/* -*- 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_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>

#include <lemon/path.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 \c 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 \c 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 \c 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 \c 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.

  ///

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

  ///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=BfsDefaultTraits<GR> >

#endif

  class Bfs {

  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

    ///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 \ref BfsDefaultTraits "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::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 &)

      {

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

        return 0; // ignore warnings

      }

    };

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

    ///\c PredMap type.

    ///

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

    ///\c PredMap type.

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

    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 &)

      {

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

        return 0; // ignore warnings

      }

    };

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

    ///\c DistMap type.

    ///

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

    ///\c DistMap type.

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

    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 &)

      {

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

        return 0; // ignore warnings

      }

    };

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

    ///\c ReachedMap type.

    ///

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

    ///\c ReachedMap type.

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

    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 &)

      {

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

        return 0; // ignore warnings

      }

    };

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

    ///\c ProcessedMap type.

    ///

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

    ///\c ProcessedMap type.

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

    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);

        return 0; // ignore warnings

      }

    };

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

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

    ///

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

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

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

    struct SetStandardProcessedMap :

      public Bfs< Digraph, SetStandardProcessedMapTraits > {

      typedef Bfs< Digraph, SetStandardProcessedMapTraits > Create;

    };

    ///@}

  public:

    ///Constructor.

    ///Constructor.

    ///\param g The digraph the algorithm runs 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 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>

    Bfs &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>

    Bfs &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>

    Bfs &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>

    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 BFS algorithm is to use one of the

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

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

    ///\ref init() first, then you can add several source nodes with

    ///\ref addSource(). Finally the actual path computation can be

    ///performed with one of the \ref start() functions.

    ///@{

    ///\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.

    ///

    ///\pre 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 if the given target node

    ///is reached. If the target node is reachable from the processed

    ///node, then the \c reach parameter will be set to \c true.

    ///

    ///\param target The target node.

    ///\retval reach Indicates if the target node is reached.

    ///It should be initially \c false.

    ///

    ///\return The processed node.

    ///

    ///\pre 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 if at least one of reached

    ///nodes has \c true value in the \c nm node map. If one node

    ///with \c true value is reachable from the processed node, then the

    ///\c rnode parameter will be set to the first of such nodes.

    ///

    ///\param nm A \c bool (or convertible) node map that indicates the

    ///possible targets.

    ///\retval rnode The reached target node.

    ///It should be initially \c INVALID.

    ///

    ///\return The processed node.

    ///

    ///\pre 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;

    }

    ///The next node to be processed.

    ///Returns the next node to be processed or \c INVALID if the queue

    ///is empty.

    Node nextNode() const

    {

      return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;

    }

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

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

    ///in the queue.

    bool emptyQueue() const { 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() const { return _queue_head-_queue_tail; }

    ///Executes the algorithm.

    ///Executes the algorithm.

    ///

    ///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 (forest),

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

    ///

    ///\pre init() must be called and at least one root node should be

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

    ///

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

    ///\code

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

    ///    b.processNextNode();

    ///  }

    ///\endcode

    void start()

    {

      while ( !emptyQueue() ) processNextNode();

    }

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

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

    ///

    ///This method runs the %BFS algorithm from the root node(s)

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

    ///

    ///The algorithm computes

    ///- the shortest path to \c t,

    ///- the distance of \c t from the root(s).

    ///

    ///\pre init() must be called and at least one root node should be

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

    ///

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

    ///\code

    ///  bool reach = false;

    ///  while ( !b.emptyQueue() && !reach ) {

    ///    b.processNextNode(t, reach);

    ///  }

    ///\endcode

    void start(Node t)

    {

      bool reach = false;

      while ( !emptyQueue() && !reach ) processNextNode(t, reach);

    }

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

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

    ///

    ///This method runs the %BFS algorithm from the root node(s) in

    ///order to compute the shortest path to a node \c v with

    /// <tt>nm[v]</tt> true, if such a node can be found.

    ///

    ///\param nm A \c 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.

    ///

    ///\pre init() must be called and at least one root node should be

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

    ///

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

    ///\code

    ///  Node rnode = INVALID;

    ///  while ( !b.emptyQueue() && rnode == INVALID ) {

    ///    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 source 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 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>b.run(s,t)</tt> is just a

    ///shortcut of the following code.

    ///\code

    ///  b.init();

    ///  b.addSource(s);

    ///  b.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 %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 results of the BFS algorithm can be obtained using these

    ///functions.\n

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

    ///before using them.

    ///@{

    ///The shortest path to a node.

    ///Returns the shortest 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 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 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 shortest path tree used here is equal to the shortest path

    ///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 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 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 shortest path tree used here is equal to the shortest path

    ///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 shortest path 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 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.

    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 shortest paths.

    ///The type of the shortest paths.

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

    typedef lemon::Path<Digraph> Path;

  };

  /// Default traits class used by 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;

    //Pointer to the shortest 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.

    BfsWizardBase() : _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.

    BfsWizardBase(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 BFS algorithm.

  /// This auxiliary class is created to implement the

  /// \ref bfs() "function-type interface" of \ref Bfs algorithm.

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

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

  ///

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

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

  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;

    ///The type of the shortest paths

    typedef typename TR::Path Path;

  public:

    /// Constructor.

    BfsWizard() : TR() {}