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

 *

 * 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/bits/path_dump.h>

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/maps.h>

namespace lemon {

  ///Default traits class of Bfs class.

  ///Default traits class of Bfs class.

  ///\tparam GR Digraph type.

  template<class GR>

  struct BfsDefaultTraits

  {

    ///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 shortest paths.

    ///

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

    ///arcs of the shortest paths.

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

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

    ///Instantiates a \ref PredMap.

    ///This function instantiates a \ref PredMap.

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

    ///\ref 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 \ref 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 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 \ref 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 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 \ref 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 Digraph &g)

    {

      return new DistMap(g);

    }

  };

  ///%BFS algorithm class.

  ///\ingroup search

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

  ///

  ///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 value is \ref ListDigraph. The value of GR is not used

  ///directly by \ref Bfs, it is only passed to \ref BfsDefaultTraits.

  ///\tparam 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.

#ifdef DOXYGEN

  template <typename GR,

            typename TR>

#else

  template <typename GR=ListDigraph,

            typename TR=BfsDefaultTraits<GR> >

#endif

  class Bfs {

  public:

    ///\ref Exception for uninitialized parameters.

    ///This error represents problems in the initialization of the

    ///parameters of the algorithm.

    class UninitializedParameter : public lemon::UninitializedParameter {

    public:

      virtual const char* what() const throw() {

        return "lemon::Bfs::UninitializedParameter";

      }

    };

    ///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

    ///shortest 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 traits class.

    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::Node> _queue;

    int _queue_head,_queue_tail,_queue_next_dist;

    int _curr_dist;

    //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:

    Bfs() {}

  public:

    typedef Bfs Create;

    ///\name Named template parameters

    ///@{

    template <class T>

    struct SetPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Digraph &)

      {

        throw UninitializedParameter();

      }

    };

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

    ///\ref PredMap type.

    ///

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

    ///\ref PredMap type.

    template <class T>

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

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

    };

    template <class T>

    struct SetDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Digraph &)

      {

        throw UninitializedParameter();

      }

    };

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

    ///\ref DistMap type.

    ///

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

    ///\ref DistMap type.

    template <class T>

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

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

    };

    template <class T>

    struct SetReachedMapTraits : public Traits {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Digraph &)

      {

        throw UninitializedParameter();

      }

    };

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

    ///\ref ReachedMap type.

    ///

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

    ///\ref ReachedMap type.

    template <class T>

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

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

    };

    template <class T>

    struct SetProcessedMapTraits : public Traits {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &)

      {

        throw UninitializedParameter();

      }

    };

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

    ///\ref ProcessedMap type.

    ///

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

    ///\ref ProcessedMap type.

    template <class T>

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

      typedef Bfs< 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

    ///    b.processNextNode(nm, rnode);

    ///  }

    ///  return rnode;

    ///\endcode

    template<class NodeBoolMap>

    Node start(const NodeBoolMap &nm)

    {

      Node rnode = INVALID;

      while ( !emptyQueue() && rnode == INVALID ) {

        processNextNode(nm, rnode);

      }

      return rnode;

    }

    ///Runs the algorithm from the given node.

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

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

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

    ///

    ///\return The length of the shortest <tt>s</tt>--<tt>t</tt> path,

    ///if \c t is reachable form \c s, \c 0 otherwise.

    ///

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

    }

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

    ///This method runs the %BFS algorithm in order to

    ///compute the shortest path to each node.

    ///

    ///The algorithm computes

    ///- the shortest path tree (forest),

    ///- the distance of each node from the root(s).

    ///

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

    ///\code

    ///  b.init();

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

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

    ///      b.addSource(n);

    ///      b.start();

    ///    }

    ///  }

    ///\endcode

    void run() {

      init();

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

        if (!reached(n)) {

          addSource(n);

          start();

        }

      }

    }

    ///@}

    ///\name Query Functions

    ///The result of the %BFS algorithm can be obtained using these

    ///functions.\n

    ///Either \ref lemon::Bfs::run() "run()" or \ref lemon::Bfs::start()

    ///"start()" must be called before using them.

    ///@{

    ///The shortest path to a node.

    ///Returns the shortest path to a node.

    ///

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

    ///

    ///\pre Either \ref run() or \ref start() 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 reachable from the root(s), then

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

    ///

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

    ///using this function.

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

    ///Returns the 'previous arc' of the shortest path tree for a node.

    ///This function returns the 'previous arc' of the shortest path

    ///tree for the node \c v, i.e. it returns the last arc of a

    ///shortest path from the root(s) to \c v. It is \c INVALID if \c v

    ///is not reachable from the root(s) or if \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.

    ///This function returns the 'previous node' of the shortest path

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

    ///from a shortest path from the root(s) to \c v. It is \c INVALID

    ///if \c v is not reachable from the root(s) or if \c v is 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]); }

    ///\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() 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 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(s).

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

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

    ///must be called before using this function.

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

    ///@}

  };

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

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

  ///\tparam GR Digraph type.

  template<class GR>

  struct BfsWizardDefaultTraits

  {

    ///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 shortest paths.

    ///

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

    ///arcs of the shortest paths.

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

    ///Instantiates a \ref PredMap.

    ///This function instantiates a \ref PredMap.

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

    ///\ref PredMap.

    static PredMap *createPredMap(const Digraph &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 \ref 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 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 \ref 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 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.

    ///Instantiates a \ref 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 Digraph &g)

    {

    }

  };

  /// Default traits class 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:

    //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;

    public:

    /// Constructor.

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

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

    /// Constructor.

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

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

  };

  ///

  template<class TR>

  class BfsWizard : 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 shortest 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;

  public:

    /// Constructor.

    BfsWizard() : TR() {}

    /// Constructor that requires parameters.

    /// Constructor that requires parameters.

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

    ///Copy constructor

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

    ~BfsWizard() {}

    void run()

    {

    }

    template<class T>

    struct SetPredMapBase : public Base {

      typedef T PredMap;

      static PredMap *createPredMap(const Digraph &) { return 0; };

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

    };

    ///for setting \ref PredMap object.

    ///

    ///for setting \ref PredMap object.

    template<class T>

    BfsWizard<SetPredMapBase<T> > predMap(const T &t)

    {

      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));

      return BfsWizard<SetPredMapBase<T> >(*this);

    }

    template<class T>

    struct SetReachedMapBase : public Base {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Digraph &) { return 0; };

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

    };

    ///for setting \ref ReachedMap object.

    ///

    ///for setting \ref ReachedMap object.

    template<class T>

    BfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)

    {

      Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));

      return BfsWizard<SetReachedMapBase<T> >(*this);

    }

    template<class T>

    struct SetProcessedMapBase : public Base {

      typedef T ProcessedMap;

      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };

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

    };

    ///for setting \ref ProcessedMap object.

    ///

    ///for setting \ref ProcessedMap object.

    template<class T>

    BfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)

    {

      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));

      return BfsWizard<SetProcessedMapBase<T> >(*this);

    }

    template<class T>

    };

    ///

    template<class T>

    {

    }

  };

  /// \ingroup search

  ///

  ///they are declared as the members of class \ref BfsWizard.

  ///\code

  ///\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> >

  {

  }

#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 for the source node(s) of the BFS.

    ///

    /// This function is called for the source node(s) of the BFS.

    void start(const Node& node) {}

    /// \brief Called when a node is reached first time.

    ///

    /// This function is called when a node is reached first time.

    void reach(const Node& node) {}

    /// \brief Called when a node is processed.

    ///

    /// This function is called when a node is processed.

    void process(const Node& node) {}

    /// \brief Called when an arc reaches a new node.

    ///

    /// This function is called when the BFS finds an arc whose target node

    /// is not reached yet.

    void discover(const Arc& arc) {}

    /// \brief Called when an arc is examined but its target node is

    /// already discovered.

    ///

    /// This function is called when an arc is examined but its target node is

    /// already discovered.

    void examine(const Arc& arc) {}

  };

#else

  template <typename _Digraph>

  struct BfsVisitor {

    typedef _Digraph Digraph;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::Node Node;

    void start(const Node&) {}

    void reach(const Node&) {}

    void process(const Node&) {}

    void discover(const Arc&) {}

    void examine(const Arc&) {}

    template <typename _Visitor>

    struct Constraints {

      void constraints() {

        Arc arc;

        Node node;

        visitor.start(node);

        visitor.reach(node);

        visitor.process(node);

        visitor.discover(arc);

        visitor.examine(arc);

      }

      _Visitor& visitor;

    };

  };

#endif

  /// \brief Default traits class of BfsVisit class.

  ///

  /// Default traits class of BfsVisit class.

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

  template<class _Digraph>

  struct BfsVisitDefaultTraits {

    /// \brief The type of the digraph 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::ReadWriteMap "ReadWriteMap" concept.

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

    /// \brief Instantiates a \ref 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 algorithm class with visitor interface.

  ///

  /// 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

  /// the member functions of the \c Visitor class on every BFS event.

  ///

  /// This interface of the BFS algorithm should be used in special cases

  /// when extra actions have to be performed in connection with certain

  /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()

  /// instead.

  ///

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

  /// The default value is

  /// \ref ListDigraph. The value of _Digraph is not used directly by

  /// \ref BfsVisit, it is only passed to \ref BfsVisitDefaultTraits.

  /// \tparam _Visitor The Visitor type that is used by the algorithm.

  /// \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.

  /// \tparam _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.

#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 algorithm.

    class UninitializedParameter : public lemon::UninitializedParameter {

    public:

      virtual const char* what() const throw()

      {