lemon/bfs.h
author Peter Kovacs <kpeter@inf.elte.hu>
Tue, 29 Jul 2008 14:41:16 +0200
changeset 241 92f046dd7f6c
parent 210 81cfc04531e8
child 247 f1158744a112
permissions -rw-r--r--
Improvements in dim2::BoundingBox (ticket #126)
- Rename the private varibles to start with underscore.
- Doc improvements.
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_BFS_H
    20 #define LEMON_BFS_H
    21 
    22 ///\ingroup search
    23 ///\file
    24 ///\brief Bfs algorithm.
    25 
    26 #include <lemon/list_graph.h>
    27 #include <lemon/bits/path_dump.h>
    28 #include <lemon/core.h>
    29 #include <lemon/error.h>
    30 #include <lemon/maps.h>
    31 
    32 namespace lemon {
    33 
    34 
    35 
    36   ///Default traits class of Bfs class.
    37 
    38   ///Default traits class of Bfs class.
    39   ///\tparam GR Digraph type.
    40   template<class GR>
    41   struct BfsDefaultTraits
    42   {
    43     ///The digraph type the algorithm runs on.
    44     typedef GR Digraph;
    45     ///\brief The type of the map that stores the last
    46     ///arcs of the shortest paths.
    47     ///
    48     ///The type of the map that stores the last
    49     ///arcs of the shortest paths.
    50     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    51     ///
    52     typedef typename Digraph::template NodeMap<typename GR::Arc> PredMap;
    53     ///Instantiates a PredMap.
    54 
    55     ///This function instantiates a \ref PredMap.
    56     ///\param G is the digraph, to which we would like to define the PredMap.
    57     ///\todo The digraph alone may be insufficient to initialize
    58     static PredMap *createPredMap(const GR &G)
    59     {
    60       return new PredMap(G);
    61     }
    62     ///The type of the map that indicates which nodes are processed.
    63 
    64     ///The type of the map that indicates which nodes are processed.
    65     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    66     ///\todo named parameter to set this type, function to read and write.
    67     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
    68     ///Instantiates a ProcessedMap.
    69 
    70     ///This function instantiates a \ref ProcessedMap.
    71     ///\param g is the digraph, to which
    72     ///we would like to define the \ref ProcessedMap
    73 #ifdef DOXYGEN
    74     static ProcessedMap *createProcessedMap(const GR &g)
    75 #else
    76     static ProcessedMap *createProcessedMap(const GR &)
    77 #endif
    78     {
    79       return new ProcessedMap();
    80     }
    81     ///The type of the map that indicates which nodes are reached.
    82 
    83     ///The type of the map that indicates which nodes are reached.
    84     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    85     ///\todo named parameter to set this type, function to read and write.
    86     typedef typename Digraph::template NodeMap<bool> ReachedMap;
    87     ///Instantiates a ReachedMap.
    88 
    89     ///This function instantiates a \ref ReachedMap.
    90     ///\param G is the digraph, to which
    91     ///we would like to define the \ref ReachedMap.
    92     static ReachedMap *createReachedMap(const GR &G)
    93     {
    94       return new ReachedMap(G);
    95     }
    96     ///The type of the map that stores the dists of the nodes.
    97 
    98     ///The type of the map that stores the dists of the nodes.
    99     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   100     ///
   101     typedef typename Digraph::template NodeMap<int> DistMap;
   102     ///Instantiates a DistMap.
   103 
   104     ///This function instantiates a \ref DistMap.
   105     ///\param G is the digraph, to which we would like to define
   106     ///the \ref DistMap
   107     static DistMap *createDistMap(const GR &G)
   108     {
   109       return new DistMap(G);
   110     }
   111   };
   112 
   113   ///%BFS algorithm class.
   114 
   115   ///\ingroup search
   116   ///This class provides an efficient implementation of the %BFS algorithm.
   117   ///
   118   ///\tparam GR The digraph type the algorithm runs on. The default value is
   119   ///\ref ListDigraph. The value of GR is not used directly by Bfs, it
   120   ///is only passed to \ref BfsDefaultTraits.
   121   ///\tparam TR Traits class to set various data types used by the algorithm.
   122   ///The default traits class is
   123   ///\ref BfsDefaultTraits "BfsDefaultTraits<GR>".
   124   ///See \ref BfsDefaultTraits for the documentation of
   125   ///a Bfs traits class.
   126 
   127 #ifdef DOXYGEN
   128   template <typename GR,
   129             typename TR>
   130 #else
   131   template <typename GR=ListDigraph,
   132             typename TR=BfsDefaultTraits<GR> >
   133 #endif
   134   class Bfs {
   135   public:
   136     /**
   137      * \brief \ref Exception for uninitialized parameters.
   138      *
   139      * This error represents problems in the initialization
   140      * of the parameters of the algorithms.
   141      */
   142     class UninitializedParameter : public lemon::UninitializedParameter {
   143     public:
   144       virtual const char* what() const throw() {
   145         return "lemon::Bfs::UninitializedParameter";
   146       }
   147     };
   148 
   149     typedef TR Traits;
   150     ///The type of the underlying digraph.
   151     typedef typename TR::Digraph Digraph;
   152 
   153     ///\brief The type of the map that stores the last
   154     ///arcs of the shortest paths.
   155     typedef typename TR::PredMap PredMap;
   156     ///The type of the map indicating which nodes are reached.
   157     typedef typename TR::ReachedMap ReachedMap;
   158     ///The type of the map indicating which nodes are processed.
   159     typedef typename TR::ProcessedMap ProcessedMap;
   160     ///The type of the map that stores the dists of the nodes.
   161     typedef typename TR::DistMap DistMap;
   162   private:
   163 
   164     typedef typename Digraph::Node Node;
   165     typedef typename Digraph::NodeIt NodeIt;
   166     typedef typename Digraph::Arc Arc;
   167     typedef typename Digraph::OutArcIt OutArcIt;
   168 
   169     /// Pointer to the underlying digraph.
   170     const Digraph *G;
   171     ///Pointer to the map of predecessors arcs.
   172     PredMap *_pred;
   173     ///Indicates if \ref _pred is locally allocated (\c true) or not.
   174     bool local_pred;
   175     ///Pointer to the map of distances.
   176     DistMap *_dist;
   177     ///Indicates if \ref _dist is locally allocated (\c true) or not.
   178     bool local_dist;
   179     ///Pointer to the map of reached status of the nodes.
   180     ReachedMap *_reached;
   181     ///Indicates if \ref _reached is locally allocated (\c true) or not.
   182     bool local_reached;
   183     ///Pointer to the map of processed status of the nodes.
   184     ProcessedMap *_processed;
   185     ///Indicates if \ref _processed is locally allocated (\c true) or not.
   186     bool local_processed;
   187 
   188     std::vector<typename Digraph::Node> _queue;
   189     int _queue_head,_queue_tail,_queue_next_dist;
   190     int _curr_dist;
   191 
   192     ///Creates the maps if necessary.
   193 
   194     ///\todo Better memory allocation (instead of new).
   195     void create_maps()
   196     {
   197       if(!_pred) {
   198         local_pred = true;
   199         _pred = Traits::createPredMap(*G);
   200       }
   201       if(!_dist) {
   202         local_dist = true;
   203         _dist = Traits::createDistMap(*G);
   204       }
   205       if(!_reached) {
   206         local_reached = true;
   207         _reached = Traits::createReachedMap(*G);
   208       }
   209       if(!_processed) {
   210         local_processed = true;
   211         _processed = Traits::createProcessedMap(*G);
   212       }
   213     }
   214 
   215   protected:
   216 
   217     Bfs() {}
   218 
   219   public:
   220 
   221     typedef Bfs Create;
   222 
   223     ///\name Named template parameters
   224 
   225     ///@{
   226 
   227     template <class T>
   228     struct DefPredMapTraits : public Traits {
   229       typedef T PredMap;
   230       static PredMap *createPredMap(const Digraph &)
   231       {
   232         throw UninitializedParameter();
   233       }
   234     };
   235     ///\brief \ref named-templ-param "Named parameter" for setting
   236     ///PredMap type
   237     ///
   238     ///\ref named-templ-param "Named parameter" for setting PredMap type
   239     ///
   240     template <class T>
   241     struct DefPredMap : public Bfs< Digraph, DefPredMapTraits<T> > {
   242       typedef Bfs< Digraph, DefPredMapTraits<T> > Create;
   243     };
   244 
   245     template <class T>
   246     struct DefDistMapTraits : public Traits {
   247       typedef T DistMap;
   248       static DistMap *createDistMap(const Digraph &)
   249       {
   250         throw UninitializedParameter();
   251       }
   252     };
   253     ///\brief \ref named-templ-param "Named parameter" for setting
   254     ///DistMap type
   255     ///
   256     ///\ref named-templ-param "Named parameter" for setting DistMap type
   257     ///
   258     template <class T>
   259     struct DefDistMap : public Bfs< Digraph, DefDistMapTraits<T> > {
   260       typedef Bfs< Digraph, DefDistMapTraits<T> > Create;
   261     };
   262 
   263     template <class T>
   264     struct DefReachedMapTraits : public Traits {
   265       typedef T ReachedMap;
   266       static ReachedMap *createReachedMap(const Digraph &)
   267       {
   268         throw UninitializedParameter();
   269       }
   270     };
   271     ///\brief \ref named-templ-param "Named parameter" for setting
   272     ///ReachedMap type
   273     ///
   274     ///\ref named-templ-param "Named parameter" for setting ReachedMap type
   275     ///
   276     template <class T>
   277     struct DefReachedMap : public Bfs< Digraph, DefReachedMapTraits<T> > {
   278       typedef Bfs< Digraph, DefReachedMapTraits<T> > Create;
   279     };
   280 
   281     template <class T>
   282     struct DefProcessedMapTraits : public Traits {
   283       typedef T ProcessedMap;
   284       static ProcessedMap *createProcessedMap(const Digraph &)
   285       {
   286         throw UninitializedParameter();
   287       }
   288     };
   289     ///\brief \ref named-templ-param "Named parameter" for setting
   290     ///ProcessedMap type
   291     ///
   292     ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
   293     ///
   294     template <class T>
   295     struct DefProcessedMap : public Bfs< Digraph, DefProcessedMapTraits<T> > {
   296       typedef Bfs< Digraph, DefProcessedMapTraits<T> > Create;
   297     };
   298 
   299     struct DefDigraphProcessedMapTraits : public Traits {
   300       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   301       static ProcessedMap *createProcessedMap(const Digraph &G)
   302       {
   303         return new ProcessedMap(G);
   304       }
   305     };
   306     ///\brief \ref named-templ-param "Named parameter"
   307     ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
   308     ///
   309     ///\ref named-templ-param "Named parameter"
   310     ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.
   311     ///If you don't set it explicitly, it will be automatically allocated.
   312     template <class T>
   313     struct DefProcessedMapToBeDefaultMap :
   314       public Bfs< Digraph, DefDigraphProcessedMapTraits> {
   315       typedef Bfs< Digraph, DefDigraphProcessedMapTraits> Create;
   316     };
   317 
   318     ///@}
   319 
   320   public:
   321 
   322     ///Constructor.
   323 
   324     ///\param _G the digraph the algorithm will run on.
   325     ///
   326     Bfs(const Digraph& _G) :
   327       G(&_G),
   328       _pred(NULL), local_pred(false),
   329       _dist(NULL), local_dist(false),
   330       _reached(NULL), local_reached(false),
   331       _processed(NULL), local_processed(false)
   332     { }
   333 
   334     ///Destructor.
   335     ~Bfs()
   336     {
   337       if(local_pred) delete _pred;
   338       if(local_dist) delete _dist;
   339       if(local_reached) delete _reached;
   340       if(local_processed) delete _processed;
   341     }
   342 
   343     ///Sets the map storing the predecessor arcs.
   344 
   345     ///Sets the map storing the predecessor arcs.
   346     ///If you don't use this function before calling \ref run(),
   347     ///it will allocate one. The destructor deallocates this
   348     ///automatically allocated map, of course.
   349     ///\return <tt> (*this) </tt>
   350     Bfs &predMap(PredMap &m)
   351     {
   352       if(local_pred) {
   353         delete _pred;
   354         local_pred=false;
   355       }
   356       _pred = &m;
   357       return *this;
   358     }
   359 
   360     ///Sets the map indicating the reached nodes.
   361 
   362     ///Sets the map indicating the reached nodes.
   363     ///If you don't use this function before calling \ref run(),
   364     ///it will allocate one. The destructor deallocates this
   365     ///automatically allocated map, of course.
   366     ///\return <tt> (*this) </tt>
   367     Bfs &reachedMap(ReachedMap &m)
   368     {
   369       if(local_reached) {
   370         delete _reached;
   371         local_reached=false;
   372       }
   373       _reached = &m;
   374       return *this;
   375     }
   376 
   377     ///Sets the map indicating the processed nodes.
   378 
   379     ///Sets the map indicating the processed nodes.
   380     ///If you don't use this function before calling \ref run(),
   381     ///it will allocate one. The destructor deallocates this
   382     ///automatically allocated map, of course.
   383     ///\return <tt> (*this) </tt>
   384     Bfs &processedMap(ProcessedMap &m)
   385     {
   386       if(local_processed) {
   387         delete _processed;
   388         local_processed=false;
   389       }
   390       _processed = &m;
   391       return *this;
   392     }
   393 
   394     ///Sets the map storing the distances calculated by the algorithm.
   395 
   396     ///Sets the map storing the distances calculated by the algorithm.
   397     ///If you don't use this function before calling \ref run(),
   398     ///it will allocate one. The destructor deallocates this
   399     ///automatically allocated map, of course.
   400     ///\return <tt> (*this) </tt>
   401     Bfs &distMap(DistMap &m)
   402     {
   403       if(local_dist) {
   404         delete _dist;
   405         local_dist=false;
   406       }
   407       _dist = &m;
   408       return *this;
   409     }
   410 
   411   public:
   412     ///\name Execution control
   413     ///The simplest way to execute the algorithm is to use
   414     ///one of the member functions called \c run(...).
   415     ///\n
   416     ///If you need more control on the execution,
   417     ///first you must call \ref init(), then you can add several source nodes
   418     ///with \ref addSource().
   419     ///Finally \ref start() will perform the actual path
   420     ///computation.
   421 
   422     ///@{
   423 
   424     ///\brief Initializes the internal data structures.
   425     ///
   426     ///Initializes the internal data structures.
   427     ///
   428     void init()
   429     {
   430       create_maps();
   431       _queue.resize(countNodes(*G));
   432       _queue_head=_queue_tail=0;
   433       _curr_dist=1;
   434       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   435         _pred->set(u,INVALID);
   436         _reached->set(u,false);
   437         _processed->set(u,false);
   438       }
   439     }
   440 
   441     ///Adds a new source node.
   442 
   443     ///Adds a new source node to the set of nodes to be processed.
   444     ///
   445     void addSource(Node s)
   446     {
   447       if(!(*_reached)[s])
   448         {
   449           _reached->set(s,true);
   450           _pred->set(s,INVALID);
   451           _dist->set(s,0);
   452           _queue[_queue_head++]=s;
   453           _queue_next_dist=_queue_head;
   454         }
   455     }
   456 
   457     ///Processes the next node.
   458 
   459     ///Processes the next node.
   460     ///
   461     ///\return The processed node.
   462     ///
   463     ///\warning The queue must not be empty!
   464     Node processNextNode()
   465     {
   466       if(_queue_tail==_queue_next_dist) {
   467         _curr_dist++;
   468         _queue_next_dist=_queue_head;
   469       }
   470       Node n=_queue[_queue_tail++];
   471       _processed->set(n,true);
   472       Node m;
   473       for(OutArcIt e(*G,n);e!=INVALID;++e)
   474         if(!(*_reached)[m=G->target(e)]) {
   475           _queue[_queue_head++]=m;
   476           _reached->set(m,true);
   477           _pred->set(m,e);
   478           _dist->set(m,_curr_dist);
   479         }
   480       return n;
   481     }
   482 
   483     ///Processes the next node.
   484 
   485     ///Processes the next node. And checks that the given target node
   486     ///is reached. If the target node is reachable from the processed
   487     ///node then the reached parameter will be set true. The reached
   488     ///parameter should be initially false.
   489     ///
   490     ///\param target The target node.
   491     ///\retval reach Indicates that the target node is reached.
   492     ///\return The processed node.
   493     ///
   494     ///\warning The queue must not be empty!
   495     Node processNextNode(Node target, bool& reach)
   496     {
   497       if(_queue_tail==_queue_next_dist) {
   498         _curr_dist++;
   499         _queue_next_dist=_queue_head;
   500       }
   501       Node n=_queue[_queue_tail++];
   502       _processed->set(n,true);
   503       Node m;
   504       for(OutArcIt e(*G,n);e!=INVALID;++e)
   505         if(!(*_reached)[m=G->target(e)]) {
   506           _queue[_queue_head++]=m;
   507           _reached->set(m,true);
   508           _pred->set(m,e);
   509           _dist->set(m,_curr_dist);
   510           reach = reach || (target == m);
   511         }
   512       return n;
   513     }
   514 
   515     ///Processes the next node.
   516 
   517     ///Processes the next node. And checks that at least one of
   518     ///reached node has true value in the \c nm node map. If one node
   519     ///with true value is reachable from the processed node then the
   520     ///rnode parameter will be set to the first of such nodes.
   521     ///
   522     ///\param nm The node map of possible targets.
   523     ///\retval rnode The reached target node.
   524     ///\return The processed node.
   525     ///
   526     ///\warning The queue must not be empty!
   527     template<class NM>
   528     Node processNextNode(const NM& nm, Node& rnode)
   529     {
   530       if(_queue_tail==_queue_next_dist) {
   531         _curr_dist++;
   532         _queue_next_dist=_queue_head;
   533       }
   534       Node n=_queue[_queue_tail++];
   535       _processed->set(n,true);
   536       Node m;
   537       for(OutArcIt e(*G,n);e!=INVALID;++e)
   538         if(!(*_reached)[m=G->target(e)]) {
   539           _queue[_queue_head++]=m;
   540           _reached->set(m,true);
   541           _pred->set(m,e);
   542           _dist->set(m,_curr_dist);
   543           if (nm[m] && rnode == INVALID) rnode = m;
   544         }
   545       return n;
   546     }
   547 
   548     ///Next node to be processed.
   549 
   550     ///Next node to be processed.
   551     ///
   552     ///\return The next node to be processed or INVALID if the queue is
   553     /// empty.
   554     Node nextNode()
   555     {
   556       return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
   557     }
   558 
   559     ///\brief Returns \c false if there are nodes
   560     ///to be processed in the queue
   561     ///
   562     ///Returns \c false if there are nodes
   563     ///to be processed in the queue
   564     bool emptyQueue() { return _queue_tail==_queue_head; }
   565     ///Returns the number of the nodes to be processed.
   566 
   567     ///Returns the number of the nodes to be processed in the queue.
   568     int queueSize() { return _queue_head-_queue_tail; }
   569 
   570     ///Executes the algorithm.
   571 
   572     ///Executes the algorithm.
   573     ///
   574     ///\pre init() must be called and at least one node should be added
   575     ///with addSource() before using this function.
   576     ///
   577     ///This method runs the %BFS algorithm from the root node(s)
   578     ///in order to
   579     ///compute the
   580     ///shortest path to each node. The algorithm computes
   581     ///- The shortest path tree.
   582     ///- The distance of each node from the root(s).
   583     void start()
   584     {
   585       while ( !emptyQueue() ) processNextNode();
   586     }
   587 
   588     ///Executes the algorithm until \c dest is reached.
   589 
   590     ///Executes the algorithm until \c dest is reached.
   591     ///
   592     ///\pre init() must be called and at least one node should be added
   593     ///with addSource() before using this function.
   594     ///
   595     ///This method runs the %BFS algorithm from the root node(s)
   596     ///in order to compute the shortest path to \c dest.
   597     ///The algorithm computes
   598     ///- The shortest path to \c  dest.
   599     ///- The distance of \c dest from the root(s).
   600     void start(Node dest)
   601     {
   602       bool reach = false;
   603       while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
   604     }
   605 
   606     ///Executes the algorithm until a condition is met.
   607 
   608     ///Executes the algorithm until a condition is met.
   609     ///
   610     ///\pre init() must be called and at least one node should be added
   611     ///with addSource() before using this function.
   612     ///
   613     ///\param nm must be a bool (or convertible) node map. The
   614     ///algorithm will stop when it reaches a node \c v with
   615     /// <tt>nm[v]</tt> true.
   616     ///
   617     ///\return The reached node \c v with <tt>nm[v]</tt> true or
   618     ///\c INVALID if no such node was found.
   619     template<class NM>
   620     Node start(const NM &nm)
   621     {
   622       Node rnode = INVALID;
   623       while ( !emptyQueue() && rnode == INVALID ) {
   624         processNextNode(nm, rnode);
   625       }
   626       return rnode;
   627     }
   628 
   629     ///Runs %BFS algorithm from node \c s.
   630 
   631     ///This method runs the %BFS algorithm from a root node \c s
   632     ///in order to
   633     ///compute the
   634     ///shortest path to each node. The algorithm computes
   635     ///- The shortest path tree.
   636     ///- The distance of each node from the root.
   637     ///
   638     ///\note b.run(s) is just a shortcut of the following code.
   639     ///\code
   640     ///  b.init();
   641     ///  b.addSource(s);
   642     ///  b.start();
   643     ///\endcode
   644     void run(Node s) {
   645       init();
   646       addSource(s);
   647       start();
   648     }
   649 
   650     ///Finds the shortest path between \c s and \c t.
   651 
   652     ///Finds the shortest path between \c s and \c t.
   653     ///
   654     ///\return The length of the shortest s---t path if there exists one,
   655     ///0 otherwise.
   656     ///\note Apart from the return value, b.run(s) is
   657     ///just a shortcut of the following code.
   658     ///\code
   659     ///  b.init();
   660     ///  b.addSource(s);
   661     ///  b.start(t);
   662     ///\endcode
   663     int run(Node s,Node t) {
   664       init();
   665       addSource(s);
   666       start(t);
   667       return reached(t) ? _curr_dist : 0;
   668     }
   669 
   670     ///@}
   671 
   672     ///\name Query Functions
   673     ///The result of the %BFS algorithm can be obtained using these
   674     ///functions.\n
   675     ///Before the use of these functions,
   676     ///either run() or start() must be calleb.
   677 
   678     ///@{
   679 
   680     typedef PredMapPath<Digraph, PredMap> Path;
   681 
   682     ///Gives back the shortest path.
   683 
   684     ///Gives back the shortest path.
   685     ///\pre The \c t should be reachable from the source.
   686     Path path(Node t)
   687     {
   688       return Path(*G, *_pred, t);
   689     }
   690 
   691     ///The distance of a node from the root(s).
   692 
   693     ///Returns the distance of a node from the root(s).
   694     ///\pre \ref run() must be called before using this function.
   695     ///\warning If node \c v in unreachable from the root(s) the return value
   696     ///of this function is undefined.
   697     int dist(Node v) const { return (*_dist)[v]; }
   698 
   699     ///Returns the 'previous arc' of the shortest path tree.
   700 
   701     ///For a node \c v it returns the 'previous arc'
   702     ///of the shortest path tree,
   703     ///i.e. it returns the last arc of a shortest path from the root(s) to \c
   704     ///v. It is \ref INVALID
   705     ///if \c v is unreachable from the root(s) or \c v is a root. The
   706     ///shortest path tree used here is equal to the shortest path tree used in
   707     ///\ref predNode().
   708     ///\pre Either \ref run() or \ref start() must be called before using
   709     ///this function.
   710     Arc predArc(Node v) const { return (*_pred)[v];}
   711 
   712     ///Returns the 'previous node' of the shortest path tree.
   713 
   714     ///For a node \c v it returns the 'previous node'
   715     ///of the shortest path tree,
   716     ///i.e. it returns the last but one node from a shortest path from the
   717     ///root(a) to \c /v.
   718     ///It is INVALID if \c v is unreachable from the root(s) or
   719     ///if \c v itself a root.
   720     ///The shortest path tree used here is equal to the shortest path
   721     ///tree used in \ref predArc().
   722     ///\pre Either \ref run() or \ref start() must be called before
   723     ///using this function.
   724     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   725                                   G->source((*_pred)[v]); }
   726 
   727     ///Returns a reference to the NodeMap of distances.
   728 
   729     ///Returns a reference to the NodeMap of distances.
   730     ///\pre Either \ref run() or \ref init() must
   731     ///be called before using this function.
   732     const DistMap &distMap() const { return *_dist;}
   733 
   734     ///Returns a reference to the shortest path tree map.
   735 
   736     ///Returns a reference to the NodeMap of the arcs of the
   737     ///shortest path tree.
   738     ///\pre Either \ref run() or \ref init()
   739     ///must be called before using this function.
   740     const PredMap &predMap() const { return *_pred;}
   741 
   742     ///Checks if a node is reachable from the root.
   743 
   744     ///Returns \c true if \c v is reachable from the root.
   745     ///\warning The source nodes are indicated as unreached.
   746     ///\pre Either \ref run() or \ref start()
   747     ///must be called before using this function.
   748     ///
   749     bool reached(Node v) { return (*_reached)[v]; }
   750 
   751     ///@}
   752   };
   753 
   754   ///Default traits class of Bfs function.
   755 
   756   ///Default traits class of Bfs function.
   757   ///\tparam GR Digraph type.
   758   template<class GR>
   759   struct BfsWizardDefaultTraits
   760   {
   761     ///The digraph type the algorithm runs on.
   762     typedef GR Digraph;
   763     ///\brief The type of the map that stores the last
   764     ///arcs of the shortest paths.
   765     ///
   766     ///The type of the map that stores the last
   767     ///arcs of the shortest paths.
   768     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   769     ///
   770     typedef NullMap<typename Digraph::Node,typename GR::Arc> PredMap;
   771     ///Instantiates a PredMap.
   772 
   773     ///This function instantiates a \ref PredMap.
   774     ///\param g is the digraph, to which we would like to define the PredMap.
   775     ///\todo The digraph alone may be insufficient to initialize
   776 #ifdef DOXYGEN
   777     static PredMap *createPredMap(const GR &g)
   778 #else
   779     static PredMap *createPredMap(const GR &)
   780 #endif
   781     {
   782       return new PredMap();
   783     }
   784 
   785     ///The type of the map that indicates which nodes are processed.
   786 
   787     ///The type of the map that indicates which nodes are processed.
   788     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   789     ///\todo named parameter to set this type, function to read and write.
   790     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   791     ///Instantiates a ProcessedMap.
   792 
   793     ///This function instantiates a \ref ProcessedMap.
   794     ///\param g is the digraph, to which
   795     ///we would like to define the \ref ProcessedMap
   796 #ifdef DOXYGEN
   797     static ProcessedMap *createProcessedMap(const GR &g)
   798 #else
   799     static ProcessedMap *createProcessedMap(const GR &)
   800 #endif
   801     {
   802       return new ProcessedMap();
   803     }
   804     ///The type of the map that indicates which nodes are reached.
   805 
   806     ///The type of the map that indicates which nodes are reached.
   807     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   808     ///\todo named parameter to set this type, function to read and write.
   809     typedef typename Digraph::template NodeMap<bool> ReachedMap;
   810     ///Instantiates a ReachedMap.
   811 
   812     ///This function instantiates a \ref ReachedMap.
   813     ///\param G is the digraph, to which
   814     ///we would like to define the \ref ReachedMap.
   815     static ReachedMap *createReachedMap(const GR &G)
   816     {
   817       return new ReachedMap(G);
   818     }
   819     ///The type of the map that stores the dists of the nodes.
   820 
   821     ///The type of the map that stores the dists of the nodes.
   822     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   823     ///
   824     typedef NullMap<typename Digraph::Node,int> DistMap;
   825     ///Instantiates a DistMap.
   826 
   827     ///This function instantiates a \ref DistMap.
   828     ///\param g is the digraph, to which we would like to define
   829     ///the \ref DistMap
   830 #ifdef DOXYGEN
   831     static DistMap *createDistMap(const GR &g)
   832 #else
   833     static DistMap *createDistMap(const GR &)
   834 #endif
   835     {
   836       return new DistMap();
   837     }
   838   };
   839 
   840   /// Default traits used by \ref BfsWizard
   841 
   842   /// To make it easier to use Bfs algorithm
   843   ///we have created a wizard class.
   844   /// This \ref BfsWizard class needs default traits,
   845   ///as well as the \ref Bfs class.
   846   /// The \ref BfsWizardBase is a class to be the default traits of the
   847   /// \ref BfsWizard class.
   848   template<class GR>
   849   class BfsWizardBase : public BfsWizardDefaultTraits<GR>
   850   {
   851 
   852     typedef BfsWizardDefaultTraits<GR> Base;
   853   protected:
   854     /// Type of the nodes in the digraph.
   855     typedef typename Base::Digraph::Node Node;
   856 
   857     /// Pointer to the underlying digraph.
   858     void *_g;
   859     ///Pointer to the map of reached nodes.
   860     void *_reached;
   861     ///Pointer to the map of processed nodes.
   862     void *_processed;
   863     ///Pointer to the map of predecessors arcs.
   864     void *_pred;
   865     ///Pointer to the map of distances.
   866     void *_dist;
   867     ///Pointer to the source node.
   868     Node _source;
   869 
   870     public:
   871     /// Constructor.
   872 
   873     /// This constructor does not require parameters, therefore it initiates
   874     /// all of the attributes to default values (0, INVALID).
   875     BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
   876                            _dist(0), _source(INVALID) {}
   877 
   878     /// Constructor.
   879 
   880     /// This constructor requires some parameters,
   881     /// listed in the parameters list.
   882     /// Others are initiated to 0.
   883     /// \param g is the initial value of  \ref _g
   884     /// \param s is the initial value of  \ref _source
   885     BfsWizardBase(const GR &g, Node s=INVALID) :
   886       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
   887       _reached(0), _processed(0), _pred(0), _dist(0), _source(s) {}
   888 
   889   };
   890 
   891   /// A class to make the usage of Bfs algorithm easier
   892 
   893   /// This class is created to make it easier to use Bfs algorithm.
   894   /// It uses the functions and features of the plain \ref Bfs,
   895   /// but it is much simpler to use it.
   896   ///
   897   /// Simplicity means that the way to change the types defined
   898   /// in the traits class is based on functions that returns the new class
   899   /// and not on templatable built-in classes.
   900   /// When using the plain \ref Bfs
   901   /// the new class with the modified type comes from
   902   /// the original class by using the ::
   903   /// operator. In the case of \ref BfsWizard only
   904   /// a function have to be called and it will
   905   /// return the needed class.
   906   ///
   907   /// It does not have own \ref run method. When its \ref run method is called
   908   /// it initiates a plain \ref Bfs class, and calls the \ref Bfs::run
   909   /// method of it.
   910   template<class TR>
   911   class BfsWizard : public TR
   912   {
   913     typedef TR Base;
   914 
   915     ///The type of the underlying digraph.
   916     typedef typename TR::Digraph Digraph;
   917     //\e
   918     typedef typename Digraph::Node Node;
   919     //\e
   920     typedef typename Digraph::NodeIt NodeIt;
   921     //\e
   922     typedef typename Digraph::Arc Arc;
   923     //\e
   924     typedef typename Digraph::OutArcIt OutArcIt;
   925 
   926     ///\brief The type of the map that stores
   927     ///the reached nodes
   928     typedef typename TR::ReachedMap ReachedMap;
   929     ///\brief The type of the map that stores
   930     ///the processed nodes
   931     typedef typename TR::ProcessedMap ProcessedMap;
   932     ///\brief The type of the map that stores the last
   933     ///arcs of the shortest paths.
   934     typedef typename TR::PredMap PredMap;
   935     ///The type of the map that stores the dists of the nodes.
   936     typedef typename TR::DistMap DistMap;
   937 
   938   public:
   939     /// Constructor.
   940     BfsWizard() : TR() {}
   941 
   942     /// Constructor that requires parameters.
   943 
   944     /// Constructor that requires parameters.
   945     /// These parameters will be the default values for the traits class.
   946     BfsWizard(const Digraph &g, Node s=INVALID) :
   947       TR(g,s) {}
   948 
   949     ///Copy constructor
   950     BfsWizard(const TR &b) : TR(b) {}
   951 
   952     ~BfsWizard() {}
   953 
   954     ///Runs Bfs algorithm from a given node.
   955 
   956     ///Runs Bfs algorithm from a given node.
   957     ///The node can be given by the \ref source function.
   958     void run()
   959     {
   960       if(Base::_source==INVALID) throw UninitializedParameter();
   961       Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
   962       if(Base::_reached)
   963         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
   964       if(Base::_processed)
   965         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
   966       if(Base::_pred)
   967         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
   968       if(Base::_dist)
   969         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
   970       alg.run(Base::_source);
   971     }
   972 
   973     ///Runs Bfs algorithm from the given node.
   974 
   975     ///Runs Bfs algorithm from the given node.
   976     ///\param s is the given source.
   977     void run(Node s)
   978     {
   979       Base::_source=s;
   980       run();
   981     }
   982 
   983     template<class T>
   984     struct DefPredMapBase : public Base {
   985       typedef T PredMap;
   986       static PredMap *createPredMap(const Digraph &) { return 0; };
   987       DefPredMapBase(const TR &b) : TR(b) {}
   988     };
   989 
   990     ///\brief \ref named-templ-param "Named parameter"
   991     ///function for setting PredMap
   992     ///
   993     /// \ref named-templ-param "Named parameter"
   994     ///function for setting PredMap
   995     ///
   996     template<class T>
   997     BfsWizard<DefPredMapBase<T> > predMap(const T &t)
   998     {
   999       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1000       return BfsWizard<DefPredMapBase<T> >(*this);
  1001     }
  1002 
  1003 
  1004     template<class T>
  1005     struct DefReachedMapBase : public Base {
  1006       typedef T ReachedMap;
  1007       static ReachedMap *createReachedMap(const Digraph &) { return 0; };
  1008       DefReachedMapBase(const TR &b) : TR(b) {}
  1009     };
  1010 
  1011     ///\brief \ref named-templ-param "Named parameter"
  1012     ///function for setting ReachedMap
  1013     ///
  1014     /// \ref named-templ-param "Named parameter"
  1015     ///function for setting ReachedMap
  1016     ///
  1017     template<class T>
  1018     BfsWizard<DefReachedMapBase<T> > reachedMap(const T &t)
  1019     {
  1020       Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
  1021       return BfsWizard<DefReachedMapBase<T> >(*this);
  1022     }
  1023 
  1024 
  1025     template<class T>
  1026     struct DefProcessedMapBase : public Base {
  1027       typedef T ProcessedMap;
  1028       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1029       DefProcessedMapBase(const TR &b) : TR(b) {}
  1030     };
  1031 
  1032     ///\brief \ref named-templ-param "Named parameter"
  1033     ///function for setting ProcessedMap
  1034     ///
  1035     /// \ref named-templ-param "Named parameter"
  1036     ///function for setting ProcessedMap
  1037     ///
  1038     template<class T>
  1039     BfsWizard<DefProcessedMapBase<T> > processedMap(const T &t)
  1040     {
  1041       Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
  1042       return BfsWizard<DefProcessedMapBase<T> >(*this);
  1043     }
  1044 
  1045 
  1046     template<class T>
  1047     struct DefDistMapBase : public Base {
  1048       typedef T DistMap;
  1049       static DistMap *createDistMap(const Digraph &) { return 0; };
  1050       DefDistMapBase(const TR &b) : TR(b) {}
  1051     };
  1052 
  1053     ///\brief \ref named-templ-param "Named parameter"
  1054     ///function for setting DistMap type
  1055     ///
  1056     /// \ref named-templ-param "Named parameter"
  1057     ///function for setting DistMap type
  1058     ///
  1059     template<class T>
  1060     BfsWizard<DefDistMapBase<T> > distMap(const T &t)
  1061     {
  1062       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1063       return BfsWizard<DefDistMapBase<T> >(*this);
  1064     }
  1065 
  1066     /// Sets the source node, from which the Bfs algorithm runs.
  1067 
  1068     /// Sets the source node, from which the Bfs algorithm runs.
  1069     /// \param s is the source node.
  1070     BfsWizard<TR> &source(Node s)
  1071     {
  1072       Base::_source=s;
  1073       return *this;
  1074     }
  1075 
  1076   };
  1077 
  1078   ///Function type interface for Bfs algorithm.
  1079 
  1080   /// \ingroup search
  1081   ///Function type interface for Bfs algorithm.
  1082   ///
  1083   ///This function also has several
  1084   ///\ref named-templ-func-param "named parameters",
  1085   ///they are declared as the members of class \ref BfsWizard.
  1086   ///The following
  1087   ///example shows how to use these parameters.
  1088   ///\code
  1089   ///  bfs(g,source).predMap(preds).run();
  1090   ///\endcode
  1091   ///\warning Don't forget to put the \ref BfsWizard::run() "run()"
  1092   ///to the end of the parameter list.
  1093   ///\sa BfsWizard
  1094   ///\sa Bfs
  1095   template<class GR>
  1096   BfsWizard<BfsWizardBase<GR> >
  1097   bfs(const GR &g,typename GR::Node s=INVALID)
  1098   {
  1099     return BfsWizard<BfsWizardBase<GR> >(g,s);
  1100   }
  1101 
  1102 #ifdef DOXYGEN
  1103   /// \brief Visitor class for bfs.
  1104   ///
  1105   /// This class defines the interface of the BfsVisit events, and
  1106   /// it could be the base of a real Visitor class.
  1107   template <typename _Digraph>
  1108   struct BfsVisitor {
  1109     typedef _Digraph Digraph;
  1110     typedef typename Digraph::Arc Arc;
  1111     typedef typename Digraph::Node Node;
  1112     /// \brief Called when the arc reach a node.
  1113     ///
  1114     /// It is called when the bfs find an arc which target is not
  1115     /// reached yet.
  1116     void discover(const Arc& arc) {}
  1117     /// \brief Called when the node reached first time.
  1118     ///
  1119     /// It is Called when the node reached first time.
  1120     void reach(const Node& node) {}
  1121     /// \brief Called when the arc examined but target of the arc
  1122     /// already discovered.
  1123     ///
  1124     /// It called when the arc examined but the target of the arc
  1125     /// already discovered.
  1126     void examine(const Arc& arc) {}
  1127     /// \brief Called for the source node of the bfs.
  1128     ///
  1129     /// It is called for the source node of the bfs.
  1130     void start(const Node& node) {}
  1131     /// \brief Called when the node processed.
  1132     ///
  1133     /// It is Called when the node processed.
  1134     void process(const Node& node) {}
  1135   };
  1136 #else
  1137   template <typename _Digraph>
  1138   struct BfsVisitor {
  1139     typedef _Digraph Digraph;
  1140     typedef typename Digraph::Arc Arc;
  1141     typedef typename Digraph::Node Node;
  1142     void discover(const Arc&) {}
  1143     void reach(const Node&) {}
  1144     void examine(const Arc&) {}
  1145     void start(const Node&) {}
  1146     void process(const Node&) {}
  1147 
  1148     template <typename _Visitor>
  1149     struct Constraints {
  1150       void constraints() {
  1151         Arc arc;
  1152         Node node;
  1153         visitor.discover(arc);
  1154         visitor.reach(node);
  1155         visitor.examine(arc);
  1156         visitor.start(node);
  1157         visitor.process(node);
  1158       }
  1159       _Visitor& visitor;
  1160     };
  1161   };
  1162 #endif
  1163 
  1164   /// \brief Default traits class of BfsVisit class.
  1165   ///
  1166   /// Default traits class of BfsVisit class.
  1167   /// \tparam _Digraph Digraph type.
  1168   template<class _Digraph>
  1169   struct BfsVisitDefaultTraits {
  1170 
  1171     /// \brief The digraph type the algorithm runs on.
  1172     typedef _Digraph Digraph;
  1173 
  1174     /// \brief The type of the map that indicates which nodes are reached.
  1175     ///
  1176     /// The type of the map that indicates which nodes are reached.
  1177     /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
  1178     /// \todo named parameter to set this type, function to read and write.
  1179     typedef typename Digraph::template NodeMap<bool> ReachedMap;
  1180 
  1181     /// \brief Instantiates a ReachedMap.
  1182     ///
  1183     /// This function instantiates a \ref ReachedMap.
  1184     /// \param digraph is the digraph, to which
  1185     /// we would like to define the \ref ReachedMap.
  1186     static ReachedMap *createReachedMap(const Digraph &digraph) {
  1187       return new ReachedMap(digraph);
  1188     }
  1189 
  1190   };
  1191 
  1192   /// \ingroup search
  1193   ///
  1194   /// \brief %BFS Visit algorithm class.
  1195   ///
  1196   /// This class provides an efficient implementation of the %BFS algorithm
  1197   /// with visitor interface.
  1198   ///
  1199   /// The %BfsVisit class provides an alternative interface to the Bfs
  1200   /// class. It works with callback mechanism, the BfsVisit object calls
  1201   /// on every bfs event the \c Visitor class member functions.
  1202   ///
  1203   /// \tparam _Digraph The digraph type the algorithm runs on.
  1204   /// The default value is
  1205   /// \ref ListDigraph. The value of _Digraph is not used directly by Bfs, it
  1206   /// is only passed to \ref BfsDefaultTraits.
  1207   /// \tparam _Visitor The Visitor object for the algorithm. The
  1208   /// \ref BfsVisitor "BfsVisitor<_Digraph>" is an empty Visitor which
  1209   /// does not observe the Bfs events. If you want to observe the bfs
  1210   /// events you should implement your own Visitor class.
  1211   /// \tparam _Traits Traits class to set various data types used by the
  1212   /// algorithm. The default traits class is
  1213   /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Digraph>".
  1214   /// See \ref BfsVisitDefaultTraits for the documentation of
  1215   /// a Bfs visit traits class.
  1216 #ifdef DOXYGEN
  1217   template <typename _Digraph, typename _Visitor, typename _Traits>
  1218 #else
  1219   template <typename _Digraph = ListDigraph,
  1220             typename _Visitor = BfsVisitor<_Digraph>,
  1221             typename _Traits = BfsDefaultTraits<_Digraph> >
  1222 #endif
  1223   class BfsVisit {
  1224   public:
  1225 
  1226     /// \brief \ref Exception for uninitialized parameters.
  1227     ///
  1228     /// This error represents problems in the initialization
  1229     /// of the parameters of the algorithms.
  1230     class UninitializedParameter : public lemon::UninitializedParameter {
  1231     public:
  1232       virtual const char* what() const throw()
  1233       {
  1234         return "lemon::BfsVisit::UninitializedParameter";
  1235       }
  1236     };
  1237 
  1238     typedef _Traits Traits;
  1239 
  1240     typedef typename Traits::Digraph Digraph;
  1241 
  1242     typedef _Visitor Visitor;
  1243 
  1244     ///The type of the map indicating which nodes are reached.
  1245     typedef typename Traits::ReachedMap ReachedMap;
  1246 
  1247   private:
  1248 
  1249     typedef typename Digraph::Node Node;
  1250     typedef typename Digraph::NodeIt NodeIt;
  1251     typedef typename Digraph::Arc Arc;
  1252     typedef typename Digraph::OutArcIt OutArcIt;
  1253 
  1254     /// Pointer to the underlying digraph.
  1255     const Digraph *_digraph;
  1256     /// Pointer to the visitor object.
  1257     Visitor *_visitor;
  1258     ///Pointer to the map of reached status of the nodes.
  1259     ReachedMap *_reached;
  1260     ///Indicates if \ref _reached is locally allocated (\c true) or not.
  1261     bool local_reached;
  1262 
  1263     std::vector<typename Digraph::Node> _list;
  1264     int _list_front, _list_back;
  1265 
  1266     /// \brief Creates the maps if necessary.
  1267     ///
  1268     /// Creates the maps if necessary.
  1269     void create_maps() {
  1270       if(!_reached) {
  1271         local_reached = true;
  1272         _reached = Traits::createReachedMap(*_digraph);
  1273       }
  1274     }
  1275 
  1276   protected:
  1277 
  1278     BfsVisit() {}
  1279 
  1280   public:
  1281 
  1282     typedef BfsVisit Create;
  1283 
  1284     /// \name Named template parameters
  1285 
  1286     ///@{
  1287     template <class T>
  1288     struct DefReachedMapTraits : public Traits {
  1289       typedef T ReachedMap;
  1290       static ReachedMap *createReachedMap(const Digraph &digraph) {
  1291         throw UninitializedParameter();
  1292       }
  1293     };
  1294     /// \brief \ref named-templ-param "Named parameter" for setting
  1295     /// ReachedMap type
  1296     ///
  1297     /// \ref named-templ-param "Named parameter" for setting ReachedMap type
  1298     template <class T>
  1299     struct DefReachedMap : public BfsVisit< Digraph, Visitor,
  1300                                             DefReachedMapTraits<T> > {
  1301       typedef BfsVisit< Digraph, Visitor, DefReachedMapTraits<T> > Create;
  1302     };
  1303     ///@}
  1304 
  1305   public:
  1306 
  1307     /// \brief Constructor.
  1308     ///
  1309     /// Constructor.
  1310     ///
  1311     /// \param digraph the digraph the algorithm will run on.
  1312     /// \param visitor The visitor of the algorithm.
  1313     ///
  1314     BfsVisit(const Digraph& digraph, Visitor& visitor)
  1315       : _digraph(&digraph), _visitor(&visitor),
  1316         _reached(0), local_reached(false) {}
  1317 
  1318     /// \brief Destructor.
  1319     ///
  1320     /// Destructor.
  1321     ~BfsVisit() {
  1322       if(local_reached) delete _reached;
  1323     }
  1324 
  1325     /// \brief Sets the map indicating if a node is reached.
  1326     ///
  1327     /// Sets the map indicating if a node is reached.
  1328     /// If you don't use this function before calling \ref run(),
  1329     /// it will allocate one. The destuctor deallocates this
  1330     /// automatically allocated map, of course.
  1331     /// \return <tt> (*this) </tt>
  1332     BfsVisit &reachedMap(ReachedMap &m) {
  1333       if(local_reached) {
  1334         delete _reached;
  1335         local_reached = false;
  1336       }
  1337       _reached = &m;
  1338       return *this;
  1339     }
  1340 
  1341   public:
  1342     /// \name Execution control
  1343     /// The simplest way to execute the algorithm is to use
  1344     /// one of the member functions called \c run(...).
  1345     /// \n
  1346     /// If you need more control on the execution,
  1347     /// first you must call \ref init(), then you can adda source node
  1348     /// with \ref addSource().
  1349     /// Finally \ref start() will perform the actual path
  1350     /// computation.
  1351 
  1352     /// @{
  1353     /// \brief Initializes the internal data structures.
  1354     ///
  1355     /// Initializes the internal data structures.
  1356     ///
  1357     void init() {
  1358       create_maps();
  1359       _list.resize(countNodes(*_digraph));
  1360       _list_front = _list_back = -1;
  1361       for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
  1362         _reached->set(u, false);
  1363       }
  1364     }
  1365 
  1366     /// \brief Adds a new source node.
  1367     ///
  1368     /// Adds a new source node to the set of nodes to be processed.
  1369     void addSource(Node s) {
  1370       if(!(*_reached)[s]) {
  1371           _reached->set(s,true);
  1372           _visitor->start(s);
  1373           _visitor->reach(s);
  1374           _list[++_list_back] = s;
  1375         }
  1376     }
  1377 
  1378     /// \brief Processes the next node.
  1379     ///
  1380     /// Processes the next node.
  1381     ///
  1382     /// \return The processed node.
  1383     ///
  1384     /// \pre The queue must not be empty!
  1385     Node processNextNode() {
  1386       Node n = _list[++_list_front];
  1387       _visitor->process(n);
  1388       Arc e;
  1389       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1390         Node m = _digraph->target(e);
  1391         if (!(*_reached)[m]) {
  1392           _visitor->discover(e);
  1393           _visitor->reach(m);
  1394           _reached->set(m, true);
  1395           _list[++_list_back] = m;
  1396         } else {
  1397           _visitor->examine(e);
  1398         }
  1399       }
  1400       return n;
  1401     }
  1402 
  1403     /// \brief Processes the next node.
  1404     ///
  1405     /// Processes the next node. And checks that the given target node
  1406     /// is reached. If the target node is reachable from the processed
  1407     /// node then the reached parameter will be set true. The reached
  1408     /// parameter should be initially false.
  1409     ///
  1410     /// \param target The target node.
  1411     /// \retval reach Indicates that the target node is reached.
  1412     /// \return The processed node.
  1413     ///
  1414     /// \warning The queue must not be empty!
  1415     Node processNextNode(Node target, bool& reach) {
  1416       Node n = _list[++_list_front];
  1417       _visitor->process(n);
  1418       Arc e;
  1419       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1420         Node m = _digraph->target(e);
  1421         if (!(*_reached)[m]) {
  1422           _visitor->discover(e);
  1423           _visitor->reach(m);
  1424           _reached->set(m, true);
  1425           _list[++_list_back] = m;
  1426           reach = reach || (target == m);
  1427         } else {
  1428           _visitor->examine(e);
  1429         }
  1430       }
  1431       return n;
  1432     }
  1433 
  1434     /// \brief Processes the next node.
  1435     ///
  1436     /// Processes the next node. And checks that at least one of
  1437     /// reached node has true value in the \c nm node map. If one node
  1438     /// with true value is reachable from the processed node then the
  1439     /// rnode parameter will be set to the first of such nodes.
  1440     ///
  1441     /// \param nm The node map of possible targets.
  1442     /// \retval rnode The reached target node.
  1443     /// \return The processed node.
  1444     ///
  1445     /// \warning The queue must not be empty!
  1446     template <typename NM>
  1447     Node processNextNode(const NM& nm, Node& rnode) {
  1448       Node n = _list[++_list_front];
  1449       _visitor->process(n);
  1450       Arc e;
  1451       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1452         Node m = _digraph->target(e);
  1453         if (!(*_reached)[m]) {
  1454           _visitor->discover(e);
  1455           _visitor->reach(m);
  1456           _reached->set(m, true);
  1457           _list[++_list_back] = m;
  1458           if (nm[m] && rnode == INVALID) rnode = m;
  1459         } else {
  1460           _visitor->examine(e);
  1461         }
  1462       }
  1463       return n;
  1464     }
  1465 
  1466     /// \brief Next node to be processed.
  1467     ///
  1468     /// Next node to be processed.
  1469     ///
  1470     /// \return The next node to be processed or INVALID if the stack is
  1471     /// empty.
  1472     Node nextNode() {
  1473       return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
  1474     }
  1475 
  1476     /// \brief Returns \c false if there are nodes
  1477     /// to be processed in the queue
  1478     ///
  1479     /// Returns \c false if there are nodes
  1480     /// to be processed in the queue
  1481     bool emptyQueue() { return _list_front == _list_back; }
  1482 
  1483     /// \brief Returns the number of the nodes to be processed.
  1484     ///
  1485     /// Returns the number of the nodes to be processed in the queue.
  1486     int queueSize() { return _list_back - _list_front; }
  1487 
  1488     /// \brief Executes the algorithm.
  1489     ///
  1490     /// Executes the algorithm.
  1491     ///
  1492     /// \pre init() must be called and at least one node should be added
  1493     /// with addSource() before using this function.
  1494     void start() {
  1495       while ( !emptyQueue() ) processNextNode();
  1496     }
  1497 
  1498     /// \brief Executes the algorithm until \c dest is reached.
  1499     ///
  1500     /// Executes the algorithm until \c dest is reached.
  1501     ///
  1502     /// \pre init() must be called and at least one node should be added
  1503     /// with addSource() before using this function.
  1504     void start(Node dest) {
  1505       bool reach = false;
  1506       while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
  1507     }
  1508 
  1509     /// \brief Executes the algorithm until a condition is met.
  1510     ///
  1511     /// Executes the algorithm until a condition is met.
  1512     ///
  1513     /// \pre init() must be called and at least one node should be added
  1514     /// with addSource() before using this function.
  1515     ///
  1516     ///\param nm must be a bool (or convertible) node map. The
  1517     ///algorithm will stop when it reaches a node \c v with
  1518     /// <tt>nm[v]</tt> true.
  1519     ///
  1520     ///\return The reached node \c v with <tt>nm[v]</tt> true or
  1521     ///\c INVALID if no such node was found.
  1522     template <typename NM>
  1523     Node start(const NM &nm) {
  1524       Node rnode = INVALID;
  1525       while ( !emptyQueue() && rnode == INVALID ) {
  1526         processNextNode(nm, rnode);
  1527       }
  1528       return rnode;
  1529     }
  1530 
  1531     /// \brief Runs %BFSVisit algorithm from node \c s.
  1532     ///
  1533     /// This method runs the %BFS algorithm from a root node \c s.
  1534     /// \note b.run(s) is just a shortcut of the following code.
  1535     ///\code
  1536     ///   b.init();
  1537     ///   b.addSource(s);
  1538     ///   b.start();
  1539     ///\endcode
  1540     void run(Node s) {
  1541       init();
  1542       addSource(s);
  1543       start();
  1544     }
  1545 
  1546     /// \brief Runs %BFSVisit algorithm to visit all nodes in the digraph.
  1547     ///
  1548     /// This method runs the %BFS algorithm in order to
  1549     /// compute the %BFS path to each node. The algorithm computes
  1550     /// - The %BFS tree.
  1551     /// - The distance of each node from the root in the %BFS tree.
  1552     ///
  1553     ///\note b.run() is just a shortcut of the following code.
  1554     ///\code
  1555     ///  b.init();
  1556     ///  for (NodeIt it(digraph); it != INVALID; ++it) {
  1557     ///    if (!b.reached(it)) {
  1558     ///      b.addSource(it);
  1559     ///      b.start();
  1560     ///    }
  1561     ///  }
  1562     ///\endcode
  1563     void run() {
  1564       init();
  1565       for (NodeIt it(*_digraph); it != INVALID; ++it) {
  1566         if (!reached(it)) {
  1567           addSource(it);
  1568           start();
  1569         }
  1570       }
  1571     }
  1572     ///@}
  1573 
  1574     /// \name Query Functions
  1575     /// The result of the %BFS algorithm can be obtained using these
  1576     /// functions.\n
  1577     /// Before the use of these functions,
  1578     /// either run() or start() must be called.
  1579     ///@{
  1580 
  1581     /// \brief Checks if a node is reachable from the root.
  1582     ///
  1583     /// Returns \c true if \c v is reachable from the root(s).
  1584     /// \warning The source nodes are inditated as unreachable.
  1585     /// \pre Either \ref run() or \ref start()
  1586     /// must be called before using this function.
  1587     ///
  1588     bool reached(Node v) { return (*_reached)[v]; }
  1589     ///@}
  1590   };
  1591 
  1592 } //END OF NAMESPACE LEMON
  1593 
  1594 #endif
  1595