/* -*- C++ -*-

 * lemon/dfs.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2005 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 flowalgs

///\file

///\brief Dfs algorithm.

#include <lemon/list_graph.h>

#include <lemon/graph_utils.h>

#include <lemon/invalid.h>

#include <lemon/error.h>

#include <lemon/maps.h>

namespace lemon {

  ///Default traits class of Dfs class.

  ///Default traits class of Dfs class.

  ///\param GR Graph type.

  template<class GR>

  struct DfsDefaultTraits

  {

    ///The graph type the algorithm runs on. 

    typedef GR Graph;

    ///\brief The type of the map that stores the last

    ///edges of the %DFS paths.

    /// 

    ///The type of the map that stores the last

    ///edges of the %DFS paths.

    ///It must meet the \ref concept::WriteMap "WriteMap" concept.

    ///

    typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;

    ///Instantiates a PredMap.

    ///This function instantiates a \ref PredMap. 

    ///\param G is the graph, to which we would like to define the PredMap.

    ///\todo The graph alone may be insufficient to initialize

    static PredMap *createPredMap(const GR &G) 

    {

      return new PredMap(G);

    }

//     ///\brief The type of the map that stores the last but one

//     ///nodes of the %DFS paths.

//     ///

//     ///The type of the map that stores the last but one

//     ///nodes of the %DFS paths.

//     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

//     ///

//     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;

//     ///Instantiates a PredNodeMap.

//     ///This function instantiates a \ref PredNodeMap. 

//     ///\param G is the graph, to which

//     ///we would like to define the \ref PredNodeMap

//     static PredNodeMap *createPredNodeMap(const GR &G)

//     {

//       return new PredNodeMap();

//     }

    ///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 concept::WriteMap "WriteMap" concept.

    ///\todo named parameter to set this type, function to read and write.

    typedef NullMap<typename Graph::Node,bool> ProcessedMap;

    ///Instantiates a ProcessedMap.

    ///This function instantiates a \ref ProcessedMap. 

    ///\param g is the graph, 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 concept::WriteMap "WriteMap" concept.

    ///\todo named parameter to set this type, function to read and write.

    typedef typename Graph::template NodeMap<bool> ReachedMap;

    ///Instantiates a ReachedMap.

    ///This function instantiates a \ref ReachedMap. 

    ///\param G is the graph, 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 concept::WriteMap "WriteMap" concept.

    ///

    typedef typename Graph::template NodeMap<int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap. 

    ///\param G is the graph, to which we would like to define the \ref DistMap

    static DistMap *createDistMap(const GR &G)

    {

      return new DistMap(G);

    }

  };

  ///%DFS algorithm class.

  ///\ingroup flowalgs

  ///This class provides an efficient implementation of the %DFS algorithm.

  ///

  ///\param GR The graph type the algorithm runs on. The default value is

  ///\ref ListGraph. 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

  ///\todo A compare object would be nice.

#ifdef DOXYGEN

  template <typename GR,

	    typename TR>

#else

  template <typename GR=ListGraph,

	    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* exceptionName() const {

	return "lemon::Dfs::UninitializedParameter";

      }

    };

    typedef TR Traits;

    ///The type of the underlying graph.

    typedef typename TR::Graph Graph;

    ///\e

    typedef typename Graph::Node Node;

    ///\e

    typedef typename Graph::NodeIt NodeIt;

    ///\e

    typedef typename Graph::Edge Edge;

    ///\e

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    ///\brief The type of the map that stores the last

    ///edges of the %DFS paths.

    typedef typename TR::PredMap PredMap;

//     ///\brief The type of the map that stores the last but one

//     ///nodes of the %DFS paths.

//     typedef typename TR::PredNodeMap PredNodeMap;

    ///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 graph.

    const Graph *G;

    ///Pointer to the map of predecessors edges.

    PredMap *_pred;

    ///Indicates if \ref _pred is locally allocated (\c true) or not.

    bool local_pred;

//     ///Pointer to the map of predecessors nodes.

//     PredNodeMap *_predNode;

//     ///Indicates if \ref _predNode is locally allocated (\c true) or not.

//     bool local_predNode;

    ///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 Graph::OutEdgeIt> _stack;

    int _stack_head;

//     ///The source node of the last execution.

//     Node source;

    ///Creates the maps if necessary.

    ///\todo Error if \c G are \c NULL.

    ///\todo Better memory allocation (instead of new).

    void create_maps() 

    {

      if(!_pred) {

	local_pred = true;

	_pred = Traits::createPredMap(*G);

      }

//       if(!_predNode) {

// 	local_predNode = true;

// 	_predNode = Traits::createPredNodeMap(*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);

      }

    }

  public :

    ///\name Named template parameters

    ///@{

    template <class T>

    struct DefPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Graph &G) 

      {

	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>

    class DefPredMap : public Dfs< Graph,

					DefPredMapTraits<T> > { };

//     template <class T>

//     struct DefPredNodeMapTraits : public Traits {

//       typedef T PredNodeMap;

//       static PredNodeMap *createPredNodeMap(const Graph &G) 

//       {

// 	throw UninitializedParameter();

//       }

//     };

//     ///\ref named-templ-param "Named parameter" for setting PredNodeMap type

//     ///\ref named-templ-param "Named parameter" for setting PredNodeMap type

//     ///

//     template <class T>

//     class DefPredNodeMap : public Dfs< Graph,

// 					    LengthMap,

// 					    DefPredNodeMapTraits<T> > { };

    template <class T>

    struct DefDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Graph &G) 

      {

	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>

    class DefDistMap : public Dfs< Graph,

				   DefDistMapTraits<T> > { };

    template <class T>

    struct DefReachedMapTraits : public Traits {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Graph &G) 

      {

	throw UninitializedParameter();

      }

    };

    ///\ref named-templ-param "Named parameter" for setting ReachedMap type

    ///\ref named-templ-param "Named parameter" for setting ReachedMap type

    ///

    template <class T>

    class DefReachedMap : public Dfs< Graph,

				      DefReachedMapTraits<T> > { };

    struct DefGraphReachedMapTraits : public Traits {

      typedef typename Graph::template NodeMap<bool> ReachedMap;

      static ReachedMap *createReachedMap(const Graph &G) 

      {

	return new ReachedMap(G);

      }

    };

    template <class T>

    struct DefProcessedMapTraits : public Traits {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Graph &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>

    class DefProcessedMap : public Dfs< Graph,

					DefProcessedMapTraits<T> > { };

    struct DefGraphProcessedMapTraits : public Traits {

      typedef typename Graph::template NodeMap<bool> ProcessedMap;

      static ProcessedMap *createProcessedMap(const Graph &G) 

      {

	return new ProcessedMap(G);

      }

    };

    ///\brief \ref named-templ-param "Named parameter"

    ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.

    ///

    ///\ref named-templ-param "Named parameter"

    ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.

    ///If you don't set it explicitely, it will be automatically allocated.

    template <class T>

    class DefProcessedMapToBeDefaultMap :

      public Dfs< Graph,

		  DefGraphProcessedMapTraits> { };

    ///@}

  public:      

    ///Constructor.

    ///\param _G the graph the algorithm will run on.

    ///

    Dfs(const Graph& _G) :

      G(&_G),

      _pred(NULL), local_pred(false),

//       _predNode(NULL), local_predNode(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_predNode) delete _predNode;

      if(local_dist) delete _dist;

      if(local_reached) delete _reached;

      if(local_processed) delete _processed;

    }

    ///Sets the map storing the predecessor edges.

    ///Sets the map storing the predecessor edges.

    ///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 predecessor nodes.

//     ///Sets the map storing the predecessor nodes.

//     ///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 &predNodeMap(PredNodeMap &m) 

//     {

//       if(local_predNode) {

// 	delete _predNode;

// 	local_predNode=false;

//       }

//       _predNode = &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 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();

      _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.

    ///

    ///\bug 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);

	  // _predNode->set(u,INVALID);

	  _stack[++_stack_head]=OutEdgeIt(*G,s);

	  _dist->set(s,_stack_head);

	}

    }

    ///Processes the next edge.

    ///Processes the next edge.

    ///

    ///\return The processed edge.

    ///

    ///\pre The stack must not be empty!

    Edge processNextEdge()

    { 

      Node m;

      Edge e=_stack[_stack_head];

      if(!(*_reached)[m=G->target(e)]) {

	_pred->set(m,e);

	_reached->set(m,true);

	//	  _pred_node->set(m,G->source(e));

	++_stack_head;

	_stack[_stack_head] = OutEdgeIt(*G, m);

	_dist->set(m,_stack_head);

      }

      else {

	Node n;

	while(_stack_head>=0 &&

	      (n=G->source(_stack[_stack_head]),

	       ++_stack[_stack_head]==INVALID))

	  {

	    _processed->set(n,true);

	    --_stack_head;

	  }

      }

      return e;

    }

    ///\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() ) processNextEdge();

    }

    ///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 ) 

	processNextEdge();

    }

    ///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) edge map. The algorithm

    ///will stop when it reaches an edge \c e with <tt>nm[e]==true</tt>.

    ///

    ///\warning Contrary to \ref Dfs and \ref Dijkstra, \c nm is an edge map,

    ///not a node map.

    template<class NM>

      void start(const NM &nm)

      {

	while ( !emptyQueue() && !nm[_stack[_stack_head]] ) processNextEdge();

      }

    ///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) 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.

    ///@{

    ///Copies the path to \c t on the DFS tree into \c p

    ///This function copies the path to \c t on the DFS tree  into \c p.

    ///If \c t is a source itself or unreachable, then it does not

    ///alter \c p.

    ///\todo Is this the right way to handle unreachable nodes?

    ///

    ///\return Returns \c true if a path to \c t was actually copied to \c p,

    ///\c false otherwise.

    ///\sa DirPath

    template<class P>

    bool getPath(P &p,Node t) 

    {

      if(reached(t)) {

	p.clear();

	typename P::Builder b(p);

	for(b.setStartNode(t);pred(t)!=INVALID;t=predNode(t))

	  b.pushFront(pred(t));

	b.commit();

	return true;

      }

      return false;

    }

    ///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 edge' of the %DFS tree.

    ///For a node \c v it returns the 'previous edge'

    ///of the %DFS path,

    ///i.e. it returns the last edge 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(Node v).

    ///\pre Either \ref run() or \ref start() must be called before using

    ///this function.

    ///\todo predEdge could be a better name.

    Edge pred(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(a) 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 pred(Node v).

    ///\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 edge-tree map.

    ///Returns a reference to the NodeMap of the edges of the

    ///%DFS tree.

    ///\pre Either \ref run() or \ref init()

    ///must be called before using this function.

    const PredMap &predMap() const { return *_pred;}

//     ///Returns a reference to the map of nodes of %DFS paths.

//     ///Returns a reference to the NodeMap of the last but one nodes of the

//     ///%DFS tree.

//     ///\pre \ref run() must be called before using this function.

//     const PredNodeMap &predNodeMap() const { return *_predNode;}

    ///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 Graph type.

  template<class GR>

  struct DfsWizardDefaultTraits

  {

    ///The graph type the algorithm runs on. 

    typedef GR Graph;

    ///\brief The type of the map that stores the last

    ///edges of the %DFS paths.

    /// 

    ///The type of the map that stores the last

    ///edges of the %DFS paths.

    ///It must meet the \ref concept::WriteMap "WriteMap" concept.

    ///

    typedef NullMap<typename Graph::Node,typename GR::Edge> PredMap;

    ///Instantiates a PredMap.

    ///This function instantiates a \ref PredMap. 

    ///\param g is the graph, to which we would like to define the PredMap.

    ///\todo The graph alone may be insufficient to initialize

#ifdef DOXYGEN

    static PredMap *createPredMap(const GR &g) 

#else

    static PredMap *createPredMap(const GR &) 

#endif

    {

      return new PredMap();

    }

//     ///\brief The type of the map that stores the last but one

//     ///nodes of the %DFS paths.

//     ///

//     ///The type of the map that stores the last but one

//     ///nodes of the %DFS paths.

//     ///It must meet the \ref concept::WriteMap "WriteMap" concept.

//     ///

//     typedef NullMap<typename Graph::Node,typename Graph::Node> PredNodeMap;

//     ///Instantiates a PredNodeMap.

//     ///This function instantiates a \ref PredNodeMap. 

//     ///\param G is the graph, to which

//     ///we would like to define the \ref PredNodeMap

//     static PredNodeMap *createPredNodeMap(const GR &G)

//     {

//       return new PredNodeMap();

//     }

    ///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 concept::WriteMap "WriteMap" concept.

    ///\todo named parameter to set this type, function to read and write.

    typedef NullMap<typename Graph::Node,bool> ProcessedMap;

    ///Instantiates a ProcessedMap.

    ///This function instantiates a \ref ProcessedMap. 

    ///\param g is the graph, 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 concept::WriteMap "WriteMap" concept.

    ///\todo named parameter to set this type, function to read and write.

    typedef typename Graph::template NodeMap<bool> ReachedMap;

    ///Instantiates a ReachedMap.

    ///This function instantiates a \ref ReachedMap. 

    ///\param G is the graph, 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 concept::WriteMap "WriteMap" concept.

    ///

    typedef NullMap<typename Graph::Node,int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap. 

    ///\param g is the graph, 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 graph.

    typedef typename Base::Graph::Node Node;

    /// Pointer to the underlying graph.

    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 edges.

    void *_pred;

//     ///Pointer to the map of predecessors nodes.

//     void *_predNode;

    ///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),

// 			   _predNode(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((void *)&g), _reached(0), _processed(0), _pred(0),

//       _predNode(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 graph.

    typedef typename TR::Graph Graph;

    //\e

    typedef typename Graph::Node Node;

    //\e

    typedef typename Graph::NodeIt NodeIt;

    //\e

    typedef typename Graph::Edge Edge;

    //\e

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    ///\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

    ///edges of the %DFS paths.

    typedef typename TR::PredMap PredMap;

//     ///\brief The type of the map that stores the last but one

//     ///nodes of the %DFS paths.

//     typedef typename TR::PredNodeMap PredNodeMap;

    ///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 Graph &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()