
+    ///@}
+
+    ///\name Query Functions
+    ///The result of the %DFS algorithm can be obtained using these
+    ///functions.\n
+    ///Before the use of these functions,
+    ///either run() or start() must be called.
+    
+    ///@{
+
+    typedef PredMapPath<Digraph, PredMap> Path;
+
+    ///Gives back the shortest path.
+    
+    ///Gives back the shortest path.
+    ///\pre The \c t should be reachable from the source.
+    Path path(Node t) 
+    {
+      return Path(*G, *_pred, t);
+    }
+
+    ///The distance of a node from the root(s).
+
+    ///Returns the distance of a node from the root(s).
+    ///\pre \ref run() must be called before using this function.
+    ///\warning If node \c v is unreachable from the root(s) then the return 
+    ///value of this funcion is undefined.
+    int dist(Node v) const { return (*_dist)[v]; }
+
+    ///Returns the 'previous arc' of the %DFS tree.
+
+    ///For a node \c v it returns the 'previous arc'
+    ///of the %DFS path,
+    ///i.e. it returns the last arc of a %DFS path from the root(s) to \c
+    ///v. It is \ref INVALID
+    ///if \c v is unreachable from the root(s) or \c v is a root. The
+    ///%DFS tree used here is equal to the %DFS tree used in
+    ///\ref predNode().
+    ///\pre Either \ref run() or \ref start() must be called before using
+    ///this function.
+    Arc predArc(Node v) const { return (*_pred)[v];}
+
+    ///Returns the 'previous node' of the %DFS tree.
+
+    ///For a node \c v it returns the 'previous node'
+    ///of the %DFS tree,
+    ///i.e. it returns the last but one node from a %DFS path from the
+    ///root(s) to \c v.
+    ///It is INVALID if \c v is unreachable from the root(s) or
+    ///if \c v itself a root.
+    ///The %DFS tree used here is equal to the %DFS
+    ///tree used in \ref predArc().
+    ///\pre Either \ref run() or \ref start() must be called before
+    ///using this function.
+    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
+				  G->source((*_pred)[v]); }
+    
+    ///Returns a reference to the NodeMap of distances.
+
+    ///Returns a reference to the NodeMap of distances.
+    ///\pre Either \ref run() or \ref init() must
+    ///be called before using this function.
+    const DistMap &distMap() const { return *_dist;}
+ 
+    ///Returns a reference to the %DFS arc-tree map.
+
+    ///Returns a reference to the NodeMap of the arcs of the
+    ///%DFS tree.
+    ///\pre Either \ref run() or \ref init()
+    ///must be called before using this function.
+    const PredMap &predMap() const { return *_pred;}
+ 
+    ///Checks if a node is reachable from the root.
+
+    ///Returns \c true if \c v is reachable from the root(s).
+    ///\warning The source nodes are inditated as unreachable.
+    ///\pre Either \ref run() or \ref start()
+    ///must be called before using this function.
+    ///
+    bool reached(Node v) { return (*_reached)[v]; }
+    
+    ///@}
+  };
+
+  ///Default traits class of Dfs function.
+
+  ///Default traits class of Dfs function.
+  ///\param GR Digraph type.
+  template<class GR>
+  struct DfsWizardDefaultTraits
+  {
+    ///The digraph type the algorithm runs on. 
+    typedef GR Digraph;
+    ///\brief The type of the map that stores the last
+    ///arcs of the %DFS paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the %DFS paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap<typename Digraph::Node,typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \ref PredMap. 
+    ///\param g is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient to initialize
+#ifdef DOXYGEN
+    static PredMap *createPredMap(const GR &g) 
+#else
+    static PredMap *createPredMap(const GR &) 
+#endif
+    {
+      return new PredMap();
+    }
+
+    ///The type of the map that indicates which nodes are processed.
+ 
+    ///The type of the map that indicates which nodes are processed.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \ref ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \ref ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that indicates which nodes are reached.
+ 
+    ///The type of the map that indicates which nodes are reached.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef typename Digraph::template NodeMap<bool> ReachedMap;
+    ///Instantiates a ReachedMap.
+ 
+    ///This function instantiates a \ref ReachedMap. 
+    ///\param G is the digraph, to which
+    ///we would like to define the \ref ReachedMap.
+    static ReachedMap *createReachedMap(const GR &G)
+    {
+      return new ReachedMap(G);
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap<typename Digraph::Node,int> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param g is the digraph, to which we would like to define the \ref DistMap
+#ifdef DOXYGEN
+    static DistMap *createDistMap(const GR &g)
+#else
+    static DistMap *createDistMap(const GR &)
+#endif
+    {
+      return new DistMap();
+    }
+  };
+  
+  /// Default traits used by \ref DfsWizard
+
+  /// To make it easier to use Dfs algorithm
+  ///we have created a wizard class.
+  /// This \ref DfsWizard class needs default traits,
+  ///as well as the \ref Dfs class.
+  /// The \ref DfsWizardBase is a class to be the default traits of the
+  /// \ref DfsWizard class.
+  template<class GR>
+  class DfsWizardBase : public DfsWizardDefaultTraits<GR>
+  {
+
+    typedef DfsWizardDefaultTraits<GR> Base;
+  protected:
+    /// Type of the nodes in the digraph.
+    typedef typename Base::Digraph::Node Node;
+
+    /// Pointer to the underlying digraph.
+    void *_g;
+    ///Pointer to the map of reached nodes.
+    void *_reached;
+    ///Pointer to the map of processed nodes.
+    void *_processed;
+    ///Pointer to the map of predecessors arcs.
+    void *_pred;
+    ///Pointer to the map of distances.
+    void *_dist;
+    ///Pointer to the source node.
+    Node _source;
+    
+    public:
+    /// Constructor.
+    
+    /// This constructor does not require parameters, therefore it initiates
+    /// all of the attributes to default values (0, INVALID).
+    DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
+			   _dist(0), _source(INVALID) {}
+
+    /// Constructor.
+    
+    /// This constructor requires some parameters,
+    /// listed in the parameters list.
+    /// Others are initiated to 0.
+    /// \param g is the initial value of  \ref _g
+    /// \param s is the initial value of  \ref _source
+    DfsWizardBase(const GR &g, Node s=INVALID) :
+      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))), 
+      _reached(0), _processed(0), _pred(0), _dist(0), _source(s) {}
+
+  };
+  
+  /// A class to make the usage of the Dfs algorithm easier
+
+  /// This class is created to make it easier to use the Dfs algorithm.
+  /// It uses the functions and features of the plain \ref Dfs,
+  /// but it is much simpler to use it.
+  ///
+  /// Simplicity means that the way to change the types defined
+  /// in the traits class is based on functions that returns the new class
+  /// and not on templatable built-in classes.
+  /// When using the plain \ref Dfs
+  /// the new class with the modified type comes from
+  /// the original class by using the ::
+  /// operator. In the case of \ref DfsWizard only
+  /// a function have to be called and it will
+  /// return the needed class.
+  ///
+  /// It does not have own \ref run method. When its \ref run method is called
+  /// it initiates a plain \ref Dfs object, and calls the \ref Dfs::run
+  /// method of it.
+  template<class TR>
+  class DfsWizard : public TR
+  {
+    typedef TR Base;
+
+    ///The type of the underlying digraph.
+    typedef typename TR::Digraph Digraph;
+    //\e
+    typedef typename Digraph::Node Node;
+    //\e
+    typedef typename Digraph::NodeIt NodeIt;
+    //\e
+    typedef typename Digraph::Arc Arc;
+    //\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///\brief The type of the map that stores
+    ///the reached nodes
+    typedef typename TR::ReachedMap ReachedMap;
+    ///\brief The type of the map that stores
+    ///the processed nodes
+    typedef typename TR::ProcessedMap ProcessedMap;
+    ///\brief The type of the map that stores the last
+    ///arcs of the %DFS paths.
+    typedef typename TR::PredMap PredMap;
+    ///The type of the map that stores the distances of the nodes.
+    typedef typename TR::DistMap DistMap;
+
+  public:
+    /// Constructor.
+    DfsWizard() : TR() {}
+
+    /// Constructor that requires parameters.
+
+    /// Constructor that requires parameters.
+    /// These parameters will be the default values for the traits class.
+    DfsWizard(const Digraph &g, Node s=INVALID) :
+      TR(g,s) {}
+
+    ///Copy constructor
+    DfsWizard(const TR &b) : TR(b) {}
+
+    ~DfsWizard() {}
+
+    ///Runs Dfs algorithm from a given node.
+    
+    ///Runs Dfs algorithm from a given node.
+    ///The node can be given by the \ref source function.
+    void run()
+    {
+      if(Base::_source==INVALID) throw UninitializedParameter();
+      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
+      if(Base::_reached) 
+        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
+      if(Base::_processed) 
+        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
+      if(Base::_pred) 
+        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
+      if(Base::_dist) 
+        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
+      alg.run(Base::_source);
+    }
+
+    ///Runs Dfs algorithm from the given node.
+
+    ///Runs Dfs algorithm from the given node.
+    ///\param s is the given source.
+    void run(Node s)
+    {
+      Base::_source=s;
+      run();
+    }
+
+    template<class T>
+    struct DefPredMapBase : public Base {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &) { return 0; };
+      DefPredMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting PredMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting PredMap type
+    ///
+    template<class T>
+    DfsWizard<DefPredMapBase<T> > predMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DfsWizard<DefPredMapBase<T> >(*this);
+    }
+    
+ 
+    template<class T>
+    struct DefReachedMapBase : public Base {
+      typedef T ReachedMap;
+      static ReachedMap *createReachedMap(const Digraph &) { return 0; };
+      DefReachedMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting ReachedMap
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting ReachedMap
+    ///
+    template<class T>
+    DfsWizard<DefReachedMapBase<T> > reachedMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DfsWizard<DefReachedMapBase<T> >(*this);
+    }
+    
+
+    template<class T>
+    struct DefProcessedMapBase : public Base {
+      typedef T ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
+      DefProcessedMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting ProcessedMap
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting ProcessedMap
+    ///
+    template<class T>
+    DfsWizard<DefProcessedMapBase<T> > processedMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DfsWizard<DefProcessedMapBase<T> >(*this);
+    }
+    
+    template<class T>
+    struct DefDistMapBase : public Base {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) { return 0; };
+      DefDistMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    template<class T>
+    DfsWizard<DefDistMapBase<T> > distMap(const T &t) 
+    {
+      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DfsWizard<DefDistMapBase<T> >(*this);
+    }
+    
+    /// Sets the source node, from which the Dfs algorithm runs.
+
+    /// Sets the source node, from which the Dfs algorithm runs.
+    /// \param s is the source node.
+    DfsWizard<TR> &source(Node s) 
+    {
+      Base::_source=s;
+      return *this;
+    }
+    
+  };
+  
+  ///Function type interface for Dfs algorithm.
+
+  ///\ingroup search
+  ///Function type interface for Dfs algorithm.
+  ///
+  ///This function also has several
+  ///\ref named-templ-func-param "named parameters",
+  ///they are declared as the members of class \ref DfsWizard.
+  ///The following
+  ///example shows how to use these parameters.
+  ///\code
+  ///  dfs(g,source).predMap(preds).run();
+  ///\endcode
+  ///\warning Don't forget to put the \ref DfsWizard::run() "run()"
+  ///to the end of the parameter list.
+  ///\sa DfsWizard
+  ///\sa Dfs
+  template<class GR>
+  DfsWizard<DfsWizardBase<GR> >
+  dfs(const GR &g,typename GR::Node s=INVALID)
+  {
+    return DfsWizard<DfsWizardBase<GR> >(g,s);
+  }
+
+#ifdef DOXYGEN
+  /// \brief Visitor class for dfs.
+  ///  
+  /// It gives a simple interface for a functional interface for dfs 
+  /// traversal. The traversal on a linear data structure. 
+  template <typename _Digraph>
+  struct DfsVisitor {
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::Node Node;
+    /// \brief Called when the arc reach a node.
+    /// 
+    /// It is called when the dfs find an arc which target is not
+    /// reached yet.
+    void discover(const Arc& arc) {}
+    /// \brief Called when the node reached first time.
+    /// 
+    /// It is Called when the node reached first time.
+    void reach(const Node& node) {}
+    /// \brief Called when we step back on an arc.
+    /// 
+    /// It is called when the dfs should step back on the arc.
+    void backtrack(const Arc& arc) {}
+    /// \brief Called when we step back from the node.
+    /// 
+    /// It is called when we step back from the node.
+    void leave(const Node& node) {}
+    /// \brief Called when the arc examined but target of the arc 
+    /// already discovered.
+    /// 
+    /// It called when the arc examined but the target of the arc 
+    /// already discovered.
+    void examine(const Arc& arc) {}
+    /// \brief Called for the source node of the dfs.
+    /// 
+    /// It is called for the source node of the dfs.
+    void start(const Node& node) {}
+    /// \brief Called when we leave the source node of the dfs.
+    /// 
+    /// It is called when we leave the source node of the dfs.
+    void stop(const Node& node) {}
+
+  };
+#else
+  template <typename _Digraph>
+  struct DfsVisitor {
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::Node Node;
+    void discover(const Arc&) {}
+    void reach(const Node&) {}
+    void backtrack(const Arc&) {}
+    void leave(const Node&) {}
+    void examine(const Arc&) {}
+    void start(const Node&) {}
+    void stop(const Node&) {}
+
+    template <typename _Visitor>
+    struct Constraints {
+      void constraints() {
+	Arc arc;
+	Node node;
+	visitor.discover(arc);
+	visitor.reach(node);
+	visitor.backtrack(arc);
+	visitor.leave(node);
+	visitor.examine(arc);
+	visitor.start(node);
+	visitor.stop(arc);
+      }
+      _Visitor& visitor;
+    };
+  };
+#endif
+
+  /// \brief Default traits class of DfsVisit class.
+  ///
+  /// Default traits class of DfsVisit class.
+  /// \param _Digraph Digraph type.
+  template<class _Digraph>
+  struct DfsVisitDefaultTraits {
+
+    /// \brief The digraph type the algorithm runs on. 
+    typedef _Digraph Digraph;
+
+    /// \brief The type of the map that indicates which nodes are reached.
+    /// 
+    /// The type of the map that indicates which nodes are reached.
+    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    /// \todo named parameter to set this type, function to read and write.
+    typedef typename Digraph::template NodeMap<bool> ReachedMap;
+
+    /// \brief Instantiates a ReachedMap.
+    ///
+    /// This function instantiates a \ref ReachedMap. 
+    /// \param digraph is the digraph, to which
+    /// we would like to define the \ref ReachedMap.
+    static ReachedMap *createReachedMap(const Digraph &digraph) {
+      return new ReachedMap(digraph);
+    }
+
+  };
+  
+  /// %DFS Visit algorithm class.
+  
+  /// \ingroup search
+  /// This class provides an efficient implementation of the %DFS algorithm
+  /// with visitor interface.
+  ///
+  /// The %DfsVisit class provides an alternative interface to the Dfs
+  /// class. It works with callback mechanism, the DfsVisit object calls
+  /// on every dfs event the \c Visitor class member functions. 
+  ///
+  /// \param _Digraph The digraph type the algorithm runs on. The default value is
+  /// \ref ListDigraph. The value of _Digraph is not used directly by Dfs, it
+  /// is only passed to \ref DfsDefaultTraits.
+  /// \param _Visitor The Visitor object for the algorithm. The 
+  /// \ref DfsVisitor "DfsVisitor<_Digraph>" is an empty Visitor which
+  /// does not observe the Dfs events. If you want to observe the dfs
+  /// events you should implement your own Visitor class.
+  /// \param _Traits Traits class to set various data types used by the 
+  /// algorithm. The default traits class is
+  /// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<_Digraph>".
+  /// See \ref DfsVisitDefaultTraits for the documentation of
+  /// a Dfs visit traits class.
+  ///
+  /// \author Jacint Szabo, Alpar Juttner and Balazs Dezso
+#ifdef DOXYGEN
+  template <typename _Digraph, typename _Visitor, typename _Traits>
+#else
+  template <typename _Digraph = ListDigraph,
+	    typename _Visitor = DfsVisitor<_Digraph>,
+	    typename _Traits = DfsDefaultTraits<_Digraph> >
+#endif
+  class DfsVisit {
+  public:
+    
+    /// \brief \ref Exception for uninitialized parameters.
+    ///
+    /// This error represents problems in the initialization
+    /// of the parameters of the algorithms.
+    class UninitializedParameter : public lemon::UninitializedParameter {
+    public:
+      virtual const char* what() const throw() 
+      {
+	return "lemon::DfsVisit::UninitializedParameter";
+      }
+    };
+
+    typedef _Traits Traits;
+
+    typedef typename Traits::Digraph Digraph;
+
+    typedef _Visitor Visitor;
+
+    ///The type of the map indicating which nodes are reached.
+    typedef typename Traits::ReachedMap ReachedMap;
+
+  private:
+
+    typedef typename Digraph::Node Node;
+    typedef typename Digraph::NodeIt NodeIt;
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::OutArcIt OutArcIt;
+
+    /// Pointer to the underlying digraph.
+    const Digraph *_digraph;
+    /// Pointer to the visitor object.
+    Visitor *_visitor;
+    ///Pointer to the map of reached status of the nodes.
+    ReachedMap *_reached;
+    ///Indicates if \ref _reached is locally allocated (\c true) or not.
+    bool local_reached;
+
+    std::vector<typename Digraph::Arc> _stack;
+    int _stack_head;
+
+    /// \brief Creates the maps if necessary.
+    ///
+    /// Creates the maps if necessary.
+    void create_maps() {
+      if(!_reached) {
+	local_reached = true;
+	_reached = Traits::createReachedMap(*_digraph);
+      }
+    }
+
+  protected:
+
+    DfsVisit() {}
+    
+  public:
+
+    typedef DfsVisit Create;
+
+    /// \name Named template parameters
+
+    ///@{
+    template <class T>
+    struct DefReachedMapTraits : public Traits {
+      typedef T ReachedMap;
+      static ReachedMap *createReachedMap(const Digraph &digraph) {
+	throw UninitializedParameter();
+      }
+    };
+    /// \brief \ref named-templ-param "Named parameter" for setting 
+    /// ReachedMap type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting ReachedMap type
+    template <class T>
+    struct DefReachedMap : public DfsVisit< Digraph, Visitor,
+					    DefReachedMapTraits<T> > {
+      typedef DfsVisit< Digraph, Visitor, DefReachedMapTraits<T> > Create;
+    };
+    ///@}
+
+  public:      
+    
+    /// \brief Constructor.
+    ///
+    /// Constructor.
+    ///
+    /// \param digraph the digraph the algorithm will run on.
+    /// \param visitor The visitor of the algorithm.
+    ///
+    DfsVisit(const Digraph& digraph, Visitor& visitor) 
+      : _digraph(&digraph), _visitor(&visitor),
+	_reached(0), local_reached(false) {}
+    
+    /// \brief Destructor.
+    ///
+    /// Destructor.
+    ~DfsVisit() {
+      if(local_reached) delete _reached;
+    }
+
+    /// \brief Sets the map indicating if a node is reached.
+    ///
+    /// Sets the map indicating if a node is reached.
+    /// If you don't use this function before calling \ref run(),
+    /// it will allocate one. The destuctor deallocates this
+    /// automatically allocated map, of course.
+    /// \return <tt> (*this) </tt>
+    DfsVisit &reachedMap(ReachedMap &m) {
+      if(local_reached) {
+	delete _reached;
+	local_reached=false;
+      }
+      _reached = &m;
+      return *this;
+    }
+
+  public:
+    /// \name Execution control
+    /// The simplest way to execute the algorithm is to use
+    /// one of the member functions called \c run(...).
+    /// \n
+    /// If you need more control on the execution,
+    /// first you must call \ref init(), then you can adda source node
+    /// with \ref addSource().
+    /// Finally \ref start() will perform the actual path
+    /// computation.
+
+    /// @{
+    /// \brief Initializes the internal data structures.
+    ///
+    /// Initializes the internal data structures.
+    ///
+    void init() {
+      create_maps();
+      _stack.resize(countNodes(*_digraph));
+      _stack_head = -1;
+      for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
+	_reached->set(u, false);
+      }
+    }
+    
+    /// \brief Adds a new source node.
+    ///
+    /// Adds a new source node to the set of nodes to be processed.
+    void addSource(Node s) {
+      if(!(*_reached)[s]) {
+	  _reached->set(s,true);
+	  _visitor->start(s);
+	  _visitor->reach(s);
+	  Arc e; 
+	  _digraph->firstOut(e, s);
+	  if (e != INVALID) {
+	    _stack[++_stack_head] = e;
+	  } else {
+	    _visitor->leave(s);
+	  }
+	}
+    }
+    
+    /// \brief Processes the next arc.
+    ///
+    /// Processes the next arc.
+    ///
+    /// \return The processed arc.
+    ///
+    /// \pre The stack must not be empty!
+    Arc processNextArc() { 
+      Arc e = _stack[_stack_head];
+      Node m = _digraph->target(e);
+      if(!(*_reached)[m]) {
+	_visitor->discover(e);
+	_visitor->reach(m);
+	_reached->set(m, true);
+	_digraph->firstOut(_stack[++_stack_head], m);
+      } else {
+	_visitor->examine(e);
+	m = _digraph->source(e);
+	_digraph->nextOut(_stack[_stack_head]);
+      }
+      while (_stack_head>=0 && _stack[_stack_head] == INVALID) {
+	_visitor->leave(m);
+	--_stack_head;
+	if (_stack_head >= 0) {
+	  _visitor->backtrack(_stack[_stack_head]);
+	  m = _digraph->source(_stack[_stack_head]);
+	  _digraph->nextOut(_stack[_stack_head]);
+	} else {
+	  _visitor->stop(m);	  
+	}
+      }
+      return e;
+    }
+
+    /// \brief Next arc to be processed.
+    ///
+    /// Next arc to be processed.
+    ///
+    /// \return The next arc to be processed or INVALID if the stack is
+    /// empty.
+    Arc nextArc() { 
+      return _stack_head >= 0 ? _stack[_stack_head] : INVALID;
+    }
+
+    /// \brief Returns \c false if there are nodes
+    /// to be processed in the queue
+    ///
+    /// Returns \c false if there are nodes
+    /// to be processed in the queue
+    bool emptyQueue() { return _stack_head < 0; }
+
+    /// \brief Returns the number of the nodes to be processed.
+    ///
+    /// Returns the number of the nodes to be processed in the queue.
+    int queueSize() { return _stack_head + 1; }
+    
+    /// \brief Executes the algorithm.
+    ///
+    /// Executes the algorithm.
+    ///
+    /// \pre init() must be called and at least one node should be added
+    /// with addSource() before using this function.
+    void start() {
+      while ( !emptyQueue() ) processNextArc();
+    }
+    
+    /// \brief Executes the algorithm until \c dest is reached.
+    ///
+    /// Executes the algorithm until \c dest is reached.
+    ///
+    /// \pre init() must be called and at least one node should be added
+    /// with addSource() before using this function.
+    void start(Node dest) {
+      while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != dest ) 
+	processNextArc();
+    }
+    
+    /// \brief Executes the algorithm until a condition is met.
+    ///
+    /// Executes the algorithm until a condition is met.
+    ///
+    /// \pre init() must be called and at least one node should be added
+    /// with addSource() before using this function.
+    ///
+    /// \param em must be a bool (or convertible) arc map. The algorithm
+    /// will stop when it reaches an arc \c e with <tt>em[e]</tt> true.
+    ///
+    ///\return The reached arc \c e with <tt>em[e]</tt> true or
+    ///\c INVALID if no such arc was found.
+    ///
+    /// \warning Contrary to \ref Bfs and \ref Dijkstra, \c em is an arc map,
+    /// not a node map.
+    template <typename EM>
+    Arc start(const EM &em) {
+      while ( !emptyQueue() && !em[_stack[_stack_head]] )
+        processNextArc();
+      return emptyQueue() ? INVALID : _stack[_stack_head];
+    }
+
+    /// \brief Runs %DFSVisit algorithm from node \c s.
+    ///
+    /// This method runs the %DFS algorithm from a root node \c s.
+    /// \note d.run(s) is just a shortcut of the following code.
+    ///\code
+    ///   d.init();
+    ///   d.addSource(s);
+    ///   d.start();
+    ///\endcode
+    void run(Node s) {
+      init();
+      addSource(s);
+      start();
+    }
+
+    /// \brief Runs %DFSVisit algorithm to visit all nodes in the digraph.
+    
+    /// This method runs the %DFS algorithm in order to
+    /// compute the %DFS path to each node. The algorithm computes
+    /// - The %DFS tree.
+    /// - The distance of each node from the root in the %DFS tree.
+    ///
+    ///\note d.run() is just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  for (NodeIt it(digraph); it != INVALID; ++it) {
+    ///    if (!d.reached(it)) {
+    ///      d.addSource(it);
+    ///      d.start();
+    ///    }
+    ///  }
+    ///\endcode
+    void run() {
+      init();
+      for (NodeIt it(*_digraph); it != INVALID; ++it) {
+        if (!reached(it)) {
+          addSource(it);
+          start();
+        }
+      }
+    }
+    ///@}
+
+    /// \name Query Functions
+    /// The result of the %DFS algorithm can be obtained using these
+    /// functions.\n
+    /// Before the use of these functions,
+    /// either run() or start() must be called.
+    ///@{
+    /// \brief Checks if a node is reachable from the root.
+    ///
+    /// Returns \c true if \c v is reachable from the root(s).
+    /// \warning The source nodes are inditated as unreachable.
+    /// \pre Either \ref run() or \ref start()
+    /// must be called before using this function.
+    ///
+    bool reached(Node v) { return (*_reached)[v]; }
+    ///@}
+  };
+
+
+} //END OF NAMESPACE LEMON
+
+#endif
+
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/dijkstra.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/dijkstra.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,1209 @@
+/* -*- 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_DIJKSTRA_H
+#define LEMON_DIJKSTRA_H
+
+///\ingroup shortest_path
+///\file
+///\brief Dijkstra algorithm.
+///
+
+#include <lemon/list_digraph.h>
+#include <lemon/bin_heap.h>
+#include <lemon/bits/path_dump.h>
+#include <lemon/bits/invalid.h>
+#include <lemon/error.h>
+#include <lemon/maps.h>
+
+
+namespace lemon {
+
+  /// \brief Default OperationTraits for the Dijkstra algorithm class.
+  ///  
+  /// It defines all computational operations and constants which are
+  /// used in the Dijkstra algorithm.
+  template <typename Value>
+  struct DijkstraDefaultOperationTraits {
+    /// \brief Gives back the zero value of the type.
+    static Value zero() {
+      return static_cast<Value>(0);
+    }
+    /// \brief Gives back the sum of the given two elements.
+    static Value plus(const Value& left, const Value& right) {
+      return left + right;
+    }
+    /// \brief Gives back true only if the first value less than the second.
+    static bool less(const Value& left, const Value& right) {
+      return left < right;
+    }
+  };
+
+  /// \brief Widest path OperationTraits for the Dijkstra algorithm class.
+  ///  
+  /// It defines all computational operations and constants which are
+  /// used in the Dijkstra algorithm for widest path computation.
+  template <typename Value>
+  struct DijkstraWidestPathOperationTraits {
+    /// \brief Gives back the maximum value of the type.
+    static Value zero() {
+      return std::numeric_limits<Value>::max();
+    }
+    /// \brief Gives back the minimum of the given two elements.
+    static Value plus(const Value& left, const Value& right) {
+      return std::min(left, right);
+    }
+    /// \brief Gives back true only if the first value less than the second.
+    static bool less(const Value& left, const Value& right) {
+      return left < right;
+    }
+  };
+  
+  ///Default traits class of Dijkstra class.
+
+  ///Default traits class of Dijkstra class.
+  ///\param GR Digraph type.
+  ///\param LM Type of length map.
+  template<class GR, class LM>
+  struct DijkstraDefaultTraits
+  {
+    ///The digraph type the algorithm runs on. 
+    typedef GR Digraph;
+    ///The type of the map that stores the arc lengths.
+
+    ///The type of the map that stores the arc lengths.
+    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef LM LengthMap;
+    //The type of the length of the arcs.
+    typedef typename LM::Value Value;
+    /// Operation traits for Dijkstra algorithm.
+
+    /// It defines the used operation by the algorithm.
+    /// \see DijkstraDefaultOperationTraits
+    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
+    /// The cross reference type used by heap.
+
+
+    /// The cross reference type used by heap.
+    /// Usually it is \c Digraph::NodeMap<int>.
+    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
+    ///Instantiates a HeapCrossRef.
+
+    ///This function instantiates a \c HeapCrossRef. 
+    /// \param G is the digraph, to which we would like to define the 
+    /// HeapCrossRef.
+    static HeapCrossRef *createHeapCrossRef(const GR &G) 
+    {
+      return new HeapCrossRef(G);
+    }
+    
+    ///The heap type used by Dijkstra algorithm.
+
+    ///The heap type used by Dijkstra algorithm.
+    ///
+    ///\sa BinHeap
+    ///\sa Dijkstra
+    typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;
+
+    static Heap *createHeap(HeapCrossRef& R) 
+    {
+      return new Heap(R);
+    }
+
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the shortest paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \c PredMap. 
+    ///\param G is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient for the initialization
+    static PredMap *createPredMap(const GR &G) 
+    {
+      return new PredMap(G);
+    }
+
+    ///The type of the map that stores whether a nodes is processed.
+ 
+    ///The type of the map that stores whether a nodes is processed.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///By default it is a NullMap.
+    ///\todo If it is set to a real map,
+    ///Dijkstra::processed() should read this.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \c ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \c ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param G is the digraph, to which we would like to define the \ref DistMap
+    static DistMap *createDistMap(const GR &G)
+    {
+      return new DistMap(G);
+    }
+  };
+  
+  ///%Dijkstra algorithm class.
+  
+  /// \ingroup shortest_path
+  ///This class provides an efficient implementation of %Dijkstra algorithm.
+  ///The arc lengths are passed to the algorithm using a
+  ///\ref concepts::ReadMap "ReadMap",
+  ///so it is easy to change it to any kind of length.
+  ///
+  ///The type of the length is determined by the
+  ///\ref concepts::ReadMap::Value "Value" of the length map.
+  ///
+  ///It is also possible to change the underlying priority heap.
+  ///
+  ///\param GR The digraph type the algorithm runs on. The default value
+  ///is \ref ListDigraph. The value of GR is not used directly by
+  ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits.
+  ///\param LM This read-only ArcMap determines the lengths of the
+  ///arcs. It is read once for each arc, so the map may involve in
+  ///relatively time consuming process to compute the arc length if
+  ///it is necessary. The default map type is \ref
+  ///concepts::Digraph::ArcMap "Digraph::ArcMap<int>".  The value
+  ///of LM is not used directly by Dijkstra, it is only passed to \ref
+  ///DijkstraDefaultTraits.  \param TR Traits class to set
+  ///various data types used by the algorithm.  The default traits
+  ///class is \ref DijkstraDefaultTraits
+  ///"DijkstraDefaultTraits<GR,LM>".  See \ref
+  ///DijkstraDefaultTraits for the documentation of a Dijkstra traits
+  ///class.
+  ///
+  ///\author Jacint Szabo and Alpar Juttner
+
+#ifdef DOXYGEN
+  template <typename GR, typename LM, typename TR>
+#else
+  template <typename GR=ListDigraph,
+	    typename LM=typename GR::template ArcMap<int>,
+	    typename TR=DijkstraDefaultTraits<GR,LM> >
+#endif
+  class Dijkstra {
+  public:
+    /**
+     * \brief \ref Exception for uninitialized parameters.
+     *
+     * This error represents problems in the initialization
+     * of the parameters of the algorithms.
+     */
+    class UninitializedParameter : public lemon::UninitializedParameter {
+    public:
+      virtual const char* what() const throw() {
+	return "lemon::Dijkstra::UninitializedParameter";
+      }
+    };
+
+    typedef TR Traits;
+    ///The type of the underlying digraph.
+    typedef typename TR::Digraph Digraph;
+    ///\e
+    typedef typename Digraph::Node Node;
+    ///\e
+    typedef typename Digraph::NodeIt NodeIt;
+    ///\e
+    typedef typename Digraph::Arc Arc;
+    ///\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///The type of the length of the arcs.
+    typedef typename TR::LengthMap::Value Value;
+    ///The type of the map that stores the arc lengths.
+    typedef typename TR::LengthMap LengthMap;
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    typedef typename TR::PredMap PredMap;
+    ///The type of the map indicating if a node is processed.
+    typedef typename TR::ProcessedMap ProcessedMap;
+    ///The type of the map that stores the dists of the nodes.
+    typedef typename TR::DistMap DistMap;
+    ///The cross reference type used for the current heap.
+    typedef typename TR::HeapCrossRef HeapCrossRef;
+    ///The heap type used by the dijkstra algorithm.
+    typedef typename TR::Heap Heap;
+    ///The operation traits.
+    typedef typename TR::OperationTraits OperationTraits;
+  private:
+    /// Pointer to the underlying digraph.
+    const Digraph *G;
+    /// Pointer to the length map
+    const LengthMap *length;
+    ///Pointer to the map of predecessors arcs.
+    PredMap *_pred;
+    ///Indicates if \ref _pred is locally allocated (\c true) or not.
+    bool local_pred;
+    ///Pointer to the map of distances.
+    DistMap *_dist;
+    ///Indicates if \ref _dist is locally allocated (\c true) or not.
+    bool local_dist;
+    ///Pointer to the map of processed status of the nodes.
+    ProcessedMap *_processed;
+    ///Indicates if \ref _processed is locally allocated (\c true) or not.
+    bool local_processed;
+    ///Pointer to the heap cross references.
+    HeapCrossRef *_heap_cross_ref;
+    ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.
+    bool local_heap_cross_ref;
+    ///Pointer to the heap.
+    Heap *_heap;
+    ///Indicates if \ref _heap is locally allocated (\c true) or not.
+    bool local_heap;
+
+    ///Creates the maps if necessary.
+    
+    ///\todo Better memory allocation (instead of new).
+    void create_maps() 
+    {
+      if(!_pred) {
+	local_pred = true;
+	_pred = Traits::createPredMap(*G);
+      }
+      if(!_dist) {
+	local_dist = true;
+	_dist = Traits::createDistMap(*G);
+      }
+      if(!_processed) {
+	local_processed = true;
+	_processed = Traits::createProcessedMap(*G);
+      }
+      if (!_heap_cross_ref) {
+	local_heap_cross_ref = true;
+	_heap_cross_ref = Traits::createHeapCrossRef(*G);
+      }
+      if (!_heap) {
+	local_heap = true;
+	_heap = Traits::createHeap(*_heap_cross_ref);
+      }
+    }
+    
+  public :
+
+    typedef Dijkstra Create;
+ 
+    ///\name Named template parameters
+
+    ///@{
+
+    template <class T>
+    struct DefPredMapTraits : public Traits {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &)
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\ref named-templ-param "Named parameter" for setting PredMap type
+
+    ///\ref named-templ-param "Named parameter" for setting PredMap type
+    ///
+    template <class T>
+    struct DefPredMap 
+      : public Dijkstra< Digraph,	LengthMap, DefPredMapTraits<T> > {
+      typedef Dijkstra< Digraph,	LengthMap, DefPredMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefDistMapTraits : public Traits {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &)
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\ref named-templ-param "Named parameter" for setting DistMap type
+
+    ///\ref named-templ-param "Named parameter" for setting DistMap type
+    ///
+    template <class T>
+    struct DefDistMap 
+      : public Dijkstra< Digraph, LengthMap, DefDistMapTraits<T> > { 
+      typedef Dijkstra< Digraph, LengthMap, DefDistMapTraits<T> > Create;
+    };
+    
+    template <class T>
+    struct DefProcessedMapTraits : public Traits {
+      typedef T ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &G) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
+
+    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
+    ///
+    template <class T>
+    struct DefProcessedMap 
+      : public Dijkstra< Digraph,	LengthMap, DefProcessedMapTraits<T> > { 
+      typedef Dijkstra< Digraph,	LengthMap, DefProcessedMapTraits<T> > Create;
+    };
+    
+    struct DefDigraphProcessedMapTraits : public Traits {
+      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
+      static ProcessedMap *createProcessedMap(const Digraph &G) 
+      {
+	return new ProcessedMap(G);
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///
+    ///\ref named-templ-param "Named parameter"
+    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
+    ///If you don't set it explicitely, it will be automatically allocated.
+    template <class T>
+    struct DefProcessedMapToBeDefaultMap 
+      : public Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits> {
+      typedef Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits> Create;
+    };
+
+    template <class H, class CR>
+    struct DefHeapTraits : public Traits {
+      typedef CR HeapCrossRef;
+      typedef H Heap;
+      static HeapCrossRef *createHeapCrossRef(const Digraph &) {
+	throw UninitializedParameter();
+      }
+      static Heap *createHeap(HeapCrossRef &) 
+      {
+	throw UninitializedParameter();
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///heap and cross reference type
+    ///
+    ///\ref named-templ-param "Named parameter" for setting heap and cross 
+    ///reference type
+    ///
+    template <class H, class CR = typename Digraph::template NodeMap<int> >
+    struct DefHeap
+      : public Dijkstra< Digraph,	LengthMap, DefHeapTraits<H, CR> > { 
+      typedef Dijkstra< Digraph,	LengthMap, DefHeapTraits<H, CR> > Create;
+    };
+
+    template <class H, class CR>
+    struct DefStandardHeapTraits : public Traits {
+      typedef CR HeapCrossRef;
+      typedef H Heap;
+      static HeapCrossRef *createHeapCrossRef(const Digraph &G) {
+	return new HeapCrossRef(G);
+      }
+      static Heap *createHeap(HeapCrossRef &R) 
+      {
+	return new Heap(R);
+      }
+    };
+    ///\brief \ref named-templ-param "Named parameter" for setting
+    ///heap and cross reference type with automatic allocation
+    ///
+    ///\ref named-templ-param "Named parameter" for setting heap and cross 
+    ///reference type. It can allocate the heap and the cross reference 
+    ///object if the cross reference's constructor waits for the digraph as 
+    ///parameter and the heap's constructor waits for the cross reference.
+    template <class H, class CR = typename Digraph::template NodeMap<int> >
+    struct DefStandardHeap
+      : public Dijkstra< Digraph,	LengthMap, DefStandardHeapTraits<H, CR> > { 
+      typedef Dijkstra< Digraph,	LengthMap, DefStandardHeapTraits<H, CR> > 
+      Create;
+    };
+
+    template <class T>
+    struct DefOperationTraitsTraits : public Traits {
+      typedef T OperationTraits;
+    };
+    
+    /// \brief \ref named-templ-param "Named parameter" for setting 
+    /// OperationTraits type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting OperationTraits
+    /// type
+    template <class T>
+    struct DefOperationTraits
+      : public Dijkstra<Digraph, LengthMap, DefOperationTraitsTraits<T> > {
+      typedef Dijkstra<Digraph, LengthMap, DefOperationTraitsTraits<T> >
+      Create;
+    };
+    
+    ///@}
+
+
+  protected:
+
+    Dijkstra() {}
+
+  public:      
+    
+    ///Constructor.
+    
+    ///\param _G the digraph the algorithm will run on.
+    ///\param _length the length map used by the algorithm.
+    Dijkstra(const Digraph& _G, const LengthMap& _length) :
+      G(&_G), length(&_length),
+      _pred(NULL), local_pred(false),
+      _dist(NULL), local_dist(false),
+      _processed(NULL), local_processed(false),
+      _heap_cross_ref(NULL), local_heap_cross_ref(false),
+      _heap(NULL), local_heap(false)
+    { }
+    
+    ///Destructor.
+    ~Dijkstra() 
+    {
+      if(local_pred) delete _pred;
+      if(local_dist) delete _dist;
+      if(local_processed) delete _processed;
+      if(local_heap_cross_ref) delete _heap_cross_ref;
+      if(local_heap) delete _heap;
+    }
+
+    ///Sets the length map.
+
+    ///Sets the length map.
+    ///\return <tt> (*this) </tt>
+    Dijkstra &lengthMap(const LengthMap &m) 
+    {
+      length = &m;
+      return *this;
+    }
+
+    ///Sets the map storing the predecessor arcs.
+
+    ///Sets the map storing the predecessor arcs.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Dijkstra &predMap(PredMap &m) 
+    {
+      if(local_pred) {
+	delete _pred;
+	local_pred=false;
+      }
+      _pred = &m;
+      return *this;
+    }
+
+    ///Sets the map storing the distances calculated by the algorithm.
+
+    ///Sets the map storing the distances calculated by the algorithm.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated map, of course.
+    ///\return <tt> (*this) </tt>
+    Dijkstra &distMap(DistMap &m) 
+    {
+      if(local_dist) {
+	delete _dist;
+	local_dist=false;
+      }
+      _dist = &m;
+      return *this;
+    }
+
+    ///Sets the heap and the cross reference used by algorithm.
+
+    ///Sets the heap and the cross reference used by algorithm.
+    ///If you don't use this function before calling \ref run(),
+    ///it will allocate one. The destuctor deallocates this
+    ///automatically allocated heap and cross reference, of course.
+    ///\return <tt> (*this) </tt>
+    Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
+    {
+      if(local_heap_cross_ref) {
+	delete _heap_cross_ref;
+	local_heap_cross_ref=false;
+      }
+      _heap_cross_ref = &cr;
+      if(local_heap) {
+	delete _heap;
+	local_heap=false;
+      }
+      _heap = &hp;
+      return *this;
+    }
+
+  private:
+    void finalizeNodeData(Node v,Value dst)
+    {
+      _processed->set(v,true);
+      _dist->set(v, dst);
+    }
+
+  public:
+
+    typedef PredMapPath<Digraph, PredMap> Path;
+
+    ///\name Execution control
+    ///The simplest way to execute the algorithm is to use
+    ///one of the member functions called \c run(...).
+    ///\n
+    ///If you need more control on the execution,
+    ///first you must call \ref init(), then you can add several source nodes
+    ///with \ref addSource().
+    ///Finally \ref start() will perform the actual path
+    ///computation.
+
+    ///@{
+
+    ///Initializes the internal data structures.
+
+    ///Initializes the internal data structures.
+    ///
+    void init()
+    {
+      create_maps();
+      _heap->clear();
+      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
+	_pred->set(u,INVALID);
+	_processed->set(u,false);
+	_heap_cross_ref->set(u,Heap::PRE_HEAP);
+      }
+    }
+    
+    ///Adds a new source node.
+
+    ///Adds a new source node to the priority heap.
+    ///
+    ///The optional second parameter is the initial distance of the node.
+    ///
+    ///It checks if the node has already been added to the heap and
+    ///it is pushed to the heap only if either it was not in the heap
+    ///or the shortest path found till then is shorter than \c dst.
+    void addSource(Node s,Value dst=OperationTraits::zero())
+    {
+      if(_heap->state(s) != Heap::IN_HEAP) {
+	_heap->push(s,dst);
+      } else if(OperationTraits::less((*_heap)[s], dst)) {
+	_heap->set(s,dst);
+	_pred->set(s,INVALID);
+      }
+    }
+    
+    ///Processes the next node in the priority heap
+
+    ///Processes the next node in the priority heap.
+    ///
+    ///\return The processed node.
+    ///
+    ///\warning The priority heap must not be empty!
+    Node processNextNode()
+    {
+      Node v=_heap->top(); 
+      Value oldvalue=_heap->prio();
+      _heap->pop();
+      finalizeNodeData(v,oldvalue);
+      
+      for(OutArcIt e(*G,v); e!=INVALID; ++e) {
+	Node w=G->target(e); 
+	switch(_heap->state(w)) {
+	case Heap::PRE_HEAP:
+	  _heap->push(w,OperationTraits::plus(oldvalue, (*length)[e])); 
+	  _pred->set(w,e);
+	  break;
+	case Heap::IN_HEAP:
+	  {
+	    Value newvalue = OperationTraits::plus(oldvalue, (*length)[e]);
+	    if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {
+	      _heap->decrease(w, newvalue); 
+	      _pred->set(w,e);
+	    }
+	  }
+	  break;
+	case Heap::POST_HEAP:
+	  break;
+	}
+      }
+      return v;
+    }
+
+    ///Next node to be processed.
+    
+    ///Next node to be processed.
+    ///
+    ///\return The next node to be processed or INVALID if the priority heap
+    /// is empty.
+    Node nextNode()
+    { 
+      return !_heap->empty()?_heap->top():INVALID;
+    }
+ 
+    ///\brief Returns \c false if there are nodes
+    ///to be processed in the priority heap
+    ///
+    ///Returns \c false if there are nodes
+    ///to be processed in the priority heap
+    bool emptyQueue() { return _heap->empty(); }
+    ///Returns the number of the nodes to be processed in the priority heap
+
+    ///Returns the number of the nodes to be processed in the priority heap
+    ///
+    int queueSize() { return _heap->size(); }
+    
+    ///Executes the algorithm.
+
+    ///Executes the algorithm.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///This method runs the %Dijkstra algorithm from the root node(s)
+    ///in order to
+    ///compute the
+    ///shortest path to each node. The algorithm computes
+    ///- The shortest path tree.
+    ///- The distance of each node from the root(s).
+    ///
+    void start()
+    {
+      while ( !_heap->empty() ) processNextNode();
+    }
+    
+    ///Executes the algorithm until \c dest is reached.
+
+    ///Executes the algorithm until \c dest is reached.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///This method runs the %Dijkstra algorithm from the root node(s)
+    ///in order to
+    ///compute the
+    ///shortest path to \c dest. The algorithm computes
+    ///- The shortest path to \c  dest.
+    ///- The distance of \c dest from the root(s).
+    ///
+    void start(Node dest)
+    {
+      while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();
+      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
+    }
+    
+    ///Executes the algorithm until a condition is met.
+
+    ///Executes the algorithm until a condition is met.
+    ///
+    ///\pre init() must be called and at least one node should be added
+    ///with addSource() before using this function.
+    ///
+    ///\param nm must be a bool (or convertible) node map. The algorithm
+    ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
+    ///
+    ///\return The reached node \c v with <tt>nm[v]</tt> true or
+    ///\c INVALID if no such node was found.
+    template<class NodeBoolMap>
+    Node start(const NodeBoolMap &nm)
+    {
+      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
+      if ( _heap->empty() ) return INVALID;
+      finalizeNodeData(_heap->top(),_heap->prio());
+      return _heap->top();
+    }
+    
+    ///Runs %Dijkstra algorithm from node \c s.
+    
+    ///This method runs the %Dijkstra algorithm from a root node \c s
+    ///in order to
+    ///compute the
+    ///shortest path to each node. The algorithm computes
+    ///- The shortest path tree.
+    ///- The distance of each node from the root.
+    ///
+    ///\note d.run(s) is just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  d.addSource(s);
+    ///  d.start();
+    ///\endcode
+    void run(Node s) {
+      init();
+      addSource(s);
+      start();
+    }
+    
+    ///Finds the shortest path between \c s and \c t.
+    
+    ///Finds the shortest path between \c s and \c t.
+    ///
+    ///\return The length of the shortest s---t path if there exists one,
+    ///0 otherwise.
+    ///\note Apart from the return value, d.run(s) is
+    ///just a shortcut of the following code.
+    ///\code
+    ///  d.init();
+    ///  d.addSource(s);
+    ///  d.start(t);
+    ///\endcode
+    Value run(Node s,Node t) {
+      init();
+      addSource(s);
+      start(t);
+      return (*_pred)[t]==INVALID?OperationTraits::zero():(*_dist)[t];
+    }
+    
+    ///@}
+
+    ///\name Query Functions
+    ///The result of the %Dijkstra algorithm can be obtained using these
+    ///functions.\n
+    ///Before the use of these functions,
+    ///either run() or start() must be called.
+    
+    ///@{
+
+    ///Gives back the shortest path.
+    
+    ///Gives back the shortest path.
+    ///\pre The \c t should be reachable from the source.
+    Path path(Node t) 
+    {
+      return Path(*G, *_pred, t);
+    }
+
+    ///The distance of a node from the root.
+
+    ///Returns the distance of a node from the root.
+    ///\pre \ref run() must be called before using this function.
+    ///\warning If node \c v in unreachable from the root the return value
+    ///of this funcion is undefined.
+    Value dist(Node v) const { return (*_dist)[v]; }
+
+    ///The current distance of a node from the root.
+
+    ///Returns the current distance of a node from the root.
+    ///It may be decreased in the following processes.
+    ///\pre \c node should be reached but not processed
+    Value currentDist(Node v) const { return (*_heap)[v]; }
+
+    ///Returns the 'previous arc' of the shortest path tree.
+
+    ///For a node \c v it returns the 'previous arc' of the shortest path tree,
+    ///i.e. it returns the last arc of a shortest path from the root to \c
+    ///v. It is \ref INVALID
+    ///if \c v is unreachable from the root or if \c v=s. The
+    ///shortest path tree used here is equal to the shortest path tree used in
+    ///\ref predNode().  \pre \ref run() must be called before using
+    ///this function.
+    Arc predArc(Node v) const { return (*_pred)[v]; }
+
+    ///Returns the 'previous node' of the shortest path tree.
+
+    ///For a node \c v it returns the 'previous node' of the shortest path tree,
+    ///i.e. it returns the last but one node from a shortest path from the
+    ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
+    ///\c v=s. The shortest path tree used here is equal to the shortest path
+    ///tree used in \ref predArc().  \pre \ref run() must be called before
+    ///using this function.
+    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
+				  G->source((*_pred)[v]); }
+    
+    ///Returns a reference to the NodeMap of distances.
+
+    ///Returns a reference to the NodeMap of distances. \pre \ref run() must
+    ///be called before using this function.
+    const DistMap &distMap() const { return *_dist;}
+ 
+    ///Returns a reference to the shortest path tree map.
+
+    ///Returns a reference to the NodeMap of the arcs of the
+    ///shortest path tree.
+    ///\pre \ref run() must be called before using this function.
+    const PredMap &predMap() const { return *_pred;}
+ 
+    ///Checks if a node is reachable from the root.
+
+    ///Returns \c true if \c v is reachable from the root.
+    ///\warning The source nodes are inditated as unreached.
+    ///\pre \ref run() must be called before using this function.
+    ///
+    bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }
+
+    ///Checks if a node is processed.
+
+    ///Returns \c true if \c v is processed, i.e. the shortest
+    ///path to \c v has already found.
+    ///\pre \ref run() must be called before using this function.
+    ///
+    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }
+    
+    ///@}
+  };
+
+
+
+
+ 
+  ///Default traits class of Dijkstra function.
+
+  ///Default traits class of Dijkstra function.
+  ///\param GR Digraph type.
+  ///\param LM Type of length map.
+  template<class GR, class LM>
+  struct DijkstraWizardDefaultTraits
+  {
+    ///The digraph type the algorithm runs on. 
+    typedef GR Digraph;
+    ///The type of the map that stores the arc lengths.
+
+    ///The type of the map that stores the arc lengths.
+    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef LM LengthMap;
+    //The type of the length of the arcs.
+    typedef typename LM::Value Value;
+    /// Operation traits for Dijkstra algorithm.
+
+    /// It defines the used operation by the algorithm.
+    /// \see DijkstraDefaultOperationTraits
+    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
+    ///The heap type used by Dijkstra algorithm.
+
+    /// The cross reference type used by heap.
+
+    /// The cross reference type used by heap.
+    /// Usually it is \c Digraph::NodeMap<int>.
+    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
+    ///Instantiates a HeapCrossRef.
+
+    ///This function instantiates a \ref HeapCrossRef. 
+    /// \param G is the digraph, to which we would like to define the 
+    /// HeapCrossRef.
+    /// \todo The digraph alone may be insufficient for the initialization
+    static HeapCrossRef *createHeapCrossRef(const GR &G) 
+    {
+      return new HeapCrossRef(G);
+    }
+    
+    ///The heap type used by Dijkstra algorithm.
+
+    ///The heap type used by Dijkstra algorithm.
+    ///
+    ///\sa BinHeap
+    ///\sa Dijkstra
+    typedef BinHeap<typename LM::Value, typename GR::template NodeMap<int>,
+		    std::less<Value> > Heap;
+
+    static Heap *createHeap(HeapCrossRef& R) 
+    {
+      return new Heap(R);
+    }
+
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    /// 
+    ///The type of the map that stores the last
+    ///arcs of the shortest paths.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap <typename GR::Node,typename GR::Arc> PredMap;
+    ///Instantiates a PredMap.
+ 
+    ///This function instantiates a \ref PredMap. 
+    ///\param g is the digraph, to which we would like to define the PredMap.
+    ///\todo The digraph alone may be insufficient for the initialization
+#ifdef DOXYGEN
+    static PredMap *createPredMap(const GR &g) 
+#else
+    static PredMap *createPredMap(const GR &) 
+#endif
+    {
+      return new PredMap();
+    }
+    ///The type of the map that stores whether a nodes is processed.
+ 
+    ///The type of the map that stores whether a nodes is processed.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///By default it is a NullMap.
+    ///\todo If it is set to a real map,
+    ///Dijkstra::processed() should read this.
+    ///\todo named parameter to set this type, function to read and write.
+    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
+    ///Instantiates a ProcessedMap.
+ 
+    ///This function instantiates a \ref ProcessedMap. 
+    ///\param g is the digraph, to which
+    ///we would like to define the \ref ProcessedMap
+#ifdef DOXYGEN
+    static ProcessedMap *createProcessedMap(const GR &g)
+#else
+    static ProcessedMap *createProcessedMap(const GR &)
+#endif
+    {
+      return new ProcessedMap();
+    }
+    ///The type of the map that stores the dists of the nodes.
+ 
+    ///The type of the map that stores the dists of the nodes.
+    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
+    ///
+    typedef NullMap<typename Digraph::Node,typename LM::Value> DistMap;
+    ///Instantiates a DistMap.
+ 
+    ///This function instantiates a \ref DistMap. 
+    ///\param g is the digraph, to which we would like to define the \ref DistMap
+#ifdef DOXYGEN
+    static DistMap *createDistMap(const GR &g)
+#else
+    static DistMap *createDistMap(const GR &)
+#endif
+    {
+      return new DistMap();
+    }
+  };
+  
+  /// Default traits used by \ref DijkstraWizard
+
+  /// To make it easier to use Dijkstra algorithm
+  ///we have created a wizard class.
+  /// This \ref DijkstraWizard class needs default traits,
+  ///as well as the \ref Dijkstra class.
+  /// The \ref DijkstraWizardBase is a class to be the default traits of the
+  /// \ref DijkstraWizard class.
+  /// \todo More named parameters are required...
+  template<class GR,class LM>
+  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
+  {
+
+    typedef DijkstraWizardDefaultTraits<GR,LM> Base;
+  protected:
+    /// Type of the nodes in the digraph.
+    typedef typename Base::Digraph::Node Node;
+
+    /// Pointer to the underlying digraph.
+    void *_g;
+    /// Pointer to the length map
+    void *_length;
+    ///Pointer to the map of predecessors arcs.
+    void *_pred;
+    ///Pointer to the map of distances.
+    void *_dist;
+    ///Pointer to the source node.
+    Node _source;
+
+    public:
+    /// Constructor.
+    
+    /// This constructor does not require parameters, therefore it initiates
+    /// all of the attributes to default values (0, INVALID).
+    DijkstraWizardBase() : _g(0), _length(0), _pred(0),
+			   _dist(0), _source(INVALID) {}
+
+    /// Constructor.
+    
+    /// This constructor requires some parameters,
+    /// listed in the parameters list.
+    /// Others are initiated to 0.
+    /// \param g is the initial value of  \ref _g
+    /// \param l is the initial value of  \ref _length
+    /// \param s is the initial value of  \ref _source
+    DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
+      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))), 
+      _length(reinterpret_cast<void*>(const_cast<LM*>(&l))), 
+      _pred(0), _dist(0), _source(s) {}
+
+  };
+  
+  /// A class to make the usage of Dijkstra algorithm easier
+
+  /// This class is created to make it easier to use Dijkstra algorithm.
+  /// It uses the functions and features of the plain \ref Dijkstra,
+  /// but it is much simpler to use it.
+  ///
+  /// Simplicity means that the way to change the types defined
+  /// in the traits class is based on functions that returns the new class
+  /// and not on templatable built-in classes.
+  /// When using the plain \ref Dijkstra
+  /// the new class with the modified type comes from
+  /// the original class by using the ::
+  /// operator. In the case of \ref DijkstraWizard only
+  /// a function have to be called and it will
+  /// return the needed class.
+  ///
+  /// It does not have own \ref run method. When its \ref run method is called
+  /// it initiates a plain \ref Dijkstra class, and calls the \ref 
+  /// Dijkstra::run method of it.
+  template<class TR>
+  class DijkstraWizard : public TR
+  {
+    typedef TR Base;
+
+    ///The type of the underlying digraph.
+    typedef typename TR::Digraph Digraph;
+    //\e
+    typedef typename Digraph::Node Node;
+    //\e
+    typedef typename Digraph::NodeIt NodeIt;
+    //\e
+    typedef typename Digraph::Arc Arc;
+    //\e
+    typedef typename Digraph::OutArcIt OutArcIt;
+    
+    ///The type of the map that stores the arc lengths.
+    typedef typename TR::LengthMap LengthMap;
+    ///The type of the length of the arcs.
+    typedef typename LengthMap::Value Value;
+    ///\brief The type of the map that stores the last
+    ///arcs of the shortest paths.
+    typedef typename TR::PredMap PredMap;
+    ///The type of the map that stores the dists of the nodes.
+    typedef typename TR::DistMap DistMap;
+    ///The heap type used by the dijkstra algorithm.
+    typedef typename TR::Heap Heap;
+  public:
+    /// Constructor.
+    DijkstraWizard() : TR() {}
+
+    /// Constructor that requires parameters.
+
+    /// Constructor that requires parameters.
+    /// These parameters will be the default values for the traits class.
+    DijkstraWizard(const Digraph &g,const LengthMap &l, Node s=INVALID) :
+      TR(g,l,s) {}
+
+    ///Copy constructor
+    DijkstraWizard(const TR &b) : TR(b) {}
+
+    ~DijkstraWizard() {}
+
+    ///Runs Dijkstra algorithm from a given node.
+    
+    ///Runs Dijkstra algorithm from a given node.
+    ///The node can be given by the \ref source function.
+    void run()
+    {
+      if(Base::_source==INVALID) throw UninitializedParameter();
+      Dijkstra<Digraph,LengthMap,TR> 
+	dij(*reinterpret_cast<const Digraph*>(Base::_g),
+            *reinterpret_cast<const LengthMap*>(Base::_length));
+      if(Base::_pred) dij.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
+      if(Base::_dist) dij.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
+      dij.run(Base::_source);
+    }
+
+    ///Runs Dijkstra algorithm from the given node.
+
+    ///Runs Dijkstra algorithm from the given node.
+    ///\param s is the given source.
+    void run(Node s)
+    {
+      Base::_source=s;
+      run();
+    }
+
+    template<class T>
+    struct DefPredMapBase : public Base {
+      typedef T PredMap;
+      static PredMap *createPredMap(const Digraph &) { return 0; };
+      DefPredMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting PredMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting PredMap type
+    ///
+    template<class T>
+    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t) 
+    {
+      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DijkstraWizard<DefPredMapBase<T> >(*this);
+    }
+    
+    template<class T>
+    struct DefDistMapBase : public Base {
+      typedef T DistMap;
+      static DistMap *createDistMap(const Digraph &) { return 0; };
+      DefDistMapBase(const TR &b) : TR(b) {}
+    };
+    
+    ///\brief \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    /// \ref named-templ-param "Named parameter"
+    ///function for setting DistMap type
+    ///
+    template<class T>
+    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t) 
+    {
+      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
+      return DijkstraWizard<DefDistMapBase<T> >(*this);
+    }
+    
+    /// Sets the source node, from which the Dijkstra algorithm runs.
+
+    /// Sets the source node, from which the Dijkstra algorithm runs.
+    /// \param s is the source node.
+    DijkstraWizard<TR> &source(Node s) 
+    {
+      Base::_source=s;
+      return *this;
+    }
+    
+  };
+  
+  ///Function type interface for Dijkstra algorithm.
+
+  /// \ingroup shortest_path
+  ///Function type interface for Dijkstra algorithm.
+  ///
+  ///This function also has several
+  ///\ref named-templ-func-param "named parameters",
+  ///they are declared as the members of class \ref DijkstraWizard.
+  ///The following
+  ///example shows how to use these parameters.
+  ///\code
+  ///  dijkstra(g,length,source).predMap(preds).run();
+  ///\endcode
+  ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
+  ///to the end of the parameter list.
+  ///\sa DijkstraWizard
+  ///\sa Dijkstra
+  template<class GR, class LM>
+  DijkstraWizard<DijkstraWizardBase<GR,LM> >
+  dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
+  {
+    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
+  }
+
+} //END OF NAMESPACE LEMON
+
+#endif
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/graph_utils.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/graph_utils.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,3179 @@
+/* -*- 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_GRAPH_UTILS_H
+#define LEMON_GRAPH_UTILS_H
+
+#include <iterator>
+#include <vector>
+#include <map>
+#include <cmath>
+#include <algorithm>
+
+#include <lemon/bits/invalid.h>
+#include <lemon/bits/utility.h>
+#include <lemon/maps.h>
+#include <lemon/bits/traits.h>
+
+#include <lemon/bits/alteration_notifier.h>
+#include <lemon/bits/default_map.h>
+
+///\ingroup gutils
+///\file
+///\brief Digraph utilities.
+
+namespace lemon {
+
+  /// \addtogroup gutils
+  /// @{
+
+  ///Creates convenience typedefs for the digraph types and iterators
+
+  ///This \c \#define creates convenience typedefs for the following types
+  ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
+  ///\c OutArcIt
+  ///\note If \c G it a template parameter, it should be used in this way.
+  ///\code
+  ///  GRAPH_TYPEDEFS(typename G);
+  ///\endcode
+  ///
+  ///\warning There are no typedefs for the digraph maps because of the lack of
+  ///template typedefs in C++.
+#define GRAPH_TYPEDEFS(Digraph)				\
+  typedef Digraph::     Node      Node;			\
+    typedef Digraph::   NodeIt    NodeIt;			\
+    typedef Digraph::   Arc      Arc;			\
+    typedef Digraph::   ArcIt    ArcIt;			\
+    typedef Digraph:: InArcIt  InArcIt;			\
+    typedef Digraph::OutArcIt OutArcIt
+
+  ///Creates convenience typedefs for the graph types and iterators
+
+  ///This \c \#define creates the same convenience typedefs as defined by
+  ///\ref GRAPH_TYPEDEFS(Digraph) and three more, namely it creates
+  ///\c Edge, \c EdgeIt, \c IncArcIt,
+  ///
+  ///\note If \c G it a template parameter, it should be used in this way.
+  ///\code
+  ///  UGRAPH_TYPEDEFS(typename G);
+  ///\endcode
+  ///
+  ///\warning There are no typedefs for the digraph maps because of the lack of
+  ///template typedefs in C++.
+#define UGRAPH_TYPEDEFS(Digraph)				\
+  GRAPH_TYPEDEFS(Digraph);				\
+    typedef Digraph:: Edge   Edge;			\
+    typedef Digraph:: EdgeIt EdgeIt;			\
+    typedef Digraph:: IncArcIt   IncArcIt
+
+  ///\brief Creates convenience typedefs for the bipartite digraph 
+  ///types and iterators
+
+  ///This \c \#define creates the same convenience typedefs as defined by
+  ///\ref UGRAPH_TYPEDEFS(Digraph) and two more, namely it creates
+  ///\c RedIt, \c BlueIt, 
+  ///
+  ///\note If \c G it a template parameter, it should be used in this way.
+  ///\code
+  ///  BPUGRAPH_TYPEDEFS(typename G);
+  ///\endcode
+  ///
+  ///\warning There are no typedefs for the digraph maps because of the lack of
+  ///template typedefs in C++.
+#define BPUGRAPH_TYPEDEFS(Digraph)            \
+  UGRAPH_TYPEDEFS(Digraph);		    \
+    typedef Digraph::Red Red;             \
+    typedef Digraph::Blue Blue;             \
+    typedef Digraph::RedIt RedIt;	    \
+    typedef Digraph::BlueIt BlueIt
+
+  /// \brief Function to count the items in the digraph.
+  ///
+  /// This function counts the items (nodes, arcs etc) in the digraph.
+  /// The complexity of the function is O(n) because
+  /// it iterates on all of the items.
+
+  template <typename Digraph, typename Item>
+  inline int countItems(const Digraph& g) {
+    typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+    int num = 0;
+    for (ItemIt it(g); it != INVALID; ++it) {
+      ++num;
+    }
+    return num;
+  }
+
+  // Node counting:
+
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct CountNodesSelector {
+      static int count(const Digraph &g) {
+        return countItems<Digraph, typename Digraph::Node>(g);
+      }
+    };
+
+    template <typename Digraph>
+    struct CountNodesSelector<
+      Digraph, typename 
+      enable_if<typename Digraph::NodeNumTag, void>::type> 
+    {
+      static int count(const Digraph &g) {
+        return g.nodeNum();
+      }
+    };    
+  }
+
+  /// \brief Function to count the nodes in the digraph.
+  ///
+  /// This function counts the nodes in the digraph.
+  /// The complexity of the function is O(n) but for some
+  /// digraph structures it is specialized to run in O(1).
+  ///
+  /// If the digraph contains a \e nodeNum() member function and a 
+  /// \e NodeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the node set.
+  template <typename Digraph>
+  inline int countNodes(const Digraph& g) {
+    return _digraph_utils_bits::CountNodesSelector<Digraph>::count(g);
+  }
+
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct CountRedsSelector {
+      static int count(const Digraph &g) {
+        return countItems<Digraph, typename Digraph::Red>(g);
+      }
+    };
+
+    template <typename Digraph>
+    struct CountRedsSelector<
+      Digraph, typename 
+      enable_if<typename Digraph::NodeNumTag, void>::type> 
+    {
+      static int count(const Digraph &g) {
+        return g.redNum();
+      }
+    };    
+  }
+
+  /// \brief Function to count the reds in the digraph.
+  ///
+  /// This function counts the reds in the digraph.
+  /// The complexity of the function is O(an) but for some
+  /// digraph structures it is specialized to run in O(1).
+  ///
+  /// If the digraph contains an \e redNum() member function and a 
+  /// \e NodeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the A-node set.
+  template <typename Digraph>
+  inline int countReds(const Digraph& g) {
+    return _digraph_utils_bits::CountRedsSelector<Digraph>::count(g);
+  }
+
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct CountBluesSelector {
+      static int count(const Digraph &g) {
+        return countItems<Digraph, typename Digraph::Blue>(g);
+      }
+    };
+
+    template <typename Digraph>
+    struct CountBluesSelector<
+      Digraph, typename 
+      enable_if<typename Digraph::NodeNumTag, void>::type> 
+    {
+      static int count(const Digraph &g) {
+        return g.blueNum();
+      }
+    };    
+  }
+
+  /// \brief Function to count the blues in the digraph.
+  ///
+  /// This function counts the blues in the digraph.
+  /// The complexity of the function is O(bn) but for some
+  /// digraph structures it is specialized to run in O(1).
+  ///
+  /// If the digraph contains a \e blueNum() member function and a 
+  /// \e NodeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the B-node set.
+  template <typename Digraph>
+  inline int countBlues(const Digraph& g) {
+    return _digraph_utils_bits::CountBluesSelector<Digraph>::count(g);
+  }
+
+
+  // Arc counting:
+
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct CountArcsSelector {
+      static int count(const Digraph &g) {
+        return countItems<Digraph, typename Digraph::Arc>(g);
+      }
+    };
+
+    template <typename Digraph>
+    struct CountArcsSelector<
+      Digraph, 
+      typename enable_if<typename Digraph::ArcNumTag, void>::type> 
+    {
+      static int count(const Digraph &g) {
+        return g.arcNum();
+      }
+    };    
+  }
+
+  /// \brief Function to count the arcs in the digraph.
+  ///
+  /// This function counts the arcs in the digraph.
+  /// The complexity of the function is O(e) but for some
+  /// digraph structures it is specialized to run in O(1).
+  ///
+  /// If the digraph contains a \e arcNum() member function and a 
+  /// \e ArcNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the arc set.
+  template <typename Digraph>
+  inline int countArcs(const Digraph& g) {
+    return _digraph_utils_bits::CountArcsSelector<Digraph>::count(g);
+  }
+
+  // Undirected arc counting:
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct CountEdgesSelector {
+      static int count(const Digraph &g) {
+        return countItems<Digraph, typename Digraph::Edge>(g);
+      }
+    };
+
+    template <typename Digraph>
+    struct CountEdgesSelector<
+      Digraph, 
+      typename enable_if<typename Digraph::ArcNumTag, void>::type> 
+    {
+      static int count(const Digraph &g) {
+        return g.edgeNum();
+      }
+    };    
+  }
+
+  /// \brief Function to count the edges in the digraph.
+  ///
+  /// This function counts the edges in the digraph.
+  /// The complexity of the function is O(e) but for some
+  /// digraph structures it is specialized to run in O(1).
+  ///
+  /// If the digraph contains a \e edgeNum() member function and a 
+  /// \e ArcNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the edge set.
+  template <typename Digraph>
+  inline int countEdges(const Digraph& g) {
+    return _digraph_utils_bits::CountEdgesSelector<Digraph>::count(g);
+
+  }
+
+
+  template <typename Digraph, typename DegIt>
+  inline int countNodeDegree(const Digraph& _g, const typename Digraph::Node& _n) {
+    int num = 0;
+    for (DegIt it(_g, _n); it != INVALID; ++it) {
+      ++num;
+    }
+    return num;
+  }
+
+  /// \brief Function to count the number of the out-arcs from node \c n.
+  ///
+  /// This function counts the number of the out-arcs from node \c n
+  /// in the digraph.  
+  template <typename Digraph>
+  inline int countOutArcs(const Digraph& _g,  const typename Digraph::Node& _n) {
+    return countNodeDegree<Digraph, typename Digraph::OutArcIt>(_g, _n);
+  }
+
+  /// \brief Function to count the number of the in-arcs to node \c n.
+  ///
+  /// This function counts the number of the in-arcs to node \c n
+  /// in the digraph.  
+  template <typename Digraph>
+  inline int countInArcs(const Digraph& _g,  const typename Digraph::Node& _n) {
+    return countNodeDegree<Digraph, typename Digraph::InArcIt>(_g, _n);
+  }
+
+  /// \brief Function to count the number of the inc-arcs to node \c n.
+  ///
+  /// This function counts the number of the inc-arcs to node \c n
+  /// in the digraph.  
+  template <typename Digraph>
+  inline int countIncArcs(const Digraph& _g,  const typename Digraph::Node& _n) {
+    return countNodeDegree<Digraph, typename Digraph::IncArcIt>(_g, _n);
+  }
+
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct FindArcSelector {
+      typedef typename Digraph::Node Node;
+      typedef typename Digraph::Arc Arc;
+      static Arc find(const Digraph &g, Node u, Node v, Arc e) {
+        if (e == INVALID) {
+          g.firstOut(e, u);
+        } else {
+          g.nextOut(e);
+        }
+        while (e != INVALID && g.target(e) != v) {
+          g.nextOut(e);
+        }
+        return e;
+      }
+    };
+
+    template <typename Digraph>
+    struct FindArcSelector<
+      Digraph, 
+      typename enable_if<typename Digraph::FindArcTag, void>::type> 
+    {
+      typedef typename Digraph::Node Node;
+      typedef typename Digraph::Arc Arc;
+      static Arc find(const Digraph &g, Node u, Node v, Arc prev) {
+        return g.findArc(u, v, prev);
+      }
+    };    
+  }
+
+  /// \brief Finds an arc between two nodes of a digraph.
+  ///
+  /// Finds an arc from node \c u to node \c v in digraph \c g.
+  ///
+  /// If \c prev is \ref INVALID (this is the default value), then
+  /// it finds the first arc from \c u to \c v. Otherwise it looks for
+  /// the next arc from \c u to \c v after \c prev.
+  /// \return The found arc or \ref INVALID if there is no such an arc.
+  ///
+  /// Thus you can iterate through each arc from \c u to \c v as it follows.
+  ///\code
+  /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa ArcLookUp
+  ///\sa AllArcLookUp
+  ///\sa DynArcLookUp
+  ///\sa ConArcIt
+  template <typename Digraph>
+  inline typename Digraph::Arc 
+  findArc(const Digraph &g, typename Digraph::Node u, typename Digraph::Node v,
+           typename Digraph::Arc prev = INVALID) {
+    return _digraph_utils_bits::FindArcSelector<Digraph>::find(g, u, v, prev);
+  }
+
+  /// \brief Iterator for iterating on arcs connected the same nodes.
+  ///
+  /// Iterator for iterating on arcs connected the same nodes. It is 
+  /// higher level interface for the findArc() function. You can
+  /// use it the following way:
+  ///\code
+  /// for (ConArcIt<Digraph> it(g, src, trg); it != INVALID; ++it) {
+  ///   ...
+  /// }
+  ///\endcode
+  /// 
+  ///\sa findArc()
+  ///\sa ArcLookUp
+  ///\sa AllArcLookUp
+  ///\sa DynArcLookUp
+  ///
+  /// \author Balazs Dezso 
+  template <typename _Digraph>
+  class ConArcIt : public _Digraph::Arc {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Parent;
+
+    typedef typename Digraph::Arc Arc;
+    typedef typename Digraph::Node Node;
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConArcIt iterating on the arcs which
+    /// connects the \c u and \c v node.
+    ConArcIt(const Digraph& g, Node u, Node v) : digraph(g) {
+      Parent::operator=(findArc(digraph, u, v));
+    }
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConArcIt which continues the iterating from 
+    /// the \c e arc.
+    ConArcIt(const Digraph& g, Arc e) : Parent(e), digraph(g) {}
+    
+    /// \brief Increment operator.
+    ///
+    /// It increments the iterator and gives back the next arc.
+    ConArcIt& operator++() {
+      Parent::operator=(findArc(digraph, digraph.source(*this), 
+				 digraph.target(*this), *this));
+      return *this;
+    }
+  private:
+    const Digraph& digraph;
+  };
+
+  namespace _digraph_utils_bits {
+    
+    template <typename Digraph, typename Enable = void>
+    struct FindEdgeSelector {
+      typedef typename Digraph::Node Node;
+      typedef typename Digraph::Edge Edge;
+      static Edge find(const Digraph &g, Node u, Node v, Edge e) {
+        bool b;
+        if (u != v) {
+          if (e == INVALID) {
+            g.firstInc(e, b, u);
+          } else {
+            b = g.source(e) == u;
+            g.nextInc(e, b);
+          }
+          while (e != INVALID && (b ? g.target(e) : g.source(e)) != v) {
+            g.nextInc(e, b);
+          }
+        } else {
+          if (e == INVALID) {
+            g.firstInc(e, b, u);
+          } else {
+            b = true;
+            g.nextInc(e, b);
+          }
+          while (e != INVALID && (!b || g.target(e) != v)) {
+            g.nextInc(e, b);
+          }
+        }
+        return e;
+      }
+    };
+
+    template <typename Digraph>
+    struct FindEdgeSelector<
+      Digraph, 
+      typename enable_if<typename Digraph::FindArcTag, void>::type> 
+    {
+      typedef typename Digraph::Node Node;
+      typedef typename Digraph::Edge Edge;
+      static Edge find(const Digraph &g, Node u, Node v, Edge prev) {
+        return g.findEdge(u, v, prev);
+      }
+    };    
+  }
+
+  /// \brief Finds an edge between two nodes of a digraph.
+  ///
+  /// Finds an edge from node \c u to node \c v in digraph \c g.
+  /// If the node \c u and node \c v is equal then each loop arc
+  /// will be enumerated.
+  ///
+  /// If \c prev is \ref INVALID (this is the default value), then
+  /// it finds the first arc from \c u to \c v. Otherwise it looks for
+  /// the next arc from \c u to \c v after \c prev.
+  /// \return The found arc or \ref INVALID if there is no such an arc.
+  ///
+  /// Thus you can iterate through each arc from \c u to \c v as it follows.
+  ///\code
+  /// for(Edge e = findEdge(g,u,v); e != INVALID; 
+  ///     e = findEdge(g,u,v,e)) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa ConArcIt
+
+  template <typename Digraph>
+  inline typename Digraph::Edge 
+  findEdge(const Digraph &g, typename Digraph::Node u, typename Digraph::Node v,
+            typename Digraph::Edge p = INVALID) {
+    return _digraph_utils_bits::FindEdgeSelector<Digraph>::find(g, u, v, p);
+  }
+
+  /// \brief Iterator for iterating on edges connected the same nodes.
+  ///
+  /// Iterator for iterating on edges connected the same nodes. It is 
+  /// higher level interface for the findEdge() function. You can
+  /// use it the following way:
+  ///\code
+  /// for (ConEdgeIt<Digraph> it(g, src, trg); it != INVALID; ++it) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\sa findEdge()
+  ///
+  /// \author Balazs Dezso 
+  template <typename _Digraph>
+  class ConEdgeIt : public _Digraph::Edge {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Edge Parent;
+
+    typedef typename Digraph::Edge Edge;
+    typedef typename Digraph::Node Node;
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConEdgeIt iterating on the arcs which
+    /// connects the \c u and \c v node.
+    ConEdgeIt(const Digraph& g, Node u, Node v) : digraph(g) {
+      Parent::operator=(findEdge(digraph, u, v));
+    }
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConEdgeIt which continues the iterating from 
+    /// the \c e arc.
+    ConEdgeIt(const Digraph& g, Edge e) : Parent(e), digraph(g) {}
+    
+    /// \brief Increment operator.
+    ///
+    /// It increments the iterator and gives back the next arc.
+    ConEdgeIt& operator++() {
+      Parent::operator=(findEdge(digraph, digraph.source(*this), 
+				      digraph.target(*this), *this));
+      return *this;
+    }
+  private:
+    const Digraph& digraph;
+  };
+
+  /// \brief Copy a map.
+  ///
+  /// This function copies the \c from map to the \c to map. It uses the
+  /// given iterator to iterate on the data structure and it uses the \c ref
+  /// mapping to convert the from's keys to the to's keys.
+  template <typename To, typename From, 
+	    typename ItemIt, typename Ref>	    
+  void copyMap(To& to, const From& from, 
+	       ItemIt it, const Ref& ref) {
+    for (; it != INVALID; ++it) {
+      to[ref[it]] = from[it];
+    }
+  }
+
+  /// \brief Copy the from map to the to map.
+  ///
+  /// Copy the \c from map to the \c to map. It uses the given iterator
+  /// to iterate on the data structure.
+  template <typename To, typename From, typename ItemIt>	    
+  void copyMap(To& to, const From& from, ItemIt it) {
+    for (; it != INVALID; ++it) {
+      to[it] = from[it];
+    }
+  }
+
+  namespace _digraph_utils_bits {
+
+    template <typename Digraph, typename Item, typename RefMap>
+    class MapCopyBase {
+    public:
+      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
+      
+      virtual ~MapCopyBase() {}
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, 
+              typename ToMap, typename FromMap>
+    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      MapCopy(ToMap& tmap, const FromMap& map) 
+        : _tmap(tmap), _map(map) {}
+      
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _tmap.set(refMap[it], _map[it]);
+        }
+      }
+
+    private:
+      ToMap& _tmap;
+      const FromMap& _map;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, typename It>
+    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
+      
+      virtual void copy(const Digraph&, const RefMap& refMap) {
+        _it = refMap[_item];
+      }
+
+    private:
+      It& _it;
+      Item _item;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, typename Ref>
+    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      RefCopy(Ref& map) : _map(map) {}
+      
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _map.set(it, refMap[it]);
+        }
+      }
+
+    private:
+      Ref& _map;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, 
+              typename CrossRef>
+    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
+      
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _cmap.set(refMap[it], it);
+        }
+      }
+
+    private:
+      CrossRef& _cmap;
+    };
+
+    template <typename Digraph, typename Enable = void>
+    struct DigraphCopySelector {
+      template <typename From, typename NodeRefMap, typename ArcRefMap>
+      static void copy(Digraph &to, const From& from,
+                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+        for (typename From::NodeIt it(from); it != INVALID; ++it) {
+          nodeRefMap[it] = to.addNode();
+        }
+        for (typename From::ArcIt it(from); it != INVALID; ++it) {
+          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
+                                          nodeRefMap[from.target(it)]);
+        }
+      }
+    };
+
+    template <typename Digraph>
+    struct DigraphCopySelector<
+      Digraph, 
+      typename enable_if<typename Digraph::BuildTag, void>::type> 
+    {
+      template <typename From, typename NodeRefMap, typename ArcRefMap>
+      static void copy(Digraph &to, const From& from,
+                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+        to.build(from, nodeRefMap, arcRefMap);
+      }
+    };
+
+    template <typename Graph, typename Enable = void>
+    struct GraphCopySelector {
+      template <typename From, typename NodeRefMap, typename EdgeRefMap>
+      static void copy(Graph &to, const From& from,
+                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+        for (typename From::NodeIt it(from); it != INVALID; ++it) {
+          nodeRefMap[it] = to.addNode();
+        }
+        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
+          edgeRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 
+				       nodeRefMap[from.target(it)]);
+        }
+      }
+    };
+
+    template <typename Graph>
+    struct GraphCopySelector<
+      Graph, 
+      typename enable_if<typename Graph::BuildTag, void>::type> 
+    {
+      template <typename From, typename NodeRefMap, typename EdgeRefMap>
+      static void copy(Graph &to, const From& from,
+                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+        to.build(from, nodeRefMap, edgeRefMap);
+      }
+    };
+
+    template <typename BpGraph, typename Enable = void>
+    struct BpGraphCopySelector {
+      template <typename From, typename RedRefMap, 
+                typename BlueRefMap, typename EdgeRefMap>
+      static void copy(BpGraph &to, const From& from,
+                       RedRefMap& redRefMap, BlueRefMap& blueRefMap,
+                       EdgeRefMap& edgeRefMap) {
+        for (typename From::RedIt it(from); it != INVALID; ++it) {
+          redRefMap[it] = to.addRed();
+        }
+        for (typename From::BlueIt it(from); it != INVALID; ++it) {
+          blueRefMap[it] = to.addBlue();
+        }
+        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
+          edgeRefMap[it] = to.addArc(redRefMap[from.red(it)], 
+                                           blueRefMap[from.blue(it)]);
+        }
+      }
+    };
+
+    template <typename BpGraph>
+    struct BpGraphCopySelector<
+      BpGraph, 
+      typename enable_if<typename BpGraph::BuildTag, void>::type> 
+    {
+      template <typename From, typename RedRefMap, 
+                typename BlueRefMap, typename EdgeRefMap>
+      static void copy(BpGraph &to, const From& from,
+                       RedRefMap& redRefMap, BlueRefMap& blueRefMap,
+                       EdgeRefMap& edgeRefMap) {
+        to.build(from, redRefMap, blueRefMap, edgeRefMap);
+      }
+    };
+    
+
+  }
+
+  /// \brief Class to copy a digraph.
+  ///
+  /// Class to copy a digraph to another digraph (duplicate a digraph). The
+  /// simplest way of using it is through the \c copyDigraph() function.
+  template <typename To, typename From>
+  class DigraphCopy {
+  private:
+
+    typedef typename From::Node Node;
+    typedef typename From::NodeIt NodeIt;
+    typedef typename From::Arc Arc;
+    typedef typename From::ArcIt ArcIt;
+
+    typedef typename To::Node TNode;
+    typedef typename To::Arc TArc;
+
+    typedef typename From::template NodeMap<TNode> NodeRefMap;
+    typedef typename From::template ArcMap<TArc> ArcRefMap;
+    
+    
+  public: 
+
+
+    /// \brief Constructor for the DigraphCopy.
+    ///
+    /// It copies the content of the \c _from digraph into the
+    /// \c _to digraph.
+    DigraphCopy(To& _to, const From& _from) 
+      : from(_from), to(_to) {}
+
+    /// \brief Destructor of the DigraphCopy
+    ///
+    /// Destructor of the DigraphCopy
+    ~DigraphCopy() {
+      for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+        delete nodeMapCopies[i];
+      }
+      for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+        delete arcMapCopies[i];
+      }
+
+    }
+
+    /// \brief Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map.
+    template <typename NodeRef>
+    DigraphCopy& nodeRef(NodeRef& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Node, 
+                              NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map.
+    template <typename NodeCrossRef>
+    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, Node,
+                              NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's node type,
+    /// and the copied map's key type is the from digraph's node
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Node, 
+                              NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    DigraphCopy& node(TNode& tnode, const Node& snode) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Node, 
+                              NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    DigraphCopy& arcRef(ArcRef& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Arc, 
+                              ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, Arc,
+                              ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's arc type,
+    /// and the copied map's key type is the from digraph's arc
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Arc, 
+                              ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      arcMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Arc, 
+                              ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      NodeRefMap nodeRefMap(from);
+      ArcRefMap arcRefMap(from);
+      _digraph_utils_bits::DigraphCopySelector<To>::
+        copy(to, from, nodeRefMap, arcRefMap);
+      for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+        nodeMapCopies[i]->copy(from, nodeRefMap);
+      }
+      for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+        arcMapCopies[i]->copy(from, arcRefMap);
+      }      
+    }
+
+  protected:
+
+
+    const From& from;
+    To& to;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
+    nodeMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
+    arcMapCopies;
+
+  };
+
+  /// \brief Copy a digraph to another digraph.
+  ///
+  /// Copy a digraph to another digraph.
+  /// The usage of the function:
+  /// 
+  ///\code
+  /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+  ///\endcode
+  /// 
+  /// After the copy the \c nr map will contain the mapping from the
+  /// nodes of the \c from digraph to the nodes of the \c to digraph and
+  /// \c ecr will contain the mapping from the arcs of the \c to digraph
+  /// to the arcs of the \c from digraph.
+  ///
+  /// \see DigraphCopy 
+  template <typename To, typename From>
+  DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
+    return DigraphCopy<To, From>(to, from);
+  }
+
+  /// \brief Class to copy an graph.
+  ///
+  /// Class to copy an graph to another digraph (duplicate a digraph).
+  /// The simplest way of using it is through the \c copyGraph() function.
+  template <typename To, typename From>
+  class GraphCopy {
+  private:
+
+    typedef typename From::Node Node;
+    typedef typename From::NodeIt NodeIt;
+    typedef typename From::Arc Arc;
+    typedef typename From::ArcIt ArcIt;
+    typedef typename From::Edge Edge;
+    typedef typename From::EdgeIt EdgeIt;
+
+    typedef typename To::Node TNode;
+    typedef typename To::Arc TArc;
+    typedef typename To::Edge TEdge;
+
+    typedef typename From::template NodeMap<TNode> NodeRefMap;
+    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
+
+    struct ArcRefMap {
+      ArcRefMap(const To& _to, const From& _from,
+                 const EdgeRefMap& _edge_ref, const NodeRefMap& _node_ref) 
+        : to(_to), from(_from), 
+          edge_ref(_edge_ref), node_ref(_node_ref) {}
+
+      typedef typename From::Arc Key;
+      typedef typename To::Arc Value;
+
+      Value operator[](const Key& key) const {
+        bool forward = 
+          (from.direction(key) == 
+           (node_ref[from.source(static_cast<const Edge&>(key))] == 
+            to.source(edge_ref[static_cast<const Edge&>(key)])));
+	return to.direct(edge_ref[key], forward); 
+      }
+      
+      const To& to;
+      const From& from;
+      const EdgeRefMap& edge_ref;
+      const NodeRefMap& node_ref;
+    };
+
+    
+  public: 
+
+
+    /// \brief Constructor for the DigraphCopy.
+    ///
+    /// It copies the content of the \c _from digraph into the
+    /// \c _to digraph.
+    GraphCopy(To& _to, const From& _from) 
+      : from(_from), to(_to) {}
+
+    /// \brief Destructor of the DigraphCopy
+    ///
+    /// Destructor of the DigraphCopy
+    ~GraphCopy() {
+      for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+        delete nodeMapCopies[i];
+      }
+      for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+        delete arcMapCopies[i];
+      }
+      for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+        delete edgeMapCopies[i];
+      }
+
+    }
+
+    /// \brief Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map.
+    template <typename NodeRef>
+    GraphCopy& nodeRef(NodeRef& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Node, 
+                              NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map.
+    template <typename NodeCrossRef>
+    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, Node,
+                              NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's node type,
+    /// and the copied map's key type is the from digraph's node
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Node, 
+                              NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    GraphCopy& node(TNode& tnode, const Node& snode) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Node, 
+                              NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    GraphCopy& arcRef(ArcRef& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Arc, 
+                              ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    GraphCopy& arcCrossRef(ArcCrossRef& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, Arc,
+                              ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's arc type,
+    /// and the copied map's key type is the from digraph's arc
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Arc, 
+                              ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    GraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      arcMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Arc, 
+                              ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Copies the edge references into the given map.
+    ///
+    /// Copies the edge references into the given map.
+    template <typename EdgeRef>
+    GraphCopy& edgeRef(EdgeRef& map) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Edge, 
+                               EdgeRefMap, EdgeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the edge cross references into the given map.
+    ///
+    /// Copies the edge cross references (reverse
+    /// references) into the given map.
+    template <typename EdgeCrossRef>
+    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, 
+                               Edge, EdgeRefMap, EdgeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's edge type,
+    /// and the copied map's key type is the from digraph's edge
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Edge, 
+                               EdgeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given edge.
+    ///
+    /// Make a copy of the given edge.
+    GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Edge, 
+                               EdgeRefMap, TEdge>(tedge, sedge));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      NodeRefMap nodeRefMap(from);
+      EdgeRefMap edgeRefMap(from);
+      ArcRefMap arcRefMap(to, from, edgeRefMap, nodeRefMap);
+      _digraph_utils_bits::GraphCopySelector<To>::
+        copy(to, from, nodeRefMap, edgeRefMap);
+      for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+        nodeMapCopies[i]->copy(from, nodeRefMap);
+      }
+      for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+        edgeMapCopies[i]->copy(from, edgeRefMap);
+      }
+      for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+        arcMapCopies[i]->copy(from, arcRefMap);
+      }
+    }
+
+  private:
+    
+    const From& from;
+    To& to;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
+    nodeMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
+    arcMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* > 
+    edgeMapCopies;
+
+  };
+
+  /// \brief Copy an graph to another digraph.
+  ///
+  /// Copy an graph to another digraph.
+  /// The usage of the function:
+  /// 
+  ///\code
+  /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+  ///\endcode
+  /// 
+  /// After the copy the \c nr map will contain the mapping from the
+  /// nodes of the \c from digraph to the nodes of the \c to digraph and
+  /// \c ecr will contain the mapping from the arcs of the \c to digraph
+  /// to the arcs of the \c from digraph.
+  ///
+  /// \see GraphCopy 
+  template <typename To, typename From>
+  GraphCopy<To, From> 
+  copyGraph(To& to, const From& from) {
+    return GraphCopy<To, From>(to, from);
+  }
+
+  /// \brief Class to copy a bipartite digraph.
+  ///
+  /// Class to copy a bipartite digraph to another digraph
+  /// (duplicate a digraph).  The simplest way of using it is through
+  /// the \c copyBpGraph() function.
+  template <typename To, typename From>
+  class BpGraphCopy {
+  private:
+
+    typedef typename From::Node Node;
+    typedef typename From::Red Red;
+    typedef typename From::Blue Blue;
+    typedef typename From::NodeIt NodeIt;
+    typedef typename From::Arc Arc;
+    typedef typename From::ArcIt ArcIt;
+    typedef typename From::Edge Edge;
+    typedef typename From::EdgeIt EdgeIt;
+
+    typedef typename To::Node TNode;
+    typedef typename To::Arc TArc;
+    typedef typename To::Edge TEdge;
+
+    typedef typename From::template RedMap<TNode> RedRefMap;
+    typedef typename From::template BlueMap<TNode> BlueRefMap;
+    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
+
+    struct NodeRefMap {
+      NodeRefMap(const From& _from, const RedRefMap& _red_ref,
+                 const BlueRefMap& _blue_ref)
+        : from(_from), red_ref(_red_ref), blue_ref(_blue_ref) {}
+
+      typedef typename From::Node Key;
+      typedef typename To::Node Value;
+
+      Value operator[](const Key& key) const {
+	return from.red(key) ? red_ref[key] : blue_ref[key]; 
+      }
+      
+      const From& from;
+      const RedRefMap& red_ref;
+      const BlueRefMap& blue_ref;
+    };
+
+    struct ArcRefMap {
+      ArcRefMap(const To& _to, const From& _from,
+                 const EdgeRefMap& _edge_ref, const NodeRefMap& _node_ref) 
+        : to(_to), from(_from), 
+          edge_ref(_edge_ref), node_ref(_node_ref) {}
+
+      typedef typename From::Arc Key;
+      typedef typename To::Arc Value;
+
+      Value operator[](const Key& key) const {
+        bool forward = 
+          (from.direction(key) == 
+           (node_ref[from.source(static_cast<const Edge&>(key))] == 
+            to.source(edge_ref[static_cast<const Edge&>(key)])));
+	return to.direct(edge_ref[key], forward); 
+      }
+      
+      const To& to;
+      const From& from;
+      const EdgeRefMap& edge_ref;
+      const NodeRefMap& node_ref;
+    };
+    
+  public: 
+
+
+    /// \brief Constructor for the DigraphCopy.
+    ///
+    /// It copies the content of the \c _from digraph into the
+    /// \c _to digraph.
+    BpGraphCopy(To& _to, const From& _from) 
+      : from(_from), to(_to) {}
+
+    /// \brief Destructor of the DigraphCopy
+    ///
+    /// Destructor of the DigraphCopy
+    ~BpGraphCopy() {
+      for (int i = 0; i < int(redMapCopies.size()); ++i) {
+        delete redMapCopies[i];
+      }
+      for (int i = 0; i < int(blueMapCopies.size()); ++i) {
+        delete blueMapCopies[i];
+      }
+      for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+        delete nodeMapCopies[i];
+      }
+      for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+        delete arcMapCopies[i];
+      }
+      for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+        delete edgeMapCopies[i];
+      }
+
+    }
+
+    /// \brief Copies the A-node references into the given map.
+    ///
+    /// Copies the A-node references into the given map.
+    template <typename RedRef>
+    BpGraphCopy& redRef(RedRef& map) {
+      redMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Red, 
+                               RedRefMap, RedRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the A-node cross references into the given map.
+    ///
+    /// Copies the A-node cross references (reverse references) into
+    /// the given map.
+    template <typename RedCrossRef>
+    BpGraphCopy& redCrossRef(RedCrossRef& map) {
+      redMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, 
+                               Red, RedRefMap, RedCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given A-node map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's node type,
+    /// and the copied map's key type is the from digraph's node
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    BpGraphCopy& redMap(ToMap& tmap, const FromMap& map) {
+      redMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Red, 
+                               RedRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Copies the B-node references into the given map.
+    ///
+    /// Copies the B-node references into the given map.
+    template <typename BlueRef>
+    BpGraphCopy& blueRef(BlueRef& map) {
+      blueMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Blue, 
+                               BlueRefMap, BlueRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the B-node cross references into the given map.
+    ///
+    ///  Copies the B-node cross references (reverse references) into
+    ///  the given map.
+    template <typename BlueCrossRef>
+    BpGraphCopy& blueCrossRef(BlueCrossRef& map) {
+      blueMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, 
+                              Blue, BlueRefMap, BlueCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given B-node map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's node type,
+    /// and the copied map's key type is the from digraph's node
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    BpGraphCopy& blueMap(ToMap& tmap, const FromMap& map) {
+      blueMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Blue, 
+                               BlueRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+    /// \brief Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map.
+    template <typename NodeRef>
+    BpGraphCopy& nodeRef(NodeRef& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Node, 
+                              NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map.
+    template <typename NodeCrossRef>
+    BpGraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, Node,
+                              NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's node type,
+    /// and the copied map's key type is the from digraph's node
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    BpGraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Node, 
+                              NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    BpGraphCopy& node(TNode& tnode, const Node& snode) {
+      nodeMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Node, 
+                              NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    BpGraphCopy& arcRef(ArcRef& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Arc, 
+                              ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    BpGraphCopy& arcCrossRef(ArcCrossRef& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, Arc,
+                              ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's arc type,
+    /// and the copied map's key type is the from digraph's arc
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    BpGraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      arcMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Arc, 
+                              ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    BpGraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      arcMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Arc, 
+                              ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Copies the edge references into the given map.
+    ///
+    /// Copies the edge references into the given map.
+    template <typename EdgeRef>
+    BpGraphCopy& edgeRef(EdgeRef& map) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Edge, 
+                               EdgeRefMap, EdgeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the edge cross references into the given map.
+    ///
+    /// Copies the edge cross references (reverse
+    /// references) into the given map.
+    template <typename EdgeCrossRef>
+    BpGraphCopy& edgeCrossRef(EdgeCrossRef& map) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From, 
+                               Edge, EdgeRefMap, EdgeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph. 
+    /// The new map's key type is the to digraph's edge type,
+    /// and the copied map's key type is the from digraph's edge
+    /// type.  
+    template <typename ToMap, typename FromMap>
+    BpGraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Edge, 
+                               EdgeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given edge.
+    ///
+    /// Make a copy of the given edge.
+    BpGraphCopy& edge(TEdge& tedge, const Edge& sedge) {
+      edgeMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Edge, 
+                               EdgeRefMap, TEdge>(tedge, sedge));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      RedRefMap redRefMap(from);
+      BlueRefMap blueRefMap(from);
+      NodeRefMap nodeRefMap(from, redRefMap, blueRefMap);
+      EdgeRefMap edgeRefMap(from);
+      ArcRefMap arcRefMap(to, from, edgeRefMap, nodeRefMap);
+      _digraph_utils_bits::BpGraphCopySelector<To>::
+        copy(to, from, redRefMap, blueRefMap, edgeRefMap);
+      for (int i = 0; i < int(redMapCopies.size()); ++i) {
+        redMapCopies[i]->copy(from, redRefMap);
+      }
+      for (int i = 0; i < int(blueMapCopies.size()); ++i) {
+        blueMapCopies[i]->copy(from, blueRefMap);
+      }
+      for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+        nodeMapCopies[i]->copy(from, nodeRefMap);
+      }
+      for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+        edgeMapCopies[i]->copy(from, edgeRefMap);
+      }
+      for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+        arcMapCopies[i]->copy(from, arcRefMap);
+      }
+    }
+
+  private:
+    
+    const From& from;
+    To& to;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Red, RedRefMap>* > 
+    redMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Blue, BlueRefMap>* > 
+    blueMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* > 
+    nodeMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* > 
+    arcMapCopies;
+
+    std::vector<_digraph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* > 
+    edgeMapCopies;
+
+  };
+
+  /// \brief Copy a bipartite digraph to another digraph.
+  ///
+  /// Copy a bipartite digraph to another digraph.
+  /// The usage of the function:
+  /// 
+  ///\code
+  /// copyBpGraph(trg, src).redRef(anr).arcCrossRef(ecr).run();
+  ///\endcode
+  /// 
+  /// After the copy the \c nr map will contain the mapping from the
+  /// nodes of the \c from digraph to the nodes of the \c to digraph and
+  /// \c ecr will contain the mapping from the arcs of the \c to digraph
+  /// to the arcs of the \c from digraph.
+  ///
+  /// \see BpGraphCopy
+  template <typename To, typename From>
+  BpGraphCopy<To, From> 
+  copyBpGraph(To& to, const From& from) {
+    return BpGraphCopy<To, From>(to, from);
+  }
+
+
+  /// @}
+
+  /// \addtogroup digraph_maps
+  /// @{
+
+  /// Provides an immutable and unique id for each item in the digraph.
+
+  /// The IdMap class provides a unique and immutable id for each item of the
+  /// same type (e.g. node) in the digraph. This id is <ul><li>\b unique:
+  /// different items (nodes) get different ids <li>\b immutable: the id of an
+  /// item (node) does not change (even if you delete other nodes).  </ul>
+  /// Through this map you get access (i.e. can read) the inner id values of
+  /// the items stored in the digraph. This map can be inverted with its member
+  /// class \c InverseMap.
+  ///
+  template <typename _Digraph, typename _Item>
+  class IdMap {
+  public:
+    typedef _Digraph Digraph;
+    typedef int Value;
+    typedef _Item Item;
+    typedef _Item Key;
+
+    /// \brief Constructor.
+    ///
+    /// Constructor of the map.
+    explicit IdMap(const Digraph& _digraph) : digraph(&_digraph) {}
+
+    /// \brief Gives back the \e id of the item.
+    ///
+    /// Gives back the immutable and unique \e id of the item.
+    int operator[](const Item& item) const { return digraph->id(item);}
+
+    /// \brief Gives back the item by its id.
+    ///
+    /// Gives back the item by its id.
+    Item operator()(int id) { return digraph->fromId(id, Item()); }
+
+  private:
+    const Digraph* digraph;
+
+  public:
+
+    /// \brief The class represents the inverse of its owner (IdMap).
+    ///
+    /// The class represents the inverse of its owner (IdMap).
+    /// \see inverse()
+    class InverseMap {
+    public:
+
+      /// \brief Constructor.
+      ///
+      /// Constructor for creating an id-to-item map.
+      explicit InverseMap(const Digraph& _digraph) : digraph(&_digraph) {}
+
+      /// \brief Constructor.
+      ///
+      /// Constructor for creating an id-to-item map.
+      explicit InverseMap(const IdMap& idMap) : digraph(idMap.digraph) {}
+
+      /// \brief Gives back the given item from its id.
+      ///
+      /// Gives back the given item from its id.
+      /// 
+      Item operator[](int id) const { return digraph->fromId(id, Item());}
+
+    private:
+      const Digraph* digraph;
+    };
+
+    /// \brief Gives back the inverse of the map.
+    ///
+    /// Gives back the inverse of the IdMap.
+    InverseMap inverse() const { return InverseMap(*digraph);} 
+
+  };
+
+  
+  /// \brief General invertable digraph-map type.
+
+  /// This type provides simple invertable digraph-maps. 
+  /// The InvertableMap wraps an arbitrary ReadWriteMap 
+  /// and if a key is set to a new value then store it
+  /// in the inverse map.
+  ///
+  /// The values of the map can be accessed
+  /// with stl compatible forward iterator.
+  ///
+  /// \param _Digraph The digraph type.
+  /// \param _Item The item type of the digraph.
+  /// \param _Value The value type of the map.
+  ///
+  /// \see IterableValueMap
+  template <typename _Digraph, typename _Item, typename _Value>
+  class InvertableMap : protected DefaultMap<_Digraph, _Item, _Value> {
+  private:
+    
+    typedef DefaultMap<_Digraph, _Item, _Value> Map;
+    typedef _Digraph Digraph;
+
+    typedef std::map<_Value, _Item> Container;
+    Container invMap;    
+
+  public:
+ 
+    /// The key type of InvertableMap (Node, Arc, Edge).
+    typedef typename Map::Key Key;
+    /// The value type of the InvertableMap.
+    typedef typename Map::Value Value;
+
+
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new InvertableMap for the digraph.
+    ///
+    explicit InvertableMap(const Digraph& digraph) : Map(digraph) {} 
+
+    /// \brief Forward iterator for values.
+    ///
+    /// This iterator is an stl compatible forward
+    /// iterator on the values of the map. The values can
+    /// be accessed in the [beginValue, endValue) range.
+    ///
+    class ValueIterator 
+      : public std::iterator<std::forward_iterator_tag, Value> {
+      friend class InvertableMap;
+    private:
+      ValueIterator(typename Container::const_iterator _it) 
+        : it(_it) {}
+    public:
+      
+      ValueIterator() {}
+
+      ValueIterator& operator++() { ++it; return *this; }
+      ValueIterator operator++(int) { 
+        ValueIterator tmp(*this); 
+        operator++();
+        return tmp; 
+      }
+
+      const Value& operator*() const { return it->first; }
+      const Value* operator->() const { return &(it->first); }
+
+      bool operator==(ValueIterator jt) const { return it == jt.it; }
+      bool operator!=(ValueIterator jt) const { return it != jt.it; }
+      
+    private:
+      typename Container::const_iterator it;
+    };
+
+    /// \brief Returns an iterator to the first value.
+    ///
+    /// Returns an stl compatible iterator to the 
+    /// first value of the map. The values of the
+    /// map can be accessed in the [beginValue, endValue)
+    /// range.
+    ValueIterator beginValue() const {
+      return ValueIterator(invMap.begin());
+    }
+
+    /// \brief Returns an iterator after the last value.
+    ///
+    /// Returns an stl compatible iterator after the 
+    /// last value of the map. The values of the
+    /// map can be accessed in the [beginValue, endValue)
+    /// range.
+    ValueIterator endValue() const {
+      return ValueIterator(invMap.end());
+    }
+    
+    /// \brief The setter function of the map.
+    ///
+    /// Sets the mapped value.
+    void set(const Key& key, const Value& val) {
+      Value oldval = Map::operator[](key);
+      typename Container::iterator it = invMap.find(oldval);
+      if (it != invMap.end() && it->second == key) {
+	invMap.erase(it);
+      }      
+      invMap.insert(make_pair(val, key));
+      Map::set(key, val);
+    }
+
+    /// \brief The getter function of the map.
+    ///
+    /// It gives back the value associated with the key.
+    typename MapTraits<Map>::ConstReturnValue 
+    operator[](const Key& key) const {
+      return Map::operator[](key);
+    }
+
+    /// \brief Gives back the item by its value.
+    ///
+    /// Gives back the item by its value.
+    Key operator()(const Value& key) const {
+      typename Container::const_iterator it = invMap.find(key);
+      return it != invMap.end() ? it->second : INVALID;
+    }
+
+  protected:
+
+    /// \brief Erase the key from the map.
+    ///
+    /// Erase the key to the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const Key& key) {
+      Value val = Map::operator[](key);
+      typename Container::iterator it = invMap.find(val);
+      if (it != invMap.end() && it->second == key) {
+	invMap.erase(it);
+      }
+      Map::erase(key);
+    }
+
+    /// \brief Erase more keys from the map.
+    ///
+    /// Erase more keys from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const std::vector<Key>& keys) {
+      for (int i = 0; i < int(keys.size()); ++i) {
+	Value val = Map::operator[](keys[i]);
+	typename Container::iterator it = invMap.find(val);
+	if (it != invMap.end() && it->second == keys[i]) {
+	  invMap.erase(it);
+	}
+      }
+      Map::erase(keys);
+    }
+
+    /// \brief Clear the keys from the map and inverse map.
+    ///
+    /// Clear the keys from the map and inverse map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void clear() {
+      invMap.clear();
+      Map::clear();
+    }
+
+  public:
+
+    /// \brief The inverse map type.
+    ///
+    /// The inverse of this map. The subscript operator of the map
+    /// gives back always the item what was last assigned to the value. 
+    class InverseMap {
+    public:
+      /// \brief Constructor of the InverseMap.
+      ///
+      /// Constructor of the InverseMap.
+      explicit InverseMap(const InvertableMap& _inverted) 
+        : inverted(_inverted) {}
+
+      /// The value type of the InverseMap.
+      typedef typename InvertableMap::Key Value;
+      /// The key type of the InverseMap.
+      typedef typename InvertableMap::Value Key; 
+
+      /// \brief Subscript operator. 
+      ///
+      /// Subscript operator. It gives back always the item 
+      /// what was last assigned to the value.
+      Value operator[](const Key& key) const {
+	return inverted(key);
+      }
+      
+    private:
+      const InvertableMap& inverted;
+    };
+
+    /// \brief It gives back the just readable inverse map.
+    ///
+    /// It gives back the just readable inverse map.
+    InverseMap inverse() const {
+      return InverseMap(*this);
+    } 
+
+
+    
+  };
+
+  /// \brief Provides a mutable, continuous and unique descriptor for each 
+  /// item in the digraph.
+  ///
+  /// The DescriptorMap class provides a unique and continuous (but mutable)
+  /// descriptor (id) for each item of the same type (e.g. node) in the
+  /// digraph. This id is <ul><li>\b unique: different items (nodes) get
+  /// different ids <li>\b continuous: the range of the ids is the set of
+  /// integers between 0 and \c n-1, where \c n is the number of the items of
+  /// this type (e.g. nodes) (so the id of a node can change if you delete an
+  /// other node, i.e. this id is mutable).  </ul> This map can be inverted
+  /// with its member class \c InverseMap.
+  ///
+  /// \param _Digraph The digraph class the \c DescriptorMap belongs to.
+  /// \param _Item The Item is the Key of the Map. It may be Node, Arc or 
+  /// Edge.
+  template <typename _Digraph, typename _Item>
+  class DescriptorMap : protected DefaultMap<_Digraph, _Item, int> {
+
+    typedef _Item Item;
+    typedef DefaultMap<_Digraph, _Item, int> Map;
+
+  public:
+    /// The digraph class of DescriptorMap.
+    typedef _Digraph Digraph;
+
+    /// The key type of DescriptorMap (Node, Arc, Edge).
+    typedef typename Map::Key Key;
+    /// The value type of DescriptorMap.
+    typedef typename Map::Value Value;
+
+    /// \brief Constructor.
+    ///
+    /// Constructor for descriptor map.
+    explicit DescriptorMap(const Digraph& _digraph) : Map(_digraph) {
+      Item it;
+      const typename Map::Notifier* nf = Map::notifier(); 
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+	Map::set(it, invMap.size());
+	invMap.push_back(it);	
+      }      
+    }
+
+  protected:
+
+    /// \brief Add a new key to the map.
+    ///
+    /// Add a new key to the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void add(const Item& item) {
+      Map::add(item);
+      Map::set(item, invMap.size());
+      invMap.push_back(item);
+    }
+
+    /// \brief Add more new keys to the map.
+    ///
+    /// Add more new keys to the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void add(const std::vector<Item>& items) {
+      Map::add(items);
+      for (int i = 0; i < int(items.size()); ++i) {
+	Map::set(items[i], invMap.size());
+	invMap.push_back(items[i]);
+      }
+    }
+
+    /// \brief Erase the key from the map.
+    ///
+    /// Erase the key from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const Item& item) {
+      Map::set(invMap.back(), Map::operator[](item));
+      invMap[Map::operator[](item)] = invMap.back();
+      invMap.pop_back();
+      Map::erase(item);
+    }
+
+    /// \brief Erase more keys from the map.
+    ///
+    /// Erase more keys from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void erase(const std::vector<Item>& items) {
+      for (int i = 0; i < int(items.size()); ++i) {
+	Map::set(invMap.back(), Map::operator[](items[i]));
+	invMap[Map::operator[](items[i])] = invMap.back();
+	invMap.pop_back();
+      }
+      Map::erase(items);
+    }
+
+    /// \brief Build the unique map.
+    ///
+    /// Build the unique map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void build() {
+      Map::build();
+      Item it;
+      const typename Map::Notifier* nf = Map::notifier(); 
+      for (nf->first(it); it != INVALID; nf->next(it)) {
+	Map::set(it, invMap.size());
+	invMap.push_back(it);	
+      }      
+    }
+    
+    /// \brief Clear the keys from the map.
+    ///
+    /// Clear the keys from the map. It is called by the
+    /// \c AlterationNotifier.
+    virtual void clear() {
+      invMap.clear();
+      Map::clear();
+    }
+
+  public:
+
+    /// \brief Returns the maximal value plus one.
+    ///
+    /// Returns the maximal value plus one in the map.
+    unsigned int size() const {
+      return invMap.size();
+    }
+
+    /// \brief Swaps the position of the two items in the map.
+    ///
+    /// Swaps the position of the two items in the map.
+    void swap(const Item& p, const Item& q) {
+      int pi = Map::operator[](p);
+      int qi = Map::operator[](q);
+      Map::set(p, qi);
+      invMap[qi] = p;
+      Map::set(q, pi);
+      invMap[pi] = q;
+    }
+
+    /// \brief Gives back the \e descriptor of the item.
+    ///
+    /// Gives back the mutable and unique \e descriptor of the map.
+    int operator[](const Item& item) const {
+      return Map::operator[](item);
+    }
+
+    /// \brief Gives back the item by its descriptor.
+    ///
+    /// Gives back th item by its descriptor.
+    Item operator()(int id) const {
+      return invMap[id];
+    }
+    
+  private:
+
+    typedef std::vector<Item> Container;
+    Container invMap;
+
+  public:
+    /// \brief The inverse map type of DescriptorMap.
+    ///
+    /// The inverse map type of DescriptorMap.
+    class InverseMap {
+    public:
+      /// \brief Constructor of the InverseMap.
+      ///
+      /// Constructor of the InverseMap.
+      explicit InverseMap(const DescriptorMap& _inverted) 
+	: inverted(_inverted) {}
+
+
+      /// The value type of the InverseMap.
+      typedef typename DescriptorMap::Key Value;
+      /// The key type of the InverseMap.
+      typedef typename DescriptorMap::Value Key; 
+
+      /// \brief Subscript operator. 
+      ///
+      /// Subscript operator. It gives back the item 
+      /// that the descriptor belongs to currently.
+      Value operator[](const Key& key) const {
+	return inverted(key);
+      }
+
+      /// \brief Size of the map.
+      ///
+      /// Returns the size of the map.
+      unsigned int size() const {
+	return inverted.size();
+      }
+      
+    private:
+      const DescriptorMap& inverted;
+    };
+
+    /// \brief Gives back the inverse of the map.
+    ///
+    /// Gives back the inverse of the map.
+    const InverseMap inverse() const {
+      return InverseMap(*this);
+    }
+  };
+
+  /// \brief Returns the source of the given arc.
+  ///
+  /// The SourceMap gives back the source Node of the given arc. 
+  /// \see TargetMap
+  /// \author Balazs Dezso
+  template <typename Digraph>
+  class SourceMap {
+  public:
+
+    typedef typename Digraph::Node Value;
+    typedef typename Digraph::Arc Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _digraph The digraph that the map belongs to.
+    explicit SourceMap(const Digraph& _digraph) : digraph(_digraph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param arc The arc 
+    /// \return The source of the arc 
+    Value operator[](const Key& arc) const {
+      return digraph.source(arc);
+    }
+
+  private:
+    const Digraph& digraph;
+  };
+
+  /// \brief Returns a \ref SourceMap class.
+  ///
+  /// This function just returns an \ref SourceMap class.
+  /// \relates SourceMap
+  template <typename Digraph>
+  inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
+    return SourceMap<Digraph>(digraph);
+  } 
+
+  /// \brief Returns the target of the given arc.
+  ///
+  /// The TargetMap gives back the target Node of the given arc. 
+  /// \see SourceMap
+  /// \author Balazs Dezso
+  template <typename Digraph>
+  class TargetMap {
+  public:
+
+    typedef typename Digraph::Node Value;
+    typedef typename Digraph::Arc Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _digraph The digraph that the map belongs to.
+    explicit TargetMap(const Digraph& _digraph) : digraph(_digraph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param e The arc 
+    /// \return The target of the arc 
+    Value operator[](const Key& e) const {
+      return digraph.target(e);
+    }
+
+  private:
+    const Digraph& digraph;
+  };
+
+  /// \brief Returns a \ref TargetMap class.
+  ///
+  /// This function just returns a \ref TargetMap class.
+  /// \relates TargetMap
+  template <typename Digraph>
+  inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
+    return TargetMap<Digraph>(digraph);
+  }
+
+  /// \brief Returns the "forward" directed arc view of an edge.
+  ///
+  /// Returns the "forward" directed arc view of an edge.
+  /// \see BackwardMap
+  /// \author Balazs Dezso
+  template <typename Digraph>
+  class ForwardMap {
+  public:
+
+    typedef typename Digraph::Arc Value;
+    typedef typename Digraph::Edge Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _digraph The digraph that the map belongs to.
+    explicit ForwardMap(const Digraph& _digraph) : digraph(_digraph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param key An edge 
+    /// \return The "forward" directed arc view of edge 
+    Value operator[](const Key& key) const {
+      return digraph.direct(key, true);
+    }
+
+  private:
+    const Digraph& digraph;
+  };
+
+  /// \brief Returns a \ref ForwardMap class.
+  ///
+  /// This function just returns an \ref ForwardMap class.
+  /// \relates ForwardMap
+  template <typename Digraph>
+  inline ForwardMap<Digraph> forwardMap(const Digraph& digraph) {
+    return ForwardMap<Digraph>(digraph);
+  }
+
+  /// \brief Returns the "backward" directed arc view of an edge.
+  ///
+  /// Returns the "backward" directed arc view of an edge.
+  /// \see ForwardMap
+  /// \author Balazs Dezso
+  template <typename Digraph>
+  class BackwardMap {
+  public:
+
+    typedef typename Digraph::Arc Value;
+    typedef typename Digraph::Edge Key;
+
+    /// \brief Constructor
+    ///
+    /// Constructor
+    /// \param _digraph The digraph that the map belongs to.
+    explicit BackwardMap(const Digraph& _digraph) : digraph(_digraph) {}
+
+    /// \brief The subscript operator.
+    ///
+    /// The subscript operator.
+    /// \param key An edge 
+    /// \return The "backward" directed arc view of edge 
+    Value operator[](const Key& key) const {
+      return digraph.direct(key, false);
+    }
+
+  private:
+    const Digraph& digraph;
+  };
+
+  /// \brief Returns a \ref BackwardMap class
+
+  /// This function just returns a \ref BackwardMap class.
+  /// \relates BackwardMap
+  template <typename Digraph>
+  inline BackwardMap<Digraph> backwardMap(const Digraph& digraph) {
+    return BackwardMap<Digraph>(digraph);
+  }
+
+  /// \brief Potential difference map
+  ///
+  /// If there is an potential map on the nodes then we
+  /// can get an arc map as we get the substraction of the
+  /// values of the target and source.
+  template <typename Digraph, typename NodeMap>
+  class PotentialDifferenceMap {
+  public:
+    typedef typename Digraph::Arc Key;
+    typedef typename NodeMap::Value Value;
+
+    /// \brief Constructor
+    ///
+    /// Contructor of the map
+    explicit PotentialDifferenceMap(const Digraph& _digraph, 
+                                    const NodeMap& _potential) 
+      : digraph(_digraph), potential(_potential) {}
+
+    /// \brief Const subscription operator
+    ///
+    /// Const subscription operator
+    Value operator[](const Key& arc) const {
+      return potential[digraph.target(arc)] - potential[digraph.source(arc)];
+    }
+
+  private:
+    const Digraph& digraph;
+    const NodeMap& potential;
+  };
+
+  /// \brief Returns a PotentialDifferenceMap.
+  ///
+  /// This function just returns a PotentialDifferenceMap.
+  /// \relates PotentialDifferenceMap
+  template <typename Digraph, typename NodeMap>
+  PotentialDifferenceMap<Digraph, NodeMap> 
+  potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
+    return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
+  }
+
+  /// \brief Map of the node in-degrees.
+  ///
+  /// This map returns the in-degree of a node. Once it is constructed,
+  /// the degrees are stored in a standard NodeMap, so each query is done
+  /// in constant time. On the other hand, the values are updated automatically
+  /// whenever the digraph changes.
+  ///
+  /// \warning Besides addNode() and addArc(), a digraph structure may provide
+  /// alternative ways to modify the digraph. The correct behavior of InDegMap
+  /// is not guarantied if these additional features are used. For example
+  /// the functions \ref ListDigraph::changeSource() "changeSource()",
+  /// \ref ListDigraph::changeTarget() "changeTarget()" and
+  /// \ref ListDigraph::reverseArc() "reverseArc()"
+  /// of \ref ListDigraph will \e not update the degree values correctly.
+  ///
+  /// \sa OutDegMap
+
+  template <typename _Digraph>
+  class InDegMap  
+    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
+      ::ItemNotifier::ObserverBase {
+
+  public:
+    
+    typedef _Digraph Digraph;
+    typedef int Value;
+    typedef typename Digraph::Node Key;
+
+    typedef typename ItemSetTraits<_Digraph, typename _Digraph::Arc>
+    ::ItemNotifier::ObserverBase Parent;
+
+  private:
+
+    class AutoNodeMap : public DefaultMap<_Digraph, Key, int> {
+    public:
+
+      typedef DefaultMap<_Digraph, Key, int> Parent;
+      typedef typename Parent::Digraph Digraph;
+
+      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
+      
+      virtual void add(const Key& key) {
+	Parent::add(key);
+	Parent::set(key, 0);
+      }
+
+      virtual void add(const std::vector<Key>& keys) {
+	Parent::add(keys);
+	for (int i = 0; i < int(keys.size()); ++i) {
+	  Parent::set(keys[i], 0);
+	}
+      }
+
+      virtual void build() {
+	Parent::build();
+	Key it;
+	typename Parent::Notifier* nf = Parent::notifier();
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  Parent::set(it, 0);
+	}
+      }
+    };
+
+  public:
+
+    /// \brief Constructor.
+    ///
+    /// Constructor for creating in-degree map.
+    explicit InDegMap(const Digraph& _digraph) : digraph(_digraph), deg(_digraph) {
+      Parent::attach(digraph.notifier(typename _Digraph::Arc()));
+      
+      for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countInArcs(digraph, it);
+      }
+    }
+    
+    /// Gives back the in-degree of a Node.
+    int operator[](const Key& key) const {
+      return deg[key];
+    }
+
+  protected:
+    
+    typedef typename Digraph::Arc Arc;
+
+    virtual void add(const Arc& arc) {
+      ++deg[digraph.target(arc)];
+    }
+
+    virtual void add(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        ++deg[digraph.target(arcs[i])];
+      }
+    }
+
+    virtual void erase(const Arc& arc) {
+      --deg[digraph.target(arc)];
+    }
+
+    virtual void erase(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        --deg[digraph.target(arcs[i])];
+      }
+    }
+
+    virtual void build() {
+      for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countInArcs(digraph, it);
+      }      
+    }
+
+    virtual void clear() {
+      for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = 0;
+      }
+    }
+  private:
+    
+    const _Digraph& digraph;
+    AutoNodeMap deg;
+  };
+
+  /// \brief Map of the node out-degrees.
+  ///
+  /// This map returns the out-degree of a node. Once it is constructed,
+  /// the degrees are stored in a standard NodeMap, so each query is done
+  /// in constant time. On the other hand, the values are updated automatically
+  /// whenever the digraph changes.
+  ///
+  /// \warning Besides addNode() and addArc(), a digraph structure may provide
+  /// alternative ways to modify the digraph. The correct behavior of OutDegMap
+  /// is not guarantied if these additional features are used. For example
+  /// the functions \ref ListDigraph::changeSource() "changeSource()",
+  /// \ref ListDigraph::changeTarget() "changeTarget()" and
+  /// \ref ListDigraph::reverseArc() "reverseArc()"
+  /// of \ref ListDigraph will \e not update the degree values correctly.
+  ///
+  /// \sa InDegMap
+
+  template <typename _Digraph>
+  class OutDegMap  
+    : protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
+      ::ItemNotifier::ObserverBase {
+
+  public:
+
+    typedef typename ItemSetTraits<_Digraph, typename _Digraph::Arc>
+    ::ItemNotifier::ObserverBase Parent;
+    
+    typedef _Digraph Digraph;
+    typedef int Value;
+    typedef typename Digraph::Node Key;
+
+  private:
+
+    class AutoNodeMap : public DefaultMap<_Digraph, Key, int> {
+    public:
+
+      typedef DefaultMap<_Digraph, Key, int> Parent;
+      typedef typename Parent::Digraph Digraph;
+
+      AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
+      
+      virtual void add(const Key& key) {
+	Parent::add(key);
+	Parent::set(key, 0);
+      }
+      virtual void add(const std::vector<Key>& keys) {
+	Parent::add(keys);
+	for (int i = 0; i < int(keys.size()); ++i) {
+	  Parent::set(keys[i], 0);
+	}
+      }
+      virtual void build() {
+	Parent::build();
+	Key it;
+	typename Parent::Notifier* nf = Parent::notifier();
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  Parent::set(it, 0);
+	}
+      }
+    };
+
+  public:
+
+    /// \brief Constructor.
+    ///
+    /// Constructor for creating out-degree map.
+    explicit OutDegMap(const Digraph& _digraph) : digraph(_digraph), deg(_digraph) {
+      Parent::attach(digraph.notifier(typename _Digraph::Arc()));
+      
+      for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countOutArcs(digraph, it);
+      }
+    }
+
+    /// Gives back the out-degree of a Node.
+    int operator[](const Key& key) const {
+      return deg[key];
+    }
+
+  protected:
+    
+    typedef typename Digraph::Arc Arc;
+
+    virtual void add(const Arc& arc) {
+      ++deg[digraph.source(arc)];
+    }
+
+    virtual void add(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        ++deg[digraph.source(arcs[i])];
+      }
+    }
+
+    virtual void erase(const Arc& arc) {
+      --deg[digraph.source(arc)];
+    }
+
+    virtual void erase(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+        --deg[digraph.source(arcs[i])];
+      }
+    }
+
+    virtual void build() {
+      for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countOutArcs(digraph, it);
+      }      
+    }
+
+    virtual void clear() {
+      for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = 0;
+      }
+    }
+  private:
+    
+    const _Digraph& digraph;
+    AutoNodeMap deg;
+  };
+
+
+  ///Dynamic arc look up between given endpoints.
+  
+  ///\ingroup gutils
+  ///Using this class, you can find an arc in a digraph from a given
+  ///source to a given target in amortized time <em>O(log d)</em>,
+  ///where <em>d</em> is the out-degree of the source node.
+  ///
+  ///It is possible to find \e all parallel arcs between two nodes with
+  ///the \c findFirst() and \c findNext() members.
+  ///
+  ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
+  ///digraph do not changed so frequently.
+  ///
+  ///This class uses a self-adjusting binary search tree, Sleator's
+  ///and Tarjan's Splay tree for guarantee the logarithmic amortized
+  ///time bound for arc lookups. This class also guarantees the
+  ///optimal time bound in a constant factor for any distribution of
+  ///queries.
+  ///
+  ///\param G The type of the underlying digraph.  
+  ///
+  ///\sa ArcLookUp  
+  ///\sa AllArcLookUp  
+  template<class G>
+  class DynArcLookUp 
+    : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
+  {
+  public:
+    typedef typename ItemSetTraits<G, typename G::Arc>
+    ::ItemNotifier::ObserverBase Parent;
+
+    GRAPH_TYPEDEFS(typename G);
+    typedef G Digraph;
+
+  protected:
+
+    class AutoNodeMap : public DefaultMap<G, Node, Arc> {
+    public:
+
+      typedef DefaultMap<G, Node, Arc> Parent;
+
+      AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
+      
+      virtual void add(const Node& node) {
+	Parent::add(node);
+	Parent::set(node, INVALID);
+      }
+
+      virtual void add(const std::vector<Node>& nodes) {
+	Parent::add(nodes);
+	for (int i = 0; i < int(nodes.size()); ++i) {
+	  Parent::set(nodes[i], INVALID);
+	}
+      }
+
+      virtual void build() {
+	Parent::build();
+	Node it;
+	typename Parent::Notifier* nf = Parent::notifier();
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  Parent::set(it, INVALID);
+	}
+      }
+    };
+
+    const Digraph &_g;
+    AutoNodeMap _head;
+    typename Digraph::template ArcMap<Arc> _parent;
+    typename Digraph::template ArcMap<Arc> _left;
+    typename Digraph::template ArcMap<Arc> _right;
+    
+    class ArcLess {
+      const Digraph &g;
+    public:
+      ArcLess(const Digraph &_g) : g(_g) {}
+      bool operator()(Arc a,Arc b) const 
+      {
+	return g.target(a)<g.target(b);
+      }
+    };
+    
+  public:
+    
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database.
+    DynArcLookUp(const Digraph &g) 
+      : _g(g),_head(g),_parent(g),_left(g),_right(g) 
+    { 
+      Parent::attach(_g.notifier(typename Digraph::Arc()));
+      refresh(); 
+    }
+    
+  protected:
+
+    virtual void add(const Arc& arc) {
+      insert(arc);
+    }
+
+    virtual void add(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+	insert(arcs[i]);
+      }
+    }
+
+    virtual void erase(const Arc& arc) {
+      remove(arc);
+    }
+
+    virtual void erase(const std::vector<Arc>& arcs) {
+      for (int i = 0; i < int(arcs.size()); ++i) {
+	remove(arcs[i]);
+      }     
+    }
+
+    virtual void build() {
+      refresh();
+    }
+
+    virtual void clear() {
+      for(NodeIt n(_g);n!=INVALID;++n) {
+	_head.set(n, INVALID);
+      }
+    }
+
+    void insert(Arc arc) {
+      Node s = _g.source(arc);
+      Node t = _g.target(arc);
+      _left.set(arc, INVALID);
+      _right.set(arc, INVALID);
+      
+      Arc e = _head[s];
+      if (e == INVALID) {
+	_head.set(s, arc);
+	_parent.set(arc, INVALID);
+	return;
+      }
+      while (true) {
+	if (t < _g.target(e)) {
+	  if (_left[e] == INVALID) {
+	    _left.set(e, arc);
+	    _parent.set(arc, e);
+	    splay(arc);
+	    return;
+	  } else {
+	    e = _left[e];
+	  }
+	} else {
+	  if (_right[e] == INVALID) {
+	    _right.set(e, arc);
+	    _parent.set(arc, e);
+	    splay(arc);
+	    return;
+	  } else {
+	    e = _right[e];
+	  }
+	}
+      }
+    }
+
+    void remove(Arc arc) {
+      if (_left[arc] == INVALID) {
+	if (_right[arc] != INVALID) {
+	  _parent.set(_right[arc], _parent[arc]);
+	}
+	if (_parent[arc] != INVALID) {
+	  if (_left[_parent[arc]] == arc) {
+	    _left.set(_parent[arc], _right[arc]);
+	  } else {
+	    _right.set(_parent[arc], _right[arc]);
+	  }
+	} else {
+	  _head.set(_g.source(arc), _right[arc]);
+	}
+      } else if (_right[arc] == INVALID) {
+	_parent.set(_left[arc], _parent[arc]);
+	if (_parent[arc] != INVALID) {
+	  if (_left[_parent[arc]] == arc) {
+	    _left.set(_parent[arc], _left[arc]);
+	  } else {
+	    _right.set(_parent[arc], _left[arc]);
+	  }
+	} else {
+	  _head.set(_g.source(arc), _left[arc]);
+	}
+      } else {
+	Arc e = _left[arc];
+	if (_right[e] != INVALID) {
+	  e = _right[e];	  
+	  while (_right[e] != INVALID) {
+	    e = _right[e];
+	  }
+	  Arc s = _parent[e];
+	  _right.set(_parent[e], _left[e]);
+	  if (_left[e] != INVALID) {
+	    _parent.set(_left[e], _parent[e]);
+	  }
+	  
+	  _left.set(e, _left[arc]);
+	  _parent.set(_left[arc], e);
+	  _right.set(e, _right[arc]);
+	  _parent.set(_right[arc], e);
+
+	  _parent.set(e, _parent[arc]);
+	  if (_parent[arc] != INVALID) {
+	    if (_left[_parent[arc]] == arc) {
+	      _left.set(_parent[arc], e);
+	    } else {
+	      _right.set(_parent[arc], e);
+	    }
+	  }
+	  splay(s);
+	} else {
+	  _right.set(e, _right[arc]);
+	  _parent.set(_right[arc], e);
+
+	  if (_parent[arc] != INVALID) {
+	    if (_left[_parent[arc]] == arc) {
+	      _left.set(_parent[arc], e);
+	    } else {
+	      _right.set(_parent[arc], e);
+	    }
+	  } else {
+	    _head.set(_g.source(arc), e);
+	  }
+	}
+      }
+    }
+
+    Arc refreshRec(std::vector<Arc> &v,int a,int b) 
+    {
+      int m=(a+b)/2;
+      Arc me=v[m];
+      if (a < m) {
+	Arc left = refreshRec(v,a,m-1);
+	_left.set(me, left);
+	_parent.set(left, me);
+      } else {
+	_left.set(me, INVALID);
+      }
+      if (m < b) {
+	Arc right = refreshRec(v,m+1,b);
+	_right.set(me, right);
+	_parent.set(right, me);
+      } else {
+	_right.set(me, INVALID);
+      }
+      return me;
+    }
+
+    void refresh() {
+      for(NodeIt n(_g);n!=INVALID;++n) {
+	std::vector<Arc> v;
+	for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
+	if(v.size()) {
+	  std::sort(v.begin(),v.end(),ArcLess(_g));
+	  Arc head = refreshRec(v,0,v.size()-1);
+	  _head.set(n, head);
+	  _parent.set(head, INVALID);
+	}
+	else _head.set(n, INVALID);
+      }
+    }
+
+    void zig(Arc v) {        
+      Arc w = _parent[v];
+      _parent.set(v, _parent[w]);
+      _parent.set(w, v);
+      _left.set(w, _right[v]);
+      _right.set(v, w);
+      if (_parent[v] != INVALID) {
+	if (_right[_parent[v]] == w) {
+	  _right.set(_parent[v], v);
+	} else {
+	  _left.set(_parent[v], v);
+	}
+      }
+      if (_left[w] != INVALID){
+	_parent.set(_left[w], w);
+      }
+    }
+
+    void zag(Arc v) {        
+      Arc w = _parent[v];
+      _parent.set(v, _parent[w]);
+      _parent.set(w, v);
+      _right.set(w, _left[v]);
+      _left.set(v, w);
+      if (_parent[v] != INVALID){
+	if (_left[_parent[v]] == w) {
+	  _left.set(_parent[v], v);
+	} else {
+	  _right.set(_parent[v], v);
+	}
+      }
+      if (_right[w] != INVALID){
+	_parent.set(_right[w], w);
+      }
+    }
+
+    void splay(Arc v) {
+      while (_parent[v] != INVALID) {
+	if (v == _left[_parent[v]]) {
+	  if (_parent[_parent[v]] == INVALID) {
+	    zig(v);
+	  } else {
+	    if (_parent[v] == _left[_parent[_parent[v]]]) {
+	      zig(_parent[v]);
+	      zig(v);
+	    } else {
+	      zig(v);
+	      zag(v);
+	    }
+	  }
+	} else {
+	  if (_parent[_parent[v]] == INVALID) {
+	    zag(v);
+	  } else {
+	    if (_parent[v] == _left[_parent[_parent[v]]]) {
+	      zag(v);
+	      zig(v);
+	    } else {
+	      zag(_parent[v]);
+	      zag(v);
+	    }
+	  }
+	}
+      }
+      _head[_g.source(v)] = v;
+    }
+
+
+  public:
+    
+    ///Find an arc between two nodes.
+    
+    ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
+    /// <em>d</em> is the number of outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists,
+    ///\ref INVALID otherwise.
+    Arc operator()(Node s, Node t) const
+    {
+      Arc e = _head[s];
+      while (true) {
+	if (_g.target(e) == t) {
+	  const_cast<DynArcLookUp&>(*this).splay(e);
+	  return e;
+	} else if (t < _g.target(e)) {
+	  if (_left[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return INVALID;
+	  } else {
+	    e = _left[e];
+	  }
+	} else  {
+	  if (_right[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return INVALID;
+	  } else {
+	    e = _right[e];
+	  }
+	}
+      }
+    }
+
+    ///Find the first arc between two nodes.
+    
+    ///Find the first arc between two nodes in time
+    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+    /// outgoing arcs of \c s.  
+    ///\param s The source node 
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists, \ref INVALID
+    /// otherwise.
+    Arc findFirst(Node s, Node t) const
+    {
+      Arc e = _head[s];
+      Arc r = INVALID;
+      while (true) {
+	if (_g.target(e) < t) {
+	  if (_right[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return r;
+	  } else {
+	    e = _right[e];
+	  }
+	} else {
+	  if (_g.target(e) == t) {
+	    r = e;
+	  }
+	  if (_left[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return r;
+	  } else {
+	    e = _left[e];
+	  }
+	}
+      }
+    }
+
+    ///Find the next arc between two nodes.
+    
+    ///Find the next arc between two nodes in time
+    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+    /// outgoing arcs of \c s.  
+    ///\param s The source node 
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists, \ref INVALID
+    /// otherwise.
+
+    ///\note If \c e is not the result of the previous \c findFirst()
+    ///operation then the amorized time bound can not be guaranteed.
+#ifdef DOXYGEN
+    Arc findNext(Node s, Node t, Arc e) const
+#else
+    Arc findNext(Node, Node t, Arc e) const
+#endif
+    {
+      if (_right[e] != INVALID) {
+	e = _right[e];
+	while (_left[e] != INVALID) {
+	  e = _left[e];
+	}
+	const_cast<DynArcLookUp&>(*this).splay(e);
+      } else {
+	while (_parent[e] != INVALID && _right[_parent[e]] ==  e) {
+	  e = _parent[e];
+	}
+	if (_parent[e] == INVALID) {
+	  return INVALID;
+	} else {
+	  e = _parent[e];
+	  const_cast<DynArcLookUp&>(*this).splay(e);
+	}
+      }
+      if (_g.target(e) == t) return e;
+      else return INVALID;    
+    }
+
+  };
+
+  ///Fast arc look up between given endpoints.
+  
+  ///\ingroup gutils
+  ///Using this class, you can find an arc in a digraph from a given
+  ///source to a given target in time <em>O(log d)</em>,
+  ///where <em>d</em> is the out-degree of the source node.
+  ///
+  ///It is not possible to find \e all parallel arcs between two nodes.
+  ///Use \ref AllArcLookUp for this purpose.
+  ///
+  ///\warning This class is static, so you should refresh() (or at least
+  ///refresh(Node)) this data structure
+  ///whenever the digraph changes. This is a time consuming (superlinearly
+  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+  ///
+  ///\param G The type of the underlying digraph.
+  ///
+  ///\sa DynArcLookUp
+  ///\sa AllArcLookUp  
+  template<class G>
+  class ArcLookUp 
+  {
+  public:
+    GRAPH_TYPEDEFS(typename G);
+    typedef G Digraph;
+
+  protected:
+    const Digraph &_g;
+    typename Digraph::template NodeMap<Arc> _head;
+    typename Digraph::template ArcMap<Arc> _left;
+    typename Digraph::template ArcMap<Arc> _right;
+    
+    class ArcLess {
+      const Digraph &g;
+    public:
+      ArcLess(const Digraph &_g) : g(_g) {}
+      bool operator()(Arc a,Arc b) const 
+      {
+	return g.target(a)<g.target(b);
+      }
+    };
+    
+  public:
+    
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database, which remains valid until the digraph
+    ///changes.
+    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
+    
+  private:
+    Arc refreshRec(std::vector<Arc> &v,int a,int b) 
+    {
+      int m=(a+b)/2;
+      Arc me=v[m];
+      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
+      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
+      return me;
+    }
+  public:
+    ///Refresh the data structure at a node.
+
+    ///Build up the search database of node \c n.
+    ///
+    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+    ///the number of the outgoing arcs of \c n.
+    void refresh(Node n) 
+    {
+      std::vector<Arc> v;
+      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
+      if(v.size()) {
+	std::sort(v.begin(),v.end(),ArcLess(_g));
+	_head[n]=refreshRec(v,0,v.size()-1);
+      }
+      else _head[n]=INVALID;
+    }
+    ///Refresh the full data structure.
+
+    ///Build up the full search database. In fact, it simply calls
+    ///\ref refresh(Node) "refresh(n)" for each node \c n.
+    ///
+    ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
+    ///the number of the arcs of \c n and <em>D</em> is the maximum
+    ///out-degree of the digraph.
+
+    void refresh() 
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
+    }
+    
+    ///Find an arc between two nodes.
+    
+    ///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
+    /// <em>d</em> is the number of outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists,
+    ///\ref INVALID otherwise.
+    ///
+    ///\warning If you change the digraph, refresh() must be called before using
+    ///this operator. If you change the outgoing arcs of
+    ///a single node \c n, then
+    ///\ref refresh(Node) "refresh(n)" is enough.
+    ///
+    Arc operator()(Node s, Node t) const
+    {
+      Arc e;
+      for(e=_head[s];
+	  e!=INVALID&&_g.target(e)!=t;
+	  e = t < _g.target(e)?_left[e]:_right[e]) ;
+      return e;
+    }
+
+  };
+
+  ///Fast look up of all arcs between given endpoints.
+  
+  ///\ingroup gutils
+  ///This class is the same as \ref ArcLookUp, with the addition
+  ///that it makes it possible to find all arcs between given endpoints.
+  ///
+  ///\warning This class is static, so you should refresh() (or at least
+  ///refresh(Node)) this data structure
+  ///whenever the digraph changes. This is a time consuming (superlinearly
+  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+  ///
+  ///\param G The type of the underlying digraph.
+  ///
+  ///\sa DynArcLookUp
+  ///\sa ArcLookUp  
+  template<class G>
+  class AllArcLookUp : public ArcLookUp<G>
+  {
+    using ArcLookUp<G>::_g;
+    using ArcLookUp<G>::_right;
+    using ArcLookUp<G>::_left;
+    using ArcLookUp<G>::_head;
+
+    GRAPH_TYPEDEFS(typename G);
+    typedef G Digraph;
+    
+    typename Digraph::template ArcMap<Arc> _next;
+    
+    Arc refreshNext(Arc head,Arc next=INVALID)
+    {
+      if(head==INVALID) return next;
+      else {
+	next=refreshNext(_right[head],next);
+// 	_next[head]=next;
+	_next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
+	  ? next : INVALID;
+	return refreshNext(_left[head],head);
+      }
+    }
+    
+    void refreshNext()
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
+    }
+    
+  public:
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database, which remains valid until the digraph
+    ///changes.
+    AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
+
+    ///Refresh the data structure at a node.
+
+    ///Build up the search database of node \c n.
+    ///
+    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+    ///the number of the outgoing arcs of \c n.
+    
+    void refresh(Node n) 
+    {
+      ArcLookUp<G>::refresh(n);
+      refreshNext(_head[n]);
+    }
+    
+    ///Refresh the full data structure.
+
+    ///Build up the full search database. In fact, it simply calls
+    ///\ref refresh(Node) "refresh(n)" for each node \c n.
+    ///
+    ///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
+    ///the number of the arcs of \c n and <em>D</em> is the maximum
+    ///out-degree of the digraph.
+
+    void refresh() 
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
+    }
+    
+    ///Find an arc between two nodes.
+    
+    ///Find an arc between two nodes.
+    ///\param s The source node
+    ///\param t The target node
+    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
+    ///not given, the operator finds the first appropriate arc.
+    ///\return An arc from \c s to \c t after \c prev or
+    ///\ref INVALID if there is no more.
+    ///
+    ///For example, you can count the number of arcs from \c u to \c v in the
+    ///following way.
+    ///\code
+    ///AllArcLookUp<ListDigraph> ae(g);
+    ///...
+    ///int n=0;
+    ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
+    ///\endcode
+    ///
+    ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
+    /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
+    ///consecutive arcs are found in constant time.
+    ///
+    ///\warning If you change the digraph, refresh() must be called before using
+    ///this operator. If you change the outgoing arcs of
+    ///a single node \c n, then
+    ///\ref refresh(Node) "refresh(n)" is enough.
+    ///
+#ifdef DOXYGEN
+    Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
+#else
+    using ArcLookUp<G>::operator() ;
+    Arc operator()(Node s, Node t, Arc prev) const
+    {
+      return prev==INVALID?(*this)(s,t):_next[prev];
+    }
+#endif
+      
+  };
+
+  /// @}
+
+} //END OF NAMESPACE LEMON
+
+#endif
diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/path.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/path.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,1079 @@
+/* -*- 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.
+ *
+ */
+
+///\ingroup paths
+///\file
+///\brief Classes for representing paths in digraphs.
+///
+
+#ifndef LEMON_PATH_H
+#define LEMON_PATH_H
+
+#include <vector>
+#include <algorithm>
+
+#include <lemon/error.h>
+#include <lemon/bits/invalid.h>
+#include <lemon/concepts/path.h>
+
+namespace lemon {
+
+  /// \addtogroup paths
+  /// @{
+
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence, it
+  /// cannot enumerate the nodes of the path and the source node of
+  /// a zero length path is undefined.
+  ///
+  /// This implementation is a back and front insertable and erasable
+  /// path type. It can be indexed in O(1) time. The front and back
+  /// insertion and erase is done in O(1) (amortized) time. The
+  /// implementation uses two vectors for storing the front and back
+  /// insertions.
+  template <typename _Digraph>
+  class Path {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    Path() {}
+
+    /// \brief Template copy constructor
+    ///
+    /// This constuctor initializes the path from any other path type.
+    /// It simply makes a copy of the given path.
+    template <typename CPath>
+    Path(const CPath& cpath) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This operator makes a copy of a path of any other type.
+    template <typename CPath>
+    Path& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Lemon style iterator for path arcs
+    ///
+    /// This class is used to iterate on the arcs of the paths.
+    class ArcIt {
+      friend class Path;
+    public:
+      /// \brief Default constructor
+      ArcIt() {}
+      /// \brief Invalid constructor
+      ArcIt(Invalid) : path(0), idx(-1) {}
+      /// \brief Initializate the iterator to the first arc of path
+      ArcIt(const Path &_path) 
+        : path(&_path), idx(_path.empty() ? -1 : 0) {}
+
+    private:
+
+      ArcIt(const Path &_path, int _idx) 
+        : path(&_path), idx(_idx) {}
+
+    public:
+
+      /// \brief Conversion to Arc
+      operator const Arc&() const {
+        return path->nth(idx);
+      }
+
+      /// \brief Next arc
+      ArcIt& operator++() { 
+        ++idx;
+        if (idx >= path->length()) idx = -1; 
+        return *this; 
+      }
+
+      /// \brief Comparison operator
+      bool operator==(const ArcIt& e) const { return idx==e.idx; }
+      /// \brief Comparison operator
+      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }
+      /// \brief Comparison operator
+      bool operator<(const ArcIt& e) const { return idx<e.idx; }
+
+    private:
+      const Path *path;
+      int idx;
+    };
+
+    /// \brief Length of the path.
+    int length() const { return head.size() + tail.size(); }
+    /// \brief Return whether the path is empty.
+    bool empty() const { return head.empty() && tail.empty(); }
+
+    /// \brief Reset the path to an empty one.
+    void clear() { head.clear(); tail.clear(); }
+
+    /// \brief The nth arc.
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      return n < int(head.size()) ? *(head.rbegin() + n) :
+        *(tail.begin() + (n - head.size()));
+    }
+
+    /// \brief Initialize arc iterator to point to the nth arc
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    ArcIt nthIt(int n) const {
+      return ArcIt(*this, n);
+    }
+
+    /// \brief The first arc of the path
+    const Arc& front() const {
+      return head.empty() ? tail.front() : head.back();
+    }
+
+    /// \brief Add a new arc before the current path
+    void addFront(const Arc& arc) {
+      head.push_back(arc);
+    }
+
+    /// \brief Erase the first arc of the path
+    void eraseFront() {
+      if (!head.empty()) {
+        head.pop_back();
+      } else {
+        head.clear();
+        int halfsize = tail.size() / 2;
+        head.resize(halfsize);
+        std::copy(tail.begin() + 1, tail.begin() + halfsize + 1,
+                  head.rbegin());
+        std::copy(tail.begin() + halfsize + 1, tail.end(), tail.begin());
+        tail.resize(tail.size() - halfsize - 1);
+      }
+    }
+
+    /// \brief The last arc of the path
+    const Arc& back() const {
+      return tail.empty() ? head.front() : tail.back();
+    }
+
+    /// \brief Add a new arc behind the current path
+    void addBack(const Arc& arc) {
+      tail.push_back(arc);
+    }
+
+    /// \brief Erase the last arc of the path
+    void eraseBack() {
+      if (!tail.empty()) {
+        tail.pop_back();
+      } else {
+        int halfsize = head.size() / 2;
+        tail.resize(halfsize);
+        std::copy(head.begin() + 1, head.begin() + halfsize + 1,
+                  tail.rbegin());
+        std::copy(head.begin() + halfsize + 1, head.end(), head.begin());
+        head.resize(head.size() - halfsize - 1);
+      }
+    }
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      int len = path.length();
+      tail.reserve(len);
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        tail.push_back(it);
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      int len = path.length();
+      head.reserve(len);
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        head.push_back(it);
+      }
+    }
+
+  protected:
+    typedef std::vector<Arc> Container;
+    Container head, tail;
+
+  };
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence it
+  /// cannot enumerate the nodes in the path and the zero length paths
+  /// cannot store the source.
+  ///
+  /// This implementation is a just back insertable and erasable path
+  /// type. It can be indexed in O(1) time. The back insertion and
+  /// erasure is amortized O(1) time. This implementation is faster
+  /// then the \c Path type because it use just one vector for the
+  /// arcs.
+  template <typename _Digraph>
+  class SimplePath {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    SimplePath() {}
+
+    /// \brief Template copy constructor
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    SimplePath(const CPath& cpath) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    SimplePath& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Iterator class to iterate on the arcs of the paths
+    ///
+    /// This class is used to iterate on the arcs of the paths
+    ///
+    /// Of course it converts to Digraph::Arc
+    class ArcIt {
+      friend class SimplePath;
+    public:
+      /// Default constructor
+      ArcIt() {}
+      /// Invalid constructor
+      ArcIt(Invalid) : path(0), idx(-1) {}
+      /// \brief Initializate the constructor to the first arc of path
+      ArcIt(const SimplePath &_path) 
+        : path(&_path), idx(_path.empty() ? -1 : 0) {}
+
+    private:
+
+      /// Constructor with starting point
+      ArcIt(const SimplePath &_path, int _idx) 
+        : idx(_idx), path(&_path) {}
+
+    public:
+
+      ///Conversion to Digraph::Arc
+      operator const Arc&() const {
+        return path->nth(idx);
+      }
+
+      /// Next arc
+      ArcIt& operator++() { 
+        ++idx;
+        if (idx >= path->length()) idx = -1; 
+        return *this; 
+      }
+
+      /// Comparison operator
+      bool operator==(const ArcIt& e) const { return idx==e.idx; }
+      /// Comparison operator
+      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }
+      /// Comparison operator
+      bool operator<(const ArcIt& e) const { return idx<e.idx; }
+
+    private:
+      const SimplePath *path;
+      int idx;
+    };
+
+    /// \brief Length of the path.
+    int length() const { return data.size(); }
+    /// \brief Return true if the path is empty.
+    bool empty() const { return data.empty(); }
+
+    /// \brief Reset the path to an empty one.
+    void clear() { data.clear(); }
+
+    /// \brief The nth arc.
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      return data[n];
+    }
+
+    /// \brief  Initializes arc iterator to point to the nth arc.
+    ArcIt nthIt(int n) const {
+      return ArcIt(*this, n);
+    }
+
+    /// \brief The first arc of the path.
+    const Arc& front() const {
+      return data.front();
+    }
+
+    /// \brief The last arc of the path.
+    const Arc& back() const {
+      return data.back();
+    }
+
+    /// \brief Add a new arc behind the current path.
+    void addBack(const Arc& arc) {
+      data.push_back(arc);
+    }
+
+    /// \brief Erase the last arc of the path
+    void eraseBack() {
+      data.pop_back();
+    }
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      int len = path.length();
+      data.resize(len);
+      int index = 0;
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        data[index] = it;;
+        ++index;
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      int len = path.length();
+      data.resize(len);
+      int index = len;
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        --index;
+        data[index] = it;;
+      }
+    }
+
+  protected:
+    typedef std::vector<Arc> Container;
+    Container data;
+
+  };
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence it
+  /// cannot enumerate the nodes in the path and the zero length paths
+  /// cannot store the source.
+  ///
+  /// This implementation is a back and front insertable and erasable
+  /// path type. It can be indexed in O(k) time, where k is the rank
+  /// of the arc in the path. The length can be computed in O(n)
+  /// time. The front and back insertion and erasure is O(1) time
+  /// and it can be splited and spliced in O(1) time.
+  template <typename _Digraph>
+  class ListPath {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+  protected:
+
+    // the std::list<> is incompatible 
+    // hard to create invalid iterator
+    struct Node {
+      Arc arc;
+      Node *next, *prev;
+    };
+
+    Node *first, *last;
+
+    std::allocator<Node> alloc;
+
+  public:
+ 
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    ListPath() : first(0), last(0) {}
+
+    /// \brief Template copy constructor
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    ListPath(const CPath& cpath) : first(0), last(0) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Destructor of the path
+    ///
+    /// Destructor of the path
+    ~ListPath() {
+      clear();
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    ListPath& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Iterator class to iterate on the arcs of the paths
+    ///
+    /// This class is used to iterate on the arcs of the paths
+    ///
+    /// Of course it converts to Digraph::Arc
+    class ArcIt {
+      friend class ListPath;
+    public:
+      /// Default constructor
+      ArcIt() {}
+      /// Invalid constructor
+      ArcIt(Invalid) : path(0), node(0) {}
+      /// \brief Initializate the constructor to the first arc of path
+      ArcIt(const ListPath &_path) 
+        : path(&_path), node(_path.first) {}
+
+    protected:
+
+      ArcIt(const ListPath &_path, Node *_node) 
+        : path(&_path), node(_node) {}
+
+
+    public:
+
+      ///Conversion to Digraph::Arc
+      operator const Arc&() const {
+        return node->arc;
+      }
+
+      /// Next arc
+      ArcIt& operator++() { 
+        node = node->next;
+        return *this; 
+      }
+
+      /// Comparison operator
+      bool operator==(const ArcIt& e) const { return node==e.node; }
+      /// Comparison operator
+      bool operator!=(const ArcIt& e) const { return node!=e.node; }
+      /// Comparison operator
+      bool operator<(const ArcIt& e) const { return node<e.node; }
+
+    private:
+      const ListPath *path;
+      Node *node;
+    };
+
+    /// \brief The nth arc.
+    ///
+    /// This function looks for the nth arc in O(n) time.
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      Node *node = first;
+      for (int i = 0; i < n; ++i) {
+        node = node->next;
+      }
+      return node->arc;
+    }
+
+    /// \brief Initializes arc iterator to point to the nth arc.
+    ArcIt nthIt(int n) const {
+      Node *node = first;
+      for (int i = 0; i < n; ++i) {
+        node = node->next;
+      }
+      return ArcIt(*this, node);
+    }
+
+    /// \brief Length of the path.
+    int length() const {
+      int len = 0;
+      Node *node = first;
+      while (node != 0) {
+        node = node->next;
+        ++len;
+      }
+      return len;
+    }
+
+    /// \brief Return true if the path is empty.
+    bool empty() const { return first == 0; }
+
+    /// \brief Reset the path to an empty one.
+    void clear() {
+      while (first != 0) {
+        last = first->next;
+        alloc.destroy(first);
+        alloc.deallocate(first, 1);
+        first = last;
+      }
+    }
+
+    /// \brief The first arc of the path
+    const Arc& front() const {
+      return first->arc;
+    }
+
+    /// \brief Add a new arc before the current path
+    void addFront(const Arc& arc) {
+      Node *node = alloc.allocate(1);
+      alloc.construct(node, Node());
+      node->prev = 0;
+      node->next = first;
+      node->arc = arc;
+      if (first) {
+        first->prev = node;
+        first = node;
+      } else {
+        first = last = node;
+      }
+    }
+
+    /// \brief Erase the first arc of the path
+    void eraseFront() {
+      Node *node = first;
+      first = first->next;
+      if (first) {
+        first->prev = 0;
+      } else {
+        last = 0;
+      }
+      alloc.destroy(node);
+      alloc.deallocate(node, 1);
+    }
+
+    /// \brief The last arc of the path.
+    const Arc& back() const {
+      return last->arc;
+    }
+
+    /// \brief Add a new arc behind the current path.
+    void addBack(const Arc& arc) {
+      Node *node = alloc.allocate(1);
+      alloc.construct(node, Node());
+      node->next = 0;
+      node->prev = last;
+      node->arc = arc;
+      if (last) {
+        last->next = node;
+        last = node;
+      } else {
+        last = first = node;
+      }
+    }
+
+    /// \brief Erase the last arc of the path
+    void eraseBack() {
+      Node *node = last;
+      last = last->prev;
+      if (last) {
+        last->next = 0;
+      } else {
+        first = 0;
+      }
+      alloc.destroy(node);
+      alloc.deallocate(node, 1);
+    }
+
+    /// \brief Splice a path to the back of the current path.
+    ///
+    /// It splices \c tpath to the back of the current path and \c
+    /// tpath becomes empty. The time complexity of this function is
+    /// O(1).
+    void spliceBack(ListPath& tpath) {
+      if (first) {
+        if (tpath.first) {
+          last->next = tpath.first;
+          tpath.first->prev = last;
+          last = tpath.last;
+        }
+      } else {
+        first = tpath.first;
+        last = tpath.last;
+      }
+      tpath.first = tpath.last = 0;
+    }
+
+    /// \brief Splice a path to the front of the current path.
+    ///
+    /// It splices \c tpath before the current path and \c tpath
+    /// becomes empty. The time complexity of this function
+    /// is O(1).
+    void spliceFront(ListPath& tpath) {
+      if (first) {
+        if (tpath.first) {
+          first->prev = tpath.last;
+          tpath.last->next = first;
+          first = tpath.first;
+        }
+      } else {
+        first = tpath.first;
+        last = tpath.last;
+      }
+      tpath.first = tpath.last = 0;
+    }
+
+    /// \brief Splice a path into the current path.
+    ///
+    /// It splices the \c tpath into the current path before the
+    /// position of \c it iterator and \c tpath becomes empty. The
+    /// time complexity of this function is O(1). If the \c it is
+    /// \c INVALID then it will splice behind the current path.
+    void splice(ArcIt it, ListPath& tpath) {
+      if (it.node) {
+        if (tpath.first) {
+          tpath.first->prev = it.node->prev;
+          if (it.node->prev) {
+            it.node->prev->next = tpath.first;
+          } else {
+            first = tpath.first;
+          }
+          it.node->prev = tpath.last;
+          tpath.last->next = it.node;
+        }
+      } else {
+        if (first) {
+          if (tpath.first) {
+            last->next = tpath.first;
+            tpath.first->prev = last;
+            last = tpath.last;
+          }
+        } else {
+          first = tpath.first;
+          last = tpath.last;
+        }
+      }
+      tpath.first = tpath.last = 0;
+    }
+
+    /// \brief Split the current path.
+    ///
+    /// It splits the current path into two parts. The part before
+    /// the iterator \c it will remain in the current path and the part
+    /// starting with
+    /// \c it will put into \c tpath. If \c tpath have arcs
+    /// before the operation they are removed first.  The time
+    /// complexity of this function is O(1) plus the the time of emtying
+    /// \c tpath. If \c it is \c INVALID then it just clears \c tpath
+    void split(ArcIt it, ListPath& tpath) {
+      tpath.clear();
+      if (it.node) {
+        tpath.first = it.node;
+        tpath.last = last;
+        if (it.node->prev) {
+          last = it.node->prev;
+          last->next = 0;
+        } else {
+          first = last = 0;
+        }
+        it.node->prev = 0;
+      }
+    }
+
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        addBack(it);
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        addFront(it);
+      }
+    }
+
+  };
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence it
+  /// cannot enumerate the nodes in the path and the source node of
+  /// a zero length path is undefined.
+  ///
+  /// This implementation is completly static, i.e. it can be copy constucted
+  /// or copy assigned from another path, but otherwise it cannot be
+  /// modified.
+  ///
+  /// Being the the most memory efficient path type in LEMON,
+  /// it is intented to be
+  /// used when you want to store a large number of paths.
+  template <typename _Digraph>
+  class StaticPath {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    StaticPath() : len(0), arcs(0) {}
+    
+    /// \brief Template copy constructor
+    ///
+    /// This path can be initialized from any other path type.
+    template <typename CPath>
+    StaticPath(const CPath& cpath) : arcs(0) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Destructor of the path
+    ///
+    /// Destructor of the path
+    ~StaticPath() {
+      if (arcs) delete[] arcs;
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This path can be made equal to any other path type. It simply
+    /// makes a copy of the given path.
+    template <typename CPath>
+    StaticPath& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Iterator class to iterate on the arcs of the paths
+    ///
+    /// This class is used to iterate on the arcs of the paths
+    ///
+    /// Of course it converts to Digraph::Arc
+    class ArcIt {
+      friend class StaticPath;
+    public:
+      /// Default constructor
+      ArcIt() {}
+      /// Invalid constructor
+      ArcIt(Invalid) : path(0), idx(-1) {}
+      /// Initializate the constructor to the first arc of path
+      ArcIt(const StaticPath &_path) 
+        : path(&_path), idx(_path.empty() ? -1 : 0) {}
+
+    private:
+
+      /// Constructor with starting point
+      ArcIt(const StaticPath &_path, int _idx) 
+        : idx(_idx), path(&_path) {}
+
+    public:
+
+      ///Conversion to Digraph::Arc
+      operator const Arc&() const {
+        return path->nth(idx);
+      }
+
+      /// Next arc
+      ArcIt& operator++() { 
+        ++idx;
+        if (idx >= path->length()) idx = -1; 
+        return *this; 
+      }
+
+      /// Comparison operator
+      bool operator==(const ArcIt& e) const { return idx==e.idx; }
+      /// Comparison operator
+      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }
+      /// Comparison operator
+      bool operator<(const ArcIt& e) const { return idx<e.idx; }
+
+    private:
+      const StaticPath *path;
+      int idx;
+    };
+
+    /// \brief The nth arc.
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      return arcs[n];
+    }
+
+    /// \brief The arc iterator pointing to the nth arc.
+    ArcIt nthIt(int n) const {
+      return ArcIt(*this, n);
+    }
+
+    /// \brief The length of the path.
+    int length() const { return len; }
+
+    /// \brief Return true when the path is empty.
+    int empty() const { return len == 0; }
+
+    /// \break Erase all arcs in the digraph.
+    void clear() {
+      len = 0;
+      if (arcs) delete[] arcs;
+      arcs = 0;
+    }
+
+    /// \brief The first arc of the path.
+    const Arc& front() const {
+      return arcs[0];
+    }
+
+    /// \brief The last arc of the path.
+    const Arc& back() const {
+      return arcs[len - 1];
+    }
+
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      len = path.length();
+      arcs = new Arc[len];
+      int index = 0;
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        arcs[index] = it;
+        ++index;
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      len = path.length();
+      arcs = new Arc[len];
+      int index = len;
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        --index;
+        arcs[index] = it;
+      }
+    }
+
+  private:
+    int len;
+    Arc* arcs;
+  };
+
+  ///////////////////////////////////////////////////////////////////////
+  // Additional utilities
+  ///////////////////////////////////////////////////////////////////////
+
+  namespace _path_bits {
+
+    template <typename Path, typename Enable = void>
+    struct RevTagIndicator {
+      static const bool value = false;
+    };
+
+    template <typename Digraph>
+    struct RevTagIndicator<
+      Digraph, 
+      typename enable_if<typename Digraph::RevTag, void>::type
+    > {
+      static const bool value = true;
+    };
+
+    template <typename Target, typename Source,
+              typename BuildEnable = void, typename RevEnable = void>
+    struct PathCopySelector {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        for (typename Source::ArcIt it(source); it != INVALID; ++it) {
+          target.addBack(it);
+        }
+      }
+    };
+
+    template <typename Target, typename Source, typename BuildEnable>
+    struct PathCopySelector<
+      Target, Source, BuildEnable, 
+      typename enable_if<typename Source::RevPathTag, void>::type> {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        for (typename Source::RevArcIt it(source); it != INVALID; ++it) {
+          target.addFront(it);
+        }
+      }
+    };
+
+    template <typename Target, typename Source, typename RevEnable>
+    struct PathCopySelector<
+      Target, Source, 
+      typename enable_if<typename Target::BuildTag, void>::type, RevEnable> {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        target.build(source);
+      }
+    };
+
+    template <typename Target, typename Source>
+    struct PathCopySelector<
+      Target, Source, 
+      typename enable_if<typename Target::BuildTag, void>::type,
+      typename enable_if<typename Source::RevPathTag, void>::type> {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        target.buildRev(source);
+      }
+    };
+
+  }
+
+
+  /// \brief Make a copy of a path.
+  ///
+  ///  This function makes a copy of a path.
+  template <typename Target, typename Source>
+  void copyPath(Target& target, const Source& source) {
+    checkConcept<concepts::PathDumper<typename Source::Digraph>, Source>();
+    _path_bits::PathCopySelector<Target, Source>::copy(target, source);
+  }
+
+  /// \brief Check the consistency of a path.
+  ///
+  /// This function checks that the target of each arc is the same
+  /// as the source of the next one. 
+  /// 
+  template <typename Digraph, typename Path>
+  bool checkPath(const Digraph& digraph, const Path& path) {
+    typename Path::ArcIt it(path);
+    if (it == INVALID) return true;
+    typename Digraph::Node node = digraph.target(it);
+    ++it;
+    while (it != INVALID) {
+      if (digraph.source(it) != node) return false;
+      node = digraph.target(it);
+      ++it;
+    }
+    return true;
+  }
+
+  /// \brief The source of a path
+  ///
+  /// This function returns the source of the given path.
+  template <typename Digraph, typename Path>
+  typename Digraph::Node pathSource(const Digraph& digraph, const Path& path) {
+    return digraph.source(path.front());
+  }
+
+  /// \brief The target of a path
+  ///
+  /// This function returns the target of the given path.
+  template <typename Digraph, typename Path>
+  typename Digraph::Node pathTarget(const Digraph& digraph, const Path& path) {
+    return digraph.target(path.back());
+  }
+
+  /// \brief Class which helps to iterate through the nodes of a path
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores only this list. As a consequence, it
+  /// cannot enumerate the nodes in the path and the zero length paths
+  /// cannot have a source node.
+  ///
+  /// This class implements the node iterator of a path structure. To
+  /// provide this feature, the underlying digraph should be passed to
+  /// the constructor of the iterator.
+  template <typename Path>
+  class PathNodeIt {
+  private:
+    const typename Path::Digraph *_digraph;
+    typename Path::ArcIt _it;
+    typename Path::Digraph::Node _nd;
+
+  public:
+
+    typedef typename Path::Digraph Digraph;
+    typedef typename Digraph::Node Node;
+    
+    /// Default constructor
+    PathNodeIt() {}
+    /// Invalid constructor
+    PathNodeIt(Invalid) 
+      : _digraph(0), _it(INVALID), _nd(INVALID) {}
+    /// Constructor
+    PathNodeIt(const Digraph& digraph, const Path& path) 
+      : _digraph(&digraph), _it(path) {
+      _nd = (_it != INVALID ? _digraph->source(_it) : INVALID);
+    }
+    /// Constructor
+    PathNodeIt(const Digraph& digraph, const Path& path, const Node& src) 
+      : _digraph(&digraph), _it(path), _nd(src) {}
+
+    ///Conversion to Digraph::Node
+    operator Node() const {
+      return _nd;
+    }
+
+    /// Next node
+    PathNodeIt& operator++() {
+      if (_it == INVALID) _nd = INVALID;
+      else {
+	_nd = _digraph->target(_it);
+	++_it;
+      }
+      return *this;
+    }
+
+    /// Comparison operator
+    bool operator==(const PathNodeIt& n) const { 
+      return _it == n._it && _nd == n._nd; 
+    }
+    /// Comparison operator
+    bool operator!=(const PathNodeIt& n) const { 
+      return _it != n._it || _nd != n._nd; 
+    }
+    /// Comparison operator
+    bool operator<(const PathNodeIt& n) const { 
+      return (_it < n._it && _nd != INVALID);
+    }
+    
+  };
+  
+  ///@}
+
+} // namespace lemon
+
+#endif // LEMON_PATH_H
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/Makefile.am
--- a/test/Makefile.am	Tue Mar 18 16:45:21 2008 +0100
+++ b/test/Makefile.am	Thu Mar 20 12:12:24 2008 +0000
@@ -3,26 +3,34 @@
 
 noinst_HEADERS += \
 	test/digraph_test.h \
+	test/heap_test.h \
 	test/map_test.h \
         test/test_tools.h
 
 check_PROGRAMS += \
+	test/bfs_test \
+	test/dfs_test \
 	test/digraph_test \
         test/dim_test \
 	test/graph_test \
         test/maps_test \
         test/random_test \
+        test/path_test \
         test/test_tools_fail \
         test/test_tools_pass
 
 TESTS += $(check_PROGRAMS)
 XFAIL_TESTS += test/test_tools_fail$(EXEEXT)
 
+test_bfs_test_SOURCES = test/bfs_test.cc
+test_dfs_test_SOURCES = test/dfs_test.cc
 test_digraph_test_SOURCES = test/digraph_test.cc
 test_dim_test_SOURCES = test/dim_test.cc
 #test_error_test_SOURCES = test/error_test.cc
 test_graph_test_SOURCES = test/graph_test.cc
+# test_heap_test_SOURCES = test/heap_test.cc
 test_maps_test_SOURCES = test/maps_test.cc
+test_path_test_SOURCES = test/path_test.cc
 test_random_test_SOURCES = test/random_test.cc
 test_test_tools_fail_SOURCES = test/test_tools_fail.cc
 test_test_tools_pass_SOURCES = test/test_tools_pass.cc
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/bfs_test.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/bfs_test.cc	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,141 @@
+/* -*- 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.
+ *
+ */
+
+#include "test_tools.h"
+//#include <lemon/smart_graph.h>
+#include <lemon/list_graph.h>
+#include <lemon/bfs.h>
+#include <lemon/path.h>
+#include<lemon/concepts/digraph.h>
+
+using namespace lemon;
+
+const int PET_SIZE =5;
+
+
+void check_Bfs_Compile() 
+{
+  typedef concepts::Digraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+ 
+  typedef Bfs<Digraph> BType;
+  
+  Digraph G;
+  Node n;
+  Arc e;
+  int l;
+  bool b;
+  BType::DistMap d(G);
+  BType::PredMap p(G);
+  //  BType::PredNodeMap pn(G);
+  
+  BType bfs_test(G);
+  
+  bfs_test.run(n);
+  
+  l  = bfs_test.dist(n);
+  e  = bfs_test.predArc(n);
+  n  = bfs_test.predNode(n);
+  d  = bfs_test.distMap();
+  p  = bfs_test.predMap();
+  //  pn = bfs_test.predNodeMap();
+  b  = bfs_test.reached(n);
+
+  Path<Digraph> pp = bfs_test.path(n);
+}
+
+void check_Bfs_Function_Compile() 
+{
+  typedef int VType;
+  typedef concepts::Digraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+  typedef concepts::ReadMap<Arc,VType> LengthMap;
+   
+  Digraph g;
+  bfs(g,Node()).run();
+  bfs(g).source(Node()).run();
+  bfs(g)
+    .predMap(concepts::WriteMap<Node,Arc>())
+    .distMap(concepts::WriteMap<Node,VType>())
+    .reachedMap(concepts::ReadWriteMap<Node,bool>())
+    .processedMap(concepts::WriteMap<Node,bool>())
+    .run(Node());
+  
+}
+
+int main()
+{
+    
+  // typedef SmartDigraph Digraph;
+  typedef ListDigraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+  typedef Digraph::ArcMap<int> LengthMap;
+
+  Digraph G;
+  Node s, t;
+  PetStruct<Digraph> ps = addPetersen(G,PET_SIZE);
+   
+  s=ps.outer[2];
+  t=ps.inner[0];
+  
+  Bfs<Digraph> bfs_test(G);
+  bfs_test.run(s);
+  
+  check(bfs_test.dist(t)==3,"Bfs found a wrong path. " << bfs_test.dist(t));
+
+  Path<Digraph> p = bfs_test.path(t);
+  check(p.length()==3,"getPath() found a wrong path.");
+  check(checkPath(G, p),"path() found a wrong path.");
+  check(pathSource(G, p) == s,"path() found a wrong path.");
+  check(pathTarget(G, p) == t,"path() found a wrong path.");
+  
+
+  for(ArcIt e(G); e==INVALID; ++e) {
+    Node u=G.source(e);
+    Node v=G.target(e);
+    check( !bfs_test.reached(u) ||
+	   (bfs_test.dist(v) > bfs_test.dist(u)+1),
+	   "Wrong output.");
+  }
+
+  for(NodeIt v(G); v==INVALID; ++v) {
+    check(bfs_test.reached(v),"Each node should be reached.");
+    if ( bfs_test.predArc(v)!=INVALID ) {
+      Arc e=bfs_test.predArc(v);
+      Node u=G.source(e);
+      check(u==bfs_test.predNode(v),"Wrong tree.");
+      check(bfs_test.dist(v) - bfs_test.dist(u) == 1,
+	    "Wrong distance. Difference: " 
+	    << std::abs(bfs_test.dist(v) - bfs_test.dist(u) 
+			- 1));
+    }
+  }
+}
+
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/dfs_test.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/dfs_test.cc	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,130 @@
+/* -*- 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.
+ *
+ */
+
+#include "test_tools.h"
+// #include <lemon/smart_graph.h>
+#include <lemon/list_graph.h>
+#include <lemon/dfs.h>
+#include <lemon/path.h>
+#include <lemon/concepts/digraph.h>
+
+using namespace lemon;
+
+const int PET_SIZE =5;
+
+
+void check_Dfs_SmartDigraph_Compile() 
+{
+  typedef concepts::Digraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+ 
+  typedef Dfs<Digraph> DType;
+  
+  Digraph G;
+  Node n;
+  Arc e;
+  int l;
+  bool b;
+  DType::DistMap d(G);
+  DType::PredMap p(G);
+  //  DType::PredNodeMap pn(G);
+  
+  DType dfs_test(G);
+  
+  dfs_test.run(n);
+  
+  l  = dfs_test.dist(n);
+  e  = dfs_test.predArc(n);
+  n  = dfs_test.predNode(n);
+  d  = dfs_test.distMap();
+  p  = dfs_test.predMap();
+  //  pn = dfs_test.predNodeMap();
+  b  = dfs_test.reached(n);
+
+  Path<Digraph> pp = dfs_test.path(n);
+}
+
+
+void check_Dfs_Function_Compile() 
+{
+  typedef int VType;
+  typedef concepts::Digraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+  typedef concepts::ReadMap<Arc,VType> LengthMap;
+   
+  Digraph g;
+  dfs(g,Node()).run();
+  dfs(g).source(Node()).run();
+  dfs(g)
+    .predMap(concepts::WriteMap<Node,Arc>())
+    .distMap(concepts::WriteMap<Node,VType>())
+    .reachedMap(concepts::ReadWriteMap<Node,bool>())
+    .processedMap(concepts::WriteMap<Node,bool>())
+    .run(Node());
+  
+}
+
+int main()
+{
+    
+  // typedef SmartDigraph Digraph;
+  typedef ListDigraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+  typedef Digraph::ArcMap<int> LengthMap;
+
+  Digraph G;
+  Node s, t;
+  PetStruct<Digraph> ps = addPetersen(G,PET_SIZE);
+   
+  s=ps.outer[2];
+  t=ps.inner[0];
+  
+  Dfs<Digraph> dfs_test(G);
+  dfs_test.run(s);  
+  
+  Path<Digraph> p = dfs_test.path(t);
+  check(p.length()==dfs_test.dist(t),"path() found a wrong path.");
+  check(checkPath(G, p),"path() found a wrong path.");
+  check(pathSource(G, p) == s,"path() found a wrong path.");
+  check(pathTarget(G, p) == t,"path() found a wrong path.");
+  
+  for(NodeIt v(G); v!=INVALID; ++v) {
+    check(dfs_test.reached(v),"Each node should be reached.");
+    if ( dfs_test.predArc(v)!=INVALID ) {
+      Arc e=dfs_test.predArc(v);
+      Node u=G.source(e);
+      check(u==dfs_test.predNode(v),"Wrong tree.");
+      check(dfs_test.dist(v) - dfs_test.dist(u) == 1,
+	    "Wrong distance. (" << dfs_test.dist(u) << "->" 
+	    <<dfs_test.dist(v) << ')');
+    }
+  }
+}
+
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/heap_test.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/heap_test.cc	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,140 @@
+/* -*- 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.
+ *
+ */
+
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <vector>
+
+#include <lemon/concept_check.h>
+#include <lemon/concepts/heap.h>
+
+#include <lemon/list_graph.h>
+
+#include <lemon/digraph_reader.h>
+
+#include <lemon/bin_heap.h>
+#include <lemon/fib_heap.h>
+#include <lemon/radix_heap.h>
+#include <lemon/bucket_heap.h>
+
+#include "test_tools.h"
+
+#include "heap_test.h"
+
+#include <lemon/time_measure.h>
+
+using namespace lemon;
+using namespace lemon::concepts;
+
+
+int main() {
+
+  typedef int Item;
+  typedef int Prio;
+  typedef IntIntMap ItemIntMap;
+
+  typedef ListDigraph Digraph;
+
+  typedef Digraph::Arc Arc;
+  typedef Digraph::Node Node;
+  typedef Digraph::ArcIt ArcIt;
+  typedef Digraph::NodeIt NodeIt;
+  typedef Digraph::ArcMap<int> LengthMap;
+
+  Digraph digraph;
+  LengthMap length(digraph);
+  Node start;
+
+  /// \todo create own test digraph
+
+  std::string f_name;
+  if( getenv("srcdir") )
+    f_name = std::string(getenv("srcdir"));
+  else f_name = ".";
+  f_name += "/test/dijkstra_test.lgf";
+  
+  std::ifstream input(f_name.c_str());
+  check(input, "Input file '" << f_name << "' not found.");
+  DigraphReader<Digraph>(input, digraph).
+    readArcMap("capacity", length).
+    readNode("source", start).
+    run();  
+ 
+  {
+    std::cerr << "Checking Bin Heap" << std::endl;
+
+    typedef BinHeap<Prio, ItemIntMap> IntHeap;
+    checkConcept<Heap<Prio, ItemIntMap>, IntHeap>();
+    heapSortTest<IntHeap>(100);
+    heapIncreaseTest<IntHeap>(100);
+    
+    typedef FibHeap<Prio, Digraph::NodeMap<int> > NodeHeap;
+    checkConcept<Heap<Prio, Digraph::NodeMap<int> >, NodeHeap>();
+    Timer timer;
+    dijkstraHeapTest<Digraph, LengthMap, NodeHeap>(digraph, length, start);
+    std::cout << timer << std::endl;
+  }
+  {
+    std::cerr << "Checking Fib Heap" << std::endl;
+
+    typedef FibHeap<Prio, ItemIntMap> IntHeap;
+    checkConcept<Heap<Prio, ItemIntMap>, IntHeap>();
+    heapSortTest<IntHeap>(100);
+    heapIncreaseTest<IntHeap>(100);
+
+    typedef FibHeap<Prio, Digraph::NodeMap<int> > NodeHeap;
+    checkConcept<Heap<Prio, Digraph::NodeMap<int> >, NodeHeap>();
+    Timer timer;
+    dijkstraHeapTest<Digraph, LengthMap, NodeHeap>(digraph, length, start);
+    std::cout << timer << std::endl;
+  }
+  {
+    std::cerr << "Checking Radix Heap" << std::endl;
+
+    typedef RadixHeap<ItemIntMap> IntHeap;
+    checkConcept<Heap<Prio, ItemIntMap>, IntHeap>();
+    heapSortTest<IntHeap>(100);
+    heapIncreaseTest<IntHeap>(100);
+
+    typedef RadixHeap<Digraph::NodeMap<int> > NodeHeap;
+    checkConcept<Heap<Prio, Digraph::NodeMap<int> >, NodeHeap>();
+    Timer timer;
+    dijkstraHeapTest<Digraph, LengthMap, NodeHeap>(digraph, length, start);
+    std::cout << timer << std::endl;
+  }
+
+  {
+    std::cerr << "Checking Bucket Heap" << std::endl;
+
+    typedef BucketHeap<ItemIntMap> IntHeap;
+    checkConcept<Heap<Prio, ItemIntMap>, IntHeap>();
+    heapSortTest<IntHeap>(100);
+    heapIncreaseTest<IntHeap>(100);
+
+    typedef BucketHeap<Digraph::NodeMap<int> > NodeHeap;
+    checkConcept<Heap<Prio, Digraph::NodeMap<int> >, NodeHeap>();
+    Timer timer;
+    dijkstraHeapTest<Digraph, LengthMap, NodeHeap>(digraph, length, start);
+    std::cout << timer << std::endl;
+  }
+
+  std::cout << __FILE__ ": All tests passed.\n";
+
+  return 0;
+}
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/heap_test.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/heap_test.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,123 @@
+/* -*- 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.
+ *
+ */
+
+#include <vector>
+#include <algorithm>
+
+#include <lemon/dijkstra.h>
+
+class IntIntMap : public std::vector<int> {
+public:
+  typedef std::vector<int> Parent;
+
+  typedef int Key;
+  typedef int Value;
+
+  IntIntMap() : Parent() {}
+  IntIntMap(int n) : Parent(n) {}
+  IntIntMap(int n, int v) : Parent(n, v) {}
+
+  void set(int key, int value) {
+    Parent::operator[](key) = value;
+  }
+};
+
+
+template <typename _Heap>
+void heapSortTest(int n) {
+  typedef _Heap Heap;
+  IntIntMap map(n, -1);
+
+  Heap heap(map);
+  
+  std::vector<int> v(n);
+
+  for (int i = 0; i < n; ++i) {
+    v[i] = rnd[1000];
+    heap.push(i, v[i]);
+  }
+  std::sort(v.begin(), v.end());
+  for (int i = 0; i < n; ++i) {
+    check(v[i] == heap.prio() ,"Wrong order in heap sort.");
+    heap.pop();
+  }
+}
+
+template <typename _Heap>
+void heapIncreaseTest(int n) {
+  typedef _Heap Heap;
+  IntIntMap map(n, -1);
+
+  Heap heap(map);
+  
+  std::vector<int> v(n);
+
+  for (int i = 0; i < n; ++i) {
+    v[i] = rnd[1000];
+    heap.push(i, v[i]);
+  }
+  for (int i = 0; i < n; ++i) {
+    v[i] += rnd[1000];
+    heap.increase(i, v[i]);
+  }
+  std::sort(v.begin(), v.end());
+  for (int i = 0; i < n; ++i) {
+    check(v[i] == heap.prio() ,"Wrong order in heap increase test.");
+    heap.pop();
+  }
+}
+
+
+
+template <typename _Digraph, typename _LengthMap, typename _Heap>
+void dijkstraHeapTest(_Digraph& digraph, _LengthMap& length,
+		      typename _Digraph::Node& start) {
+
+  typedef _Heap Heap;
+  typedef _Digraph Digraph;
+  typedef _LengthMap LengthMap;
+
+  typedef typename Digraph::Node Node;
+  typedef typename Digraph::Arc Arc;
+  typedef typename Digraph::NodeIt NodeIt;
+  typedef typename Digraph::ArcIt ArcIt;
+
+  typename Dijkstra<Digraph, LengthMap>::template DefStandardHeap<Heap>::
+    Create dijkstra(digraph, length);
+
+  dijkstra.run(start);
+
+  for(ArcIt e(digraph); e!=INVALID; ++e) {
+    Node u=digraph.source(e); 
+    Node v=digraph.target(e);
+    if (dijkstra.reached(u)) {
+      check( dijkstra.dist(v) - dijkstra.dist(u) <= length[e],
+      	     "Error in a shortest path tree arc!");
+    }
+  }
+
+  for(NodeIt v(digraph); v!=INVALID; ++v) {
+    if ( dijkstra.reached(v) && dijkstra.predArc(v) != INVALID ) {
+      Arc e=dijkstra.predArc(v);
+      Node u=digraph.source(e);
+      check( dijkstra.dist(v) - dijkstra .dist(u) == length[e],
+	     "Error in a shortest path tree arc!");
+    }
+  }
+
+}
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/path_test.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/path_test.cc	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,44 @@
+/* -*- 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.
+ *
+ */
+
+#include <string>
+#include <iostream>
+
+#include <lemon/concepts/path.h>
+#include <lemon/concepts/digraph.h>
+
+#include <lemon/path.h>
+#include <lemon/list_graph.h>
+
+#include "test_tools.h"
+
+using namespace std;
+using namespace lemon;
+
+void check_concepts() {
+  checkConcept<concepts::Path<ListDigraph>, concepts::Path<ListDigraph> >();
+  checkConcept<concepts::Path<ListDigraph>, Path<ListDigraph> >();
+  checkConcept<concepts::Path<ListDigraph>, SimplePath<ListDigraph> >();
+  checkConcept<concepts::Path<ListDigraph>, StaticPath<ListDigraph> >();
+  checkConcept<concepts::Path<ListDigraph>, ListPath<ListDigraph> >();
+}
+
+int main() {
+  check_concepts();  
+  return 0;
+}
diff -r cc7e6b8b59bf -r 70f3967ca6eb test/test_tools.h
--- a/test/test_tools.h	Tue Mar 18 16:45:21 2008 +0100
+++ b/test/test_tools.h	Thu Mar 20 12:12:24 2008 +0000
@@ -20,6 +20,17 @@
 #define LEMON_TEST_TEST_TOOLS_H
 
 #include <iostream>
+#include <vector>
+
+#include <cstdlib>
+#include <ctime>
+
+#include <lemon/concept_check.h>
+#include <lemon/concepts/digraph.h>
+
+#include <lemon/random.h>
+
+using namespace lemon;
 
 //! \ingroup misc
 //! \file
@@ -36,7 +47,7 @@
 ///For example
 ///\code check(0==1,"This is obviously false.");\endcode will
 ///print this (and then exits).
-///\verbatim graph_test.cc:123: error: This is obviously false. \endverbatim
+///\verbatim digraph_test.cc:123: error: This is obviously false. \endverbatim
 ///
 ///\todo It should be in \c error.h
 #define check(rc, msg) \
@@ -45,4 +56,126 @@
     abort(); \
   } else { } \
 
+///Structure returned by \ref addPetersen().
+
+///Structure returned by \ref addPetersen().
+///
+template<class Digraph> struct PetStruct
+{
+  ///Vector containing the outer nodes.
+  std::vector<typename Digraph::Node> outer;
+  ///Vector containing the inner nodes.
+  std::vector<typename Digraph::Node> inner;
+  ///Vector containing the arcs of the inner circle.
+  std::vector<typename Digraph::Arc> incir;
+  ///Vector containing the arcs of the outer circle.
+  std::vector<typename Digraph::Arc> outcir;
+  ///Vector containing the chord arcs.
+  std::vector<typename Digraph::Arc> chords;
+};
+
+
+
+///Adds a Petersen digraph to \c G.
+
+///Adds a Petersen digraph to \c G.
+///\return The nodes and arcs of the generated digraph.
+
+template<typename Digraph>
+PetStruct<Digraph> addPetersen(Digraph &G,int num = 5)
+{
+  PetStruct<Digraph> n;
+
+  for(int i=0;i<num;i++) {
+    n.outer.push_back(G.addNode());
+    n.inner.push_back(G.addNode());
+  }
+
+ for(int i=0;i<num;i++) {
+   n.chords.push_back(G.addArc(n.outer[i],n.inner[i]));
+   n.outcir.push_back(G.addArc(n.outer[i],n.outer[(i+1) % num]));
+   n.incir.push_back(G.addArc(n.inner[i],n.inner[(i+2) % num]));
+  }
+ return n;
+}
+
+/// \brief Adds to the digraph the reverse pair of all arcs.
+///
+/// Adds to the digraph the reverse pair of all arcs.
+///
+template<class Digraph> void bidirDigraph(Digraph &G)
+{
+  typedef typename Digraph::Arc Arc;
+  typedef typename Digraph::ArcIt ArcIt;
+  
+  std::vector<Arc> ee;
+  
+  for(ArcIt e(G);e!=INVALID;++e) ee.push_back(e);
+
+  for(typename std::vector<Arc>::iterator p=ee.begin();p!=ee.end();p++)
+    G.addArc(G.target(*p),G.source(*p));
+}
+
+
+/// \brief Checks the bidirectioned Petersen digraph.
+///
+///  Checks the bidirectioned Petersen digraph.
+///
+template<class Digraph> void checkBidirPetersen(Digraph &G, int num = 5)
+{
+  typedef typename Digraph::Node Node;
+
+  typedef typename Digraph::ArcIt ArcIt;
+  typedef typename Digraph::NodeIt NodeIt;
+
+  checkDigraphNodeList(G, 2 * num);
+  checkDigraphArcList(G, 6 * num);
+
+  for(NodeIt n(G);n!=INVALID;++n) {
+    checkDigraphInArcList(G, n, 3);
+    checkDigraphOutArcList(G, n, 3);
+  }  
+}
+
+///Structure returned by \ref addUPetersen().
+
+///Structure returned by \ref addUPetersen().
+///
+template<class Digraph> struct UPetStruct
+{
+  ///Vector containing the outer nodes.
+  std::vector<typename Digraph::Node> outer;
+  ///Vector containing the inner nodes.
+  std::vector<typename Digraph::Node> inner;
+  ///Vector containing the arcs of the inner circle.
+  std::vector<typename Digraph::Edge> incir;
+  ///Vector containing the arcs of the outer circle.
+  std::vector<typename Digraph::Edge> outcir;
+  ///Vector containing the chord arcs.
+  std::vector<typename Digraph::Edge> chords;
+};
+
+///Adds a Petersen digraph to the undirected \c G.
+
+///Adds a Petersen digraph to the undirected \c G.
+///\return The nodes and arcs of the generated digraph.
+
+template<typename Digraph>
+UPetStruct<Digraph> addUPetersen(Digraph &G,int num=5)
+{
+  UPetStruct<Digraph> n;
+
+  for(int i=0;i<num;i++) {
+    n.outer.push_back(G.addNode());
+    n.inner.push_back(G.addNode());
+  }
+
+ for(int i=0;i<num;i++) {
+   n.chords.push_back(G.addArc(n.outer[i],n.inner[i]));
+   n.outcir.push_back(G.addArc(n.outer[i],n.outer[(i+1)%5]));
+   n.incir.push_back(G.addArc(n.inner[i],n.inner[(i+2)%5]));
+ }
+ return n;
+}
+
 #endif