COIN-OR::LEMON - Graph Library

source: lemon/lemon/dfs.h @ 301:9db8964f0cf6

Last change on this file since 301:9db8964f0cf6 was 301:9db8964f0cf6, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Fix several doxygen warings

File size: 50.2 KB
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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/bits/path_dump.h>
28#include <lemon/core.h>
29#include <lemon/error.h>
30#include <lemon/assert.h>
31#include <lemon/maps.h>
32#include <lemon/path.h>
33
34namespace lemon {
35
36  ///Default traits class of Dfs class.
37
38  ///Default traits class of Dfs class.
39  ///\tparam GR Digraph type.
40  template<class GR>
41  struct DfsDefaultTraits
42  {
43    ///The type of the digraph the algorithm runs on.
44    typedef GR Digraph;
45
46    ///\brief The type of the map that stores the predecessor
47    ///arcs of the %DFS paths.
48    ///
49    ///The type of the map that stores the predecessor
50    ///arcs of the %DFS paths.
51    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
52    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
53    ///Instantiates a PredMap.
54
55    ///This function instantiates a PredMap.
56    ///\param g is the digraph, to which we would like to define the
57    ///PredMap.
58    static PredMap *createPredMap(const Digraph &g)
59    {
60      return new PredMap(g);
61    }
62
63    ///The type of the map that indicates which nodes are processed.
64
65    ///The type of the map that indicates which nodes are processed.
66    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
67    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
68    ///Instantiates a ProcessedMap.
69
70    ///This function instantiates a ProcessedMap.
71    ///\param g is the digraph, to which
72    ///we would like to define the ProcessedMap
73#ifdef DOXYGEN
74    static ProcessedMap *createProcessedMap(const Digraph &g)
75#else
76    static ProcessedMap *createProcessedMap(const Digraph &)
77#endif
78    {
79      return new ProcessedMap();
80    }
81
82    ///The type of the map that indicates which nodes are reached.
83
84    ///The type of the map that indicates which nodes are reached.
85    ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
86    typedef typename Digraph::template NodeMap<bool> ReachedMap;
87    ///Instantiates a ReachedMap.
88
89    ///This function instantiates a ReachedMap.
90    ///\param g is the digraph, to which
91    ///we would like to define the ReachedMap.
92    static ReachedMap *createReachedMap(const Digraph &g)
93    {
94      return new ReachedMap(g);
95    }
96
97    ///The type of the map that stores the distances of the nodes.
98
99    ///The type of the map that stores the distances of the nodes.
100    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
101    typedef typename Digraph::template NodeMap<int> DistMap;
102    ///Instantiates a DistMap.
103
104    ///This function instantiates a DistMap.
105    ///\param g is the digraph, to which we would like to define the
106    ///DistMap.
107    static DistMap *createDistMap(const Digraph &g)
108    {
109      return new DistMap(g);
110    }
111  };
112
113  ///%DFS algorithm class.
114
115  ///\ingroup search
116  ///This class provides an efficient implementation of the %DFS algorithm.
117  ///
118  ///There is also a \ref dfs() "function-type interface" for the DFS
119  ///algorithm, which is convenient in the simplier cases and it can be
120  ///used easier.
121  ///
122  ///\tparam GR The type of the digraph the algorithm runs on.
123  ///The default value is \ref ListDigraph. The value of GR is not used
124  ///directly by \ref Dfs, it is only passed to \ref DfsDefaultTraits.
125  ///\tparam TR Traits class to set various data types used by the algorithm.
126  ///The default traits class is
127  ///\ref DfsDefaultTraits "DfsDefaultTraits<GR>".
128  ///See \ref DfsDefaultTraits for the documentation of
129  ///a Dfs traits class.
130#ifdef DOXYGEN
131  template <typename GR,
132            typename TR>
133#else
134  template <typename GR=ListDigraph,
135            typename TR=DfsDefaultTraits<GR> >
136#endif
137  class Dfs {
138  public:
139
140    ///The type of the digraph the algorithm runs on.
141    typedef typename TR::Digraph Digraph;
142
143    ///\brief The type of the map that stores the predecessor arcs of the
144    ///DFS paths.
145    typedef typename TR::PredMap PredMap;
146    ///The type of the map that stores the distances of the nodes.
147    typedef typename TR::DistMap DistMap;
148    ///The type of the map that indicates which nodes are reached.
149    typedef typename TR::ReachedMap ReachedMap;
150    ///The type of the map that indicates which nodes are processed.
151    typedef typename TR::ProcessedMap ProcessedMap;
152    ///The type of the paths.
153    typedef PredMapPath<Digraph, PredMap> Path;
154
155    ///The traits class.
156    typedef TR Traits;
157
158  private:
159
160    typedef typename Digraph::Node Node;
161    typedef typename Digraph::NodeIt NodeIt;
162    typedef typename Digraph::Arc Arc;
163    typedef typename Digraph::OutArcIt OutArcIt;
164
165    //Pointer to the underlying digraph.
166    const Digraph *G;
167    //Pointer to the map of predecessor arcs.
168    PredMap *_pred;
169    //Indicates if _pred is locally allocated (true) or not.
170    bool local_pred;
171    //Pointer to the map of distances.
172    DistMap *_dist;
173    //Indicates if _dist is locally allocated (true) or not.
174    bool local_dist;
175    //Pointer to the map of reached status of the nodes.
176    ReachedMap *_reached;
177    //Indicates if _reached is locally allocated (true) or not.
178    bool local_reached;
179    //Pointer to the map of processed status of the nodes.
180    ProcessedMap *_processed;
181    //Indicates if _processed is locally allocated (true) or not.
182    bool local_processed;
183
184    std::vector<typename Digraph::OutArcIt> _stack;
185    int _stack_head;
186
187    //Creates the maps if necessary.
188    void create_maps()
189    {
190      if(!_pred) {
191        local_pred = true;
192        _pred = Traits::createPredMap(*G);
193      }
194      if(!_dist) {
195        local_dist = true;
196        _dist = Traits::createDistMap(*G);
197      }
198      if(!_reached) {
199        local_reached = true;
200        _reached = Traits::createReachedMap(*G);
201      }
202      if(!_processed) {
203        local_processed = true;
204        _processed = Traits::createProcessedMap(*G);
205      }
206    }
207
208  protected:
209
210    Dfs() {}
211
212  public:
213
214    typedef Dfs Create;
215
216    ///\name Named template parameters
217
218    ///@{
219
220    template <class T>
221    struct SetPredMapTraits : public Traits {
222      typedef T PredMap;
223      static PredMap *createPredMap(const Digraph &)
224      {
225        LEMON_ASSERT(false, "PredMap is not initialized");
226        return 0; // ignore warnings
227      }
228    };
229    ///\brief \ref named-templ-param "Named parameter" for setting
230    ///PredMap type.
231    ///
232    ///\ref named-templ-param "Named parameter" for setting
233    ///PredMap type.
234    template <class T>
235    struct SetPredMap : public Dfs<Digraph, SetPredMapTraits<T> > {
236      typedef Dfs<Digraph, SetPredMapTraits<T> > Create;
237    };
238
239    template <class T>
240    struct SetDistMapTraits : public Traits {
241      typedef T DistMap;
242      static DistMap *createDistMap(const Digraph &)
243      {
244        LEMON_ASSERT(false, "DistMap is not initialized");
245        return 0; // ignore warnings
246      }
247    };
248    ///\brief \ref named-templ-param "Named parameter" for setting
249    ///DistMap type.
250    ///
251    ///\ref named-templ-param "Named parameter" for setting
252    ///DistMap type.
253    template <class T>
254    struct SetDistMap : public Dfs< Digraph, SetDistMapTraits<T> > {
255      typedef Dfs<Digraph, SetDistMapTraits<T> > Create;
256    };
257
258    template <class T>
259    struct SetReachedMapTraits : public Traits {
260      typedef T ReachedMap;
261      static ReachedMap *createReachedMap(const Digraph &)
262      {
263        LEMON_ASSERT(false, "ReachedMap is not initialized");
264        return 0; // ignore warnings
265      }
266    };
267    ///\brief \ref named-templ-param "Named parameter" for setting
268    ///ReachedMap type.
269    ///
270    ///\ref named-templ-param "Named parameter" for setting
271    ///ReachedMap type.
272    template <class T>
273    struct SetReachedMap : public Dfs< Digraph, SetReachedMapTraits<T> > {
274      typedef Dfs< Digraph, SetReachedMapTraits<T> > Create;
275    };
276
277    template <class T>
278    struct SetProcessedMapTraits : public Traits {
279      typedef T ProcessedMap;
280      static ProcessedMap *createProcessedMap(const Digraph &)
281      {
282        LEMON_ASSERT(false, "ProcessedMap is not initialized");
283        return 0; // ignore warnings
284      }
285    };
286    ///\brief \ref named-templ-param "Named parameter" for setting
287    ///ProcessedMap type.
288    ///
289    ///\ref named-templ-param "Named parameter" for setting
290    ///ProcessedMap type.
291    template <class T>
292    struct SetProcessedMap : public Dfs< Digraph, SetProcessedMapTraits<T> > {
293      typedef Dfs< Digraph, SetProcessedMapTraits<T> > Create;
294    };
295
296    struct SetStandardProcessedMapTraits : public Traits {
297      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
298      static ProcessedMap *createProcessedMap(const Digraph &g)
299      {
300        return new ProcessedMap(g);
301      }
302    };
303    ///\brief \ref named-templ-param "Named parameter" for setting
304    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
305    ///
306    ///\ref named-templ-param "Named parameter" for setting
307    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
308    ///If you don't set it explicitly, it will be automatically allocated.
309    struct SetStandardProcessedMap :
310      public Dfs< Digraph, SetStandardProcessedMapTraits > {
311      typedef Dfs< Digraph, SetStandardProcessedMapTraits > Create;
312    };
313
314    ///@}
315
316  public:
317
318    ///Constructor.
319
320    ///Constructor.
321    ///\param g The digraph the algorithm runs on.
322    Dfs(const Digraph &g) :
323      G(&g),
324      _pred(NULL), local_pred(false),
325      _dist(NULL), local_dist(false),
326      _reached(NULL), local_reached(false),
327      _processed(NULL), local_processed(false)
328    { }
329
330    ///Destructor.
331    ~Dfs()
332    {
333      if(local_pred) delete _pred;
334      if(local_dist) delete _dist;
335      if(local_reached) delete _reached;
336      if(local_processed) delete _processed;
337    }
338
339    ///Sets the map that stores the predecessor arcs.
340
341    ///Sets the map that stores the predecessor arcs.
342    ///If you don't use this function before calling \ref run(),
343    ///it will allocate one. The destructor deallocates this
344    ///automatically allocated map, of course.
345    ///\return <tt> (*this) </tt>
346    Dfs &predMap(PredMap &m)
347    {
348      if(local_pred) {
349        delete _pred;
350        local_pred=false;
351      }
352      _pred = &m;
353      return *this;
354    }
355
356    ///Sets the map that indicates which nodes are reached.
357
358    ///Sets the map that indicates which nodes are reached.
359    ///If you don't use this function before calling \ref run(),
360    ///it will allocate one. The destructor deallocates this
361    ///automatically allocated map, of course.
362    ///\return <tt> (*this) </tt>
363    Dfs &reachedMap(ReachedMap &m)
364    {
365      if(local_reached) {
366        delete _reached;
367        local_reached=false;
368      }
369      _reached = &m;
370      return *this;
371    }
372
373    ///Sets the map that indicates which nodes are processed.
374
375    ///Sets the map that indicates which nodes are processed.
376    ///If you don't use this function before calling \ref run(),
377    ///it will allocate one. The destructor deallocates this
378    ///automatically allocated map, 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(),
395    ///it will allocate one. The destructor deallocates this
396    ///automatically allocated map, of course.
397    ///\return <tt> (*this) </tt>
398    Dfs &distMap(DistMap &m)
399    {
400      if(local_dist) {
401        delete _dist;
402        local_dist=false;
403      }
404      _dist = &m;
405      return *this;
406    }
407
408  public:
409
410    ///\name Execution control
411    ///The simplest way to execute the algorithm is to use
412    ///one of the member functions called \ref lemon::Dfs::run() "run()".
413    ///\n
414    ///If you need more control on the execution, first you must call
415    ///\ref lemon::Dfs::init() "init()", then you can add a source node
416    ///with \ref lemon::Dfs::addSource() "addSource()".
417    ///Finally \ref lemon::Dfs::start() "start()" will perform the
418    ///actual path computation.
419
420    ///@{
421
422    ///Initializes the internal data structures.
423
424    ///Initializes the internal data structures.
425    ///
426    void init()
427    {
428      create_maps();
429      _stack.resize(countNodes(*G));
430      _stack_head=-1;
431      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
432        _pred->set(u,INVALID);
433        _reached->set(u,false);
434        _processed->set(u,false);
435      }
436    }
437
438    ///Adds a new source node.
439
440    ///Adds a new source node to the set of nodes to be processed.
441    ///
442    ///\pre The stack must be empty. (Otherwise the algorithm gives
443    ///false results.)
444    ///
445    ///\warning Distances will be wrong (or at least strange) in case of
446    ///multiple sources.
447    void addSource(Node s)
448    {
449      LEMON_DEBUG(emptyQueue(), "The stack is not empty.");
450      if(!(*_reached)[s])
451        {
452          _reached->set(s,true);
453          _pred->set(s,INVALID);
454          OutArcIt e(*G,s);
455          if(e!=INVALID) {
456            _stack[++_stack_head]=e;
457            _dist->set(s,_stack_head);
458          }
459          else {
460            _processed->set(s,true);
461            _dist->set(s,0);
462          }
463        }
464    }
465
466    ///Processes the next arc.
467
468    ///Processes the next arc.
469    ///
470    ///\return The processed arc.
471    ///
472    ///\pre The stack must not be empty.
473    Arc processNextArc()
474    {
475      Node m;
476      Arc e=_stack[_stack_head];
477      if(!(*_reached)[m=G->target(e)]) {
478        _pred->set(m,e);
479        _reached->set(m,true);
480        ++_stack_head;
481        _stack[_stack_head] = OutArcIt(*G, m);
482        _dist->set(m,_stack_head);
483      }
484      else {
485        m=G->source(e);
486        ++_stack[_stack_head];
487      }
488      while(_stack_head>=0 && _stack[_stack_head]==INVALID) {
489        _processed->set(m,true);
490        --_stack_head;
491        if(_stack_head>=0) {
492          m=G->source(_stack[_stack_head]);
493          ++_stack[_stack_head];
494        }
495      }
496      return e;
497    }
498
499    ///Next arc to be processed.
500
501    ///Next arc to be processed.
502    ///
503    ///\return The next arc to be processed or \c INVALID if the stack
504    ///is empty.
505    OutArcIt nextArc() const
506    {
507      return _stack_head>=0?_stack[_stack_head]:INVALID;
508    }
509
510    ///\brief Returns \c false if there are nodes
511    ///to be processed.
512    ///
513    ///Returns \c false if there are nodes
514    ///to be processed in the queue (stack).
515    bool emptyQueue() const { return _stack_head<0; }
516
517    ///Returns the number of the nodes to be processed.
518
519    ///Returns the number of the nodes to be processed in the queue (stack).
520    int queueSize() const { return _stack_head+1; }
521
522    ///Executes the algorithm.
523
524    ///Executes the algorithm.
525    ///
526    ///This method runs the %DFS algorithm from the root node
527    ///in order to compute the DFS path to each node.
528    ///
529    /// The algorithm computes
530    ///- the %DFS tree,
531    ///- the distance of each node from the root in the %DFS tree.
532    ///
533    ///\pre init() must be called and a root node should be
534    ///added with addSource() before using this function.
535    ///
536    ///\note <tt>d.start()</tt> is just a shortcut of the following code.
537    ///\code
538    ///  while ( !d.emptyQueue() ) {
539    ///    d.processNextArc();
540    ///  }
541    ///\endcode
542    void start()
543    {
544      while ( !emptyQueue() ) processNextArc();
545    }
546
547    ///Executes the algorithm until the given target node is reached.
548
549    ///Executes the algorithm until the given target node is reached.
550    ///
551    ///This method runs the %DFS algorithm from the root node
552    ///in order to compute the DFS path to \c t.
553    ///
554    ///The algorithm computes
555    ///- the %DFS path to \c t,
556    ///- the distance of \c t from the root in the %DFS tree.
557    ///
558    ///\pre init() must be called and a root node should be
559    ///added with addSource() before using this function.
560    void start(Node t)
561    {
562      while ( !emptyQueue() && G->target(_stack[_stack_head])!=t )
563        processNextArc();
564    }
565
566    ///Executes the algorithm until a condition is met.
567
568    ///Executes the algorithm until a condition is met.
569    ///
570    ///This method runs the %DFS algorithm from the root node
571    ///until an arc \c a with <tt>am[a]</tt> true is found.
572    ///
573    ///\param am A \c bool (or convertible) arc map. The algorithm
574    ///will stop when it reaches an arc \c a with <tt>am[a]</tt> true.
575    ///
576    ///\return The reached arc \c a with <tt>am[a]</tt> true or
577    ///\c INVALID if no such arc was found.
578    ///
579    ///\pre init() must be called and a root node should be
580    ///added with addSource() before using this function.
581    ///
582    ///\warning Contrary to \ref Bfs and \ref Dijkstra, \c am is an arc map,
583    ///not a node map.
584    template<class ArcBoolMap>
585    Arc start(const ArcBoolMap &am)
586    {
587      while ( !emptyQueue() && !am[_stack[_stack_head]] )
588        processNextArc();
589      return emptyQueue() ? INVALID : _stack[_stack_head];
590    }
591
592    ///Runs the algorithm from the given source node.
593
594    ///This method runs the %DFS algorithm from node \c s
595    ///in order to compute the DFS path to each node.
596    ///
597    ///The algorithm computes
598    ///- the %DFS tree,
599    ///- the distance of each node from the root in the %DFS tree.
600    ///
601    ///\note <tt>d.run(s)</tt> is just a shortcut of the following code.
602    ///\code
603    ///  d.init();
604    ///  d.addSource(s);
605    ///  d.start();
606    ///\endcode
607    void run(Node s) {
608      init();
609      addSource(s);
610      start();
611    }
612
613    ///Finds the %DFS path between \c s and \c t.
614
615    ///This method runs the %DFS algorithm from node \c s
616    ///in order to compute the DFS path to node \c t
617    ///(it stops searching when \c t is processed)
618    ///
619    ///\return \c true if \c t is reachable form \c s.
620    ///
621    ///\note Apart from the return value, <tt>d.run(s,t)</tt> is
622    ///just a shortcut of the following code.
623    ///\code
624    ///  d.init();
625    ///  d.addSource(s);
626    ///  d.start(t);
627    ///\endcode
628    bool run(Node s,Node t) {
629      init();
630      addSource(s);
631      start(t);
632      return reached(t);
633    }
634
635    ///Runs the algorithm to visit all nodes in the digraph.
636
637    ///This method runs the %DFS algorithm in order to compute the
638    ///%DFS path to each node.
639    ///
640    ///The algorithm computes
641    ///- the %DFS tree,
642    ///- the distance of each node from the root in the %DFS tree.
643    ///
644    ///\note <tt>d.run()</tt> is just a shortcut of the following code.
645    ///\code
646    ///  d.init();
647    ///  for (NodeIt n(digraph); n != INVALID; ++n) {
648    ///    if (!d.reached(n)) {
649    ///      d.addSource(n);
650    ///      d.start();
651    ///    }
652    ///  }
653    ///\endcode
654    void run() {
655      init();
656      for (NodeIt it(*G); it != INVALID; ++it) {
657        if (!reached(it)) {
658          addSource(it);
659          start();
660        }
661      }
662    }
663
664    ///@}
665
666    ///\name Query Functions
667    ///The result of the %DFS algorithm can be obtained using these
668    ///functions.\n
669    ///Either \ref lemon::Dfs::run() "run()" or \ref lemon::Dfs::start()
670    ///"start()" must be called before using them.
671
672    ///@{
673
674    ///The DFS path to a node.
675
676    ///Returns the DFS path to a node.
677    ///
678    ///\warning \c t should be reachable from the root.
679    ///
680    ///\pre Either \ref run() or \ref start() must be called before
681    ///using this function.
682    Path path(Node t) const { return Path(*G, *_pred, t); }
683
684    ///The distance of a node from the root.
685
686    ///Returns the distance of a node from the root.
687    ///
688    ///\warning If node \c v is not reachable from the root, then
689    ///the return value of this function is undefined.
690    ///
691    ///\pre Either \ref run() or \ref start() must be called before
692    ///using this function.
693    int dist(Node v) const { return (*_dist)[v]; }
694
695    ///Returns the 'previous arc' of the %DFS tree for a node.
696
697    ///This function returns the 'previous arc' of the %DFS tree for the
698    ///node \c v, i.e. it returns the last arc of a %DFS path from the
699    ///root to \c v. It is \c INVALID
700    ///if \c v is not reachable from the root(s) or if \c v is a root.
701    ///
702    ///The %DFS tree used here is equal to the %DFS tree used in
703    ///\ref predNode().
704    ///
705    ///\pre Either \ref run() or \ref start() must be called before using
706    ///this function.
707    Arc predArc(Node v) const { return (*_pred)[v];}
708
709    ///Returns the 'previous node' of the %DFS tree.
710
711    ///This function returns the 'previous node' of the %DFS
712    ///tree for the node \c v, i.e. it returns the last but one node
713    ///from a %DFS path from the root to \c v. It is \c INVALID
714    ///if \c v is not reachable from the root(s) or if \c v is a root.
715    ///
716    ///The %DFS tree used here is equal to the %DFS tree used in
717    ///\ref predArc().
718    ///
719    ///\pre Either \ref run() or \ref start() must be called before
720    ///using this function.
721    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
722                                  G->source((*_pred)[v]); }
723
724    ///\brief Returns a const reference to the node map that stores the
725    ///distances of the nodes.
726    ///
727    ///Returns a const reference to the node map that stores the
728    ///distances of the nodes calculated by the algorithm.
729    ///
730    ///\pre Either \ref run() or \ref init()
731    ///must be called before using this function.
732    const DistMap &distMap() const { return *_dist;}
733
734    ///\brief Returns a const reference to the node map that stores the
735    ///predecessor arcs.
736    ///
737    ///Returns a const reference to the node map that stores the predecessor
738    ///arcs, which form the DFS tree.
739    ///
740    ///\pre Either \ref run() or \ref init()
741    ///must be called before using this function.
742    const PredMap &predMap() const { return *_pred;}
743
744    ///Checks if a node is reachable from the root(s).
745
746    ///Returns \c true if \c v is reachable from the root(s).
747    ///\pre Either \ref run() or \ref start()
748    ///must be called before using this function.
749    bool reached(Node v) const { return (*_reached)[v]; }
750
751    ///@}
752  };
753
754  ///Default traits class of dfs() function.
755
756  ///Default traits class of dfs() function.
757  ///\tparam GR Digraph type.
758  template<class GR>
759  struct DfsWizardDefaultTraits
760  {
761    ///The type of the digraph the algorithm runs on.
762    typedef GR Digraph;
763
764    ///\brief The type of the map that stores the predecessor
765    ///arcs of the %DFS paths.
766    ///
767    ///The type of the map that stores the predecessor
768    ///arcs of the %DFS paths.
769    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
770    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
771    ///Instantiates a PredMap.
772
773    ///This function instantiates a PredMap.
774    ///\param g is the digraph, to which we would like to define the
775    ///PredMap.
776    static PredMap *createPredMap(const Digraph &g)
777    {
778      return new PredMap(g);
779    }
780
781    ///The type of the map that indicates which nodes are processed.
782
783    ///The type of the map that indicates which nodes are processed.
784    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
785    ///By default it is a NullMap.
786    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
787    ///Instantiates a ProcessedMap.
788
789    ///This function instantiates a ProcessedMap.
790    ///\param g is the digraph, to which
791    ///we would like to define the ProcessedMap.
792#ifdef DOXYGEN
793    static ProcessedMap *createProcessedMap(const Digraph &g)
794#else
795    static ProcessedMap *createProcessedMap(const Digraph &)
796#endif
797    {
798      return new ProcessedMap();
799    }
800
801    ///The type of the map that indicates which nodes are reached.
802
803    ///The type of the map that indicates which nodes are reached.
804    ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
805    typedef typename Digraph::template NodeMap<bool> ReachedMap;
806    ///Instantiates a ReachedMap.
807
808    ///This function instantiates a ReachedMap.
809    ///\param g is the digraph, to which
810    ///we would like to define the ReachedMap.
811    static ReachedMap *createReachedMap(const Digraph &g)
812    {
813      return new ReachedMap(g);
814    }
815
816    ///The type of the map that stores the distances of the nodes.
817
818    ///The type of the map that stores the distances of the nodes.
819    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
820    typedef typename Digraph::template NodeMap<int> DistMap;
821    ///Instantiates a DistMap.
822
823    ///This function instantiates a DistMap.
824    ///\param g is the digraph, to which we would like to define
825    ///the DistMap
826    static DistMap *createDistMap(const Digraph &g)
827    {
828      return new DistMap(g);
829    }
830
831    ///The type of the DFS paths.
832
833    ///The type of the DFS paths.
834    ///It must meet the \ref concepts::Path "Path" concept.
835    typedef lemon::Path<Digraph> Path;
836  };
837
838  /// Default traits class used by \ref DfsWizard
839
840  /// To make it easier to use Dfs algorithm
841  /// we have created a wizard class.
842  /// This \ref DfsWizard class needs default traits,
843  /// as well as the \ref Dfs class.
844  /// The \ref DfsWizardBase is a class to be the default traits of the
845  /// \ref DfsWizard class.
846  template<class GR>
847  class DfsWizardBase : public DfsWizardDefaultTraits<GR>
848  {
849
850    typedef DfsWizardDefaultTraits<GR> Base;
851  protected:
852    //The type of the nodes in the digraph.
853    typedef typename Base::Digraph::Node Node;
854
855    //Pointer to the digraph the algorithm runs on.
856    void *_g;
857    //Pointer to the map of reached nodes.
858    void *_reached;
859    //Pointer to the map of processed nodes.
860    void *_processed;
861    //Pointer to the map of predecessors arcs.
862    void *_pred;
863    //Pointer to the map of distances.
864    void *_dist;
865    //Pointer to the DFS path to the target node.
866    void *_path;
867    //Pointer to the distance of the target node.
868    int *_di;
869
870    public:
871    /// Constructor.
872
873    /// This constructor does not require parameters, therefore it initiates
874    /// all of the attributes to \c 0.
875    DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
876                      _dist(0), _path(0), _di(0) {}
877
878    /// Constructor.
879
880    /// This constructor requires one parameter,
881    /// others are initiated to \c 0.
882    /// \param g The digraph the algorithm runs on.
883    DfsWizardBase(const GR &g) :
884      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
885      _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
886
887  };
888
889  /// Auxiliary class for the function-type interface of DFS algorithm.
890
891  /// This auxiliary class is created to implement the
892  /// \ref dfs() "function-type interface" of \ref Dfs algorithm.
893  /// It does not have own \ref run() method, it uses the functions
894  /// and features of the plain \ref Dfs.
895  ///
896  /// This class should only be used through the \ref dfs() function,
897  /// which makes it easier to use the algorithm.
898  template<class TR>
899  class DfsWizard : public TR
900  {
901    typedef TR Base;
902
903    ///The type of the digraph the algorithm runs on.
904    typedef typename TR::Digraph Digraph;
905
906    typedef typename Digraph::Node Node;
907    typedef typename Digraph::NodeIt NodeIt;
908    typedef typename Digraph::Arc Arc;
909    typedef typename Digraph::OutArcIt OutArcIt;
910
911    ///\brief The type of the map that stores the predecessor
912    ///arcs of the DFS paths.
913    typedef typename TR::PredMap PredMap;
914    ///\brief The type of the map that stores the distances of the nodes.
915    typedef typename TR::DistMap DistMap;
916    ///\brief The type of the map that indicates which nodes are reached.
917    typedef typename TR::ReachedMap ReachedMap;
918    ///\brief The type of the map that indicates which nodes are processed.
919    typedef typename TR::ProcessedMap ProcessedMap;
920    ///The type of the DFS paths
921    typedef typename TR::Path Path;
922
923  public:
924
925    /// Constructor.
926    DfsWizard() : TR() {}
927
928    /// Constructor that requires parameters.
929
930    /// Constructor that requires parameters.
931    /// These parameters will be the default values for the traits class.
932    /// \param g The digraph the algorithm runs on.
933    DfsWizard(const Digraph &g) :
934      TR(g) {}
935
936    ///Copy constructor
937    DfsWizard(const TR &b) : TR(b) {}
938
939    ~DfsWizard() {}
940
941    ///Runs DFS algorithm from the given source node.
942
943    ///This method runs DFS algorithm from node \c s
944    ///in order to compute the DFS path to each node.
945    void run(Node s)
946    {
947      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
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      if (Base::_reached)
953        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
954      if (Base::_processed)
955        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
956      if (s!=INVALID)
957        alg.run(s);
958      else
959        alg.run();
960    }
961
962    ///Finds the DFS path between \c s and \c t.
963
964    ///This method runs DFS algorithm from node \c s
965    ///in order to compute the DFS path to node \c t
966    ///(it stops searching when \c t is processed).
967    ///
968    ///\return \c true if \c t is reachable form \c s.
969    bool run(Node s, Node t)
970    {
971      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
972      if (Base::_pred)
973        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
974      if (Base::_dist)
975        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
976      if (Base::_reached)
977        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
978      if (Base::_processed)
979        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
980      alg.run(s,t);
981      if (Base::_path)
982        *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
983      if (Base::_di)
984        *Base::_di = alg.dist(t);
985      return alg.reached(t);
986      }
987
988    ///Runs DFS algorithm to visit all nodes in the digraph.
989
990    ///This method runs DFS algorithm in order to compute
991    ///the DFS path to each node.
992    void run()
993    {
994      run(INVALID);
995    }
996
997    template<class T>
998    struct SetPredMapBase : public Base {
999      typedef T PredMap;
1000      static PredMap *createPredMap(const Digraph &) { return 0; };
1001      SetPredMapBase(const TR &b) : TR(b) {}
1002    };
1003    ///\brief \ref named-func-param "Named parameter"
1004    ///for setting PredMap object.
1005    ///
1006    ///\ref named-func-param "Named parameter"
1007    ///for setting PredMap object.
1008    template<class T>
1009    DfsWizard<SetPredMapBase<T> > predMap(const T &t)
1010    {
1011      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
1012      return DfsWizard<SetPredMapBase<T> >(*this);
1013    }
1014
1015    template<class T>
1016    struct SetReachedMapBase : public Base {
1017      typedef T ReachedMap;
1018      static ReachedMap *createReachedMap(const Digraph &) { return 0; };
1019      SetReachedMapBase(const TR &b) : TR(b) {}
1020    };
1021    ///\brief \ref named-func-param "Named parameter"
1022    ///for setting ReachedMap object.
1023    ///
1024    /// \ref named-func-param "Named parameter"
1025    ///for setting ReachedMap object.
1026    template<class T>
1027    DfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
1028    {
1029      Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
1030      return DfsWizard<SetReachedMapBase<T> >(*this);
1031    }
1032
1033    template<class T>
1034    struct SetDistMapBase : public Base {
1035      typedef T DistMap;
1036      static DistMap *createDistMap(const Digraph &) { return 0; };
1037      SetDistMapBase(const TR &b) : TR(b) {}
1038    };
1039    ///\brief \ref named-func-param "Named parameter"
1040    ///for setting DistMap object.
1041    ///
1042    /// \ref named-func-param "Named parameter"
1043    ///for setting DistMap object.
1044    template<class T>
1045    DfsWizard<SetDistMapBase<T> > distMap(const T &t)
1046    {
1047      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
1048      return DfsWizard<SetDistMapBase<T> >(*this);
1049    }
1050
1051    template<class T>
1052    struct SetProcessedMapBase : public Base {
1053      typedef T ProcessedMap;
1054      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
1055      SetProcessedMapBase(const TR &b) : TR(b) {}
1056    };
1057    ///\brief \ref named-func-param "Named parameter"
1058    ///for setting ProcessedMap object.
1059    ///
1060    /// \ref named-func-param "Named parameter"
1061    ///for setting ProcessedMap object.
1062    template<class T>
1063    DfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
1064    {
1065      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
1066      return DfsWizard<SetProcessedMapBase<T> >(*this);
1067    }
1068
1069    template<class T>
1070    struct SetPathBase : public Base {
1071      typedef T Path;
1072      SetPathBase(const TR &b) : TR(b) {}
1073    };
1074    ///\brief \ref named-func-param "Named parameter"
1075    ///for getting the DFS path to the target node.
1076    ///
1077    ///\ref named-func-param "Named parameter"
1078    ///for getting the DFS path to the target node.
1079    template<class T>
1080    DfsWizard<SetPathBase<T> > path(const T &t)
1081    {
1082      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
1083      return DfsWizard<SetPathBase<T> >(*this);
1084    }
1085
1086    ///\brief \ref named-func-param "Named parameter"
1087    ///for getting the distance of the target node.
1088    ///
1089    ///\ref named-func-param "Named parameter"
1090    ///for getting the distance of the target node.
1091    DfsWizard dist(const int &d)
1092    {
1093      Base::_di=const_cast<int*>(&d);
1094      return *this;
1095    }
1096
1097  };
1098
1099  ///Function-type interface for DFS algorithm.
1100
1101  ///\ingroup search
1102  ///Function-type interface for DFS algorithm.
1103  ///
1104  ///This function also has several \ref named-func-param "named parameters",
1105  ///they are declared as the members of class \ref DfsWizard.
1106  ///The following examples show how to use these parameters.
1107  ///\code
1108  ///  // Compute the DFS tree
1109  ///  dfs(g).predMap(preds).distMap(dists).run(s);
1110  ///
1111  ///  // Compute the DFS path from s to t
1112  ///  bool reached = dfs(g).path(p).dist(d).run(s,t);
1113  ///\endcode
1114
1115  ///\warning Don't forget to put the \ref DfsWizard::run() "run()"
1116  ///to the end of the parameter list.
1117  ///\sa DfsWizard
1118  ///\sa Dfs
1119  template<class GR>
1120  DfsWizard<DfsWizardBase<GR> >
1121  dfs(const GR &digraph)
1122  {
1123    return DfsWizard<DfsWizardBase<GR> >(digraph);
1124  }
1125
1126#ifdef DOXYGEN
1127  /// \brief Visitor class for DFS.
1128  ///
1129  /// This class defines the interface of the DfsVisit events, and
1130  /// it could be the base of a real visitor class.
1131  template <typename _Digraph>
1132  struct DfsVisitor {
1133    typedef _Digraph Digraph;
1134    typedef typename Digraph::Arc Arc;
1135    typedef typename Digraph::Node Node;
1136    /// \brief Called for the source node of the DFS.
1137    ///
1138    /// This function is called for the source node of the DFS.
1139    void start(const Node& node) {}
1140    /// \brief Called when the source node is leaved.
1141    ///
1142    /// This function is called when the source node is leaved.
1143    void stop(const Node& node) {}
1144    /// \brief Called when a node is reached first time.
1145    ///
1146    /// This function is called when a node is reached first time.
1147    void reach(const Node& node) {}
1148    /// \brief Called when an arc reaches a new node.
1149    ///
1150    /// This function is called when the DFS finds an arc whose target node
1151    /// is not reached yet.
1152    void discover(const Arc& arc) {}
1153    /// \brief Called when an arc is examined but its target node is
1154    /// already discovered.
1155    ///
1156    /// This function is called when an arc is examined but its target node is
1157    /// already discovered.
1158    void examine(const Arc& arc) {}
1159    /// \brief Called when the DFS steps back from a node.
1160    ///
1161    /// This function is called when the DFS steps back from a node.
1162    void leave(const Node& node) {}
1163    /// \brief Called when the DFS steps back on an arc.
1164    ///
1165    /// This function is called when the DFS steps back on an arc.
1166    void backtrack(const Arc& arc) {}
1167  };
1168#else
1169  template <typename _Digraph>
1170  struct DfsVisitor {
1171    typedef _Digraph Digraph;
1172    typedef typename Digraph::Arc Arc;
1173    typedef typename Digraph::Node Node;
1174    void start(const Node&) {}
1175    void stop(const Node&) {}
1176    void reach(const Node&) {}
1177    void discover(const Arc&) {}
1178    void examine(const Arc&) {}
1179    void leave(const Node&) {}
1180    void backtrack(const Arc&) {}
1181
1182    template <typename _Visitor>
1183    struct Constraints {
1184      void constraints() {
1185        Arc arc;
1186        Node node;
1187        visitor.start(node);
1188        visitor.stop(arc);
1189        visitor.reach(node);
1190        visitor.discover(arc);
1191        visitor.examine(arc);
1192        visitor.leave(node);
1193        visitor.backtrack(arc);
1194      }
1195      _Visitor& visitor;
1196    };
1197  };
1198#endif
1199
1200  /// \brief Default traits class of DfsVisit class.
1201  ///
1202  /// Default traits class of DfsVisit class.
1203  /// \tparam _Digraph The type of the digraph the algorithm runs on.
1204  template<class _Digraph>
1205  struct DfsVisitDefaultTraits {
1206
1207    /// \brief The type of the digraph the algorithm runs on.
1208    typedef _Digraph Digraph;
1209
1210    /// \brief The type of the map that indicates which nodes are reached.
1211    ///
1212    /// The type of the map that indicates which nodes are reached.
1213    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
1214    typedef typename Digraph::template NodeMap<bool> ReachedMap;
1215
1216    /// \brief Instantiates a ReachedMap.
1217    ///
1218    /// This function instantiates a ReachedMap.
1219    /// \param digraph is the digraph, to which
1220    /// we would like to define the ReachedMap.
1221    static ReachedMap *createReachedMap(const Digraph &digraph) {
1222      return new ReachedMap(digraph);
1223    }
1224
1225  };
1226
1227  /// \ingroup search
1228  ///
1229  /// \brief %DFS algorithm class with visitor interface.
1230  ///
1231  /// This class provides an efficient implementation of the %DFS algorithm
1232  /// with visitor interface.
1233  ///
1234  /// The %DfsVisit class provides an alternative interface to the Dfs
1235  /// class. It works with callback mechanism, the DfsVisit object calls
1236  /// the member functions of the \c Visitor class on every DFS event.
1237  ///
1238  /// This interface of the DFS algorithm should be used in special cases
1239  /// when extra actions have to be performed in connection with certain
1240  /// events of the DFS algorithm. Otherwise consider to use Dfs or dfs()
1241  /// instead.
1242  ///
1243  /// \tparam _Digraph The type of the digraph the algorithm runs on.
1244  /// The default value is
1245  /// \ref ListDigraph. The value of _Digraph is not used directly by
1246  /// \ref DfsVisit, it is only passed to \ref DfsVisitDefaultTraits.
1247  /// \tparam _Visitor The Visitor type that is used by the algorithm.
1248  /// \ref DfsVisitor "DfsVisitor<_Digraph>" is an empty visitor, which
1249  /// does not observe the DFS events. If you want to observe the DFS
1250  /// events, you should implement your own visitor class.
1251  /// \tparam _Traits Traits class to set various data types used by the
1252  /// algorithm. The default traits class is
1253  /// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<_Digraph>".
1254  /// See \ref DfsVisitDefaultTraits for the documentation of
1255  /// a DFS visit traits class.
1256#ifdef DOXYGEN
1257  template <typename _Digraph, typename _Visitor, typename _Traits>
1258#else
1259  template <typename _Digraph = ListDigraph,
1260            typename _Visitor = DfsVisitor<_Digraph>,
1261            typename _Traits = DfsVisitDefaultTraits<_Digraph> >
1262#endif
1263  class DfsVisit {
1264  public:
1265
1266    ///The traits class.
1267    typedef _Traits Traits;
1268
1269    ///The type of the digraph the algorithm runs on.
1270    typedef typename Traits::Digraph Digraph;
1271
1272    ///The visitor type used by the algorithm.
1273    typedef _Visitor Visitor;
1274
1275    ///The type of the map that indicates which nodes are reached.
1276    typedef typename Traits::ReachedMap ReachedMap;
1277
1278  private:
1279
1280    typedef typename Digraph::Node Node;
1281    typedef typename Digraph::NodeIt NodeIt;
1282    typedef typename Digraph::Arc Arc;
1283    typedef typename Digraph::OutArcIt OutArcIt;
1284
1285    //Pointer to the underlying digraph.
1286    const Digraph *_digraph;
1287    //Pointer to the visitor object.
1288    Visitor *_visitor;
1289    //Pointer to the map of reached status of the nodes.
1290    ReachedMap *_reached;
1291    //Indicates if _reached is locally allocated (true) or not.
1292    bool local_reached;
1293
1294    std::vector<typename Digraph::Arc> _stack;
1295    int _stack_head;
1296
1297    //Creates the maps if necessary.
1298    void create_maps() {
1299      if(!_reached) {
1300        local_reached = true;
1301        _reached = Traits::createReachedMap(*_digraph);
1302      }
1303    }
1304
1305  protected:
1306
1307    DfsVisit() {}
1308
1309  public:
1310
1311    typedef DfsVisit Create;
1312
1313    /// \name Named template parameters
1314
1315    ///@{
1316    template <class T>
1317    struct SetReachedMapTraits : public Traits {
1318      typedef T ReachedMap;
1319      static ReachedMap *createReachedMap(const Digraph &digraph) {
1320        LEMON_ASSERT(false, "ReachedMap is not initialized");
1321        return 0; // ignore warnings
1322      }
1323    };
1324    /// \brief \ref named-templ-param "Named parameter" for setting
1325    /// ReachedMap type.
1326    ///
1327    /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
1328    template <class T>
1329    struct SetReachedMap : public DfsVisit< Digraph, Visitor,
1330                                            SetReachedMapTraits<T> > {
1331      typedef DfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
1332    };
1333    ///@}
1334
1335  public:
1336
1337    /// \brief Constructor.
1338    ///
1339    /// Constructor.
1340    ///
1341    /// \param digraph The digraph the algorithm runs on.
1342    /// \param visitor The visitor object of the algorithm.
1343    DfsVisit(const Digraph& digraph, Visitor& visitor)
1344      : _digraph(&digraph), _visitor(&visitor),
1345        _reached(0), local_reached(false) {}
1346
1347    /// \brief Destructor.
1348    ~DfsVisit() {
1349      if(local_reached) delete _reached;
1350    }
1351
1352    /// \brief Sets the map that indicates which nodes are reached.
1353    ///
1354    /// Sets the map that indicates which nodes are reached.
1355    /// If you don't use this function before calling \ref run(),
1356    /// it will allocate one. The destructor deallocates this
1357    /// automatically allocated map, of course.
1358    /// \return <tt> (*this) </tt>
1359    DfsVisit &reachedMap(ReachedMap &m) {
1360      if(local_reached) {
1361        delete _reached;
1362        local_reached=false;
1363      }
1364      _reached = &m;
1365      return *this;
1366    }
1367
1368  public:
1369
1370    /// \name Execution control
1371    /// The simplest way to execute the algorithm is to use
1372    /// one of the member functions called \ref lemon::DfsVisit::run()
1373    /// "run()".
1374    /// \n
1375    /// If you need more control on the execution, first you must call
1376    /// \ref lemon::DfsVisit::init() "init()", then you can add several
1377    /// source nodes with \ref lemon::DfsVisit::addSource() "addSource()".
1378    /// Finally \ref lemon::DfsVisit::start() "start()" will perform the
1379    /// actual path computation.
1380
1381    /// @{
1382
1383    /// \brief Initializes the internal data structures.
1384    ///
1385    /// Initializes the internal data structures.
1386    void init() {
1387      create_maps();
1388      _stack.resize(countNodes(*_digraph));
1389      _stack_head = -1;
1390      for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
1391        _reached->set(u, false);
1392      }
1393    }
1394
1395    ///Adds a new source node.
1396
1397    ///Adds a new source node to the set of nodes to be processed.
1398    ///
1399    ///\pre The stack must be empty. (Otherwise the algorithm gives
1400    ///false results.)
1401    ///
1402    ///\warning Distances will be wrong (or at least strange) in case of
1403    ///multiple sources.
1404    void addSource(Node s)
1405    {
1406      LEMON_DEBUG(emptyQueue(), "The stack is not empty.");
1407      if(!(*_reached)[s]) {
1408          _reached->set(s,true);
1409          _visitor->start(s);
1410          _visitor->reach(s);
1411          Arc e;
1412          _digraph->firstOut(e, s);
1413          if (e != INVALID) {
1414            _stack[++_stack_head] = e;
1415          } else {
1416            _visitor->leave(s);
1417          }
1418        }
1419    }
1420
1421    /// \brief Processes the next arc.
1422    ///
1423    /// Processes the next arc.
1424    ///
1425    /// \return The processed arc.
1426    ///
1427    /// \pre The stack must not be empty.
1428    Arc processNextArc() {
1429      Arc e = _stack[_stack_head];
1430      Node m = _digraph->target(e);
1431      if(!(*_reached)[m]) {
1432        _visitor->discover(e);
1433        _visitor->reach(m);
1434        _reached->set(m, true);
1435        _digraph->firstOut(_stack[++_stack_head], m);
1436      } else {
1437        _visitor->examine(e);
1438        m = _digraph->source(e);
1439        _digraph->nextOut(_stack[_stack_head]);
1440      }
1441      while (_stack_head>=0 && _stack[_stack_head] == INVALID) {
1442        _visitor->leave(m);
1443        --_stack_head;
1444        if (_stack_head >= 0) {
1445          _visitor->backtrack(_stack[_stack_head]);
1446          m = _digraph->source(_stack[_stack_head]);
1447          _digraph->nextOut(_stack[_stack_head]);
1448        } else {
1449          _visitor->stop(m);
1450        }
1451      }
1452      return e;
1453    }
1454
1455    /// \brief Next arc to be processed.
1456    ///
1457    /// Next arc to be processed.
1458    ///
1459    /// \return The next arc to be processed or INVALID if the stack is
1460    /// empty.
1461    Arc nextArc() const {
1462      return _stack_head >= 0 ? _stack[_stack_head] : INVALID;
1463    }
1464
1465    /// \brief Returns \c false if there are nodes
1466    /// to be processed.
1467    ///
1468    /// Returns \c false if there are nodes
1469    /// to be processed in the queue (stack).
1470    bool emptyQueue() const { return _stack_head < 0; }
1471
1472    /// \brief Returns the number of the nodes to be processed.
1473    ///
1474    /// Returns the number of the nodes to be processed in the queue (stack).
1475    int queueSize() const { return _stack_head + 1; }
1476
1477    /// \brief Executes the algorithm.
1478    ///
1479    /// Executes the algorithm.
1480    ///
1481    /// This method runs the %DFS algorithm from the root node
1482    /// in order to compute the %DFS path to each node.
1483    ///
1484    /// The algorithm computes
1485    /// - the %DFS tree,
1486    /// - the distance of each node from the root in the %DFS tree.
1487    ///
1488    /// \pre init() must be called and a root node should be
1489    /// added with addSource() before using this function.
1490    ///
1491    /// \note <tt>d.start()</tt> is just a shortcut of the following code.
1492    /// \code
1493    ///   while ( !d.emptyQueue() ) {
1494    ///     d.processNextArc();
1495    ///   }
1496    /// \endcode
1497    void start() {
1498      while ( !emptyQueue() ) processNextArc();
1499    }
1500
1501    /// \brief Executes the algorithm until the given target node is reached.
1502    ///
1503    /// Executes the algorithm until the given target node is reached.
1504    ///
1505    /// This method runs the %DFS algorithm from the root node
1506    /// in order to compute the DFS path to \c t.
1507    ///
1508    /// The algorithm computes
1509    /// - the %DFS path to \c t,
1510    /// - the distance of \c t from the root in the %DFS tree.
1511    ///
1512    /// \pre init() must be called and a root node should be added
1513    /// with addSource() before using this function.
1514    void start(Node t) {
1515      while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != t )
1516        processNextArc();
1517    }
1518
1519    /// \brief Executes the algorithm until a condition is met.
1520    ///
1521    /// Executes the algorithm until a condition is met.
1522    ///
1523    /// This method runs the %DFS algorithm from the root node
1524    /// until an arc \c a with <tt>am[a]</tt> true is found.
1525    ///
1526    /// \param am A \c bool (or convertible) arc map. The algorithm
1527    /// will stop when it reaches an arc \c a with <tt>am[a]</tt> true.
1528    ///
1529    /// \return The reached arc \c a with <tt>am[a]</tt> true or
1530    /// \c INVALID if no such arc was found.
1531    ///
1532    /// \pre init() must be called and a root node should be added
1533    /// with addSource() before using this function.
1534    ///
1535    /// \warning Contrary to \ref Bfs and \ref Dijkstra, \c am is an arc map,
1536    /// not a node map.
1537    template <typename AM>
1538    Arc start(const AM &am) {
1539      while ( !emptyQueue() && !am[_stack[_stack_head]] )
1540        processNextArc();
1541      return emptyQueue() ? INVALID : _stack[_stack_head];
1542    }
1543
1544    /// \brief Runs the algorithm from the given source node.
1545    ///
1546    /// This method runs the %DFS algorithm from node \c s.
1547    /// in order to compute the DFS path to each node.
1548    ///
1549    /// The algorithm computes
1550    /// - the %DFS tree,
1551    /// - the distance of each node from the root in the %DFS tree.
1552    ///
1553    /// \note <tt>d.run(s)</tt> is just a shortcut of the following code.
1554    ///\code
1555    ///   d.init();
1556    ///   d.addSource(s);
1557    ///   d.start();
1558    ///\endcode
1559    void run(Node s) {
1560      init();
1561      addSource(s);
1562      start();
1563    }
1564
1565    /// \brief Finds the %DFS path between \c s and \c t.
1566
1567    /// This method runs the %DFS algorithm from node \c s
1568    /// in order to compute the DFS path to node \c t
1569    /// (it stops searching when \c t is processed).
1570    ///
1571    /// \return \c true if \c t is reachable form \c s.
1572    ///
1573    /// \note Apart from the return value, <tt>d.run(s,t)</tt> is
1574    /// just a shortcut of the following code.
1575    ///\code
1576    ///   d.init();
1577    ///   d.addSource(s);
1578    ///   d.start(t);
1579    ///\endcode
1580    bool run(Node s,Node t) {
1581      init();
1582      addSource(s);
1583      start(t);
1584      return reached(t);
1585    }
1586
1587    /// \brief Runs the algorithm to visit all nodes in the digraph.
1588
1589    /// This method runs the %DFS algorithm in order to
1590    /// compute the %DFS path to each node.
1591    ///
1592    /// The algorithm computes
1593    /// - the %DFS tree,
1594    /// - the distance of each node from the root in the %DFS tree.
1595    ///
1596    /// \note <tt>d.run()</tt> is just a shortcut of the following code.
1597    ///\code
1598    ///   d.init();
1599    ///   for (NodeIt n(digraph); n != INVALID; ++n) {
1600    ///     if (!d.reached(n)) {
1601    ///       d.addSource(n);
1602    ///       d.start();
1603    ///     }
1604    ///   }
1605    ///\endcode
1606    void run() {
1607      init();
1608      for (NodeIt it(*_digraph); it != INVALID; ++it) {
1609        if (!reached(it)) {
1610          addSource(it);
1611          start();
1612        }
1613      }
1614    }
1615
1616    ///@}
1617
1618    /// \name Query Functions
1619    /// The result of the %DFS algorithm can be obtained using these
1620    /// functions.\n
1621    /// Either \ref lemon::DfsVisit::run() "run()" or
1622    /// \ref lemon::DfsVisit::start() "start()" must be called before
1623    /// using them.
1624    ///@{
1625
1626    /// \brief Checks if a node is reachable from the root(s).
1627    ///
1628    /// Returns \c true if \c v is reachable from the root(s).
1629    /// \pre Either \ref run() or \ref start()
1630    /// must be called before using this function.
1631    bool reached(Node v) { return (*_reached)[v]; }
1632
1633    ///@}
1634
1635  };
1636
1637} //END OF NAMESPACE LEMON
1638
1639#endif
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