lemon/bfs.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 08 Jan 2011 22:49:09 +0100
changeset 1032 62ba43576f85
parent 825 75e6020b19b1
child 976 426a704d7483
permissions -rw-r--r--
Doc group for TSP algorithms (#386)
     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) 2003-2010
     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 #include <lemon/path.h>
    32 
    33 namespace lemon {
    34 
    35   ///Default traits class of Bfs class.
    36 
    37   ///Default traits class of Bfs class.
    38   ///\tparam GR Digraph type.
    39   template<class GR>
    40   struct BfsDefaultTraits
    41   {
    42     ///The type of the digraph the algorithm runs on.
    43     typedef GR Digraph;
    44 
    45     ///\brief The type of the map that stores the predecessor
    46     ///arcs of the shortest paths.
    47     ///
    48     ///The type of the map that stores the predecessor
    49     ///arcs of the shortest paths.
    50     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
    51     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
    52     ///Instantiates a \c PredMap.
    53 
    54     ///This function instantiates a \ref PredMap.
    55     ///\param g is the digraph, to which we would like to define the
    56     ///\ref PredMap.
    57     static PredMap *createPredMap(const Digraph &g)
    58     {
    59       return new PredMap(g);
    60     }
    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 conform to the \ref concepts::WriteMap "WriteMap" concept.
    66     ///By default, it is a NullMap.
    67     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
    68     ///Instantiates a \c 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 Digraph &g)
    75 #else
    76     static ProcessedMap *createProcessedMap(const Digraph &)
    77 #endif
    78     {
    79       return new ProcessedMap();
    80     }
    81 
    82     ///The type of the map that indicates which nodes are reached.
    83 
    84     ///The type of the map that indicates which nodes are reached.
    85     ///It must conform to
    86     ///the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    87     typedef typename Digraph::template NodeMap<bool> ReachedMap;
    88     ///Instantiates a \c ReachedMap.
    89 
    90     ///This function instantiates a \ref ReachedMap.
    91     ///\param g is the digraph, to which
    92     ///we would like to define the \ref ReachedMap.
    93     static ReachedMap *createReachedMap(const Digraph &g)
    94     {
    95       return new ReachedMap(g);
    96     }
    97 
    98     ///The type of the map that stores the distances of the nodes.
    99 
   100     ///The type of the map that stores the distances of the nodes.
   101     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   102     typedef typename Digraph::template NodeMap<int> DistMap;
   103     ///Instantiates a \c DistMap.
   104 
   105     ///This function instantiates a \ref DistMap.
   106     ///\param g is the digraph, to which we would like to define the
   107     ///\ref DistMap.
   108     static DistMap *createDistMap(const Digraph &g)
   109     {
   110       return new DistMap(g);
   111     }
   112   };
   113 
   114   ///%BFS algorithm class.
   115 
   116   ///\ingroup search
   117   ///This class provides an efficient implementation of the %BFS algorithm.
   118   ///
   119   ///There is also a \ref bfs() "function-type interface" for the BFS
   120   ///algorithm, which is convenient in the simplier cases and it can be
   121   ///used easier.
   122   ///
   123   ///\tparam GR The type of the digraph the algorithm runs on.
   124   ///The default type is \ref ListDigraph.
   125   ///\tparam TR The traits class that defines various types used by the
   126   ///algorithm. By default, it is \ref BfsDefaultTraits
   127   ///"BfsDefaultTraits<GR>".
   128   ///In most cases, this parameter should not be set directly,
   129   ///consider to use the named template parameters instead.
   130 #ifdef DOXYGEN
   131   template <typename GR,
   132             typename TR>
   133 #else
   134   template <typename GR=ListDigraph,
   135             typename TR=BfsDefaultTraits<GR> >
   136 #endif
   137   class Bfs {
   138   public:
   139 
   140     ///The type of the digraph the algorithm runs on.
   141     typedef typename TR::Digraph Digraph;
   142 
   143     ///\brief The type of the map that stores the predecessor arcs of the
   144     ///shortest paths.
   145     typedef typename TR::PredMap PredMap;
   146     ///The type of the map that stores the distances of the nodes.
   147     typedef typename TR::DistMap DistMap;
   148     ///The type of the map that indicates which nodes are reached.
   149     typedef typename TR::ReachedMap ReachedMap;
   150     ///The type of the map that indicates which nodes are processed.
   151     typedef typename TR::ProcessedMap ProcessedMap;
   152     ///The type of the paths.
   153     typedef PredMapPath<Digraph, PredMap> Path;
   154 
   155     ///The \ref BfsDefaultTraits "traits class" of the algorithm.
   156     typedef TR Traits;
   157 
   158   private:
   159 
   160     typedef typename Digraph::Node Node;
   161     typedef typename Digraph::NodeIt NodeIt;
   162     typedef typename Digraph::Arc Arc;
   163     typedef typename Digraph::OutArcIt OutArcIt;
   164 
   165     //Pointer to the underlying digraph.
   166     const Digraph *G;
   167     //Pointer to the map of predecessor arcs.
   168     PredMap *_pred;
   169     //Indicates if _pred is locally allocated (true) or not.
   170     bool local_pred;
   171     //Pointer to the map of distances.
   172     DistMap *_dist;
   173     //Indicates if _dist is locally allocated (true) or not.
   174     bool local_dist;
   175     //Pointer to the map of reached status of the nodes.
   176     ReachedMap *_reached;
   177     //Indicates if _reached is locally allocated (true) or not.
   178     bool local_reached;
   179     //Pointer to the map of processed status of the nodes.
   180     ProcessedMap *_processed;
   181     //Indicates if _processed is locally allocated (true) or not.
   182     bool local_processed;
   183 
   184     std::vector<typename Digraph::Node> _queue;
   185     int _queue_head,_queue_tail,_queue_next_dist;
   186     int _curr_dist;
   187 
   188     //Creates the maps if necessary.
   189     void create_maps()
   190     {
   191       if(!_pred) {
   192         local_pred = true;
   193         _pred = Traits::createPredMap(*G);
   194       }
   195       if(!_dist) {
   196         local_dist = true;
   197         _dist = Traits::createDistMap(*G);
   198       }
   199       if(!_reached) {
   200         local_reached = true;
   201         _reached = Traits::createReachedMap(*G);
   202       }
   203       if(!_processed) {
   204         local_processed = true;
   205         _processed = Traits::createProcessedMap(*G);
   206       }
   207     }
   208 
   209   protected:
   210 
   211     Bfs() {}
   212 
   213   public:
   214 
   215     typedef Bfs Create;
   216 
   217     ///\name Named Template Parameters
   218 
   219     ///@{
   220 
   221     template <class T>
   222     struct SetPredMapTraits : public Traits {
   223       typedef T PredMap;
   224       static PredMap *createPredMap(const Digraph &)
   225       {
   226         LEMON_ASSERT(false, "PredMap is not initialized");
   227         return 0; // ignore warnings
   228       }
   229     };
   230     ///\brief \ref named-templ-param "Named parameter" for setting
   231     ///\c PredMap type.
   232     ///
   233     ///\ref named-templ-param "Named parameter" for setting
   234     ///\c PredMap type.
   235     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   236     template <class T>
   237     struct SetPredMap : public Bfs< Digraph, SetPredMapTraits<T> > {
   238       typedef Bfs< Digraph, SetPredMapTraits<T> > Create;
   239     };
   240 
   241     template <class T>
   242     struct SetDistMapTraits : public Traits {
   243       typedef T DistMap;
   244       static DistMap *createDistMap(const Digraph &)
   245       {
   246         LEMON_ASSERT(false, "DistMap is not initialized");
   247         return 0; // ignore warnings
   248       }
   249     };
   250     ///\brief \ref named-templ-param "Named parameter" for setting
   251     ///\c DistMap type.
   252     ///
   253     ///\ref named-templ-param "Named parameter" for setting
   254     ///\c DistMap type.
   255     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   256     template <class T>
   257     struct SetDistMap : public Bfs< Digraph, SetDistMapTraits<T> > {
   258       typedef Bfs< Digraph, SetDistMapTraits<T> > Create;
   259     };
   260 
   261     template <class T>
   262     struct SetReachedMapTraits : public Traits {
   263       typedef T ReachedMap;
   264       static ReachedMap *createReachedMap(const Digraph &)
   265       {
   266         LEMON_ASSERT(false, "ReachedMap is not initialized");
   267         return 0; // ignore warnings
   268       }
   269     };
   270     ///\brief \ref named-templ-param "Named parameter" for setting
   271     ///\c ReachedMap type.
   272     ///
   273     ///\ref named-templ-param "Named parameter" for setting
   274     ///\c ReachedMap type.
   275     ///It must conform to
   276     ///the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
   277     template <class T>
   278     struct SetReachedMap : public Bfs< Digraph, SetReachedMapTraits<T> > {
   279       typedef Bfs< Digraph, SetReachedMapTraits<T> > Create;
   280     };
   281 
   282     template <class T>
   283     struct SetProcessedMapTraits : public Traits {
   284       typedef T ProcessedMap;
   285       static ProcessedMap *createProcessedMap(const Digraph &)
   286       {
   287         LEMON_ASSERT(false, "ProcessedMap is not initialized");
   288         return 0; // ignore warnings
   289       }
   290     };
   291     ///\brief \ref named-templ-param "Named parameter" for setting
   292     ///\c ProcessedMap type.
   293     ///
   294     ///\ref named-templ-param "Named parameter" for setting
   295     ///\c ProcessedMap type.
   296     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   297     template <class T>
   298     struct SetProcessedMap : public Bfs< Digraph, SetProcessedMapTraits<T> > {
   299       typedef Bfs< Digraph, SetProcessedMapTraits<T> > Create;
   300     };
   301 
   302     struct SetStandardProcessedMapTraits : public Traits {
   303       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   304       static ProcessedMap *createProcessedMap(const Digraph &g)
   305       {
   306         return new ProcessedMap(g);
   307         return 0; // ignore warnings
   308       }
   309     };
   310     ///\brief \ref named-templ-param "Named parameter" for setting
   311     ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   312     ///
   313     ///\ref named-templ-param "Named parameter" for setting
   314     ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   315     ///If you don't set it explicitly, it will be automatically allocated.
   316     struct SetStandardProcessedMap :
   317       public Bfs< Digraph, SetStandardProcessedMapTraits > {
   318       typedef Bfs< Digraph, SetStandardProcessedMapTraits > Create;
   319     };
   320 
   321     ///@}
   322 
   323   public:
   324 
   325     ///Constructor.
   326 
   327     ///Constructor.
   328     ///\param g The digraph the algorithm runs on.
   329     Bfs(const Digraph &g) :
   330       G(&g),
   331       _pred(NULL), local_pred(false),
   332       _dist(NULL), local_dist(false),
   333       _reached(NULL), local_reached(false),
   334       _processed(NULL), local_processed(false)
   335     { }
   336 
   337     ///Destructor.
   338     ~Bfs()
   339     {
   340       if(local_pred) delete _pred;
   341       if(local_dist) delete _dist;
   342       if(local_reached) delete _reached;
   343       if(local_processed) delete _processed;
   344     }
   345 
   346     ///Sets the map that stores the predecessor arcs.
   347 
   348     ///Sets the map that stores the predecessor arcs.
   349     ///If you don't use this function before calling \ref run(Node) "run()"
   350     ///or \ref init(), an instance will be allocated automatically.
   351     ///The destructor deallocates this automatically allocated map,
   352     ///of course.
   353     ///\return <tt> (*this) </tt>
   354     Bfs &predMap(PredMap &m)
   355     {
   356       if(local_pred) {
   357         delete _pred;
   358         local_pred=false;
   359       }
   360       _pred = &m;
   361       return *this;
   362     }
   363 
   364     ///Sets the map that indicates which nodes are reached.
   365 
   366     ///Sets the map that indicates which nodes are reached.
   367     ///If you don't use this function before calling \ref run(Node) "run()"
   368     ///or \ref init(), an instance will be allocated automatically.
   369     ///The destructor deallocates this automatically allocated map,
   370     ///of course.
   371     ///\return <tt> (*this) </tt>
   372     Bfs &reachedMap(ReachedMap &m)
   373     {
   374       if(local_reached) {
   375         delete _reached;
   376         local_reached=false;
   377       }
   378       _reached = &m;
   379       return *this;
   380     }
   381 
   382     ///Sets the map that indicates which nodes are processed.
   383 
   384     ///Sets the map that indicates which nodes are processed.
   385     ///If you don't use this function before calling \ref run(Node) "run()"
   386     ///or \ref init(), an instance will be allocated automatically.
   387     ///The destructor deallocates this automatically allocated map,
   388     ///of course.
   389     ///\return <tt> (*this) </tt>
   390     Bfs &processedMap(ProcessedMap &m)
   391     {
   392       if(local_processed) {
   393         delete _processed;
   394         local_processed=false;
   395       }
   396       _processed = &m;
   397       return *this;
   398     }
   399 
   400     ///Sets the map that stores the distances of the nodes.
   401 
   402     ///Sets the map that stores the distances of the nodes calculated by
   403     ///the algorithm.
   404     ///If you don't use this function before calling \ref run(Node) "run()"
   405     ///or \ref init(), an instance will be allocated automatically.
   406     ///The destructor deallocates this automatically allocated map,
   407     ///of course.
   408     ///\return <tt> (*this) </tt>
   409     Bfs &distMap(DistMap &m)
   410     {
   411       if(local_dist) {
   412         delete _dist;
   413         local_dist=false;
   414       }
   415       _dist = &m;
   416       return *this;
   417     }
   418 
   419   public:
   420 
   421     ///\name Execution Control
   422     ///The simplest way to execute the BFS algorithm is to use one of the
   423     ///member functions called \ref run(Node) "run()".\n
   424     ///If you need better control on the execution, you have to call
   425     ///\ref init() first, then you can add several source nodes with
   426     ///\ref addSource(). Finally the actual path computation can be
   427     ///performed with one of the \ref start() functions.
   428 
   429     ///@{
   430 
   431     ///\brief Initializes the internal data structures.
   432     ///
   433     ///Initializes the internal data structures.
   434     void init()
   435     {
   436       create_maps();
   437       _queue.resize(countNodes(*G));
   438       _queue_head=_queue_tail=0;
   439       _curr_dist=1;
   440       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   441         _pred->set(u,INVALID);
   442         _reached->set(u,false);
   443         _processed->set(u,false);
   444       }
   445     }
   446 
   447     ///Adds a new source node.
   448 
   449     ///Adds a new source node to the set of nodes to be processed.
   450     ///
   451     void addSource(Node s)
   452     {
   453       if(!(*_reached)[s])
   454         {
   455           _reached->set(s,true);
   456           _pred->set(s,INVALID);
   457           _dist->set(s,0);
   458           _queue[_queue_head++]=s;
   459           _queue_next_dist=_queue_head;
   460         }
   461     }
   462 
   463     ///Processes the next node.
   464 
   465     ///Processes the next node.
   466     ///
   467     ///\return The processed node.
   468     ///
   469     ///\pre The queue must not be empty.
   470     Node processNextNode()
   471     {
   472       if(_queue_tail==_queue_next_dist) {
   473         _curr_dist++;
   474         _queue_next_dist=_queue_head;
   475       }
   476       Node n=_queue[_queue_tail++];
   477       _processed->set(n,true);
   478       Node m;
   479       for(OutArcIt e(*G,n);e!=INVALID;++e)
   480         if(!(*_reached)[m=G->target(e)]) {
   481           _queue[_queue_head++]=m;
   482           _reached->set(m,true);
   483           _pred->set(m,e);
   484           _dist->set(m,_curr_dist);
   485         }
   486       return n;
   487     }
   488 
   489     ///Processes the next node.
   490 
   491     ///Processes the next node and checks if the given target node
   492     ///is reached. If the target node is reachable from the processed
   493     ///node, then the \c reach parameter will be set to \c true.
   494     ///
   495     ///\param target The target node.
   496     ///\retval reach Indicates if the target node is reached.
   497     ///It should be initially \c false.
   498     ///
   499     ///\return The processed node.
   500     ///
   501     ///\pre The queue must not be empty.
   502     Node processNextNode(Node target, bool& reach)
   503     {
   504       if(_queue_tail==_queue_next_dist) {
   505         _curr_dist++;
   506         _queue_next_dist=_queue_head;
   507       }
   508       Node n=_queue[_queue_tail++];
   509       _processed->set(n,true);
   510       Node m;
   511       for(OutArcIt e(*G,n);e!=INVALID;++e)
   512         if(!(*_reached)[m=G->target(e)]) {
   513           _queue[_queue_head++]=m;
   514           _reached->set(m,true);
   515           _pred->set(m,e);
   516           _dist->set(m,_curr_dist);
   517           reach = reach || (target == m);
   518         }
   519       return n;
   520     }
   521 
   522     ///Processes the next node.
   523 
   524     ///Processes the next node and checks if at least one of reached
   525     ///nodes has \c true value in the \c nm node map. If one node
   526     ///with \c true value is reachable from the processed node, then the
   527     ///\c rnode parameter will be set to the first of such nodes.
   528     ///
   529     ///\param nm A \c bool (or convertible) node map that indicates the
   530     ///possible targets.
   531     ///\retval rnode The reached target node.
   532     ///It should be initially \c INVALID.
   533     ///
   534     ///\return The processed node.
   535     ///
   536     ///\pre The queue must not be empty.
   537     template<class NM>
   538     Node processNextNode(const NM& nm, Node& rnode)
   539     {
   540       if(_queue_tail==_queue_next_dist) {
   541         _curr_dist++;
   542         _queue_next_dist=_queue_head;
   543       }
   544       Node n=_queue[_queue_tail++];
   545       _processed->set(n,true);
   546       Node m;
   547       for(OutArcIt e(*G,n);e!=INVALID;++e)
   548         if(!(*_reached)[m=G->target(e)]) {
   549           _queue[_queue_head++]=m;
   550           _reached->set(m,true);
   551           _pred->set(m,e);
   552           _dist->set(m,_curr_dist);
   553           if (nm[m] && rnode == INVALID) rnode = m;
   554         }
   555       return n;
   556     }
   557 
   558     ///The next node to be processed.
   559 
   560     ///Returns the next node to be processed or \c INVALID if the queue
   561     ///is empty.
   562     Node nextNode() const
   563     {
   564       return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
   565     }
   566 
   567     ///Returns \c false if there are nodes to be processed.
   568 
   569     ///Returns \c false if there are nodes to be processed
   570     ///in the queue.
   571     bool emptyQueue() const { return _queue_tail==_queue_head; }
   572 
   573     ///Returns the number of the nodes to be processed.
   574 
   575     ///Returns the number of the nodes to be processed
   576     ///in the queue.
   577     int queueSize() const { return _queue_head-_queue_tail; }
   578 
   579     ///Executes the algorithm.
   580 
   581     ///Executes the algorithm.
   582     ///
   583     ///This method runs the %BFS algorithm from the root node(s)
   584     ///in order to compute the shortest path to each node.
   585     ///
   586     ///The algorithm computes
   587     ///- the shortest path tree (forest),
   588     ///- the distance of each node from the root(s).
   589     ///
   590     ///\pre init() must be called and at least one root node should be
   591     ///added with addSource() before using this function.
   592     ///
   593     ///\note <tt>b.start()</tt> is just a shortcut of the following code.
   594     ///\code
   595     ///  while ( !b.emptyQueue() ) {
   596     ///    b.processNextNode();
   597     ///  }
   598     ///\endcode
   599     void start()
   600     {
   601       while ( !emptyQueue() ) processNextNode();
   602     }
   603 
   604     ///Executes the algorithm until the given target node is reached.
   605 
   606     ///Executes the algorithm until the given target node is reached.
   607     ///
   608     ///This method runs the %BFS algorithm from the root node(s)
   609     ///in order to compute the shortest path to \c t.
   610     ///
   611     ///The algorithm computes
   612     ///- the shortest path to \c t,
   613     ///- the distance of \c t from the root(s).
   614     ///
   615     ///\pre init() must be called and at least one root node should be
   616     ///added with addSource() before using this function.
   617     ///
   618     ///\note <tt>b.start(t)</tt> is just a shortcut of the following code.
   619     ///\code
   620     ///  bool reach = false;
   621     ///  while ( !b.emptyQueue() && !reach ) {
   622     ///    b.processNextNode(t, reach);
   623     ///  }
   624     ///\endcode
   625     void start(Node t)
   626     {
   627       bool reach = false;
   628       while ( !emptyQueue() && !reach ) processNextNode(t, reach);
   629     }
   630 
   631     ///Executes the algorithm until a condition is met.
   632 
   633     ///Executes the algorithm until a condition is met.
   634     ///
   635     ///This method runs the %BFS algorithm from the root node(s) in
   636     ///order to compute the shortest path to a node \c v with
   637     /// <tt>nm[v]</tt> true, if such a node can be found.
   638     ///
   639     ///\param nm A \c bool (or convertible) node map. The algorithm
   640     ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
   641     ///
   642     ///\return The reached node \c v with <tt>nm[v]</tt> true or
   643     ///\c INVALID if no such node was found.
   644     ///
   645     ///\pre init() must be called and at least one root node should be
   646     ///added with addSource() before using this function.
   647     ///
   648     ///\note <tt>b.start(nm)</tt> is just a shortcut of the following code.
   649     ///\code
   650     ///  Node rnode = INVALID;
   651     ///  while ( !b.emptyQueue() && rnode == INVALID ) {
   652     ///    b.processNextNode(nm, rnode);
   653     ///  }
   654     ///  return rnode;
   655     ///\endcode
   656     template<class NodeBoolMap>
   657     Node start(const NodeBoolMap &nm)
   658     {
   659       Node rnode = INVALID;
   660       while ( !emptyQueue() && rnode == INVALID ) {
   661         processNextNode(nm, rnode);
   662       }
   663       return rnode;
   664     }
   665 
   666     ///Runs the algorithm from the given source node.
   667 
   668     ///This method runs the %BFS algorithm from node \c s
   669     ///in order to compute the shortest path to each node.
   670     ///
   671     ///The algorithm computes
   672     ///- the shortest path tree,
   673     ///- the distance of each node from the root.
   674     ///
   675     ///\note <tt>b.run(s)</tt> is just a shortcut of the following code.
   676     ///\code
   677     ///  b.init();
   678     ///  b.addSource(s);
   679     ///  b.start();
   680     ///\endcode
   681     void run(Node s) {
   682       init();
   683       addSource(s);
   684       start();
   685     }
   686 
   687     ///Finds the shortest path between \c s and \c t.
   688 
   689     ///This method runs the %BFS algorithm from node \c s
   690     ///in order to compute the shortest path to node \c t
   691     ///(it stops searching when \c t is processed).
   692     ///
   693     ///\return \c true if \c t is reachable form \c s.
   694     ///
   695     ///\note Apart from the return value, <tt>b.run(s,t)</tt> is just a
   696     ///shortcut of the following code.
   697     ///\code
   698     ///  b.init();
   699     ///  b.addSource(s);
   700     ///  b.start(t);
   701     ///\endcode
   702     bool run(Node s,Node t) {
   703       init();
   704       addSource(s);
   705       start(t);
   706       return reached(t);
   707     }
   708 
   709     ///Runs the algorithm to visit all nodes in the digraph.
   710 
   711     ///This method runs the %BFS algorithm in order to visit all nodes
   712     ///in the digraph.
   713     ///
   714     ///\note <tt>b.run(s)</tt> is just a shortcut of the following code.
   715     ///\code
   716     ///  b.init();
   717     ///  for (NodeIt n(gr); n != INVALID; ++n) {
   718     ///    if (!b.reached(n)) {
   719     ///      b.addSource(n);
   720     ///      b.start();
   721     ///    }
   722     ///  }
   723     ///\endcode
   724     void run() {
   725       init();
   726       for (NodeIt n(*G); n != INVALID; ++n) {
   727         if (!reached(n)) {
   728           addSource(n);
   729           start();
   730         }
   731       }
   732     }
   733 
   734     ///@}
   735 
   736     ///\name Query Functions
   737     ///The results of the BFS algorithm can be obtained using these
   738     ///functions.\n
   739     ///Either \ref run(Node) "run()" or \ref start() should be called
   740     ///before using them.
   741 
   742     ///@{
   743 
   744     ///The shortest path to the given node.
   745 
   746     ///Returns the shortest path to the given node from the root(s).
   747     ///
   748     ///\warning \c t should be reached from the root(s).
   749     ///
   750     ///\pre Either \ref run(Node) "run()" or \ref init()
   751     ///must be called before using this function.
   752     Path path(Node t) const { return Path(*G, *_pred, t); }
   753 
   754     ///The distance of the given node from the root(s).
   755 
   756     ///Returns the distance of the given node from the root(s).
   757     ///
   758     ///\warning If node \c v is not reached from the root(s), then
   759     ///the return value of this function is undefined.
   760     ///
   761     ///\pre Either \ref run(Node) "run()" or \ref init()
   762     ///must be called before using this function.
   763     int dist(Node v) const { return (*_dist)[v]; }
   764 
   765     ///\brief Returns the 'previous arc' of the shortest path tree for
   766     ///the given node.
   767     ///
   768     ///This function returns the 'previous arc' of the shortest path
   769     ///tree for the node \c v, i.e. it returns the last arc of a
   770     ///shortest path from a root to \c v. It is \c INVALID if \c v
   771     ///is not reached from the root(s) or if \c v is a root.
   772     ///
   773     ///The shortest path tree used here is equal to the shortest path
   774     ///tree used in \ref predNode() and \ref predMap().
   775     ///
   776     ///\pre Either \ref run(Node) "run()" or \ref init()
   777     ///must be called before using this function.
   778     Arc predArc(Node v) const { return (*_pred)[v];}
   779 
   780     ///\brief Returns the 'previous node' of the shortest path tree for
   781     ///the given node.
   782     ///
   783     ///This function returns the 'previous node' of the shortest path
   784     ///tree for the node \c v, i.e. it returns the last but one node
   785     ///of a shortest path from a root to \c v. It is \c INVALID
   786     ///if \c v is not reached from the root(s) or if \c v is a root.
   787     ///
   788     ///The shortest path tree used here is equal to the shortest path
   789     ///tree used in \ref predArc() and \ref predMap().
   790     ///
   791     ///\pre Either \ref run(Node) "run()" or \ref init()
   792     ///must be called before using this function.
   793     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   794                                   G->source((*_pred)[v]); }
   795 
   796     ///\brief Returns a const reference to the node map that stores the
   797     /// distances of the nodes.
   798     ///
   799     ///Returns a const reference to the node map that stores the distances
   800     ///of the nodes calculated by the algorithm.
   801     ///
   802     ///\pre Either \ref run(Node) "run()" or \ref init()
   803     ///must be called before using this function.
   804     const DistMap &distMap() const { return *_dist;}
   805 
   806     ///\brief Returns a const reference to the node map that stores the
   807     ///predecessor arcs.
   808     ///
   809     ///Returns a const reference to the node map that stores the predecessor
   810     ///arcs, which form the shortest path tree (forest).
   811     ///
   812     ///\pre Either \ref run(Node) "run()" or \ref init()
   813     ///must be called before using this function.
   814     const PredMap &predMap() const { return *_pred;}
   815 
   816     ///Checks if the given node is reached from the root(s).
   817 
   818     ///Returns \c true if \c v is reached from the root(s).
   819     ///
   820     ///\pre Either \ref run(Node) "run()" or \ref init()
   821     ///must be called before using this function.
   822     bool reached(Node v) const { return (*_reached)[v]; }
   823 
   824     ///@}
   825   };
   826 
   827   ///Default traits class of bfs() function.
   828 
   829   ///Default traits class of bfs() function.
   830   ///\tparam GR Digraph type.
   831   template<class GR>
   832   struct BfsWizardDefaultTraits
   833   {
   834     ///The type of the digraph the algorithm runs on.
   835     typedef GR Digraph;
   836 
   837     ///\brief The type of the map that stores the predecessor
   838     ///arcs of the shortest paths.
   839     ///
   840     ///The type of the map that stores the predecessor
   841     ///arcs of the shortest paths.
   842     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   843     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   844     ///Instantiates a PredMap.
   845 
   846     ///This function instantiates a PredMap.
   847     ///\param g is the digraph, to which we would like to define the
   848     ///PredMap.
   849     static PredMap *createPredMap(const Digraph &g)
   850     {
   851       return new PredMap(g);
   852     }
   853 
   854     ///The type of the map that indicates which nodes are processed.
   855 
   856     ///The type of the map that indicates which nodes are processed.
   857     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   858     ///By default, it is a NullMap.
   859     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   860     ///Instantiates a ProcessedMap.
   861 
   862     ///This function instantiates a ProcessedMap.
   863     ///\param g is the digraph, to which
   864     ///we would like to define the ProcessedMap.
   865 #ifdef DOXYGEN
   866     static ProcessedMap *createProcessedMap(const Digraph &g)
   867 #else
   868     static ProcessedMap *createProcessedMap(const Digraph &)
   869 #endif
   870     {
   871       return new ProcessedMap();
   872     }
   873 
   874     ///The type of the map that indicates which nodes are reached.
   875 
   876     ///The type of the map that indicates which nodes are reached.
   877     ///It must conform to
   878     ///the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
   879     typedef typename Digraph::template NodeMap<bool> ReachedMap;
   880     ///Instantiates a ReachedMap.
   881 
   882     ///This function instantiates a ReachedMap.
   883     ///\param g is the digraph, to which
   884     ///we would like to define the ReachedMap.
   885     static ReachedMap *createReachedMap(const Digraph &g)
   886     {
   887       return new ReachedMap(g);
   888     }
   889 
   890     ///The type of the map that stores the distances of the nodes.
   891 
   892     ///The type of the map that stores the distances of the nodes.
   893     ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
   894     typedef typename Digraph::template NodeMap<int> DistMap;
   895     ///Instantiates a DistMap.
   896 
   897     ///This function instantiates a DistMap.
   898     ///\param g is the digraph, to which we would like to define
   899     ///the DistMap
   900     static DistMap *createDistMap(const Digraph &g)
   901     {
   902       return new DistMap(g);
   903     }
   904 
   905     ///The type of the shortest paths.
   906 
   907     ///The type of the shortest paths.
   908     ///It must conform to the \ref concepts::Path "Path" concept.
   909     typedef lemon::Path<Digraph> Path;
   910   };
   911 
   912   /// Default traits class used by BfsWizard
   913 
   914   /// Default traits class used by BfsWizard.
   915   /// \tparam GR The type of the digraph.
   916   template<class GR>
   917   class BfsWizardBase : public BfsWizardDefaultTraits<GR>
   918   {
   919 
   920     typedef BfsWizardDefaultTraits<GR> Base;
   921   protected:
   922     //The type of the nodes in the digraph.
   923     typedef typename Base::Digraph::Node Node;
   924 
   925     //Pointer to the digraph the algorithm runs on.
   926     void *_g;
   927     //Pointer to the map of reached nodes.
   928     void *_reached;
   929     //Pointer to the map of processed nodes.
   930     void *_processed;
   931     //Pointer to the map of predecessors arcs.
   932     void *_pred;
   933     //Pointer to the map of distances.
   934     void *_dist;
   935     //Pointer to the shortest path to the target node.
   936     void *_path;
   937     //Pointer to the distance of the target node.
   938     int *_di;
   939 
   940     public:
   941     /// Constructor.
   942 
   943     /// This constructor does not require parameters, it initiates
   944     /// all of the attributes to \c 0.
   945     BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
   946                       _dist(0), _path(0), _di(0) {}
   947 
   948     /// Constructor.
   949 
   950     /// This constructor requires one parameter,
   951     /// others are initiated to \c 0.
   952     /// \param g The digraph the algorithm runs on.
   953     BfsWizardBase(const GR &g) :
   954       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
   955       _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
   956 
   957   };
   958 
   959   /// Auxiliary class for the function-type interface of BFS algorithm.
   960 
   961   /// This auxiliary class is created to implement the
   962   /// \ref bfs() "function-type interface" of \ref Bfs algorithm.
   963   /// It does not have own \ref run(Node) "run()" method, it uses the
   964   /// functions and features of the plain \ref Bfs.
   965   ///
   966   /// This class should only be used through the \ref bfs() function,
   967   /// which makes it easier to use the algorithm.
   968   ///
   969   /// \tparam TR The traits class that defines various types used by the
   970   /// algorithm.
   971   template<class TR>
   972   class BfsWizard : public TR
   973   {
   974     typedef TR Base;
   975 
   976     typedef typename TR::Digraph Digraph;
   977 
   978     typedef typename Digraph::Node Node;
   979     typedef typename Digraph::NodeIt NodeIt;
   980     typedef typename Digraph::Arc Arc;
   981     typedef typename Digraph::OutArcIt OutArcIt;
   982 
   983     typedef typename TR::PredMap PredMap;
   984     typedef typename TR::DistMap DistMap;
   985     typedef typename TR::ReachedMap ReachedMap;
   986     typedef typename TR::ProcessedMap ProcessedMap;
   987     typedef typename TR::Path Path;
   988 
   989   public:
   990 
   991     /// Constructor.
   992     BfsWizard() : TR() {}
   993 
   994     /// Constructor that requires parameters.
   995 
   996     /// Constructor that requires parameters.
   997     /// These parameters will be the default values for the traits class.
   998     /// \param g The digraph the algorithm runs on.
   999     BfsWizard(const Digraph &g) :
  1000       TR(g) {}
  1001 
  1002     ///Copy constructor
  1003     BfsWizard(const TR &b) : TR(b) {}
  1004 
  1005     ~BfsWizard() {}
  1006 
  1007     ///Runs BFS algorithm from the given source node.
  1008 
  1009     ///This method runs BFS algorithm from node \c s
  1010     ///in order to compute the shortest path to each node.
  1011     void run(Node s)
  1012     {
  1013       Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
  1014       if (Base::_pred)
  1015         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1016       if (Base::_dist)
  1017         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1018       if (Base::_reached)
  1019         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
  1020       if (Base::_processed)
  1021         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1022       if (s!=INVALID)
  1023         alg.run(s);
  1024       else
  1025         alg.run();
  1026     }
  1027 
  1028     ///Finds the shortest path between \c s and \c t.
  1029 
  1030     ///This method runs BFS algorithm from node \c s
  1031     ///in order to compute the shortest path to node \c t
  1032     ///(it stops searching when \c t is processed).
  1033     ///
  1034     ///\return \c true if \c t is reachable form \c s.
  1035     bool run(Node s, Node t)
  1036     {
  1037       Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
  1038       if (Base::_pred)
  1039         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
  1040       if (Base::_dist)
  1041         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
  1042       if (Base::_reached)
  1043         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
  1044       if (Base::_processed)
  1045         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
  1046       alg.run(s,t);
  1047       if (Base::_path)
  1048         *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
  1049       if (Base::_di)
  1050         *Base::_di = alg.dist(t);
  1051       return alg.reached(t);
  1052     }
  1053 
  1054     ///Runs BFS algorithm to visit all nodes in the digraph.
  1055 
  1056     ///This method runs BFS algorithm in order to visit all nodes
  1057     ///in the digraph.
  1058     void run()
  1059     {
  1060       run(INVALID);
  1061     }
  1062 
  1063     template<class T>
  1064     struct SetPredMapBase : public Base {
  1065       typedef T PredMap;
  1066       static PredMap *createPredMap(const Digraph &) { return 0; };
  1067       SetPredMapBase(const TR &b) : TR(b) {}
  1068     };
  1069 
  1070     ///\brief \ref named-templ-param "Named parameter" for setting
  1071     ///the predecessor map.
  1072     ///
  1073     ///\ref named-templ-param "Named parameter" function for setting
  1074     ///the map that stores the predecessor arcs of the nodes.
  1075     template<class T>
  1076     BfsWizard<SetPredMapBase<T> > predMap(const T &t)
  1077     {
  1078       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1079       return BfsWizard<SetPredMapBase<T> >(*this);
  1080     }
  1081 
  1082     template<class T>
  1083     struct SetReachedMapBase : public Base {
  1084       typedef T ReachedMap;
  1085       static ReachedMap *createReachedMap(const Digraph &) { return 0; };
  1086       SetReachedMapBase(const TR &b) : TR(b) {}
  1087     };
  1088 
  1089     ///\brief \ref named-templ-param "Named parameter" for setting
  1090     ///the reached map.
  1091     ///
  1092     ///\ref named-templ-param "Named parameter" function for setting
  1093     ///the map that indicates which nodes are reached.
  1094     template<class T>
  1095     BfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
  1096     {
  1097       Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
  1098       return BfsWizard<SetReachedMapBase<T> >(*this);
  1099     }
  1100 
  1101     template<class T>
  1102     struct SetDistMapBase : public Base {
  1103       typedef T DistMap;
  1104       static DistMap *createDistMap(const Digraph &) { return 0; };
  1105       SetDistMapBase(const TR &b) : TR(b) {}
  1106     };
  1107 
  1108     ///\brief \ref named-templ-param "Named parameter" for setting
  1109     ///the distance map.
  1110     ///
  1111     ///\ref named-templ-param "Named parameter" function for setting
  1112     ///the map that stores the distances of the nodes calculated
  1113     ///by the algorithm.
  1114     template<class T>
  1115     BfsWizard<SetDistMapBase<T> > distMap(const T &t)
  1116     {
  1117       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1118       return BfsWizard<SetDistMapBase<T> >(*this);
  1119     }
  1120 
  1121     template<class T>
  1122     struct SetProcessedMapBase : public Base {
  1123       typedef T ProcessedMap;
  1124       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1125       SetProcessedMapBase(const TR &b) : TR(b) {}
  1126     };
  1127 
  1128     ///\brief \ref named-func-param "Named parameter" for setting
  1129     ///the processed map.
  1130     ///
  1131     ///\ref named-templ-param "Named parameter" function for setting
  1132     ///the map that indicates which nodes are processed.
  1133     template<class T>
  1134     BfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
  1135     {
  1136       Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
  1137       return BfsWizard<SetProcessedMapBase<T> >(*this);
  1138     }
  1139 
  1140     template<class T>
  1141     struct SetPathBase : public Base {
  1142       typedef T Path;
  1143       SetPathBase(const TR &b) : TR(b) {}
  1144     };
  1145     ///\brief \ref named-func-param "Named parameter"
  1146     ///for getting the shortest path to the target node.
  1147     ///
  1148     ///\ref named-func-param "Named parameter"
  1149     ///for getting the shortest path to the target node.
  1150     template<class T>
  1151     BfsWizard<SetPathBase<T> > path(const T &t)
  1152     {
  1153       Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
  1154       return BfsWizard<SetPathBase<T> >(*this);
  1155     }
  1156 
  1157     ///\brief \ref named-func-param "Named parameter"
  1158     ///for getting the distance of the target node.
  1159     ///
  1160     ///\ref named-func-param "Named parameter"
  1161     ///for getting the distance of the target node.
  1162     BfsWizard dist(const int &d)
  1163     {
  1164       Base::_di=const_cast<int*>(&d);
  1165       return *this;
  1166     }
  1167 
  1168   };
  1169 
  1170   ///Function-type interface for BFS algorithm.
  1171 
  1172   /// \ingroup search
  1173   ///Function-type interface for BFS algorithm.
  1174   ///
  1175   ///This function also has several \ref named-func-param "named parameters",
  1176   ///they are declared as the members of class \ref BfsWizard.
  1177   ///The following examples show how to use these parameters.
  1178   ///\code
  1179   ///  // Compute shortest path from node s to each node
  1180   ///  bfs(g).predMap(preds).distMap(dists).run(s);
  1181   ///
  1182   ///  // Compute shortest path from s to t
  1183   ///  bool reached = bfs(g).path(p).dist(d).run(s,t);
  1184   ///\endcode
  1185   ///\warning Don't forget to put the \ref BfsWizard::run(Node) "run()"
  1186   ///to the end of the parameter list.
  1187   ///\sa BfsWizard
  1188   ///\sa Bfs
  1189   template<class GR>
  1190   BfsWizard<BfsWizardBase<GR> >
  1191   bfs(const GR &digraph)
  1192   {
  1193     return BfsWizard<BfsWizardBase<GR> >(digraph);
  1194   }
  1195 
  1196 #ifdef DOXYGEN
  1197   /// \brief Visitor class for BFS.
  1198   ///
  1199   /// This class defines the interface of the BfsVisit events, and
  1200   /// it could be the base of a real visitor class.
  1201   template <typename GR>
  1202   struct BfsVisitor {
  1203     typedef GR Digraph;
  1204     typedef typename Digraph::Arc Arc;
  1205     typedef typename Digraph::Node Node;
  1206     /// \brief Called for the source node(s) of the BFS.
  1207     ///
  1208     /// This function is called for the source node(s) of the BFS.
  1209     void start(const Node& node) {}
  1210     /// \brief Called when a node is reached first time.
  1211     ///
  1212     /// This function is called when a node is reached first time.
  1213     void reach(const Node& node) {}
  1214     /// \brief Called when a node is processed.
  1215     ///
  1216     /// This function is called when a node is processed.
  1217     void process(const Node& node) {}
  1218     /// \brief Called when an arc reaches a new node.
  1219     ///
  1220     /// This function is called when the BFS finds an arc whose target node
  1221     /// is not reached yet.
  1222     void discover(const Arc& arc) {}
  1223     /// \brief Called when an arc is examined but its target node is
  1224     /// already discovered.
  1225     ///
  1226     /// This function is called when an arc is examined but its target node is
  1227     /// already discovered.
  1228     void examine(const Arc& arc) {}
  1229   };
  1230 #else
  1231   template <typename GR>
  1232   struct BfsVisitor {
  1233     typedef GR Digraph;
  1234     typedef typename Digraph::Arc Arc;
  1235     typedef typename Digraph::Node Node;
  1236     void start(const Node&) {}
  1237     void reach(const Node&) {}
  1238     void process(const Node&) {}
  1239     void discover(const Arc&) {}
  1240     void examine(const Arc&) {}
  1241 
  1242     template <typename _Visitor>
  1243     struct Constraints {
  1244       void constraints() {
  1245         Arc arc;
  1246         Node node;
  1247         visitor.start(node);
  1248         visitor.reach(node);
  1249         visitor.process(node);
  1250         visitor.discover(arc);
  1251         visitor.examine(arc);
  1252       }
  1253       _Visitor& visitor;
  1254     };
  1255   };
  1256 #endif
  1257 
  1258   /// \brief Default traits class of BfsVisit class.
  1259   ///
  1260   /// Default traits class of BfsVisit class.
  1261   /// \tparam GR The type of the digraph the algorithm runs on.
  1262   template<class GR>
  1263   struct BfsVisitDefaultTraits {
  1264 
  1265     /// \brief The type of the digraph the algorithm runs on.
  1266     typedef GR Digraph;
  1267 
  1268     /// \brief The type of the map that indicates which nodes are reached.
  1269     ///
  1270     /// The type of the map that indicates which nodes are reached.
  1271     /// It must conform to
  1272     ///the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
  1273     typedef typename Digraph::template NodeMap<bool> ReachedMap;
  1274 
  1275     /// \brief Instantiates a ReachedMap.
  1276     ///
  1277     /// This function instantiates a ReachedMap.
  1278     /// \param digraph is the digraph, to which
  1279     /// we would like to define the ReachedMap.
  1280     static ReachedMap *createReachedMap(const Digraph &digraph) {
  1281       return new ReachedMap(digraph);
  1282     }
  1283 
  1284   };
  1285 
  1286   /// \ingroup search
  1287   ///
  1288   /// \brief BFS algorithm class with visitor interface.
  1289   ///
  1290   /// This class provides an efficient implementation of the BFS algorithm
  1291   /// with visitor interface.
  1292   ///
  1293   /// The BfsVisit class provides an alternative interface to the Bfs
  1294   /// class. It works with callback mechanism, the BfsVisit object calls
  1295   /// the member functions of the \c Visitor class on every BFS event.
  1296   ///
  1297   /// This interface of the BFS algorithm should be used in special cases
  1298   /// when extra actions have to be performed in connection with certain
  1299   /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()
  1300   /// instead.
  1301   ///
  1302   /// \tparam GR The type of the digraph the algorithm runs on.
  1303   /// The default type is \ref ListDigraph.
  1304   /// The value of GR is not used directly by \ref BfsVisit,
  1305   /// it is only passed to \ref BfsVisitDefaultTraits.
  1306   /// \tparam VS The Visitor type that is used by the algorithm.
  1307   /// \ref BfsVisitor "BfsVisitor<GR>" is an empty visitor, which
  1308   /// does not observe the BFS events. If you want to observe the BFS
  1309   /// events, you should implement your own visitor class.
  1310   /// \tparam TR The traits class that defines various types used by the
  1311   /// algorithm. By default, it is \ref BfsVisitDefaultTraits
  1312   /// "BfsVisitDefaultTraits<GR>".
  1313   /// In most cases, this parameter should not be set directly,
  1314   /// consider to use the named template parameters instead.
  1315 #ifdef DOXYGEN
  1316   template <typename GR, typename VS, typename TR>
  1317 #else
  1318   template <typename GR = ListDigraph,
  1319             typename VS = BfsVisitor<GR>,
  1320             typename TR = BfsVisitDefaultTraits<GR> >
  1321 #endif
  1322   class BfsVisit {
  1323   public:
  1324 
  1325     ///The traits class.
  1326     typedef TR Traits;
  1327 
  1328     ///The type of the digraph the algorithm runs on.
  1329     typedef typename Traits::Digraph Digraph;
  1330 
  1331     ///The visitor type used by the algorithm.
  1332     typedef VS Visitor;
  1333 
  1334     ///The type of the map that indicates which nodes are reached.
  1335     typedef typename Traits::ReachedMap ReachedMap;
  1336 
  1337   private:
  1338 
  1339     typedef typename Digraph::Node Node;
  1340     typedef typename Digraph::NodeIt NodeIt;
  1341     typedef typename Digraph::Arc Arc;
  1342     typedef typename Digraph::OutArcIt OutArcIt;
  1343 
  1344     //Pointer to the underlying digraph.
  1345     const Digraph *_digraph;
  1346     //Pointer to the visitor object.
  1347     Visitor *_visitor;
  1348     //Pointer to the map of reached status of the nodes.
  1349     ReachedMap *_reached;
  1350     //Indicates if _reached is locally allocated (true) or not.
  1351     bool local_reached;
  1352 
  1353     std::vector<typename Digraph::Node> _list;
  1354     int _list_front, _list_back;
  1355 
  1356     //Creates the maps if necessary.
  1357     void create_maps() {
  1358       if(!_reached) {
  1359         local_reached = true;
  1360         _reached = Traits::createReachedMap(*_digraph);
  1361       }
  1362     }
  1363 
  1364   protected:
  1365 
  1366     BfsVisit() {}
  1367 
  1368   public:
  1369 
  1370     typedef BfsVisit Create;
  1371 
  1372     /// \name Named Template Parameters
  1373 
  1374     ///@{
  1375     template <class T>
  1376     struct SetReachedMapTraits : public Traits {
  1377       typedef T ReachedMap;
  1378       static ReachedMap *createReachedMap(const Digraph &digraph) {
  1379         LEMON_ASSERT(false, "ReachedMap is not initialized");
  1380         return 0; // ignore warnings
  1381       }
  1382     };
  1383     /// \brief \ref named-templ-param "Named parameter" for setting
  1384     /// ReachedMap type.
  1385     ///
  1386     /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
  1387     template <class T>
  1388     struct SetReachedMap : public BfsVisit< Digraph, Visitor,
  1389                                             SetReachedMapTraits<T> > {
  1390       typedef BfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
  1391     };
  1392     ///@}
  1393 
  1394   public:
  1395 
  1396     /// \brief Constructor.
  1397     ///
  1398     /// Constructor.
  1399     ///
  1400     /// \param digraph The digraph the algorithm runs on.
  1401     /// \param visitor The visitor object of the algorithm.
  1402     BfsVisit(const Digraph& digraph, Visitor& visitor)
  1403       : _digraph(&digraph), _visitor(&visitor),
  1404         _reached(0), local_reached(false) {}
  1405 
  1406     /// \brief Destructor.
  1407     ~BfsVisit() {
  1408       if(local_reached) delete _reached;
  1409     }
  1410 
  1411     /// \brief Sets the map that indicates which nodes are reached.
  1412     ///
  1413     /// Sets the map that indicates which nodes are reached.
  1414     /// If you don't use this function before calling \ref run(Node) "run()"
  1415     /// or \ref init(), an instance will be allocated automatically.
  1416     /// The destructor deallocates this automatically allocated map,
  1417     /// of course.
  1418     /// \return <tt> (*this) </tt>
  1419     BfsVisit &reachedMap(ReachedMap &m) {
  1420       if(local_reached) {
  1421         delete _reached;
  1422         local_reached = false;
  1423       }
  1424       _reached = &m;
  1425       return *this;
  1426     }
  1427 
  1428   public:
  1429 
  1430     /// \name Execution Control
  1431     /// The simplest way to execute the BFS algorithm is to use one of the
  1432     /// member functions called \ref run(Node) "run()".\n
  1433     /// If you need better control on the execution, you have to call
  1434     /// \ref init() first, then you can add several source nodes with
  1435     /// \ref addSource(). Finally the actual path computation can be
  1436     /// performed with one of the \ref start() functions.
  1437 
  1438     /// @{
  1439 
  1440     /// \brief Initializes the internal data structures.
  1441     ///
  1442     /// Initializes the internal data structures.
  1443     void init() {
  1444       create_maps();
  1445       _list.resize(countNodes(*_digraph));
  1446       _list_front = _list_back = -1;
  1447       for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
  1448         _reached->set(u, false);
  1449       }
  1450     }
  1451 
  1452     /// \brief Adds a new source node.
  1453     ///
  1454     /// Adds a new source node to the set of nodes to be processed.
  1455     void addSource(Node s) {
  1456       if(!(*_reached)[s]) {
  1457           _reached->set(s,true);
  1458           _visitor->start(s);
  1459           _visitor->reach(s);
  1460           _list[++_list_back] = s;
  1461         }
  1462     }
  1463 
  1464     /// \brief Processes the next node.
  1465     ///
  1466     /// Processes the next node.
  1467     ///
  1468     /// \return The processed node.
  1469     ///
  1470     /// \pre The queue must not be empty.
  1471     Node processNextNode() {
  1472       Node n = _list[++_list_front];
  1473       _visitor->process(n);
  1474       Arc e;
  1475       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1476         Node m = _digraph->target(e);
  1477         if (!(*_reached)[m]) {
  1478           _visitor->discover(e);
  1479           _visitor->reach(m);
  1480           _reached->set(m, true);
  1481           _list[++_list_back] = m;
  1482         } else {
  1483           _visitor->examine(e);
  1484         }
  1485       }
  1486       return n;
  1487     }
  1488 
  1489     /// \brief Processes the next node.
  1490     ///
  1491     /// Processes the next node and checks if the given target node
  1492     /// is reached. If the target node is reachable from the processed
  1493     /// node, then the \c reach parameter will be set to \c true.
  1494     ///
  1495     /// \param target The target node.
  1496     /// \retval reach Indicates if the target node is reached.
  1497     /// It should be initially \c false.
  1498     ///
  1499     /// \return The processed node.
  1500     ///
  1501     /// \pre The queue must not be empty.
  1502     Node processNextNode(Node target, bool& reach) {
  1503       Node n = _list[++_list_front];
  1504       _visitor->process(n);
  1505       Arc e;
  1506       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1507         Node m = _digraph->target(e);
  1508         if (!(*_reached)[m]) {
  1509           _visitor->discover(e);
  1510           _visitor->reach(m);
  1511           _reached->set(m, true);
  1512           _list[++_list_back] = m;
  1513           reach = reach || (target == m);
  1514         } else {
  1515           _visitor->examine(e);
  1516         }
  1517       }
  1518       return n;
  1519     }
  1520 
  1521     /// \brief Processes the next node.
  1522     ///
  1523     /// Processes the next node and checks if at least one of reached
  1524     /// nodes has \c true value in the \c nm node map. If one node
  1525     /// with \c true value is reachable from the processed node, then the
  1526     /// \c rnode parameter will be set to the first of such nodes.
  1527     ///
  1528     /// \param nm A \c bool (or convertible) node map that indicates the
  1529     /// possible targets.
  1530     /// \retval rnode The reached target node.
  1531     /// It should be initially \c INVALID.
  1532     ///
  1533     /// \return The processed node.
  1534     ///
  1535     /// \pre The queue must not be empty.
  1536     template <typename NM>
  1537     Node processNextNode(const NM& nm, Node& rnode) {
  1538       Node n = _list[++_list_front];
  1539       _visitor->process(n);
  1540       Arc e;
  1541       for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
  1542         Node m = _digraph->target(e);
  1543         if (!(*_reached)[m]) {
  1544           _visitor->discover(e);
  1545           _visitor->reach(m);
  1546           _reached->set(m, true);
  1547           _list[++_list_back] = m;
  1548           if (nm[m] && rnode == INVALID) rnode = m;
  1549         } else {
  1550           _visitor->examine(e);
  1551         }
  1552       }
  1553       return n;
  1554     }
  1555 
  1556     /// \brief The next node to be processed.
  1557     ///
  1558     /// Returns the next node to be processed or \c INVALID if the queue
  1559     /// is empty.
  1560     Node nextNode() const {
  1561       return _list_front != _list_back ? _list[_list_front + 1] : INVALID;
  1562     }
  1563 
  1564     /// \brief Returns \c false if there are nodes
  1565     /// to be processed.
  1566     ///
  1567     /// Returns \c false if there are nodes
  1568     /// to be processed in the queue.
  1569     bool emptyQueue() const { return _list_front == _list_back; }
  1570 
  1571     /// \brief Returns the number of the nodes to be processed.
  1572     ///
  1573     /// Returns the number of the nodes to be processed in the queue.
  1574     int queueSize() const { return _list_back - _list_front; }
  1575 
  1576     /// \brief Executes the algorithm.
  1577     ///
  1578     /// Executes the algorithm.
  1579     ///
  1580     /// This method runs the %BFS algorithm from the root node(s)
  1581     /// in order to compute the shortest path to each node.
  1582     ///
  1583     /// The algorithm computes
  1584     /// - the shortest path tree (forest),
  1585     /// - the distance of each node from the root(s).
  1586     ///
  1587     /// \pre init() must be called and at least one root node should be added
  1588     /// with addSource() before using this function.
  1589     ///
  1590     /// \note <tt>b.start()</tt> is just a shortcut of the following code.
  1591     /// \code
  1592     ///   while ( !b.emptyQueue() ) {
  1593     ///     b.processNextNode();
  1594     ///   }
  1595     /// \endcode
  1596     void start() {
  1597       while ( !emptyQueue() ) processNextNode();
  1598     }
  1599 
  1600     /// \brief Executes the algorithm until the given target node is reached.
  1601     ///
  1602     /// Executes the algorithm until the given target node is reached.
  1603     ///
  1604     /// This method runs the %BFS algorithm from the root node(s)
  1605     /// in order to compute the shortest path to \c t.
  1606     ///
  1607     /// The algorithm computes
  1608     /// - the shortest path to \c t,
  1609     /// - the distance of \c t from the root(s).
  1610     ///
  1611     /// \pre init() must be called and at least one root node should be
  1612     /// added with addSource() before using this function.
  1613     ///
  1614     /// \note <tt>b.start(t)</tt> is just a shortcut of the following code.
  1615     /// \code
  1616     ///   bool reach = false;
  1617     ///   while ( !b.emptyQueue() && !reach ) {
  1618     ///     b.processNextNode(t, reach);
  1619     ///   }
  1620     /// \endcode
  1621     void start(Node t) {
  1622       bool reach = false;
  1623       while ( !emptyQueue() && !reach ) processNextNode(t, reach);
  1624     }
  1625 
  1626     /// \brief Executes the algorithm until a condition is met.
  1627     ///
  1628     /// Executes the algorithm until a condition is met.
  1629     ///
  1630     /// This method runs the %BFS algorithm from the root node(s) in
  1631     /// order to compute the shortest path to a node \c v with
  1632     /// <tt>nm[v]</tt> true, if such a node can be found.
  1633     ///
  1634     /// \param nm must be a bool (or convertible) node map. The
  1635     /// algorithm will stop when it reaches a node \c v with
  1636     /// <tt>nm[v]</tt> true.
  1637     ///
  1638     /// \return The reached node \c v with <tt>nm[v]</tt> true or
  1639     /// \c INVALID if no such node was found.
  1640     ///
  1641     /// \pre init() must be called and at least one root node should be
  1642     /// added with addSource() before using this function.
  1643     ///
  1644     /// \note <tt>b.start(nm)</tt> is just a shortcut of the following code.
  1645     /// \code
  1646     ///   Node rnode = INVALID;
  1647     ///   while ( !b.emptyQueue() && rnode == INVALID ) {
  1648     ///     b.processNextNode(nm, rnode);
  1649     ///   }
  1650     ///   return rnode;
  1651     /// \endcode
  1652     template <typename NM>
  1653     Node start(const NM &nm) {
  1654       Node rnode = INVALID;
  1655       while ( !emptyQueue() && rnode == INVALID ) {
  1656         processNextNode(nm, rnode);
  1657       }
  1658       return rnode;
  1659     }
  1660 
  1661     /// \brief Runs the algorithm from the given source node.
  1662     ///
  1663     /// This method runs the %BFS algorithm from node \c s
  1664     /// in order to compute the shortest path to each node.
  1665     ///
  1666     /// The algorithm computes
  1667     /// - the shortest path tree,
  1668     /// - the distance of each node from the root.
  1669     ///
  1670     /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
  1671     ///\code
  1672     ///   b.init();
  1673     ///   b.addSource(s);
  1674     ///   b.start();
  1675     ///\endcode
  1676     void run(Node s) {
  1677       init();
  1678       addSource(s);
  1679       start();
  1680     }
  1681 
  1682     /// \brief Finds the shortest path between \c s and \c t.
  1683     ///
  1684     /// This method runs the %BFS algorithm from node \c s
  1685     /// in order to compute the shortest path to node \c t
  1686     /// (it stops searching when \c t is processed).
  1687     ///
  1688     /// \return \c true if \c t is reachable form \c s.
  1689     ///
  1690     /// \note Apart from the return value, <tt>b.run(s,t)</tt> is just a
  1691     /// shortcut of the following code.
  1692     ///\code
  1693     ///   b.init();
  1694     ///   b.addSource(s);
  1695     ///   b.start(t);
  1696     ///\endcode
  1697     bool run(Node s,Node t) {
  1698       init();
  1699       addSource(s);
  1700       start(t);
  1701       return reached(t);
  1702     }
  1703 
  1704     /// \brief Runs the algorithm to visit all nodes in the digraph.
  1705     ///
  1706     /// This method runs the %BFS algorithm in order to visit all nodes
  1707     /// in the digraph.
  1708     ///
  1709     /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
  1710     ///\code
  1711     ///  b.init();
  1712     ///  for (NodeIt n(gr); n != INVALID; ++n) {
  1713     ///    if (!b.reached(n)) {
  1714     ///      b.addSource(n);
  1715     ///      b.start();
  1716     ///    }
  1717     ///  }
  1718     ///\endcode
  1719     void run() {
  1720       init();
  1721       for (NodeIt it(*_digraph); it != INVALID; ++it) {
  1722         if (!reached(it)) {
  1723           addSource(it);
  1724           start();
  1725         }
  1726       }
  1727     }
  1728 
  1729     ///@}
  1730 
  1731     /// \name Query Functions
  1732     /// The results of the BFS algorithm can be obtained using these
  1733     /// functions.\n
  1734     /// Either \ref run(Node) "run()" or \ref start() should be called
  1735     /// before using them.
  1736 
  1737     ///@{
  1738 
  1739     /// \brief Checks if the given node is reached from the root(s).
  1740     ///
  1741     /// Returns \c true if \c v is reached from the root(s).
  1742     ///
  1743     /// \pre Either \ref run(Node) "run()" or \ref init()
  1744     /// must be called before using this function.
  1745     bool reached(Node v) const { return (*_reached)[v]; }
  1746 
  1747     ///@}
  1748 
  1749   };
  1750 
  1751 } //END OF NAMESPACE LEMON
  1752 
  1753 #endif