lemon/dfs.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 08 Dec 2008 15:18:04 +0000
changeset 423 ff48c2738fb2
parent 420 6a2a33ad261b
parent 419 9afe81e4c543
child 440 88ed40ad0d4f
permissions -rw-r--r--
Inline the test input files into the source code
     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_DFS_H
    20 #define LEMON_DFS_H
    21 
    22 ///\ingroup search
    23 ///\file
    24 ///\brief DFS 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 Dfs class.
    36 
    37   ///Default traits class of Dfs class.
    38   ///\tparam GR Digraph type.
    39   template<class GR>
    40   struct DfsDefaultTraits
    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 %DFS paths.
    47     ///
    48     ///The type of the map that stores the predecessor
    49     ///arcs of the %DFS paths.
    50     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
    51     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
    52     ///Instantiates a PredMap.
    53 
    54     ///This function instantiates a PredMap.
    55     ///\param g is the digraph, to which we would like to define the
    56     ///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 meet the \ref concepts::WriteMap "WriteMap" concept.
    66     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
    67     ///Instantiates a ProcessedMap.
    68 
    69     ///This function instantiates a ProcessedMap.
    70     ///\param g is the digraph, to which
    71     ///we would like to define the ProcessedMap
    72 #ifdef DOXYGEN
    73     static ProcessedMap *createProcessedMap(const Digraph &g)
    74 #else
    75     static ProcessedMap *createProcessedMap(const Digraph &)
    76 #endif
    77     {
    78       return new ProcessedMap();
    79     }
    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::ReadWriteMap "ReadWriteMap" concept.
    85     typedef typename Digraph::template NodeMap<bool> ReachedMap;
    86     ///Instantiates a ReachedMap.
    87 
    88     ///This function instantiates a ReachedMap.
    89     ///\param g is the digraph, to which
    90     ///we would like to define the ReachedMap.
    91     static ReachedMap *createReachedMap(const Digraph &g)
    92     {
    93       return new ReachedMap(g);
    94     }
    95 
    96     ///The type of the map that stores the distances of the nodes.
    97 
    98     ///The type of the map that stores the distances of the nodes.
    99     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   100     typedef typename Digraph::template NodeMap<int> DistMap;
   101     ///Instantiates a DistMap.
   102 
   103     ///This function instantiates a DistMap.
   104     ///\param g is the digraph, to which we would like to define the
   105     ///DistMap.
   106     static DistMap *createDistMap(const Digraph &g)
   107     {
   108       return new DistMap(g);
   109     }
   110   };
   111 
   112   ///%DFS algorithm class.
   113 
   114   ///\ingroup search
   115   ///This class provides an efficient implementation of the %DFS algorithm.
   116   ///
   117   ///There is also a \ref dfs() "function-type interface" for the DFS
   118   ///algorithm, which is convenient in the simplier cases and it can be
   119   ///used easier.
   120   ///
   121   ///\tparam GR The type of the digraph the algorithm runs on.
   122   ///The default type is \ref ListDigraph.
   123 #ifdef DOXYGEN
   124   template <typename GR,
   125             typename TR>
   126 #else
   127   template <typename GR=ListDigraph,
   128             typename TR=DfsDefaultTraits<GR> >
   129 #endif
   130   class Dfs {
   131   public:
   132 
   133     ///The type of the digraph the algorithm runs on.
   134     typedef typename TR::Digraph Digraph;
   135 
   136     ///\brief The type of the map that stores the predecessor arcs of the
   137     ///DFS paths.
   138     typedef typename TR::PredMap PredMap;
   139     ///The type of the map that stores the distances of the nodes.
   140     typedef typename TR::DistMap DistMap;
   141     ///The type of the map that indicates which nodes are reached.
   142     typedef typename TR::ReachedMap ReachedMap;
   143     ///The type of the map that indicates which nodes are processed.
   144     typedef typename TR::ProcessedMap ProcessedMap;
   145     ///The type of the paths.
   146     typedef PredMapPath<Digraph, PredMap> Path;
   147 
   148     ///The \ref DfsDefaultTraits "traits class" of the algorithm.
   149     typedef TR Traits;
   150 
   151   private:
   152 
   153     typedef typename Digraph::Node Node;
   154     typedef typename Digraph::NodeIt NodeIt;
   155     typedef typename Digraph::Arc Arc;
   156     typedef typename Digraph::OutArcIt OutArcIt;
   157 
   158     //Pointer to the underlying digraph.
   159     const Digraph *G;
   160     //Pointer to the map of predecessor arcs.
   161     PredMap *_pred;
   162     //Indicates if _pred is locally allocated (true) or not.
   163     bool local_pred;
   164     //Pointer to the map of distances.
   165     DistMap *_dist;
   166     //Indicates if _dist is locally allocated (true) or not.
   167     bool local_dist;
   168     //Pointer to the map of reached status of the nodes.
   169     ReachedMap *_reached;
   170     //Indicates if _reached is locally allocated (true) or not.
   171     bool local_reached;
   172     //Pointer to the map of processed status of the nodes.
   173     ProcessedMap *_processed;
   174     //Indicates if _processed is locally allocated (true) or not.
   175     bool local_processed;
   176 
   177     std::vector<typename Digraph::OutArcIt> _stack;
   178     int _stack_head;
   179 
   180     //Creates the maps if necessary.
   181     void create_maps()
   182     {
   183       if(!_pred) {
   184         local_pred = true;
   185         _pred = Traits::createPredMap(*G);
   186       }
   187       if(!_dist) {
   188         local_dist = true;
   189         _dist = Traits::createDistMap(*G);
   190       }
   191       if(!_reached) {
   192         local_reached = true;
   193         _reached = Traits::createReachedMap(*G);
   194       }
   195       if(!_processed) {
   196         local_processed = true;
   197         _processed = Traits::createProcessedMap(*G);
   198       }
   199     }
   200 
   201   protected:
   202 
   203     Dfs() {}
   204 
   205   public:
   206 
   207     typedef Dfs Create;
   208 
   209     ///\name Named template parameters
   210 
   211     ///@{
   212 
   213     template <class T>
   214     struct SetPredMapTraits : public Traits {
   215       typedef T PredMap;
   216       static PredMap *createPredMap(const Digraph &)
   217       {
   218         LEMON_ASSERT(false, "PredMap is not initialized");
   219         return 0; // ignore warnings
   220       }
   221     };
   222     ///\brief \ref named-templ-param "Named parameter" for setting
   223     ///PredMap type.
   224     ///
   225     ///\ref named-templ-param "Named parameter" for setting
   226     ///PredMap type.
   227     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   228     template <class T>
   229     struct SetPredMap : public Dfs<Digraph, SetPredMapTraits<T> > {
   230       typedef Dfs<Digraph, SetPredMapTraits<T> > Create;
   231     };
   232 
   233     template <class T>
   234     struct SetDistMapTraits : public Traits {
   235       typedef T DistMap;
   236       static DistMap *createDistMap(const Digraph &)
   237       {
   238         LEMON_ASSERT(false, "DistMap is not initialized");
   239         return 0; // ignore warnings
   240       }
   241     };
   242     ///\brief \ref named-templ-param "Named parameter" for setting
   243     ///DistMap type.
   244     ///
   245     ///\ref named-templ-param "Named parameter" for setting
   246     ///DistMap type.
   247     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   248     template <class T>
   249     struct SetDistMap : public Dfs< Digraph, SetDistMapTraits<T> > {
   250       typedef Dfs<Digraph, SetDistMapTraits<T> > Create;
   251     };
   252 
   253     template <class T>
   254     struct SetReachedMapTraits : public Traits {
   255       typedef T ReachedMap;
   256       static ReachedMap *createReachedMap(const Digraph &)
   257       {
   258         LEMON_ASSERT(false, "ReachedMap is not initialized");
   259         return 0; // ignore warnings
   260       }
   261     };
   262     ///\brief \ref named-templ-param "Named parameter" for setting
   263     ///ReachedMap type.
   264     ///
   265     ///\ref named-templ-param "Named parameter" for setting
   266     ///ReachedMap type.
   267     ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
   268     template <class T>
   269     struct SetReachedMap : public Dfs< Digraph, SetReachedMapTraits<T> > {
   270       typedef Dfs< Digraph, SetReachedMapTraits<T> > Create;
   271     };
   272 
   273     template <class T>
   274     struct SetProcessedMapTraits : public Traits {
   275       typedef T ProcessedMap;
   276       static ProcessedMap *createProcessedMap(const Digraph &)
   277       {
   278         LEMON_ASSERT(false, "ProcessedMap is not initialized");
   279         return 0; // ignore warnings
   280       }
   281     };
   282     ///\brief \ref named-templ-param "Named parameter" for setting
   283     ///ProcessedMap type.
   284     ///
   285     ///\ref named-templ-param "Named parameter" for setting
   286     ///ProcessedMap type.
   287     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   288     template <class T>
   289     struct SetProcessedMap : public Dfs< Digraph, SetProcessedMapTraits<T> > {
   290       typedef Dfs< Digraph, SetProcessedMapTraits<T> > Create;
   291     };
   292 
   293     struct SetStandardProcessedMapTraits : public Traits {
   294       typedef typename Digraph::template NodeMap<bool> ProcessedMap;
   295       static ProcessedMap *createProcessedMap(const Digraph &g)
   296       {
   297         return new ProcessedMap(g);
   298       }
   299     };
   300     ///\brief \ref named-templ-param "Named parameter" for setting
   301     ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   302     ///
   303     ///\ref named-templ-param "Named parameter" for setting
   304     ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
   305     ///If you don't set it explicitly, it will be automatically allocated.
   306     struct SetStandardProcessedMap :
   307       public Dfs< Digraph, SetStandardProcessedMapTraits > {
   308       typedef Dfs< Digraph, SetStandardProcessedMapTraits > Create;
   309     };
   310 
   311     ///@}
   312 
   313   public:
   314 
   315     ///Constructor.
   316 
   317     ///Constructor.
   318     ///\param g The digraph the algorithm runs on.
   319     Dfs(const Digraph &g) :
   320       G(&g),
   321       _pred(NULL), local_pred(false),
   322       _dist(NULL), local_dist(false),
   323       _reached(NULL), local_reached(false),
   324       _processed(NULL), local_processed(false)
   325     { }
   326 
   327     ///Destructor.
   328     ~Dfs()
   329     {
   330       if(local_pred) delete _pred;
   331       if(local_dist) delete _dist;
   332       if(local_reached) delete _reached;
   333       if(local_processed) delete _processed;
   334     }
   335 
   336     ///Sets the map that stores the predecessor arcs.
   337 
   338     ///Sets the map that stores the predecessor arcs.
   339     ///If you don't use this function before calling \ref run(Node) "run()"
   340     ///or \ref init(), an instance will be allocated automatically.
   341     ///The destructor deallocates this automatically allocated map,
   342     ///of course.
   343     ///\return <tt> (*this) </tt>
   344     Dfs &predMap(PredMap &m)
   345     {
   346       if(local_pred) {
   347         delete _pred;
   348         local_pred=false;
   349       }
   350       _pred = &m;
   351       return *this;
   352     }
   353 
   354     ///Sets the map that indicates which nodes are reached.
   355 
   356     ///Sets the map that indicates which nodes are reached.
   357     ///If you don't use this function before calling \ref run(Node) "run()"
   358     ///or \ref init(), an instance will be allocated automatically.
   359     ///The destructor deallocates this automatically allocated map,
   360     ///of course.
   361     ///\return <tt> (*this) </tt>
   362     Dfs &reachedMap(ReachedMap &m)
   363     {
   364       if(local_reached) {
   365         delete _reached;
   366         local_reached=false;
   367       }
   368       _reached = &m;
   369       return *this;
   370     }
   371 
   372     ///Sets the map that indicates which nodes are processed.
   373 
   374     ///Sets the map that indicates which nodes are processed.
   375     ///If you don't use this function before calling \ref run(Node) "run()"
   376     ///or \ref init(), an instance will be allocated automatically.
   377     ///The destructor deallocates this automatically allocated map,
   378     ///of course.
   379     ///\return <tt> (*this) </tt>
   380     Dfs &processedMap(ProcessedMap &m)
   381     {
   382       if(local_processed) {
   383         delete _processed;
   384         local_processed=false;
   385       }
   386       _processed = &m;
   387       return *this;
   388     }
   389 
   390     ///Sets the map that stores the distances of the nodes.
   391 
   392     ///Sets the map that stores the distances of the nodes calculated by
   393     ///the algorithm.
   394     ///If you don't use this function before calling \ref run(Node) "run()"
   395     ///or \ref init(), an instance will be allocated automatically.
   396     ///The destructor deallocates this automatically allocated map,
   397     ///of course.
   398     ///\return <tt> (*this) </tt>
   399     Dfs &distMap(DistMap &m)
   400     {
   401       if(local_dist) {
   402         delete _dist;
   403         local_dist=false;
   404       }
   405       _dist = &m;
   406       return *this;
   407     }
   408 
   409   public:
   410 
   411     ///\name Execution Control
   412     ///The simplest way to execute the DFS algorithm is to use one of the
   413     ///member functions called \ref run(Node) "run()".\n
   414     ///If you need more control on the execution, first you have to call
   415     ///\ref init(), then you can add a source node with \ref addSource()
   416     ///and perform the actual computation with \ref start().
   417     ///This procedure can be repeated if there are nodes that have not
   418     ///been reached.
   419 
   420     ///@{
   421 
   422     ///\brief Initializes the internal data structures.
   423     ///
   424     ///Initializes the internal data structures.
   425     void init()
   426     {
   427       create_maps();
   428       _stack.resize(countNodes(*G));
   429       _stack_head=-1;
   430       for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
   431         _pred->set(u,INVALID);
   432         _reached->set(u,false);
   433         _processed->set(u,false);
   434       }
   435     }
   436 
   437     ///Adds a new source node.
   438 
   439     ///Adds a new source node to the set of nodes to be processed.
   440     ///
   441     ///\pre The stack must be empty. Otherwise the algorithm gives
   442     ///wrong results. (One of the outgoing arcs of all the source nodes
   443     ///except for the last one will not be visited and distances will
   444     ///also be wrong.)
   445     void addSource(Node s)
   446     {
   447       LEMON_DEBUG(emptyQueue(), "The stack is not empty.");
   448       if(!(*_reached)[s])
   449         {
   450           _reached->set(s,true);
   451           _pred->set(s,INVALID);
   452           OutArcIt e(*G,s);
   453           if(e!=INVALID) {
   454             _stack[++_stack_head]=e;
   455             _dist->set(s,_stack_head);
   456           }
   457           else {
   458             _processed->set(s,true);
   459             _dist->set(s,0);
   460           }
   461         }
   462     }
   463 
   464     ///Processes the next arc.
   465 
   466     ///Processes the next arc.
   467     ///
   468     ///\return The processed arc.
   469     ///
   470     ///\pre The stack must not be empty.
   471     Arc processNextArc()
   472     {
   473       Node m;
   474       Arc e=_stack[_stack_head];
   475       if(!(*_reached)[m=G->target(e)]) {
   476         _pred->set(m,e);
   477         _reached->set(m,true);
   478         ++_stack_head;
   479         _stack[_stack_head] = OutArcIt(*G, m);
   480         _dist->set(m,_stack_head);
   481       }
   482       else {
   483         m=G->source(e);
   484         ++_stack[_stack_head];
   485       }
   486       while(_stack_head>=0 && _stack[_stack_head]==INVALID) {
   487         _processed->set(m,true);
   488         --_stack_head;
   489         if(_stack_head>=0) {
   490           m=G->source(_stack[_stack_head]);
   491           ++_stack[_stack_head];
   492         }
   493       }
   494       return e;
   495     }
   496 
   497     ///Next arc to be processed.
   498 
   499     ///Next arc to be processed.
   500     ///
   501     ///\return The next arc to be processed or \c INVALID if the stack
   502     ///is empty.
   503     OutArcIt nextArc() const
   504     {
   505       return _stack_head>=0?_stack[_stack_head]:INVALID;
   506     }
   507 
   508     ///Returns \c false if there are nodes to be processed.
   509 
   510     ///Returns \c false if there are nodes to be processed
   511     ///in the queue (stack).
   512     bool emptyQueue() const { return _stack_head<0; }
   513 
   514     ///Returns the number of the nodes to be processed.
   515 
   516     ///Returns the number of the nodes to be processed
   517     ///in the queue (stack).
   518     int queueSize() const { return _stack_head+1; }
   519 
   520     ///Executes the algorithm.
   521 
   522     ///Executes the algorithm.
   523     ///
   524     ///This method runs the %DFS algorithm from the root node
   525     ///in order to compute the DFS path to each node.
   526     ///
   527     /// The algorithm computes
   528     ///- the %DFS tree,
   529     ///- the distance of each node from the root in the %DFS tree.
   530     ///
   531     ///\pre init() must be called and a root node should be
   532     ///added with addSource() before using this function.
   533     ///
   534     ///\note <tt>d.start()</tt> is just a shortcut of the following code.
   535     ///\code
   536     ///  while ( !d.emptyQueue() ) {
   537     ///    d.processNextArc();
   538     ///  }
   539     ///\endcode
   540     void start()
   541     {
   542       while ( !emptyQueue() ) processNextArc();
   543     }
   544 
   545     ///Executes the algorithm until the given target node is reached.
   546 
   547     ///Executes the algorithm until the given target node is reached.
   548     ///
   549     ///This method runs the %DFS algorithm from the root node
   550     ///in order to compute the DFS path to \c t.
   551     ///
   552     ///The algorithm computes
   553     ///- the %DFS path to \c t,
   554     ///- the distance of \c t from the root in the %DFS tree.
   555     ///
   556     ///\pre init() must be called and a root node should be
   557     ///added with addSource() before using this function.
   558     void start(Node t)
   559     {
   560       while ( !emptyQueue() && G->target(_stack[_stack_head])!=t )
   561         processNextArc();
   562     }
   563 
   564     ///Executes the algorithm until a condition is met.
   565 
   566     ///Executes the algorithm until a condition is met.
   567     ///
   568     ///This method runs the %DFS algorithm from the root node
   569     ///until an arc \c a with <tt>am[a]</tt> true is found.
   570     ///
   571     ///\param am A \c bool (or convertible) arc map. The algorithm
   572     ///will stop when it reaches an arc \c a with <tt>am[a]</tt> true.
   573     ///
   574     ///\return The reached arc \c a with <tt>am[a]</tt> true or
   575     ///\c INVALID if no such arc was found.
   576     ///
   577     ///\pre init() must be called and a root node should be
   578     ///added with addSource() before using this function.
   579     ///
   580     ///\warning Contrary to \ref Bfs and \ref Dijkstra, \c am is an arc map,
   581     ///not a node map.
   582     template<class ArcBoolMap>
   583     Arc start(const ArcBoolMap &am)
   584     {
   585       while ( !emptyQueue() && !am[_stack[_stack_head]] )
   586         processNextArc();
   587       return emptyQueue() ? INVALID : _stack[_stack_head];
   588     }
   589 
   590     ///Runs the algorithm from the given source node.
   591 
   592     ///This method runs the %DFS algorithm from node \c s
   593     ///in order to compute the DFS path to each node.
   594     ///
   595     ///The algorithm computes
   596     ///- the %DFS tree,
   597     ///- the distance of each node from the root in the %DFS tree.
   598     ///
   599     ///\note <tt>d.run(s)</tt> is just a shortcut of the following code.
   600     ///\code
   601     ///  d.init();
   602     ///  d.addSource(s);
   603     ///  d.start();
   604     ///\endcode
   605     void run(Node s) {
   606       init();
   607       addSource(s);
   608       start();
   609     }
   610 
   611     ///Finds the %DFS path between \c s and \c t.
   612 
   613     ///This method runs the %DFS algorithm from node \c s
   614     ///in order to compute the DFS path to node \c t
   615     ///(it stops searching when \c t is processed)
   616     ///
   617     ///\return \c true if \c t is reachable form \c s.
   618     ///
   619     ///\note Apart from the return value, <tt>d.run(s,t)</tt> is
   620     ///just a shortcut of the following code.
   621     ///\code
   622     ///  d.init();
   623     ///  d.addSource(s);
   624     ///  d.start(t);
   625     ///\endcode
   626     bool run(Node s,Node t) {
   627       init();
   628       addSource(s);
   629       start(t);
   630       return reached(t);
   631     }
   632 
   633     ///Runs the algorithm to visit all nodes in the digraph.
   634 
   635     ///This method runs the %DFS algorithm in order to compute the
   636     ///%DFS path to each node.
   637     ///
   638     ///The algorithm computes
   639     ///- the %DFS tree (forest),
   640     ///- the distance of each node from the root(s) in the %DFS tree.
   641     ///
   642     ///\note <tt>d.run()</tt> is just a shortcut of the following code.
   643     ///\code
   644     ///  d.init();
   645     ///  for (NodeIt n(digraph); n != INVALID; ++n) {
   646     ///    if (!d.reached(n)) {
   647     ///      d.addSource(n);
   648     ///      d.start();
   649     ///    }
   650     ///  }
   651     ///\endcode
   652     void run() {
   653       init();
   654       for (NodeIt it(*G); it != INVALID; ++it) {
   655         if (!reached(it)) {
   656           addSource(it);
   657           start();
   658         }
   659       }
   660     }
   661 
   662     ///@}
   663 
   664     ///\name Query Functions
   665     ///The results of the DFS algorithm can be obtained using these
   666     ///functions.\n
   667     ///Either \ref run(Node) "run()" or \ref start() should be called
   668     ///before using them.
   669 
   670     ///@{
   671 
   672     ///The DFS path to a node.
   673 
   674     ///Returns the DFS path to a node.
   675     ///
   676     ///\warning \c t should be reached from the root(s).
   677     ///
   678     ///\pre Either \ref run(Node) "run()" or \ref init()
   679     ///must be called before using this function.
   680     Path path(Node t) const { return Path(*G, *_pred, t); }
   681 
   682     ///The distance of a node from the root(s).
   683 
   684     ///Returns the distance of a node from the root(s).
   685     ///
   686     ///\warning If node \c v is not reached from the root(s), then
   687     ///the return value of this function is undefined.
   688     ///
   689     ///\pre Either \ref run(Node) "run()" or \ref init()
   690     ///must be called before using this function.
   691     int dist(Node v) const { return (*_dist)[v]; }
   692 
   693     ///Returns the 'previous arc' of the %DFS tree for a node.
   694 
   695     ///This function returns the 'previous arc' of the %DFS tree for the
   696     ///node \c v, i.e. it returns the last arc of a %DFS path from a
   697     ///root to \c v. It is \c INVALID if \c v is not reached from the
   698     ///root(s) or if \c v is a root.
   699     ///
   700     ///The %DFS tree used here is equal to the %DFS tree used in
   701     ///\ref predNode().
   702     ///
   703     ///\pre Either \ref run(Node) "run()" or \ref init()
   704     ///must be called before using this function.
   705     Arc predArc(Node v) const { return (*_pred)[v];}
   706 
   707     ///Returns the 'previous node' of the %DFS tree.
   708 
   709     ///This function returns the 'previous node' of the %DFS
   710     ///tree for the node \c v, i.e. it returns the last but one node
   711     ///from a %DFS path from a root to \c v. It is \c INVALID
   712     ///if \c v is not reached from the root(s) or if \c v is a root.
   713     ///
   714     ///The %DFS tree used here is equal to the %DFS tree used in
   715     ///\ref predArc().
   716     ///
   717     ///\pre Either \ref run(Node) "run()" or \ref init()
   718     ///must be called before using this function.
   719     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
   720                                   G->source((*_pred)[v]); }
   721 
   722     ///\brief Returns a const reference to the node map that stores the
   723     ///distances of the nodes.
   724     ///
   725     ///Returns a const reference to the node map that stores the
   726     ///distances of the nodes calculated by the algorithm.
   727     ///
   728     ///\pre Either \ref run(Node) "run()" or \ref init()
   729     ///must be called before using this function.
   730     const DistMap &distMap() const { return *_dist;}
   731 
   732     ///\brief Returns a const reference to the node map that stores the
   733     ///predecessor arcs.
   734     ///
   735     ///Returns a const reference to the node map that stores the predecessor
   736     ///arcs, which form the DFS tree.
   737     ///
   738     ///\pre Either \ref run(Node) "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 reached from the root(s).
   743 
   744     ///Returns \c true if \c v is reached from the root(s).
   745     ///
   746     ///\pre Either \ref run(Node) "run()" or \ref init()
   747     ///must be called before using this function.
   748     bool reached(Node v) const { return (*_reached)[v]; }
   749 
   750     ///@}
   751   };
   752 
   753   ///Default traits class of dfs() function.
   754 
   755   ///Default traits class of dfs() function.
   756   ///\tparam GR Digraph type.
   757   template<class GR>
   758   struct DfsWizardDefaultTraits
   759   {
   760     ///The type of the digraph the algorithm runs on.
   761     typedef GR Digraph;
   762 
   763     ///\brief The type of the map that stores the predecessor
   764     ///arcs of the %DFS paths.
   765     ///
   766     ///The type of the map that stores the predecessor
   767     ///arcs of the %DFS paths.
   768     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   769     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
   770     ///Instantiates a PredMap.
   771 
   772     ///This function instantiates a PredMap.
   773     ///\param g is the digraph, to which we would like to define the
   774     ///PredMap.
   775     static PredMap *createPredMap(const Digraph &g)
   776     {
   777       return new PredMap(g);
   778     }
   779 
   780     ///The type of the map that indicates which nodes are processed.
   781 
   782     ///The type of the map that indicates which nodes are processed.
   783     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   784     ///By default it is a NullMap.
   785     typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
   786     ///Instantiates a ProcessedMap.
   787 
   788     ///This function instantiates a ProcessedMap.
   789     ///\param g is the digraph, to which
   790     ///we would like to define the ProcessedMap.
   791 #ifdef DOXYGEN
   792     static ProcessedMap *createProcessedMap(const Digraph &g)
   793 #else
   794     static ProcessedMap *createProcessedMap(const Digraph &)
   795 #endif
   796     {
   797       return new ProcessedMap();
   798     }
   799 
   800     ///The type of the map that indicates which nodes are reached.
   801 
   802     ///The type of the map that indicates which nodes are reached.
   803     ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
   804     typedef typename Digraph::template NodeMap<bool> ReachedMap;
   805     ///Instantiates a ReachedMap.
   806 
   807     ///This function instantiates a ReachedMap.
   808     ///\param g is the digraph, to which
   809     ///we would like to define the ReachedMap.
   810     static ReachedMap *createReachedMap(const Digraph &g)
   811     {
   812       return new ReachedMap(g);
   813     }
   814 
   815     ///The type of the map that stores the distances of the nodes.
   816 
   817     ///The type of the map that stores the distances of the nodes.
   818     ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
   819     typedef typename Digraph::template NodeMap<int> DistMap;
   820     ///Instantiates a DistMap.
   821 
   822     ///This function instantiates a DistMap.
   823     ///\param g is the digraph, to which we would like to define
   824     ///the DistMap
   825     static DistMap *createDistMap(const Digraph &g)
   826     {
   827       return new DistMap(g);
   828     }
   829 
   830     ///The type of the DFS paths.
   831 
   832     ///The type of the DFS paths.
   833     ///It must meet the \ref concepts::Path "Path" concept.
   834     typedef lemon::Path<Digraph> Path;
   835   };
   836 
   837   /// Default traits class used by DfsWizard
   838 
   839   /// To make it easier to use Dfs algorithm
   840   /// we have created a wizard class.
   841   /// This \ref DfsWizard class needs default traits,
   842   /// as well as the \ref Dfs class.
   843   /// The \ref DfsWizardBase is a class to be the default traits of the
   844   /// \ref DfsWizard class.
   845   template<class GR>
   846   class DfsWizardBase : public DfsWizardDefaultTraits<GR>
   847   {
   848 
   849     typedef DfsWizardDefaultTraits<GR> Base;
   850   protected:
   851     //The type of the nodes in the digraph.
   852     typedef typename Base::Digraph::Node Node;
   853 
   854     //Pointer to the digraph the algorithm runs on.
   855     void *_g;
   856     //Pointer to the map of reached nodes.
   857     void *_reached;
   858     //Pointer to the map of processed nodes.
   859     void *_processed;
   860     //Pointer to the map of predecessors arcs.
   861     void *_pred;
   862     //Pointer to the map of distances.
   863     void *_dist;
   864     //Pointer to the DFS path to the target node.
   865     void *_path;
   866     //Pointer to the distance of the target node.
   867     int *_di;
   868 
   869     public:
   870     /// Constructor.
   871 
   872     /// This constructor does not require parameters, therefore it initiates
   873     /// all of the attributes to \c 0.
   874     DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
   875                       _dist(0), _path(0), _di(0) {}
   876 
   877     /// Constructor.
   878 
   879     /// This constructor requires one parameter,
   880     /// others are initiated to \c 0.
   881     /// \param g The digraph the algorithm runs on.
   882     DfsWizardBase(const GR &g) :
   883       _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
   884       _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
   885 
   886   };
   887 
   888   /// Auxiliary class for the function-type interface of DFS algorithm.
   889 
   890   /// This auxiliary class is created to implement the
   891   /// \ref dfs() "function-type interface" of \ref Dfs algorithm.
   892   /// It does not have own \ref run(Node) "run()" method, it uses the
   893   /// functions and features of the plain \ref Dfs.
   894   ///
   895   /// This class should only be used through the \ref dfs() function,
   896   /// which makes it easier to use the algorithm.
   897   template<class TR>
   898   class DfsWizard : public TR
   899   {
   900     typedef TR Base;
   901 
   902     ///The type of the digraph the algorithm runs on.
   903     typedef typename TR::Digraph Digraph;
   904 
   905     typedef typename Digraph::Node Node;
   906     typedef typename Digraph::NodeIt NodeIt;
   907     typedef typename Digraph::Arc Arc;
   908     typedef typename Digraph::OutArcIt OutArcIt;
   909 
   910     ///\brief The type of the map that stores the predecessor
   911     ///arcs of the DFS paths.
   912     typedef typename TR::PredMap PredMap;
   913     ///\brief The type of the map that stores the distances of the nodes.
   914     typedef typename TR::DistMap DistMap;
   915     ///\brief The type of the map that indicates which nodes are reached.
   916     typedef typename TR::ReachedMap ReachedMap;
   917     ///\brief The type of the map that indicates which nodes are processed.
   918     typedef typename TR::ProcessedMap ProcessedMap;
   919     ///The type of the DFS paths
   920     typedef typename TR::Path Path;
   921 
   922   public:
   923 
   924     /// Constructor.
   925     DfsWizard() : TR() {}
   926 
   927     /// Constructor that requires parameters.
   928 
   929     /// Constructor that requires parameters.
   930     /// These parameters will be the default values for the traits class.
   931     /// \param g The digraph the algorithm runs on.
   932     DfsWizard(const Digraph &g) :
   933       TR(g) {}
   934 
   935     ///Copy constructor
   936     DfsWizard(const TR &b) : TR(b) {}
   937 
   938     ~DfsWizard() {}
   939 
   940     ///Runs DFS algorithm from the given source node.
   941 
   942     ///This method runs DFS algorithm from node \c s
   943     ///in order to compute the DFS path to each node.
   944     void run(Node s)
   945     {
   946       Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
   947       if (Base::_pred)
   948         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
   949       if (Base::_dist)
   950         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
   951       if (Base::_reached)
   952         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
   953       if (Base::_processed)
   954         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
   955       if (s!=INVALID)
   956         alg.run(s);
   957       else
   958         alg.run();
   959     }
   960 
   961     ///Finds the DFS path between \c s and \c t.
   962 
   963     ///This method runs DFS algorithm from node \c s
   964     ///in order to compute the DFS path to node \c t
   965     ///(it stops searching when \c t is processed).
   966     ///
   967     ///\return \c true if \c t is reachable form \c s.
   968     bool run(Node s, Node t)
   969     {
   970       Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
   971       if (Base::_pred)
   972         alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
   973       if (Base::_dist)
   974         alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
   975       if (Base::_reached)
   976         alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
   977       if (Base::_processed)
   978         alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
   979       alg.run(s,t);
   980       if (Base::_path)
   981         *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
   982       if (Base::_di)
   983         *Base::_di = alg.dist(t);
   984       return alg.reached(t);
   985       }
   986 
   987     ///Runs DFS algorithm to visit all nodes in the digraph.
   988 
   989     ///This method runs DFS algorithm in order to compute
   990     ///the DFS path to each node.
   991     void run()
   992     {
   993       run(INVALID);
   994     }
   995 
   996     template<class T>
   997     struct SetPredMapBase : public Base {
   998       typedef T PredMap;
   999       static PredMap *createPredMap(const Digraph &) { return 0; };
  1000       SetPredMapBase(const TR &b) : TR(b) {}
  1001     };
  1002     ///\brief \ref named-func-param "Named parameter"
  1003     ///for setting PredMap object.
  1004     ///
  1005     ///\ref named-func-param "Named parameter"
  1006     ///for setting PredMap object.
  1007     template<class T>
  1008     DfsWizard<SetPredMapBase<T> > predMap(const T &t)
  1009     {
  1010       Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
  1011       return DfsWizard<SetPredMapBase<T> >(*this);
  1012     }
  1013 
  1014     template<class T>
  1015     struct SetReachedMapBase : public Base {
  1016       typedef T ReachedMap;
  1017       static ReachedMap *createReachedMap(const Digraph &) { return 0; };
  1018       SetReachedMapBase(const TR &b) : TR(b) {}
  1019     };
  1020     ///\brief \ref named-func-param "Named parameter"
  1021     ///for setting ReachedMap object.
  1022     ///
  1023     /// \ref named-func-param "Named parameter"
  1024     ///for setting ReachedMap object.
  1025     template<class T>
  1026     DfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
  1027     {
  1028       Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
  1029       return DfsWizard<SetReachedMapBase<T> >(*this);
  1030     }
  1031 
  1032     template<class T>
  1033     struct SetDistMapBase : public Base {
  1034       typedef T DistMap;
  1035       static DistMap *createDistMap(const Digraph &) { return 0; };
  1036       SetDistMapBase(const TR &b) : TR(b) {}
  1037     };
  1038     ///\brief \ref named-func-param "Named parameter"
  1039     ///for setting DistMap object.
  1040     ///
  1041     /// \ref named-func-param "Named parameter"
  1042     ///for setting DistMap object.
  1043     template<class T>
  1044     DfsWizard<SetDistMapBase<T> > distMap(const T &t)
  1045     {
  1046       Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
  1047       return DfsWizard<SetDistMapBase<T> >(*this);
  1048     }
  1049 
  1050     template<class T>
  1051     struct SetProcessedMapBase : public Base {
  1052       typedef T ProcessedMap;
  1053       static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
  1054       SetProcessedMapBase(const TR &b) : TR(b) {}
  1055     };
  1056     ///\brief \ref named-func-param "Named parameter"
  1057     ///for setting ProcessedMap object.
  1058     ///
  1059     /// \ref named-func-param "Named parameter"
  1060     ///for setting ProcessedMap object.
  1061     template<class T>
  1062     DfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
  1063     {
  1064       Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
  1065       return DfsWizard<SetProcessedMapBase<T> >(*this);
  1066     }
  1067 
  1068     template<class T>
  1069     struct SetPathBase : public Base {
  1070       typedef T Path;
  1071       SetPathBase(const TR &b) : TR(b) {}
  1072     };
  1073     ///\brief \ref named-func-param "Named parameter"
  1074     ///for getting the DFS path to the target node.
  1075     ///
  1076     ///\ref named-func-param "Named parameter"
  1077     ///for getting the DFS path to the target node.
  1078     template<class T>
  1079     DfsWizard<SetPathBase<T> > path(const T &t)
  1080     {
  1081       Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
  1082       return DfsWizard<SetPathBase<T> >(*this);
  1083     }
  1084 
  1085     ///\brief \ref named-func-param "Named parameter"
  1086     ///for getting the distance of the target node.
  1087     ///
  1088     ///\ref named-func-param "Named parameter"
  1089     ///for getting the distance of the target node.
  1090     DfsWizard dist(const int &d)
  1091     {
  1092       Base::_di=const_cast<int*>(&d);
  1093       return *this;
  1094     }
  1095 
  1096   };
  1097 
  1098   ///Function-type interface for DFS algorithm.
  1099 
  1100   ///\ingroup search
  1101   ///Function-type interface for DFS algorithm.
  1102   ///
  1103   ///This function also has several \ref named-func-param "named parameters",
  1104   ///they are declared as the members of class \ref DfsWizard.
  1105   ///The following examples show how to use these parameters.
  1106   ///\code
  1107   ///  // Compute the DFS tree
  1108   ///  dfs(g).predMap(preds).distMap(dists).run(s);
  1109   ///
  1110   ///  // Compute the DFS path from s to t
  1111   ///  bool reached = dfs(g).path(p).dist(d).run(s,t);
  1112   ///\endcode
  1113   ///\warning Don't forget to put the \ref DfsWizard::run(Node) "run()"
  1114   ///to the end of the parameter list.
  1115   ///\sa DfsWizard
  1116   ///\sa Dfs
  1117   template<class GR>
  1118   DfsWizard<DfsWizardBase<GR> >
  1119   dfs(const GR &digraph)
  1120   {
  1121     return DfsWizard<DfsWizardBase<GR> >(digraph);
  1122   }
  1123 
  1124 #ifdef DOXYGEN
  1125   /// \brief Visitor class for DFS.
  1126   ///
  1127   /// This class defines the interface of the DfsVisit events, and
  1128   /// it could be the base of a real visitor class.
  1129   template <typename _Digraph>
  1130   struct DfsVisitor {
  1131     typedef _Digraph Digraph;
  1132     typedef typename Digraph::Arc Arc;
  1133     typedef typename Digraph::Node Node;
  1134     /// \brief Called for the source node of the DFS.
  1135     ///
  1136     /// This function is called for the source node of the DFS.
  1137     void start(const Node& node) {}
  1138     /// \brief Called when the source node is leaved.
  1139     ///
  1140     /// This function is called when the source node is leaved.
  1141     void stop(const Node& node) {}
  1142     /// \brief Called when a node is reached first time.
  1143     ///
  1144     /// This function is called when a node is reached first time.
  1145     void reach(const Node& node) {}
  1146     /// \brief Called when an arc reaches a new node.
  1147     ///
  1148     /// This function is called when the DFS finds an arc whose target node
  1149     /// is not reached yet.
  1150     void discover(const Arc& arc) {}
  1151     /// \brief Called when an arc is examined but its target node is
  1152     /// already discovered.
  1153     ///
  1154     /// This function is called when an arc is examined but its target node is
  1155     /// already discovered.
  1156     void examine(const Arc& arc) {}
  1157     /// \brief Called when the DFS steps back from a node.
  1158     ///
  1159     /// This function is called when the DFS steps back from a node.
  1160     void leave(const Node& node) {}
  1161     /// \brief Called when the DFS steps back on an arc.
  1162     ///
  1163     /// This function is called when the DFS steps back on an arc.
  1164     void backtrack(const Arc& arc) {}
  1165   };
  1166 #else
  1167   template <typename _Digraph>
  1168   struct DfsVisitor {
  1169     typedef _Digraph Digraph;
  1170     typedef typename Digraph::Arc Arc;
  1171     typedef typename Digraph::Node Node;
  1172     void start(const Node&) {}
  1173     void stop(const Node&) {}
  1174     void reach(const Node&) {}
  1175     void discover(const Arc&) {}
  1176     void examine(const Arc&) {}
  1177     void leave(const Node&) {}
  1178     void backtrack(const Arc&) {}
  1179 
  1180     template <typename _Visitor>
  1181     struct Constraints {
  1182       void constraints() {
  1183         Arc arc;
  1184         Node node;
  1185         visitor.start(node);
  1186         visitor.stop(arc);
  1187         visitor.reach(node);
  1188         visitor.discover(arc);
  1189         visitor.examine(arc);
  1190         visitor.leave(node);
  1191         visitor.backtrack(arc);
  1192       }
  1193       _Visitor& visitor;
  1194     };
  1195   };
  1196 #endif
  1197 
  1198   /// \brief Default traits class of DfsVisit class.
  1199   ///
  1200   /// Default traits class of DfsVisit class.
  1201   /// \tparam _Digraph The type of the digraph the algorithm runs on.
  1202   template<class _Digraph>
  1203   struct DfsVisitDefaultTraits {
  1204 
  1205     /// \brief The type of the digraph the algorithm runs on.
  1206     typedef _Digraph Digraph;
  1207 
  1208     /// \brief The type of the map that indicates which nodes are reached.
  1209     ///
  1210     /// The type of the map that indicates which nodes are reached.
  1211     /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
  1212     typedef typename Digraph::template NodeMap<bool> ReachedMap;
  1213 
  1214     /// \brief Instantiates a ReachedMap.
  1215     ///
  1216     /// This function instantiates a ReachedMap.
  1217     /// \param digraph is the digraph, to which
  1218     /// we would like to define the ReachedMap.
  1219     static ReachedMap *createReachedMap(const Digraph &digraph) {
  1220       return new ReachedMap(digraph);
  1221     }
  1222 
  1223   };
  1224 
  1225   /// \ingroup search
  1226   ///
  1227   /// \brief %DFS algorithm class with visitor interface.
  1228   ///
  1229   /// This class provides an efficient implementation of the %DFS algorithm
  1230   /// with visitor interface.
  1231   ///
  1232   /// The %DfsVisit class provides an alternative interface to the Dfs
  1233   /// class. It works with callback mechanism, the DfsVisit object calls
  1234   /// the member functions of the \c Visitor class on every DFS event.
  1235   ///
  1236   /// This interface of the DFS algorithm should be used in special cases
  1237   /// when extra actions have to be performed in connection with certain
  1238   /// events of the DFS algorithm. Otherwise consider to use Dfs or dfs()
  1239   /// instead.
  1240   ///
  1241   /// \tparam _Digraph The type of the digraph the algorithm runs on.
  1242   /// The default value is
  1243   /// \ref ListDigraph. The value of _Digraph is not used directly by
  1244   /// \ref DfsVisit, it is only passed to \ref DfsVisitDefaultTraits.
  1245   /// \tparam _Visitor The Visitor type that is used by the algorithm.
  1246   /// \ref DfsVisitor "DfsVisitor<_Digraph>" is an empty visitor, which
  1247   /// does not observe the DFS events. If you want to observe the DFS
  1248   /// events, you should implement your own visitor class.
  1249   /// \tparam _Traits Traits class to set various data types used by the
  1250   /// algorithm. The default traits class is
  1251   /// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<_Digraph>".
  1252   /// See \ref DfsVisitDefaultTraits for the documentation of
  1253   /// a DFS visit traits class.
  1254 #ifdef DOXYGEN
  1255   template <typename _Digraph, typename _Visitor, typename _Traits>
  1256 #else
  1257   template <typename _Digraph = ListDigraph,
  1258             typename _Visitor = DfsVisitor<_Digraph>,
  1259             typename _Traits = DfsVisitDefaultTraits<_Digraph> >
  1260 #endif
  1261   class DfsVisit {
  1262   public:
  1263 
  1264     ///The traits class.
  1265     typedef _Traits Traits;
  1266 
  1267     ///The type of the digraph the algorithm runs on.
  1268     typedef typename Traits::Digraph Digraph;
  1269 
  1270     ///The visitor type used by the algorithm.
  1271     typedef _Visitor Visitor;
  1272 
  1273     ///The type of the map that indicates which nodes are reached.
  1274     typedef typename Traits::ReachedMap ReachedMap;
  1275 
  1276   private:
  1277 
  1278     typedef typename Digraph::Node Node;
  1279     typedef typename Digraph::NodeIt NodeIt;
  1280     typedef typename Digraph::Arc Arc;
  1281     typedef typename Digraph::OutArcIt OutArcIt;
  1282 
  1283     //Pointer to the underlying digraph.
  1284     const Digraph *_digraph;
  1285     //Pointer to the visitor object.
  1286     Visitor *_visitor;
  1287     //Pointer to the map of reached status of the nodes.
  1288     ReachedMap *_reached;
  1289     //Indicates if _reached is locally allocated (true) or not.
  1290     bool local_reached;
  1291 
  1292     std::vector<typename Digraph::Arc> _stack;
  1293     int _stack_head;
  1294 
  1295     //Creates the maps if necessary.
  1296     void create_maps() {
  1297       if(!_reached) {
  1298         local_reached = true;
  1299         _reached = Traits::createReachedMap(*_digraph);
  1300       }
  1301     }
  1302 
  1303   protected:
  1304 
  1305     DfsVisit() {}
  1306 
  1307   public:
  1308 
  1309     typedef DfsVisit Create;
  1310 
  1311     /// \name Named Template Parameters
  1312 
  1313     ///@{
  1314     template <class T>
  1315     struct SetReachedMapTraits : public Traits {
  1316       typedef T ReachedMap;
  1317       static ReachedMap *createReachedMap(const Digraph &digraph) {
  1318         LEMON_ASSERT(false, "ReachedMap is not initialized");
  1319         return 0; // ignore warnings
  1320       }
  1321     };
  1322     /// \brief \ref named-templ-param "Named parameter" for setting
  1323     /// ReachedMap type.
  1324     ///
  1325     /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
  1326     template <class T>
  1327     struct SetReachedMap : public DfsVisit< Digraph, Visitor,
  1328                                             SetReachedMapTraits<T> > {
  1329       typedef DfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
  1330     };
  1331     ///@}
  1332 
  1333   public:
  1334 
  1335     /// \brief Constructor.
  1336     ///
  1337     /// Constructor.
  1338     ///
  1339     /// \param digraph The digraph the algorithm runs on.
  1340     /// \param visitor The visitor object of the algorithm.
  1341     DfsVisit(const Digraph& digraph, Visitor& visitor)
  1342       : _digraph(&digraph), _visitor(&visitor),
  1343         _reached(0), local_reached(false) {}
  1344 
  1345     /// \brief Destructor.
  1346     ~DfsVisit() {
  1347       if(local_reached) delete _reached;
  1348     }
  1349 
  1350     /// \brief Sets the map that indicates which nodes are reached.
  1351     ///
  1352     /// Sets the map that indicates which nodes are reached.
  1353     /// If you don't use this function before calling \ref run(Node) "run()"
  1354     /// or \ref init(), an instance will be allocated automatically.
  1355     /// The destructor deallocates this automatically allocated map,
  1356     /// of course.
  1357     /// \return <tt> (*this) </tt>
  1358     DfsVisit &reachedMap(ReachedMap &m) {
  1359       if(local_reached) {
  1360         delete _reached;
  1361         local_reached=false;
  1362       }
  1363       _reached = &m;
  1364       return *this;
  1365     }
  1366 
  1367   public:
  1368 
  1369     /// \name Execution Control
  1370     /// The simplest way to execute the DFS algorithm is to use one of the
  1371     /// member functions called \ref run(Node) "run()".\n
  1372     /// If you need more control on the execution, first you have to call
  1373     /// \ref init(), then you can add a source node with \ref addSource()
  1374     /// and perform the actual computation with \ref start().
  1375     /// This procedure can be repeated if there are nodes that have not
  1376     /// been reached.
  1377 
  1378     /// @{
  1379 
  1380     /// \brief Initializes the internal data structures.
  1381     ///
  1382     /// Initializes the internal data structures.
  1383     void init() {
  1384       create_maps();
  1385       _stack.resize(countNodes(*_digraph));
  1386       _stack_head = -1;
  1387       for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
  1388         _reached->set(u, false);
  1389       }
  1390     }
  1391 
  1392     /// \brief Adds a new source node.
  1393     ///
  1394     /// Adds a new source node to the set of nodes to be processed.
  1395     ///
  1396     /// \pre The stack must be empty. Otherwise the algorithm gives
  1397     /// wrong results. (One of the outgoing arcs of all the source nodes
  1398     /// except for the last one will not be visited and distances will
  1399     /// also be wrong.)
  1400     void addSource(Node s)
  1401     {
  1402       LEMON_DEBUG(emptyQueue(), "The stack is not empty.");
  1403       if(!(*_reached)[s]) {
  1404           _reached->set(s,true);
  1405           _visitor->start(s);
  1406           _visitor->reach(s);
  1407           Arc e;
  1408           _digraph->firstOut(e, s);
  1409           if (e != INVALID) {
  1410             _stack[++_stack_head] = e;
  1411           } else {
  1412             _visitor->leave(s);
  1413             _visitor->stop(s);
  1414           }
  1415         }
  1416     }
  1417 
  1418     /// \brief Processes the next arc.
  1419     ///
  1420     /// Processes the next arc.
  1421     ///
  1422     /// \return The processed arc.
  1423     ///
  1424     /// \pre The stack must not be empty.
  1425     Arc processNextArc() {
  1426       Arc e = _stack[_stack_head];
  1427       Node m = _digraph->target(e);
  1428       if(!(*_reached)[m]) {
  1429         _visitor->discover(e);
  1430         _visitor->reach(m);
  1431         _reached->set(m, true);
  1432         _digraph->firstOut(_stack[++_stack_head], m);
  1433       } else {
  1434         _visitor->examine(e);
  1435         m = _digraph->source(e);
  1436         _digraph->nextOut(_stack[_stack_head]);
  1437       }
  1438       while (_stack_head>=0 && _stack[_stack_head] == INVALID) {
  1439         _visitor->leave(m);
  1440         --_stack_head;
  1441         if (_stack_head >= 0) {
  1442           _visitor->backtrack(_stack[_stack_head]);
  1443           m = _digraph->source(_stack[_stack_head]);
  1444           _digraph->nextOut(_stack[_stack_head]);
  1445         } else {
  1446           _visitor->stop(m);
  1447         }
  1448       }
  1449       return e;
  1450     }
  1451 
  1452     /// \brief Next arc to be processed.
  1453     ///
  1454     /// Next arc to be processed.
  1455     ///
  1456     /// \return The next arc to be processed or INVALID if the stack is
  1457     /// empty.
  1458     Arc nextArc() const {
  1459       return _stack_head >= 0 ? _stack[_stack_head] : INVALID;
  1460     }
  1461 
  1462     /// \brief Returns \c false if there are nodes
  1463     /// to be processed.
  1464     ///
  1465     /// Returns \c false if there are nodes
  1466     /// to be processed in the queue (stack).
  1467     bool emptyQueue() const { return _stack_head < 0; }
  1468 
  1469     /// \brief Returns the number of the nodes to be processed.
  1470     ///
  1471     /// Returns the number of the nodes to be processed in the queue (stack).
  1472     int queueSize() const { return _stack_head + 1; }
  1473 
  1474     /// \brief Executes the algorithm.
  1475     ///
  1476     /// Executes the algorithm.
  1477     ///
  1478     /// This method runs the %DFS algorithm from the root node
  1479     /// in order to compute the %DFS path to each node.
  1480     ///
  1481     /// The algorithm computes
  1482     /// - the %DFS tree,
  1483     /// - the distance of each node from the root in the %DFS tree.
  1484     ///
  1485     /// \pre init() must be called and a root node should be
  1486     /// added with addSource() before using this function.
  1487     ///
  1488     /// \note <tt>d.start()</tt> is just a shortcut of the following code.
  1489     /// \code
  1490     ///   while ( !d.emptyQueue() ) {
  1491     ///     d.processNextArc();
  1492     ///   }
  1493     /// \endcode
  1494     void start() {
  1495       while ( !emptyQueue() ) processNextArc();
  1496     }
  1497 
  1498     /// \brief Executes the algorithm until the given target node is reached.
  1499     ///
  1500     /// Executes the algorithm until the given target node is reached.
  1501     ///
  1502     /// This method runs the %DFS algorithm from the root node
  1503     /// in order to compute the DFS path to \c t.
  1504     ///
  1505     /// The algorithm computes
  1506     /// - the %DFS path to \c t,
  1507     /// - the distance of \c t from the root in the %DFS tree.
  1508     ///
  1509     /// \pre init() must be called and a root node should be added
  1510     /// with addSource() before using this function.
  1511     void start(Node t) {
  1512       while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != t )
  1513         processNextArc();
  1514     }
  1515 
  1516     /// \brief Executes the algorithm until a condition is met.
  1517     ///
  1518     /// Executes the algorithm until a condition is met.
  1519     ///
  1520     /// This method runs the %DFS algorithm from the root node
  1521     /// until an arc \c a with <tt>am[a]</tt> true is found.
  1522     ///
  1523     /// \param am A \c bool (or convertible) arc map. The algorithm
  1524     /// will stop when it reaches an arc \c a with <tt>am[a]</tt> true.
  1525     ///
  1526     /// \return The reached arc \c a with <tt>am[a]</tt> true or
  1527     /// \c INVALID if no such arc was found.
  1528     ///
  1529     /// \pre init() must be called and a root node should be added
  1530     /// with addSource() before using this function.
  1531     ///
  1532     /// \warning Contrary to \ref Bfs and \ref Dijkstra, \c am is an arc map,
  1533     /// not a node map.
  1534     template <typename AM>
  1535     Arc start(const AM &am) {
  1536       while ( !emptyQueue() && !am[_stack[_stack_head]] )
  1537         processNextArc();
  1538       return emptyQueue() ? INVALID : _stack[_stack_head];
  1539     }
  1540 
  1541     /// \brief Runs the algorithm from the given source node.
  1542     ///
  1543     /// This method runs the %DFS algorithm from node \c s.
  1544     /// in order to compute the DFS path to each node.
  1545     ///
  1546     /// The algorithm computes
  1547     /// - the %DFS tree,
  1548     /// - the distance of each node from the root in the %DFS tree.
  1549     ///
  1550     /// \note <tt>d.run(s)</tt> is just a shortcut of the following code.
  1551     ///\code
  1552     ///   d.init();
  1553     ///   d.addSource(s);
  1554     ///   d.start();
  1555     ///\endcode
  1556     void run(Node s) {
  1557       init();
  1558       addSource(s);
  1559       start();
  1560     }
  1561 
  1562     /// \brief Finds the %DFS path between \c s and \c t.
  1563 
  1564     /// This method runs the %DFS algorithm from node \c s
  1565     /// in order to compute the DFS path to node \c t
  1566     /// (it stops searching when \c t is processed).
  1567     ///
  1568     /// \return \c true if \c t is reachable form \c s.
  1569     ///
  1570     /// \note Apart from the return value, <tt>d.run(s,t)</tt> is
  1571     /// just a shortcut of the following code.
  1572     ///\code
  1573     ///   d.init();
  1574     ///   d.addSource(s);
  1575     ///   d.start(t);
  1576     ///\endcode
  1577     bool run(Node s,Node t) {
  1578       init();
  1579       addSource(s);
  1580       start(t);
  1581       return reached(t);
  1582     }
  1583 
  1584     /// \brief Runs the algorithm to visit all nodes in the digraph.
  1585 
  1586     /// This method runs the %DFS algorithm in order to
  1587     /// compute the %DFS path to each node.
  1588     ///
  1589     /// The algorithm computes
  1590     /// - the %DFS tree (forest),
  1591     /// - the distance of each node from the root(s) in the %DFS tree.
  1592     ///
  1593     /// \note <tt>d.run()</tt> is just a shortcut of the following code.
  1594     ///\code
  1595     ///   d.init();
  1596     ///   for (NodeIt n(digraph); n != INVALID; ++n) {
  1597     ///     if (!d.reached(n)) {
  1598     ///       d.addSource(n);
  1599     ///       d.start();
  1600     ///     }
  1601     ///   }
  1602     ///\endcode
  1603     void run() {
  1604       init();
  1605       for (NodeIt it(*_digraph); it != INVALID; ++it) {
  1606         if (!reached(it)) {
  1607           addSource(it);
  1608           start();
  1609         }
  1610       }
  1611     }
  1612 
  1613     ///@}
  1614 
  1615     /// \name Query Functions
  1616     /// The results of the DFS algorithm can be obtained using these
  1617     /// functions.\n
  1618     /// Either \ref run(Node) "run()" or \ref start() should be called
  1619     /// before using them.
  1620 
  1621     ///@{
  1622 
  1623     /// \brief Checks if a node is reached from the root(s).
  1624     ///
  1625     /// Returns \c true if \c v is reached from the root(s).
  1626     ///
  1627     /// \pre Either \ref run(Node) "run()" or \ref init()
  1628     /// must be called before using this function.
  1629     bool reached(Node v) const { return (*_reached)[v]; }
  1630 
  1631     ///@}
  1632 
  1633   };
  1634 
  1635 } //END OF NAMESPACE LEMON
  1636 
  1637 #endif