COIN-OR::LEMON - Graph Library

source: lemon-1.0/lemon/dijkstra.h @ 395:8a144437db7d

Last change on this file since 395:8a144437db7d was 342:62f9787c516c, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Remove DijkstraWidestPathOperationTraits? (#187)

File size: 41.8 KB
Line 
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_DIJKSTRA_H
20#define LEMON_DIJKSTRA_H
21
22///\ingroup shortest_path
23///\file
24///\brief Dijkstra algorithm.
25
26#include <limits>
27#include <lemon/list_graph.h>
28#include <lemon/bin_heap.h>
29#include <lemon/bits/path_dump.h>
30#include <lemon/core.h>
31#include <lemon/error.h>
32#include <lemon/maps.h>
33#include <lemon/path.h>
34
35namespace lemon {
36
37  /// \brief Default operation traits for the Dijkstra algorithm class.
38  ///
39  /// This operation traits class defines all computational operations and
40  /// constants which are used in the Dijkstra algorithm.
41  template <typename Value>
42  struct DijkstraDefaultOperationTraits {
43    /// \brief Gives back the zero value of the type.
44    static Value zero() {
45      return static_cast<Value>(0);
46    }
47    /// \brief Gives back the sum of the given two elements.
48    static Value plus(const Value& left, const Value& right) {
49      return left + right;
50    }
51    /// \brief Gives back true only if the first value is less than the second.
52    static bool less(const Value& left, const Value& right) {
53      return left < right;
54    }
55  };
56
57  ///Default traits class of Dijkstra class.
58
59  ///Default traits class of Dijkstra class.
60  ///\tparam GR The type of the digraph.
61  ///\tparam LM The type of the length map.
62  template<class GR, class LM>
63  struct DijkstraDefaultTraits
64  {
65    ///The type of the digraph the algorithm runs on.
66    typedef GR Digraph;
67
68    ///The type of the map that stores the arc lengths.
69
70    ///The type of the map that stores the arc lengths.
71    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
72    typedef LM LengthMap;
73    ///The type of the length of the arcs.
74    typedef typename LM::Value Value;
75
76    /// Operation traits for Dijkstra algorithm.
77
78    /// This class defines the operations that are used in the algorithm.
79    /// \see DijkstraDefaultOperationTraits
80    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
81
82    /// The cross reference type used by the heap.
83
84    /// The cross reference type used by the heap.
85    /// Usually it is \c Digraph::NodeMap<int>.
86    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
87    ///Instantiates a \ref HeapCrossRef.
88
89    ///This function instantiates a \ref HeapCrossRef.
90    /// \param g is the digraph, to which we would like to define the
91    /// \ref HeapCrossRef.
92    static HeapCrossRef *createHeapCrossRef(const Digraph &g)
93    {
94      return new HeapCrossRef(g);
95    }
96
97    ///The heap type used by the Dijkstra algorithm.
98
99    ///The heap type used by the Dijkstra algorithm.
100    ///
101    ///\sa BinHeap
102    ///\sa Dijkstra
103    typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;
104    ///Instantiates a \ref Heap.
105
106    ///This function instantiates a \ref Heap.
107    static Heap *createHeap(HeapCrossRef& r)
108    {
109      return new Heap(r);
110    }
111
112    ///\brief The type of the map that stores the predecessor
113    ///arcs of the shortest paths.
114    ///
115    ///The type of the map that stores the predecessor
116    ///arcs of the shortest paths.
117    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
118    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
119    ///Instantiates a PredMap.
120
121    ///This function instantiates a PredMap.
122    ///\param g is the digraph, to which we would like to define the
123    ///PredMap.
124    static PredMap *createPredMap(const Digraph &g)
125    {
126      return new PredMap(g);
127    }
128
129    ///The type of the map that indicates which nodes are processed.
130
131    ///The type of the map that indicates which nodes are processed.
132    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
133    ///By default it is a NullMap.
134    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
135    ///Instantiates a ProcessedMap.
136
137    ///This function instantiates a ProcessedMap.
138    ///\param g is the digraph, to which
139    ///we would like to define the ProcessedMap
140#ifdef DOXYGEN
141    static ProcessedMap *createProcessedMap(const Digraph &g)
142#else
143    static ProcessedMap *createProcessedMap(const Digraph &)
144#endif
145    {
146      return new ProcessedMap();
147    }
148
149    ///The type of the map that stores the distances of the nodes.
150
151    ///The type of the map that stores the distances of the nodes.
152    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
153    typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;
154    ///Instantiates a DistMap.
155
156    ///This function instantiates a DistMap.
157    ///\param g is the digraph, to which we would like to define
158    ///the DistMap
159    static DistMap *createDistMap(const Digraph &g)
160    {
161      return new DistMap(g);
162    }
163  };
164
165  ///%Dijkstra algorithm class.
166
167  /// \ingroup shortest_path
168  ///This class provides an efficient implementation of the %Dijkstra algorithm.
169  ///
170  ///The arc lengths are passed to the algorithm using a
171  ///\ref concepts::ReadMap "ReadMap",
172  ///so it is easy to change it to any kind of length.
173  ///The type of the length is determined by the
174  ///\ref concepts::ReadMap::Value "Value" of the length map.
175  ///It is also possible to change the underlying priority heap.
176  ///
177  ///There is also a \ref dijkstra() "function-type interface" for the
178  ///%Dijkstra algorithm, which is convenient in the simplier cases and
179  ///it can be used easier.
180  ///
181  ///\tparam GR The type of the digraph the algorithm runs on.
182  ///The default value is \ref ListDigraph.
183  ///The value of GR is not used directly by \ref Dijkstra, it is only
184  ///passed to \ref DijkstraDefaultTraits.
185  ///\tparam LM A readable arc map that determines the lengths of the
186  ///arcs. It is read once for each arc, so the map may involve in
187  ///relatively time consuming process to compute the arc lengths if
188  ///it is necessary. The default map type is \ref
189  ///concepts::Digraph::ArcMap "Digraph::ArcMap<int>".
190  ///The value of LM is not used directly by \ref Dijkstra, it is only
191  ///passed to \ref DijkstraDefaultTraits.
192  ///\tparam TR Traits class to set various data types used by the algorithm.
193  ///The default traits class is \ref DijkstraDefaultTraits
194  ///"DijkstraDefaultTraits<GR,LM>". See \ref DijkstraDefaultTraits
195  ///for the documentation of a Dijkstra traits class.
196#ifdef DOXYGEN
197  template <typename GR, typename LM, typename TR>
198#else
199  template <typename GR=ListDigraph,
200            typename LM=typename GR::template ArcMap<int>,
201            typename TR=DijkstraDefaultTraits<GR,LM> >
202#endif
203  class Dijkstra {
204  public:
205
206    ///The type of the digraph the algorithm runs on.
207    typedef typename TR::Digraph Digraph;
208
209    ///The type of the length of the arcs.
210    typedef typename TR::LengthMap::Value Value;
211    ///The type of the map that stores the arc lengths.
212    typedef typename TR::LengthMap LengthMap;
213    ///\brief The type of the map that stores the predecessor arcs of the
214    ///shortest paths.
215    typedef typename TR::PredMap PredMap;
216    ///The type of the map that stores the distances of the nodes.
217    typedef typename TR::DistMap DistMap;
218    ///The type of the map that indicates which nodes are processed.
219    typedef typename TR::ProcessedMap ProcessedMap;
220    ///The type of the paths.
221    typedef PredMapPath<Digraph, PredMap> Path;
222    ///The cross reference type used for the current heap.
223    typedef typename TR::HeapCrossRef HeapCrossRef;
224    ///The heap type used by the algorithm.
225    typedef typename TR::Heap Heap;
226    ///The operation traits class.
227    typedef typename TR::OperationTraits OperationTraits;
228
229    ///The traits class.
230    typedef TR Traits;
231
232  private:
233
234    typedef typename Digraph::Node Node;
235    typedef typename Digraph::NodeIt NodeIt;
236    typedef typename Digraph::Arc Arc;
237    typedef typename Digraph::OutArcIt OutArcIt;
238
239    //Pointer to the underlying digraph.
240    const Digraph *G;
241    //Pointer to the length map.
242    const LengthMap *length;
243    //Pointer to the map of predecessors arcs.
244    PredMap *_pred;
245    //Indicates if _pred is locally allocated (true) or not.
246    bool local_pred;
247    //Pointer to the map of distances.
248    DistMap *_dist;
249    //Indicates if _dist is locally allocated (true) or not.
250    bool local_dist;
251    //Pointer to the map of processed status of the nodes.
252    ProcessedMap *_processed;
253    //Indicates if _processed is locally allocated (true) or not.
254    bool local_processed;
255    //Pointer to the heap cross references.
256    HeapCrossRef *_heap_cross_ref;
257    //Indicates if _heap_cross_ref is locally allocated (true) or not.
258    bool local_heap_cross_ref;
259    //Pointer to the heap.
260    Heap *_heap;
261    //Indicates if _heap is locally allocated (true) or not.
262    bool local_heap;
263
264    //Creates the maps if necessary.
265    void create_maps()
266    {
267      if(!_pred) {
268        local_pred = true;
269        _pred = Traits::createPredMap(*G);
270      }
271      if(!_dist) {
272        local_dist = true;
273        _dist = Traits::createDistMap(*G);
274      }
275      if(!_processed) {
276        local_processed = true;
277        _processed = Traits::createProcessedMap(*G);
278      }
279      if (!_heap_cross_ref) {
280        local_heap_cross_ref = true;
281        _heap_cross_ref = Traits::createHeapCrossRef(*G);
282      }
283      if (!_heap) {
284        local_heap = true;
285        _heap = Traits::createHeap(*_heap_cross_ref);
286      }
287    }
288
289  public:
290
291    typedef Dijkstra Create;
292
293    ///\name Named template parameters
294
295    ///@{
296
297    template <class T>
298    struct SetPredMapTraits : public Traits {
299      typedef T PredMap;
300      static PredMap *createPredMap(const Digraph &)
301      {
302        LEMON_ASSERT(false, "PredMap is not initialized");
303        return 0; // ignore warnings
304      }
305    };
306    ///\brief \ref named-templ-param "Named parameter" for setting
307    ///PredMap type.
308    ///
309    ///\ref named-templ-param "Named parameter" for setting
310    ///PredMap type.
311    template <class T>
312    struct SetPredMap
313      : public Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > {
314      typedef Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > Create;
315    };
316
317    template <class T>
318    struct SetDistMapTraits : public Traits {
319      typedef T DistMap;
320      static DistMap *createDistMap(const Digraph &)
321      {
322        LEMON_ASSERT(false, "DistMap is not initialized");
323        return 0; // ignore warnings
324      }
325    };
326    ///\brief \ref named-templ-param "Named parameter" for setting
327    ///DistMap type.
328    ///
329    ///\ref named-templ-param "Named parameter" for setting
330    ///DistMap type.
331    template <class T>
332    struct SetDistMap
333      : public Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > {
334      typedef Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > Create;
335    };
336
337    template <class T>
338    struct SetProcessedMapTraits : public Traits {
339      typedef T ProcessedMap;
340      static ProcessedMap *createProcessedMap(const Digraph &)
341      {
342        LEMON_ASSERT(false, "ProcessedMap is not initialized");
343        return 0; // ignore warnings
344      }
345    };
346    ///\brief \ref named-templ-param "Named parameter" for setting
347    ///ProcessedMap type.
348    ///
349    ///\ref named-templ-param "Named parameter" for setting
350    ///ProcessedMap type.
351    template <class T>
352    struct SetProcessedMap
353      : public Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > {
354      typedef Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > Create;
355    };
356
357    struct SetStandardProcessedMapTraits : public Traits {
358      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
359      static ProcessedMap *createProcessedMap(const Digraph &g)
360      {
361        return new ProcessedMap(g);
362      }
363    };
364    ///\brief \ref named-templ-param "Named parameter" for setting
365    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
366    ///
367    ///\ref named-templ-param "Named parameter" for setting
368    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
369    ///If you don't set it explicitly, it will be automatically allocated.
370    struct SetStandardProcessedMap
371      : public Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits > {
372      typedef Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits >
373      Create;
374    };
375
376    template <class H, class CR>
377    struct SetHeapTraits : public Traits {
378      typedef CR HeapCrossRef;
379      typedef H Heap;
380      static HeapCrossRef *createHeapCrossRef(const Digraph &) {
381        LEMON_ASSERT(false, "HeapCrossRef is not initialized");
382        return 0; // ignore warnings
383      }
384      static Heap *createHeap(HeapCrossRef &)
385      {
386        LEMON_ASSERT(false, "Heap is not initialized");
387        return 0; // ignore warnings
388      }
389    };
390    ///\brief \ref named-templ-param "Named parameter" for setting
391    ///heap and cross reference type
392    ///
393    ///\ref named-templ-param "Named parameter" for setting heap and cross
394    ///reference type.
395    template <class H, class CR = typename Digraph::template NodeMap<int> >
396    struct SetHeap
397      : public Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > {
398      typedef Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > Create;
399    };
400
401    template <class H, class CR>
402    struct SetStandardHeapTraits : public Traits {
403      typedef CR HeapCrossRef;
404      typedef H Heap;
405      static HeapCrossRef *createHeapCrossRef(const Digraph &G) {
406        return new HeapCrossRef(G);
407      }
408      static Heap *createHeap(HeapCrossRef &R)
409      {
410        return new Heap(R);
411      }
412    };
413    ///\brief \ref named-templ-param "Named parameter" for setting
414    ///heap and cross reference type with automatic allocation
415    ///
416    ///\ref named-templ-param "Named parameter" for setting heap and cross
417    ///reference type. It can allocate the heap and the cross reference
418    ///object if the cross reference's constructor waits for the digraph as
419    ///parameter and the heap's constructor waits for the cross reference.
420    template <class H, class CR = typename Digraph::template NodeMap<int> >
421    struct SetStandardHeap
422      : public Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> > {
423      typedef Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> >
424      Create;
425    };
426
427    template <class T>
428    struct SetOperationTraitsTraits : public Traits {
429      typedef T OperationTraits;
430    };
431
432    /// \brief \ref named-templ-param "Named parameter" for setting
433    ///\c OperationTraits type
434    ///
435    ///\ref named-templ-param "Named parameter" for setting
436    ///\ref OperationTraits type.
437    template <class T>
438    struct SetOperationTraits
439      : public Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> > {
440      typedef Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> >
441      Create;
442    };
443
444    ///@}
445
446  protected:
447
448    Dijkstra() {}
449
450  public:
451
452    ///Constructor.
453
454    ///Constructor.
455    ///\param _g The digraph the algorithm runs on.
456    ///\param _length The length map used by the algorithm.
457    Dijkstra(const Digraph& _g, const LengthMap& _length) :
458      G(&_g), length(&_length),
459      _pred(NULL), local_pred(false),
460      _dist(NULL), local_dist(false),
461      _processed(NULL), local_processed(false),
462      _heap_cross_ref(NULL), local_heap_cross_ref(false),
463      _heap(NULL), local_heap(false)
464    { }
465
466    ///Destructor.
467    ~Dijkstra()
468    {
469      if(local_pred) delete _pred;
470      if(local_dist) delete _dist;
471      if(local_processed) delete _processed;
472      if(local_heap_cross_ref) delete _heap_cross_ref;
473      if(local_heap) delete _heap;
474    }
475
476    ///Sets the length map.
477
478    ///Sets the length map.
479    ///\return <tt> (*this) </tt>
480    Dijkstra &lengthMap(const LengthMap &m)
481    {
482      length = &m;
483      return *this;
484    }
485
486    ///Sets the map that stores the predecessor arcs.
487
488    ///Sets the map that stores the predecessor arcs.
489    ///If you don't use this function before calling \ref run(),
490    ///it will allocate one. The destructor deallocates this
491    ///automatically allocated map, of course.
492    ///\return <tt> (*this) </tt>
493    Dijkstra &predMap(PredMap &m)
494    {
495      if(local_pred) {
496        delete _pred;
497        local_pred=false;
498      }
499      _pred = &m;
500      return *this;
501    }
502
503    ///Sets the map that indicates which nodes are processed.
504
505    ///Sets the map that indicates which nodes are processed.
506    ///If you don't use this function before calling \ref run(),
507    ///it will allocate one. The destructor deallocates this
508    ///automatically allocated map, of course.
509    ///\return <tt> (*this) </tt>
510    Dijkstra &processedMap(ProcessedMap &m)
511    {
512      if(local_processed) {
513        delete _processed;
514        local_processed=false;
515      }
516      _processed = &m;
517      return *this;
518    }
519
520    ///Sets the map that stores the distances of the nodes.
521
522    ///Sets the map that stores the distances of the nodes calculated by the
523    ///algorithm.
524    ///If you don't use this function before calling \ref run(),
525    ///it will allocate one. The destructor deallocates this
526    ///automatically allocated map, of course.
527    ///\return <tt> (*this) </tt>
528    Dijkstra &distMap(DistMap &m)
529    {
530      if(local_dist) {
531        delete _dist;
532        local_dist=false;
533      }
534      _dist = &m;
535      return *this;
536    }
537
538    ///Sets the heap and the cross reference used by algorithm.
539
540    ///Sets the heap and the cross reference used by algorithm.
541    ///If you don't use this function before calling \ref run(),
542    ///it will allocate one. The destructor deallocates this
543    ///automatically allocated heap and cross reference, of course.
544    ///\return <tt> (*this) </tt>
545    Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
546    {
547      if(local_heap_cross_ref) {
548        delete _heap_cross_ref;
549        local_heap_cross_ref=false;
550      }
551      _heap_cross_ref = &cr;
552      if(local_heap) {
553        delete _heap;
554        local_heap=false;
555      }
556      _heap = &hp;
557      return *this;
558    }
559
560  private:
561
562    void finalizeNodeData(Node v,Value dst)
563    {
564      _processed->set(v,true);
565      _dist->set(v, dst);
566    }
567
568  public:
569
570    ///\name Execution control
571    ///The simplest way to execute the algorithm is to use one of the
572    ///member functions called \ref lemon::Dijkstra::run() "run()".
573    ///\n
574    ///If you need more control on the execution, first you must call
575    ///\ref lemon::Dijkstra::init() "init()", then you can add several
576    ///source nodes with \ref lemon::Dijkstra::addSource() "addSource()".
577    ///Finally \ref lemon::Dijkstra::start() "start()" will perform the
578    ///actual path computation.
579
580    ///@{
581
582    ///Initializes the internal data structures.
583
584    ///Initializes the internal data structures.
585    ///
586    void init()
587    {
588      create_maps();
589      _heap->clear();
590      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
591        _pred->set(u,INVALID);
592        _processed->set(u,false);
593        _heap_cross_ref->set(u,Heap::PRE_HEAP);
594      }
595    }
596
597    ///Adds a new source node.
598
599    ///Adds a new source node to the priority heap.
600    ///The optional second parameter is the initial distance of the node.
601    ///
602    ///The function checks if the node has already been added to the heap and
603    ///it is pushed to the heap only if either it was not in the heap
604    ///or the shortest path found till then is shorter than \c dst.
605    void addSource(Node s,Value dst=OperationTraits::zero())
606    {
607      if(_heap->state(s) != Heap::IN_HEAP) {
608        _heap->push(s,dst);
609      } else if(OperationTraits::less((*_heap)[s], dst)) {
610        _heap->set(s,dst);
611        _pred->set(s,INVALID);
612      }
613    }
614
615    ///Processes the next node in the priority heap
616
617    ///Processes the next node in the priority heap.
618    ///
619    ///\return The processed node.
620    ///
621    ///\warning The priority heap must not be empty.
622    Node processNextNode()
623    {
624      Node v=_heap->top();
625      Value oldvalue=_heap->prio();
626      _heap->pop();
627      finalizeNodeData(v,oldvalue);
628
629      for(OutArcIt e(*G,v); e!=INVALID; ++e) {
630        Node w=G->target(e);
631        switch(_heap->state(w)) {
632        case Heap::PRE_HEAP:
633          _heap->push(w,OperationTraits::plus(oldvalue, (*length)[e]));
634          _pred->set(w,e);
635          break;
636        case Heap::IN_HEAP:
637          {
638            Value newvalue = OperationTraits::plus(oldvalue, (*length)[e]);
639            if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {
640              _heap->decrease(w, newvalue);
641              _pred->set(w,e);
642            }
643          }
644          break;
645        case Heap::POST_HEAP:
646          break;
647        }
648      }
649      return v;
650    }
651
652    ///The next node to be processed.
653
654    ///Returns the next node to be processed or \c INVALID if the
655    ///priority heap is empty.
656    Node nextNode() const
657    {
658      return !_heap->empty()?_heap->top():INVALID;
659    }
660
661    ///\brief Returns \c false if there are nodes
662    ///to be processed.
663    ///
664    ///Returns \c false if there are nodes
665    ///to be processed in the priority heap.
666    bool emptyQueue() const { return _heap->empty(); }
667
668    ///Returns the number of the nodes to be processed in the priority heap
669
670    ///Returns the number of the nodes to be processed in the priority heap.
671    ///
672    int queueSize() const { return _heap->size(); }
673
674    ///Executes the algorithm.
675
676    ///Executes the algorithm.
677    ///
678    ///This method runs the %Dijkstra algorithm from the root node(s)
679    ///in order to compute the shortest path to each node.
680    ///
681    ///The algorithm computes
682    ///- the shortest path tree (forest),
683    ///- the distance of each node from the root(s).
684    ///
685    ///\pre init() must be called and at least one root node should be
686    ///added with addSource() before using this function.
687    ///
688    ///\note <tt>d.start()</tt> is just a shortcut of the following code.
689    ///\code
690    ///  while ( !d.emptyQueue() ) {
691    ///    d.processNextNode();
692    ///  }
693    ///\endcode
694    void start()
695    {
696      while ( !emptyQueue() ) processNextNode();
697    }
698
699    ///Executes the algorithm until the given target node is processed.
700
701    ///Executes the algorithm until the given target node is processed.
702    ///
703    ///This method runs the %Dijkstra algorithm from the root node(s)
704    ///in order to compute the shortest path to \c t.
705    ///
706    ///The algorithm computes
707    ///- the shortest path to \c t,
708    ///- the distance of \c t from the root(s).
709    ///
710    ///\pre init() must be called and at least one root node should be
711    ///added with addSource() before using this function.
712    void start(Node t)
713    {
714      while ( !_heap->empty() && _heap->top()!=t ) processNextNode();
715      if ( !_heap->empty() ) {
716        finalizeNodeData(_heap->top(),_heap->prio());
717        _heap->pop();
718      }
719    }
720
721    ///Executes the algorithm until a condition is met.
722
723    ///Executes the algorithm until a condition is met.
724    ///
725    ///This method runs the %Dijkstra algorithm from the root node(s) in
726    ///order to compute the shortest path to a node \c v with
727    /// <tt>nm[v]</tt> true, if such a node can be found.
728    ///
729    ///\param nm A \c bool (or convertible) node map. The algorithm
730    ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
731    ///
732    ///\return The reached node \c v with <tt>nm[v]</tt> true or
733    ///\c INVALID if no such node was found.
734    ///
735    ///\pre init() must be called and at least one root node should be
736    ///added with addSource() before using this function.
737    template<class NodeBoolMap>
738    Node start(const NodeBoolMap &nm)
739    {
740      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
741      if ( _heap->empty() ) return INVALID;
742      finalizeNodeData(_heap->top(),_heap->prio());
743      return _heap->top();
744    }
745
746    ///Runs the algorithm from the given source node.
747
748    ///This method runs the %Dijkstra algorithm from node \c s
749    ///in order to compute the shortest path to each node.
750    ///
751    ///The algorithm computes
752    ///- the shortest path tree,
753    ///- the distance of each node from the root.
754    ///
755    ///\note <tt>d.run(s)</tt> is just a shortcut of the following code.
756    ///\code
757    ///  d.init();
758    ///  d.addSource(s);
759    ///  d.start();
760    ///\endcode
761    void run(Node s) {
762      init();
763      addSource(s);
764      start();
765    }
766
767    ///Finds the shortest path between \c s and \c t.
768
769    ///This method runs the %Dijkstra algorithm from node \c s
770    ///in order to compute the shortest path to node \c t
771    ///(it stops searching when \c t is processed).
772    ///
773    ///\return \c true if \c t is reachable form \c s.
774    ///
775    ///\note Apart from the return value, <tt>d.run(s,t)</tt> is just a
776    ///shortcut of the following code.
777    ///\code
778    ///  d.init();
779    ///  d.addSource(s);
780    ///  d.start(t);
781    ///\endcode
782    bool run(Node s,Node t) {
783      init();
784      addSource(s);
785      start(t);
786      return (*_heap_cross_ref)[t] == Heap::POST_HEAP;
787    }
788
789    ///@}
790
791    ///\name Query Functions
792    ///The result of the %Dijkstra algorithm can be obtained using these
793    ///functions.\n
794    ///Either \ref lemon::Dijkstra::run() "run()" or
795    ///\ref lemon::Dijkstra::start() "start()" must be called before
796    ///using them.
797
798    ///@{
799
800    ///The shortest path to a node.
801
802    ///Returns the shortest path to a node.
803    ///
804    ///\warning \c t should be reachable from the root(s).
805    ///
806    ///\pre Either \ref run() or \ref start() must be called before
807    ///using this function.
808    Path path(Node t) const { return Path(*G, *_pred, t); }
809
810    ///The distance of a node from the root(s).
811
812    ///Returns the distance of a node from the root(s).
813    ///
814    ///\warning If node \c v is not reachable from the root(s), then
815    ///the return value of this function is undefined.
816    ///
817    ///\pre Either \ref run() or \ref start() must be called before
818    ///using this function.
819    Value dist(Node v) const { return (*_dist)[v]; }
820
821    ///Returns the 'previous arc' of the shortest path tree for a node.
822
823    ///This function returns the 'previous arc' of the shortest path
824    ///tree for the node \c v, i.e. it returns the last arc of a
825    ///shortest path from the root(s) to \c v. It is \c INVALID if \c v
826    ///is not reachable from the root(s) or if \c v is a root.
827    ///
828    ///The shortest path tree used here is equal to the shortest path
829    ///tree used in \ref predNode().
830    ///
831    ///\pre Either \ref run() or \ref start() must be called before
832    ///using this function.
833    Arc predArc(Node v) const { return (*_pred)[v]; }
834
835    ///Returns the 'previous node' of the shortest path tree for a node.
836
837    ///This function returns the 'previous node' of the shortest path
838    ///tree for the node \c v, i.e. it returns the last but one node
839    ///from a shortest path from the root(s) to \c v. It is \c INVALID
840    ///if \c v is not reachable from the root(s) or if \c v is a root.
841    ///
842    ///The shortest path tree used here is equal to the shortest path
843    ///tree used in \ref predArc().
844    ///
845    ///\pre Either \ref run() or \ref start() must be called before
846    ///using this function.
847    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
848                                  G->source((*_pred)[v]); }
849
850    ///\brief Returns a const reference to the node map that stores the
851    ///distances of the nodes.
852    ///
853    ///Returns a const reference to the node map that stores the distances
854    ///of the nodes calculated by the algorithm.
855    ///
856    ///\pre Either \ref run() or \ref init()
857    ///must be called before using this function.
858    const DistMap &distMap() const { return *_dist;}
859
860    ///\brief Returns a const reference to the node map that stores the
861    ///predecessor arcs.
862    ///
863    ///Returns a const reference to the node map that stores the predecessor
864    ///arcs, which form the shortest path tree.
865    ///
866    ///\pre Either \ref run() or \ref init()
867    ///must be called before using this function.
868    const PredMap &predMap() const { return *_pred;}
869
870    ///Checks if a node is reachable from the root(s).
871
872    ///Returns \c true if \c v is reachable from the root(s).
873    ///\pre Either \ref run() or \ref start()
874    ///must be called before using this function.
875    bool reached(Node v) const { return (*_heap_cross_ref)[v] !=
876                                        Heap::PRE_HEAP; }
877
878    ///Checks if a node is processed.
879
880    ///Returns \c true if \c v is processed, i.e. the shortest
881    ///path to \c v has already found.
882    ///\pre Either \ref run() or \ref init()
883    ///must be called before using this function.
884    bool processed(Node v) const { return (*_heap_cross_ref)[v] ==
885                                          Heap::POST_HEAP; }
886
887    ///The current distance of a node from the root(s).
888
889    ///Returns the current distance of a node from the root(s).
890    ///It may be decreased in the following processes.
891    ///\pre Either \ref run() or \ref init()
892    ///must be called before using this function and
893    ///node \c v must be reached but not necessarily processed.
894    Value currentDist(Node v) const {
895      return processed(v) ? (*_dist)[v] : (*_heap)[v];
896    }
897
898    ///@}
899  };
900
901
902  ///Default traits class of dijkstra() function.
903
904  ///Default traits class of dijkstra() function.
905  ///\tparam GR The type of the digraph.
906  ///\tparam LM The type of the length map.
907  template<class GR, class LM>
908  struct DijkstraWizardDefaultTraits
909  {
910    ///The type of the digraph the algorithm runs on.
911    typedef GR Digraph;
912    ///The type of the map that stores the arc lengths.
913
914    ///The type of the map that stores the arc lengths.
915    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
916    typedef LM LengthMap;
917    ///The type of the length of the arcs.
918    typedef typename LM::Value Value;
919
920    /// Operation traits for Dijkstra algorithm.
921
922    /// This class defines the operations that are used in the algorithm.
923    /// \see DijkstraDefaultOperationTraits
924    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
925
926    /// The cross reference type used by the heap.
927
928    /// The cross reference type used by the heap.
929    /// Usually it is \c Digraph::NodeMap<int>.
930    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
931    ///Instantiates a \ref HeapCrossRef.
932
933    ///This function instantiates a \ref HeapCrossRef.
934    /// \param g is the digraph, to which we would like to define the
935    /// HeapCrossRef.
936    static HeapCrossRef *createHeapCrossRef(const Digraph &g)
937    {
938      return new HeapCrossRef(g);
939    }
940
941    ///The heap type used by the Dijkstra algorithm.
942
943    ///The heap type used by the Dijkstra algorithm.
944    ///
945    ///\sa BinHeap
946    ///\sa Dijkstra
947    typedef BinHeap<Value, typename Digraph::template NodeMap<int>,
948                    std::less<Value> > Heap;
949
950    ///Instantiates a \ref Heap.
951
952    ///This function instantiates a \ref Heap.
953    /// \param r is the HeapCrossRef which is used.
954    static Heap *createHeap(HeapCrossRef& r)
955    {
956      return new Heap(r);
957    }
958
959    ///\brief The type of the map that stores the predecessor
960    ///arcs of the shortest paths.
961    ///
962    ///The type of the map that stores the predecessor
963    ///arcs of the shortest paths.
964    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
965    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
966    ///Instantiates a PredMap.
967
968    ///This function instantiates a PredMap.
969    ///\param g is the digraph, to which we would like to define the
970    ///PredMap.
971    static PredMap *createPredMap(const Digraph &g)
972    {
973      return new PredMap(g);
974    }
975
976    ///The type of the map that indicates which nodes are processed.
977
978    ///The type of the map that indicates which nodes are processed.
979    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
980    ///By default it is a NullMap.
981    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
982    ///Instantiates a ProcessedMap.
983
984    ///This function instantiates a ProcessedMap.
985    ///\param g is the digraph, to which
986    ///we would like to define the ProcessedMap.
987#ifdef DOXYGEN
988    static ProcessedMap *createProcessedMap(const Digraph &g)
989#else
990    static ProcessedMap *createProcessedMap(const Digraph &)
991#endif
992    {
993      return new ProcessedMap();
994    }
995
996    ///The type of the map that stores the distances of the nodes.
997
998    ///The type of the map that stores the distances of the nodes.
999    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
1000    typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;
1001    ///Instantiates a DistMap.
1002
1003    ///This function instantiates a DistMap.
1004    ///\param g is the digraph, to which we would like to define
1005    ///the DistMap
1006    static DistMap *createDistMap(const Digraph &g)
1007    {
1008      return new DistMap(g);
1009    }
1010
1011    ///The type of the shortest paths.
1012
1013    ///The type of the shortest paths.
1014    ///It must meet the \ref concepts::Path "Path" concept.
1015    typedef lemon::Path<Digraph> Path;
1016  };
1017
1018  /// Default traits class used by DijkstraWizard
1019
1020  /// To make it easier to use Dijkstra algorithm
1021  /// we have created a wizard class.
1022  /// This \ref DijkstraWizard class needs default traits,
1023  /// as well as the \ref Dijkstra class.
1024  /// The \ref DijkstraWizardBase is a class to be the default traits of the
1025  /// \ref DijkstraWizard class.
1026  template<class GR,class LM>
1027  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
1028  {
1029    typedef DijkstraWizardDefaultTraits<GR,LM> Base;
1030  protected:
1031    //The type of the nodes in the digraph.
1032    typedef typename Base::Digraph::Node Node;
1033
1034    //Pointer to the digraph the algorithm runs on.
1035    void *_g;
1036    //Pointer to the length map.
1037    void *_length;
1038    //Pointer to the map of processed nodes.
1039    void *_processed;
1040    //Pointer to the map of predecessors arcs.
1041    void *_pred;
1042    //Pointer to the map of distances.
1043    void *_dist;
1044    //Pointer to the shortest path to the target node.
1045    void *_path;
1046    //Pointer to the distance of the target node.
1047    void *_di;
1048
1049  public:
1050    /// Constructor.
1051
1052    /// This constructor does not require parameters, therefore it initiates
1053    /// all of the attributes to \c 0.
1054    DijkstraWizardBase() : _g(0), _length(0), _processed(0), _pred(0),
1055                           _dist(0), _path(0), _di(0) {}
1056
1057    /// Constructor.
1058
1059    /// This constructor requires two parameters,
1060    /// others are initiated to \c 0.
1061    /// \param g The digraph the algorithm runs on.
1062    /// \param l The length map.
1063    DijkstraWizardBase(const GR &g,const LM &l) :
1064      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
1065      _length(reinterpret_cast<void*>(const_cast<LM*>(&l))),
1066      _processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
1067
1068  };
1069
1070  /// Auxiliary class for the function-type interface of Dijkstra algorithm.
1071
1072  /// This auxiliary class is created to implement the
1073  /// \ref dijkstra() "function-type interface" of \ref Dijkstra algorithm.
1074  /// It does not have own \ref run() method, it uses the functions
1075  /// and features of the plain \ref Dijkstra.
1076  ///
1077  /// This class should only be used through the \ref dijkstra() function,
1078  /// which makes it easier to use the algorithm.
1079  template<class TR>
1080  class DijkstraWizard : public TR
1081  {
1082    typedef TR Base;
1083
1084    ///The type of the digraph the algorithm runs on.
1085    typedef typename TR::Digraph Digraph;
1086
1087    typedef typename Digraph::Node Node;
1088    typedef typename Digraph::NodeIt NodeIt;
1089    typedef typename Digraph::Arc Arc;
1090    typedef typename Digraph::OutArcIt OutArcIt;
1091
1092    ///The type of the map that stores the arc lengths.
1093    typedef typename TR::LengthMap LengthMap;
1094    ///The type of the length of the arcs.
1095    typedef typename LengthMap::Value Value;
1096    ///\brief The type of the map that stores the predecessor
1097    ///arcs of the shortest paths.
1098    typedef typename TR::PredMap PredMap;
1099    ///The type of the map that stores the distances of the nodes.
1100    typedef typename TR::DistMap DistMap;
1101    ///The type of the map that indicates which nodes are processed.
1102    typedef typename TR::ProcessedMap ProcessedMap;
1103    ///The type of the shortest paths
1104    typedef typename TR::Path Path;
1105    ///The heap type used by the dijkstra algorithm.
1106    typedef typename TR::Heap Heap;
1107
1108  public:
1109
1110    /// Constructor.
1111    DijkstraWizard() : TR() {}
1112
1113    /// Constructor that requires parameters.
1114
1115    /// Constructor that requires parameters.
1116    /// These parameters will be the default values for the traits class.
1117    /// \param g The digraph the algorithm runs on.
1118    /// \param l The length map.
1119    DijkstraWizard(const Digraph &g, const LengthMap &l) :
1120      TR(g,l) {}
1121
1122    ///Copy constructor
1123    DijkstraWizard(const TR &b) : TR(b) {}
1124
1125    ~DijkstraWizard() {}
1126
1127    ///Runs Dijkstra algorithm from the given source node.
1128
1129    ///This method runs %Dijkstra algorithm from the given source node
1130    ///in order to compute the shortest path to each node.
1131    void run(Node s)
1132    {
1133      Dijkstra<Digraph,LengthMap,TR>
1134        dijk(*reinterpret_cast<const Digraph*>(Base::_g),
1135             *reinterpret_cast<const LengthMap*>(Base::_length));
1136      if (Base::_pred)
1137        dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1138      if (Base::_dist)
1139        dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1140      if (Base::_processed)
1141        dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
1142      dijk.run(s);
1143    }
1144
1145    ///Finds the shortest path between \c s and \c t.
1146
1147    ///This method runs the %Dijkstra algorithm from node \c s
1148    ///in order to compute the shortest path to node \c t
1149    ///(it stops searching when \c t is processed).
1150    ///
1151    ///\return \c true if \c t is reachable form \c s.
1152    bool run(Node s, Node t)
1153    {
1154      Dijkstra<Digraph,LengthMap,TR>
1155        dijk(*reinterpret_cast<const Digraph*>(Base::_g),
1156             *reinterpret_cast<const LengthMap*>(Base::_length));
1157      if (Base::_pred)
1158        dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1159      if (Base::_dist)
1160        dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1161      if (Base::_processed)
1162        dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
1163      dijk.run(s,t);
1164      if (Base::_path)
1165        *reinterpret_cast<Path*>(Base::_path) = dijk.path(t);
1166      if (Base::_di)
1167        *reinterpret_cast<Value*>(Base::_di) = dijk.dist(t);
1168      return dijk.reached(t);
1169    }
1170
1171    template<class T>
1172    struct SetPredMapBase : public Base {
1173      typedef T PredMap;
1174      static PredMap *createPredMap(const Digraph &) { return 0; };
1175      SetPredMapBase(const TR &b) : TR(b) {}
1176    };
1177    ///\brief \ref named-func-param "Named parameter"
1178    ///for setting PredMap object.
1179    ///
1180    ///\ref named-func-param "Named parameter"
1181    ///for setting PredMap object.
1182    template<class T>
1183    DijkstraWizard<SetPredMapBase<T> > predMap(const T &t)
1184    {
1185      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
1186      return DijkstraWizard<SetPredMapBase<T> >(*this);
1187    }
1188
1189    template<class T>
1190    struct SetDistMapBase : public Base {
1191      typedef T DistMap;
1192      static DistMap *createDistMap(const Digraph &) { return 0; };
1193      SetDistMapBase(const TR &b) : TR(b) {}
1194    };
1195    ///\brief \ref named-func-param "Named parameter"
1196    ///for setting DistMap object.
1197    ///
1198    ///\ref named-func-param "Named parameter"
1199    ///for setting DistMap object.
1200    template<class T>
1201    DijkstraWizard<SetDistMapBase<T> > distMap(const T &t)
1202    {
1203      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
1204      return DijkstraWizard<SetDistMapBase<T> >(*this);
1205    }
1206
1207    template<class T>
1208    struct SetProcessedMapBase : public Base {
1209      typedef T ProcessedMap;
1210      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
1211      SetProcessedMapBase(const TR &b) : TR(b) {}
1212    };
1213    ///\brief \ref named-func-param "Named parameter"
1214    ///for setting ProcessedMap object.
1215    ///
1216    /// \ref named-func-param "Named parameter"
1217    ///for setting ProcessedMap object.
1218    template<class T>
1219    DijkstraWizard<SetProcessedMapBase<T> > processedMap(const T &t)
1220    {
1221      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
1222      return DijkstraWizard<SetProcessedMapBase<T> >(*this);
1223    }
1224
1225    template<class T>
1226    struct SetPathBase : public Base {
1227      typedef T Path;
1228      SetPathBase(const TR &b) : TR(b) {}
1229    };
1230    ///\brief \ref named-func-param "Named parameter"
1231    ///for getting the shortest path to the target node.
1232    ///
1233    ///\ref named-func-param "Named parameter"
1234    ///for getting the shortest path to the target node.
1235    template<class T>
1236    DijkstraWizard<SetPathBase<T> > path(const T &t)
1237    {
1238      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
1239      return DijkstraWizard<SetPathBase<T> >(*this);
1240    }
1241
1242    ///\brief \ref named-func-param "Named parameter"
1243    ///for getting the distance of the target node.
1244    ///
1245    ///\ref named-func-param "Named parameter"
1246    ///for getting the distance of the target node.
1247    DijkstraWizard dist(const Value &d)
1248    {
1249      Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
1250      return *this;
1251    }
1252
1253  };
1254
1255  ///Function-type interface for Dijkstra algorithm.
1256
1257  /// \ingroup shortest_path
1258  ///Function-type interface for Dijkstra algorithm.
1259  ///
1260  ///This function also has several \ref named-func-param "named parameters",
1261  ///they are declared as the members of class \ref DijkstraWizard.
1262  ///The following examples show how to use these parameters.
1263  ///\code
1264  ///  // Compute shortest path from node s to each node
1265  ///  dijkstra(g,length).predMap(preds).distMap(dists).run(s);
1266  ///
1267  ///  // Compute shortest path from s to t
1268  ///  bool reached = dijkstra(g,length).path(p).dist(d).run(s,t);
1269  ///\endcode
1270  ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
1271  ///to the end of the parameter list.
1272  ///\sa DijkstraWizard
1273  ///\sa Dijkstra
1274  template<class GR, class LM>
1275  DijkstraWizard<DijkstraWizardBase<GR,LM> >
1276  dijkstra(const GR &digraph, const LM &length)
1277  {
1278    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(digraph,length);
1279  }
1280
1281} //END OF NAMESPACE LEMON
1282
1283#endif
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