/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2009

 * 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/bits/path_dump.h>

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <lemon/path.h>

namespace lemon {

  ///Default traits class of Dfs class.

  ///Default traits class of Dfs class.

  ///\tparam GR Digraph type.

  template<class GR>

  struct DfsDefaultTraits

  {

    ///The type of the digraph the algorithm runs on.

    typedef GR Digraph;

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

    ///arcs of the %DFS paths.

    ///

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

    ///arcs of the %DFS paths.

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

    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;

    ///Instantiates a PredMap.

    ///This function instantiates a PredMap.

    ///\param g is the digraph, to which we would like to define the

    ///PredMap.

    static PredMap *createPredMap(const Digraph &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.

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

    ///Instantiates a ProcessedMap.

    ///This function instantiates a ProcessedMap.

    ///\param g is the digraph, to which

    ///we would like to define the ProcessedMap

#ifdef DOXYGEN

    static ProcessedMap *createProcessedMap(const Digraph &g)

#else

    static ProcessedMap *createProcessedMap(const Digraph &)

#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::ReadWriteMap "ReadWriteMap" concept.

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

    ///Instantiates a ReachedMap.

    ///This function instantiates a ReachedMap.

    ///\param g is the digraph, to which

    ///we would like to define the ReachedMap.

    static ReachedMap *createReachedMap(const Digraph &g)

    {

      return new ReachedMap(g);

    }

    ///The type of the map that stores the distances of the nodes.

    ///The type of the map that stores the distances 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 DistMap.

    ///\param g is the digraph, to which we would like to define the

    ///DistMap.

    static DistMap *createDistMap(const Digraph &g)

    {

      return new DistMap(g);

    }

  };

  ///%DFS algorithm class.

  ///\ingroup search

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

  ///

  ///There is also a \ref dfs() "function-type interface" for the DFS

  ///algorithm, which is convenient in the simplier cases and it can be

  ///used easier.

  ///

  ///\tparam GR The type of the digraph the algorithm runs on.

  ///The default type is \ref ListDigraph.

#ifdef DOXYGEN

  template <typename GR,

            typename TR>

#else

  template <typename GR=ListDigraph,

            typename TR=DfsDefaultTraits<GR> >

#endif

  class Dfs {

  public:

    ///The type of the digraph the algorithm runs on.

    typedef typename TR::Digraph Digraph;

    ///\brief The type of the map that stores the predecessor 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;

    ///The type of the map that indicates which nodes are reached.

    typedef typename TR::ReachedMap ReachedMap;

    ///The type of the map that indicates which nodes are processed.

    typedef typename TR::ProcessedMap ProcessedMap;

    ///The type of the paths.

    typedef PredMapPath<Digraph, PredMap> Path;

    ///The \ref DfsDefaultTraits "traits class" of the algorithm.

    typedef TR Traits;

  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 predecessor arcs.

    PredMap *_pred;

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

    bool local_pred;

    //Pointer to the map of distances.

    DistMap *_dist;

    //Indicates if _dist is locally allocated (true) or not.

    bool local_dist;

    //Pointer to the map of reached status of the nodes.

    ReachedMap *_reached;

    //Indicates if _reached is locally allocated (true) or not.

    bool local_reached;

    //Pointer to the map of processed status of the nodes.

    ProcessedMap *_processed;

    //Indicates if _processed is locally allocated (true) or not.

    bool local_processed;

    std::vector<typename Digraph::OutArcIt> _stack;

    int _stack_head;

    //Creates the maps if necessary.

    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 SetPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Digraph &)

      {

        LEMON_ASSERT(false, "PredMap is not initialized");

        return 0; // ignore warnings

      }

    };

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

    ///PredMap type.

    ///

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

    ///PredMap type.

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

    template <class T>

    struct SetPredMap : public Dfs<Digraph, SetPredMapTraits<T> > {

      typedef Dfs<Digraph, SetPredMapTraits<T> > Create;

    };

    template <class T>

    struct SetDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Digraph &)

      {

        LEMON_ASSERT(false, "DistMap is not initialized");

        return 0; // ignore warnings

      }

    };

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

    ///DistMap type.

    ///

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

    ///DistMap type.

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

    template <class T>

    struct SetDistMap : public Dfs< Digraph, SetDistMapTraits<T> > {

      typedef Dfs<Digraph, SetDistMapTraits<T> > Create;

    };

    template <class T>

    struct SetReachedMapTraits : public Traits {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Digraph &)

      {

        LEMON_ASSERT(false, "ReachedMap is not initialized");

        return 0; // ignore warnings

      }

    };

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

    ///ReachedMap type.

    ///

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

    ///ReachedMap type.

    ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    template <class T>

    struct SetReachedMap : public Dfs< Digraph, SetReachedMapTraits<T> > {

      typedef Dfs< Digraph, SetReachedMapTraits<T> > Create;

    };

    template <class T>

    struct SetProcessedMapTraits : public Traits {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &)

      {

        LEMON_ASSERT(false, "ProcessedMap is not initialized");

        return 0; // ignore warnings

      }

    };

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

    ///ProcessedMap type.

    ///

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

    ///ProcessedMap type.

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

    template <class T>

    struct SetProcessedMap : public Dfs< Digraph, SetProcessedMapTraits<T> > {

      typedef Dfs< Digraph, SetProcessedMapTraits<T> > Create;

    };

    struct SetStandardProcessedMapTraits : 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

    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.

    ///

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

    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.

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

    struct SetStandardProcessedMap :

      public Dfs< Digraph, SetStandardProcessedMapTraits > {

      typedef Dfs< Digraph, SetStandardProcessedMapTraits > Create;

    };

    ///@}

  public:

    ///Constructor.

    ///Constructor.

    ///\param g The digraph the algorithm runs 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 that stores the predecessor arcs.

    ///Sets the map that stores the predecessor arcs.

    ///If you don't use this function before calling \ref run(Node) "run()"

    ///or \ref init(), an instance will be allocated automatically.

    ///The destructor 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 that indicates which nodes are reached.

    ///Sets the map that indicates which nodes are reached.

    ///If you don't use this function before calling \ref run(Node) "run()"

    ///or \ref init(), an instance will be allocated automatically.

    ///The destructor 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 that indicates which nodes are processed.

    ///Sets the map that indicates which nodes are processed.

    ///If you don't use this function before calling \ref run(Node) "run()"

    ///or \ref init(), an instance will be allocated automatically.

    ///The destructor 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;

    }

    ///Sets the map that stores the distances of the nodes.

    ///Sets the map that stores the distances of the nodes calculated by

    ///the algorithm.

    ///If you don't use this function before calling \ref run(Node) "run()"

    ///or \ref init(), an instance will be allocated automatically.

    ///The destructor 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;

    }

  public:

    ///\name Execution Control

    ///The simplest way to execute the DFS algorithm is to use one of the

    ///member functions called \ref run(Node) "run()".\n

    ///If you need more control on the execution, first you have to call

    ///\ref init(), then you can add a source node with \ref addSource()

    ///and perform the actual computation with \ref start().

    ///This procedure can be repeated if there are nodes that have not

    ///been reached.

    ///@{

    ///\brief 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);

        _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.

    ///

    ///\pre The stack must be empty. Otherwise the algorithm gives

    ///wrong results. (One of the outgoing arcs of all the source nodes

    ///except for the last one will not be visited and distances will

    ///also be wrong.)

    void addSource(Node s)

    {

      LEMON_DEBUG(emptyQueue(), "The stack is not empty.");

      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 \c INVALID if the stack

    ///is empty.

    OutArcIt nextArc() const

    {

      return _stack_head>=0?_stack[_stack_head]:INVALID;

    }

    ///Returns \c false if there are nodes to be processed.

    ///Returns \c false if there are nodes to be processed

    ///in the queue (stack).

    bool emptyQueue() const { 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 (stack).

    int queueSize() const { return _stack_head+1; }

    ///Executes the algorithm.

    ///Executes the algorithm.

    ///

    ///This method runs the %DFS algorithm from the root node

    ///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.

    ///

    ///\pre init() must be called and a root node should be

    ///added with addSource() before using this function.

    ///

    ///\note <tt>d.start()</tt> is just a shortcut of the following code.

    ///\code

    ///  while ( !d.emptyQueue() ) {

    ///    d.processNextArc();

    ///  }

    ///\endcode

    void start()

    {

      while ( !emptyQueue() ) processNextArc();

    }

    ///Executes the algorithm until the given target node is reached.

    ///Executes the algorithm until the given target node is reached.

    ///

    ///This method runs the %DFS algorithm from the root node

    ///in order to compute the DFS path to \c t.

    ///

    ///The algorithm computes

    ///- the %DFS path to \c t,

    ///- the distance of \c t from the root in the %DFS tree.

    ///

    ///\pre init() must be called and a root node should be

    ///added with addSource() before using this function.

    void start(Node t)

    {

      while ( !emptyQueue() && G->target(_stack[_stack_head])!=t )

        processNextArc();

    }

    ///Executes the algorithm until a condition is met.

    ///Executes the algorithm until a condition is met.

    ///

    ///This method runs the %DFS algorithm from the root node

    ///until an arc \c a with <tt>am[a]</tt> true is found.

    ///

    ///\param am A \c bool (or convertible) arc map. The algorithm

    ///will stop when it reaches an arc \c a with <tt>am[a]</tt> true.

    ///

    ///\return The reached arc \c a with <tt>am[a]</tt> true or

    ///\c INVALID if no such arc was found.

    ///

    ///\pre init() must be called and a root node should be

    ///added with addSource() before using this function.

    ///

    ///\warning Contrary to \ref Bfs and \ref Dijkstra, \c am is an arc map,

    ///not a node map.

    template<class ArcBoolMap>

    Arc start(const ArcBoolMap &am)

    {

      while ( !emptyQueue() && !am[_stack[_stack_head]] )

        processNextArc();

      return emptyQueue() ? INVALID : _stack[_stack_head];

    }

    ///Runs the algorithm from the given source node.

    ///This method runs the %DFS algorithm from 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 <tt>d.run(s)</tt> 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.

    ///This method runs the %DFS algorithm from node \c s

    ///in order to compute the DFS path to node \c t

    ///(it stops searching when \c t is processed)

    ///

    ///\return \c true if \c t is reachable form \c s.

    ///

    ///\note Apart from the return value, <tt>d.run(s,t)</tt> is

    ///just a shortcut of the following code.

    ///\code

    ///  d.init();

    ///  d.addSource(s);

    ///  d.start(t);

    ///\endcode

    bool run(Node s,Node t) {

      init();

      addSource(s);

      start(t);

      return reached(t);

    }

    ///Runs the 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 (forest),

    ///- the distance of each node from the root(s) in the %DFS tree.

    ///

    ///\note <tt>d.run()</tt> is just a shortcut of the following code.

    ///\code

    ///  d.init();

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

    ///    if (!d.reached(n)) {

    ///      d.addSource(n);

    ///      d.start();

    ///    }

    ///  }

    ///\endcode

    void run() {

      init();

      for (NodeIt it(*G); it != INVALID; ++it) {

        if (!reached(it)) {

          addSource(it);

          start();

        }

      }

    }

    ///@}

    ///\name Query Functions

    ///The results of the DFS algorithm can be obtained using these

    ///functions.\n

    ///Either \ref run(Node) "run()" or \ref start() should be called

    ///before using them.

    ///@{

    ///The DFS path to a node.

    ///Returns the DFS path to a node.

    ///

    ///\warning \c t should be reached from the root(s).

    ///

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

    ///must be called before using this function.

    Path path(Node t) const { return Path(*G, *_pred, t); }

    ///The distance of a node from the root(s).

    ///Returns the distance of a node from the root(s).

    ///

    ///\warning If node \c v is not reached from the root(s), then

    ///the return value of this function is undefined.

    ///

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

    ///must be called before using this function.

    int dist(Node v) const { return (*_dist)[v]; }

    ///Returns the 'previous arc' of the %DFS tree for a node.

    ///This function returns the 'previous arc' of the %DFS tree for the

    ///node \c v, i.e. it returns the last arc of a %DFS path from a

    ///root to \c v. It is \c INVALID if \c v is not reached from the

    ///root(s) or if \c v is a root.

    ///

    ///The %DFS tree used here is equal to the %DFS tree used in

    ///\ref predNode().

    ///

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

    ///must be called before using this function.

    Arc predArc(Node v) const { return (*_pred)[v];}

    ///Returns the 'previous node' of the %DFS tree.

    ///This function returns the 'previous node' of the %DFS

    ///tree for the node \c v, i.e. it returns the last but one node

    ///from a %DFS path from a root to \c v. It is \c INVALID

    ///if \c v is not reached from the root(s) or if \c v is a root.

    ///

    ///The %DFS tree used here is equal to the %DFS tree used in

    ///\ref predArc().

    ///

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

    ///must be called before using this function.

    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:

                                  G->source((*_pred)[v]); }

    ///\brief Returns a const reference to the node map that stores the

    ///distances of the nodes.

    ///

    ///Returns a const reference to the node map that stores the

    ///distances of the nodes calculated by the algorithm.

    ///

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

    ///must be called before using this function.

    const DistMap &distMap() const { return *_dist;}

    ///\brief Returns a const reference to the node map that stores the

    ///predecessor arcs.

    ///

    ///Returns a const reference to the node map that stores the predecessor

    ///arcs, which form the DFS tree.

    ///

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

    ///must be called before using this function.

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

    ///Checks if a node is reached from the root(s).

    ///Returns \c true if \c v is reached from the root(s).

    ///

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

    ///must be called before using this function.

    bool reached(Node v) const { return (*_reached)[v]; }

    ///@}

  };

  ///Default traits class of dfs() function.

  ///Default traits class of dfs() function.

  ///\tparam GR Digraph type.

  template<class GR>

  struct DfsWizardDefaultTraits

  {

    ///The type of the digraph the algorithm runs on.

    typedef GR Digraph;

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

    ///arcs of the %DFS paths.

    ///

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

    ///arcs of the %DFS paths.

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

    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;

    ///Instantiates a PredMap.

    ///This function instantiates a PredMap.

    ///\param g is the digraph, to which we would like to define the

    ///PredMap.

    static PredMap *createPredMap(const Digraph &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.

    ///By default it is a NullMap.

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

    ///Instantiates a ProcessedMap.

    ///This function instantiates a ProcessedMap.

    ///\param g is the digraph, to which

    ///we would like to define the ProcessedMap.

#ifdef DOXYGEN

    static ProcessedMap *createProcessedMap(const Digraph &g)

#else

    static ProcessedMap *createProcessedMap(const Digraph &)

#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::ReadWriteMap "ReadWriteMap" concept.

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

    ///Instantiates a ReachedMap.

    ///This function instantiates a ReachedMap.

    ///\param g is the digraph, to which

    ///we would like to define the ReachedMap.

    static ReachedMap *createReachedMap(const Digraph &g)

    {

      return new ReachedMap(g);

    }

    ///The type of the map that stores the distances of the nodes.

    ///The type of the map that stores the distances 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 DistMap.

    ///\param g is the digraph, to which we would like to define

    ///the DistMap

    static DistMap *createDistMap(const Digraph &g)

    {

      return new DistMap(g);

    }

    ///The type of the DFS paths.

    ///The type of the DFS paths.

    ///It must meet the \ref concepts::Path "Path" concept.

    typedef lemon::Path<Digraph> Path;

  };

  /// Default traits class used by 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:

    //The type of the nodes in the digraph.

    typedef typename Base::Digraph::Node Node;

    //Pointer to the digraph the algorithm runs on.

    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 DFS path to the target node.

    void *_path;

    //Pointer to the distance of the target node.

    int *_di;

    public:

    /// Constructor.

    /// This constructor does not require parameters, therefore it initiates

    /// all of the attributes to \c 0.

    DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),

                      _dist(0), _path(0), _di(0) {}

    /// Constructor.

    /// This constructor requires one parameter,

    /// others are initiated to \c 0.

    /// \param g The digraph the algorithm runs on.

    DfsWizardBase(const GR &g) :

      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),

      _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}

  };

  /// Auxiliary class for the function-type interface of DFS algorithm.

  /// This auxiliary class is created to implement the

  /// \ref dfs() "function-type interface" of \ref Dfs algorithm.

  /// It does not have own \ref run(Node) "run()" method, it uses the

  /// functions and features of the plain \ref Dfs.

  ///

  /// This class should only be used through the \ref dfs() function,

  /// which makes it easier to use the algorithm.

  template<class TR>

  class DfsWizard : public TR

  {

    typedef TR Base;

    ///The type of the digraph the algorithm runs on.

    typedef typename TR::Digraph Digraph;

    typedef typename Digraph::Node Node;

    typedef typename Digraph::NodeIt NodeIt;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::OutArcIt OutArcIt;

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

    ///arcs of the DFS paths.

    typedef typename TR::PredMap PredMap;

    ///\brief The type of the map that stores the distances of the nodes.

    typedef typename TR::DistMap DistMap;

    ///\brief The type of the map that indicates which nodes are reached.

    typedef typename TR::ReachedMap ReachedMap;

    ///\brief The type of the map that indicates which nodes are processed.

    typedef typename TR::ProcessedMap ProcessedMap;

    ///The type of the DFS paths

    typedef typename TR::Path Path;

  public:

    /// Constructor.

    DfsWizard() : TR() {}

    /// Constructor that requires parameters.

    /// Constructor that requires parameters.

    /// These parameters will be the default values for the traits class.

    /// \param g The digraph the algorithm runs on.

    DfsWizard(const Digraph &g) :

      TR(g) {}

    ///Copy constructor

    DfsWizard(const TR &b) : TR(b) {}

    ~DfsWizard() {}

    ///Runs DFS algorithm from the given source node.

    ///This method runs DFS algorithm from node \c s

    ///in order to compute the DFS path to each node.

    void run(Node s)

    {

      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));

      if (Base::_pred)

        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));

      if (Base::_dist)

        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));

      if (Base::_reached)

        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));

      if (Base::_processed)

        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));

      if (s!=INVALID)

        alg.run(s);

      else

        alg.run();

    }

    ///Finds the DFS path between \c s and \c t.

    ///This method runs DFS algorithm from node \c s

    ///in order to compute the DFS path to node \c t

    ///(it stops searching when \c t is processed).

    ///

    ///\return \c true if \c t is reachable form \c s.

    bool run(Node s, Node t)

    {

      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));

      if (Base::_pred)

        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));

      if (Base::_dist)

        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));

      if (Base::_reached)

        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));

      if (Base::_processed)

        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));

      alg.run(s,t);

      if (Base::_path)

        *reinterpret_cast<Path*>(Base::_path) = alg.path(t);

      if (Base::_di)

        *Base::_di = alg.dist(t);

      return alg.reached(t);

      }

    ///Runs DFS algorithm to visit all nodes in the digraph.

    ///This method runs DFS algorithm in order to compute

    ///the DFS path to each node.

    void run()

    {

      run(INVALID);