COIN-OR::LEMON - Graph Library

source: lemon-1.0/lemon/dfs.h @ 209:765619b7cbb2

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