COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/dijkstra.h @ 1741:7a98fe2ed989

Last change on this file since 1741:7a98fe2ed989 was 1741:7a98fe2ed989, checked in by Balazs Dezso, 14 years ago

Some modifications on shortest path algoritms:

  • heap traits
  • checked execution
File size: 35.6 KB
Line 
1/* -*- C++ -*-
2 * lemon/dijkstra.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_DIJKSTRA_H
18#define LEMON_DIJKSTRA_H
19
20///\ingroup flowalgs
21///\file
22///\brief Dijkstra algorithm.
23///
24///\todo getPath() should be implemented! (also for BFS and DFS)
25///\todo dijkstraZero() solution should be revised.
26
27#include <lemon/list_graph.h>
28#include <lemon/bin_heap.h>
29#include <lemon/invalid.h>
30#include <lemon/error.h>
31#include <lemon/maps.h>
32
33namespace lemon {
34
35  template<class T> T dijkstraZero() {return 0;}
36 
37  ///Default traits class of Dijkstra class.
38
39  ///Default traits class of Dijkstra class.
40  ///\param GR Graph type.
41  ///\param LM Type of length map.
42  template<class GR, class LM>
43  struct DijkstraDefaultTraits
44  {
45    ///The graph type the algorithm runs on.
46    typedef GR Graph;
47    ///The type of the map that stores the edge lengths.
48
49    ///The type of the map that stores the edge lengths.
50    ///It must meet the \ref concept::ReadMap "ReadMap" concept.
51    typedef LM LengthMap;
52    //The type of the length of the edges.
53    typedef typename LM::Value Value;
54    /// The cross reference type used by heap.
55
56    /// The cross reference type used by heap.
57    /// Usually it is \c Graph::NodeMap<int>.
58    typedef typename Graph::template NodeMap<int> HeapCrossRef;
59    ///Instantiates a HeapCrossRef.
60
61    ///This function instantiates a \ref HeapCrossRef.
62    /// \param G is the graph, to which we would like to define the
63    /// HeapCrossRef.
64    static HeapCrossRef *createHeapCrossRef(const GR &G)
65    {
66      return new HeapCrossRef(G);
67    }
68   
69    ///The heap type used by Dijkstra algorithm.
70
71    ///The heap type used by Dijkstra algorithm.
72    ///
73    ///\sa BinHeap
74    ///\sa Dijkstra
75    typedef BinHeap<typename Graph::Node, typename LM::Value,
76                    HeapCrossRef, std::less<Value> > Heap;
77
78    static Heap *createHeap(HeapCrossRef& R)
79    {
80      return new Heap(R);
81    }
82
83    ///\brief The type of the map that stores the last
84    ///edges of the shortest paths.
85    ///
86    ///The type of the map that stores the last
87    ///edges of the shortest paths.
88    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
89    ///
90    typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;
91    ///Instantiates a PredMap.
92 
93    ///This function instantiates a \ref PredMap.
94    ///\param G is the graph, to which we would like to define the PredMap.
95    ///\todo The graph alone may be insufficient for the initialization
96    static PredMap *createPredMap(const GR &G)
97    {
98      return new PredMap(G);
99    }
100
101    ///The type of the map that stores whether a nodes is processed.
102 
103    ///The type of the map that stores whether a nodes is processed.
104    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
105    ///By default it is a NullMap.
106    ///\todo If it is set to a real map,
107    ///Dijkstra::processed() should read this.
108    ///\todo named parameter to set this type, function to read and write.
109    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
110    ///Instantiates a ProcessedMap.
111 
112    ///This function instantiates a \ref ProcessedMap.
113    ///\param g is the graph, to which
114    ///we would like to define the \ref ProcessedMap
115#ifdef DOXYGEN
116    static ProcessedMap *createProcessedMap(const GR &g)
117#else
118    static ProcessedMap *createProcessedMap(const GR &)
119#endif
120    {
121      return new ProcessedMap();
122    }
123    ///The type of the map that stores the dists of the nodes.
124 
125    ///The type of the map that stores the dists of the nodes.
126    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
127    ///
128    typedef typename Graph::template NodeMap<typename LM::Value> DistMap;
129    ///Instantiates a DistMap.
130 
131    ///This function instantiates a \ref DistMap.
132    ///\param G is the graph, to which we would like to define the \ref DistMap
133    static DistMap *createDistMap(const GR &G)
134    {
135      return new DistMap(G);
136    }
137  };
138 
139  ///%Dijkstra algorithm class.
140 
141  /// \ingroup flowalgs
142  ///This class provides an efficient implementation of %Dijkstra algorithm.
143  ///The edge lengths are passed to the algorithm using a
144  ///\ref concept::ReadMap "ReadMap",
145  ///so it is easy to change it to any kind of length.
146  ///
147  ///The type of the length is determined by the
148  ///\ref concept::ReadMap::Value "Value" of the length map.
149  ///
150  ///It is also possible to change the underlying priority heap.
151  ///
152  ///\param GR The graph type the algorithm runs on. The default value
153  ///is \ref ListGraph. The value of GR is not used directly by
154  ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits.
155  ///\param LM This read-only EdgeMap determines the lengths of the
156  ///edges. It is read once for each edge, so the map may involve in
157  ///relatively time consuming process to compute the edge length if
158  ///it is necessary. The default map type is \ref
159  ///concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
160  ///of LM is not used directly by Dijkstra, it is only passed to \ref
161  ///DijkstraDefaultTraits.  \param TR Traits class to set
162  ///various data types used by the algorithm.  The default traits
163  ///class is \ref DijkstraDefaultTraits
164  ///"DijkstraDefaultTraits<GR,LM>".  See \ref
165  ///DijkstraDefaultTraits for the documentation of a Dijkstra traits
166  ///class.
167  ///
168  ///\author Jacint Szabo and Alpar Juttner
169  ///\todo A compare object would be nice.
170
171#ifdef DOXYGEN
172  template <typename GR,
173            typename LM,
174            typename TR>
175#else
176  template <typename GR=ListGraph,
177            typename LM=typename GR::template EdgeMap<int>,
178            typename TR=DijkstraDefaultTraits<GR,LM> >
179#endif
180  class Dijkstra {
181  public:
182    /**
183     * \brief \ref Exception for uninitialized parameters.
184     *
185     * This error represents problems in the initialization
186     * of the parameters of the algorithms.
187     */
188    class UninitializedParameter : public lemon::UninitializedParameter {
189    public:
190      virtual const char* exceptionName() const {
191        return "lemon::Dijkstra::UninitializedParameter";
192      }
193    };
194
195    typedef TR Traits;
196    ///The type of the underlying graph.
197    typedef typename TR::Graph Graph;
198    ///\e
199    typedef typename Graph::Node Node;
200    ///\e
201    typedef typename Graph::NodeIt NodeIt;
202    ///\e
203    typedef typename Graph::Edge Edge;
204    ///\e
205    typedef typename Graph::OutEdgeIt OutEdgeIt;
206   
207    ///The type of the length of the edges.
208    typedef typename TR::LengthMap::Value Value;
209    ///The type of the map that stores the edge lengths.
210    typedef typename TR::LengthMap LengthMap;
211    ///\brief The type of the map that stores the last
212    ///edges of the shortest paths.
213    typedef typename TR::PredMap PredMap;
214    ///The type of the map indicating if a node is processed.
215    typedef typename TR::ProcessedMap ProcessedMap;
216    ///The type of the map that stores the dists of the nodes.
217    typedef typename TR::DistMap DistMap;
218    ///The cross reference type used for the current heap.
219    typedef typename TR::HeapCrossRef HeapCrossRef;
220    ///The heap type used by the dijkstra algorithm.
221    typedef typename TR::Heap Heap;
222  private:
223    /// Pointer to the underlying graph.
224    const Graph *G;
225    /// Pointer to the length map
226    const LengthMap *length;
227    ///Pointer to the map of predecessors edges.
228    PredMap *_pred;
229    ///Indicates if \ref _pred is locally allocated (\c true) or not.
230    bool local_pred;
231    ///Pointer to the map of distances.
232    DistMap *_dist;
233    ///Indicates if \ref _dist is locally allocated (\c true) or not.
234    bool local_dist;
235    ///Pointer to the map of processed status of the nodes.
236    ProcessedMap *_processed;
237    ///Indicates if \ref _processed is locally allocated (\c true) or not.
238    bool local_processed;
239    ///Pointer to the heap cross references.
240    HeapCrossRef *_heap_cross_ref;
241    ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.
242    bool local_heap_cross_ref;
243    ///Pointer to the heap.
244    Heap *_heap;
245    ///Indicates if \ref _heap is locally allocated (\c true) or not.
246    bool local_heap;
247
248    ///Creates the maps if necessary.
249   
250    ///\todo Error if \c G or are \c NULL. What about \c length?
251    ///\todo Better memory allocation (instead of new).
252    void create_maps()
253    {
254      if(!_pred) {
255        local_pred = true;
256        _pred = Traits::createPredMap(*G);
257      }
258      if(!_dist) {
259        local_dist = true;
260        _dist = Traits::createDistMap(*G);
261      }
262      if(!_processed) {
263        local_processed = true;
264        _processed = Traits::createProcessedMap(*G);
265      }
266      if (!_heap_cross_ref) {
267        local_heap_cross_ref = true;
268        _heap_cross_ref = Traits::createHeapCrossRef(*G);
269      }
270      if (!_heap) {
271        local_heap = true;
272        _heap = Traits::createHeap(*_heap_cross_ref);
273      }
274    }
275   
276  public :
277
278    typedef Dijkstra Create;
279 
280    ///\name Named template parameters
281
282    ///@{
283
284    template <class T>
285    struct DefPredMapTraits : public Traits {
286      typedef T PredMap;
287      static PredMap *createPredMap(const Graph &G)
288      {
289        throw UninitializedParameter();
290      }
291    };
292    ///\ref named-templ-param "Named parameter" for setting PredMap type
293
294    ///\ref named-templ-param "Named parameter" for setting PredMap type
295    ///
296    template <class T>
297    struct DefPredMap
298      : public Dijkstra< Graph, LengthMap, DefPredMapTraits<T> > {
299      typedef Dijkstra< Graph,  LengthMap, DefPredMapTraits<T> > Create;
300    };
301   
302    template <class T>
303    struct DefDistMapTraits : public Traits {
304      typedef T DistMap;
305      static DistMap *createDistMap(const Graph &G)
306      {
307        throw UninitializedParameter();
308      }
309    };
310    ///\ref named-templ-param "Named parameter" for setting DistMap type
311
312    ///\ref named-templ-param "Named parameter" for setting DistMap type
313    ///
314    template <class T>
315    struct DefDistMap
316      : public Dijkstra< Graph, LengthMap, DefDistMapTraits<T> > {
317      typedef Dijkstra< Graph, LengthMap, DefDistMapTraits<T> > Create;
318    };
319   
320    template <class T>
321    struct DefProcessedMapTraits : public Traits {
322      typedef T ProcessedMap;
323      static ProcessedMap *createProcessedMap(const Graph &G)
324      {
325        throw UninitializedParameter();
326      }
327    };
328    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
329
330    ///\ref named-templ-param "Named parameter" for setting ProcessedMap type
331    ///
332    template <class T>
333    struct DefProcessedMap
334      : public Dijkstra< Graph, LengthMap, DefProcessedMapTraits<T> > {
335      typedef Dijkstra< Graph,  LengthMap, DefProcessedMapTraits<T> > Create;
336    };
337   
338    struct DefGraphProcessedMapTraits : public Traits {
339      typedef typename Graph::template NodeMap<bool> ProcessedMap;
340      static ProcessedMap *createProcessedMap(const Graph &G)
341      {
342        return new ProcessedMap(G);
343      }
344    };
345    ///\brief \ref named-templ-param "Named parameter"
346    ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.
347    ///
348    ///\ref named-templ-param "Named parameter"
349    ///for setting the ProcessedMap type to be Graph::NodeMap<bool>.
350    ///If you don't set it explicitely, it will be automatically allocated.
351    template <class T>
352    struct DefProcessedMapToBeDefaultMap
353      : public Dijkstra< Graph, LengthMap, DefGraphProcessedMapTraits> {
354      typedef Dijkstra< Graph, LengthMap, DefGraphProcessedMapTraits> Create;
355    };
356
357    template <class H, class CR>
358    struct DefHeapTraits : public Traits {
359      typedef CR HeapCrossRef;
360      typedef H Heap;
361      static HeapCrossRef *createHeapCrossRef(const Graph &) {
362        throw UninitializedParameter();
363      }
364      static Heap *createHeap(HeapCrossRef &)
365      {
366        throw UninitializedParameter();
367      }
368    };
369    ///\ref named-templ-param "Named parameter" for setting heap and cross
370    ///reference type
371
372    ///\ref named-templ-param "Named parameter" for setting heap and cross
373    ///reference type
374    ///
375    template <class H, class CR = typename Graph::template NodeMap<int> >
376    struct DefHeap
377      : public Dijkstra< Graph, LengthMap, DefHeapTraits<H, CR> > {
378      typedef Dijkstra< Graph,  LengthMap, DefHeapTraits<H, CR> > Create;
379    };
380
381    template <class H, class CR>
382    struct DefStandardHeapTraits : public Traits {
383      typedef CR HeapCrossRef;
384      typedef H Heap;
385      static HeapCrossRef *createHeapCrossRef(const Graph &G) {
386        return new HeapCrossRef(G);
387      }
388      static Heap *createHeap(HeapCrossRef &R)
389      {
390        return new Heap(R);
391      }
392    };
393    ///\ref named-templ-param "Named parameter" for setting heap and cross
394    ///reference type with automatic allocation
395
396    ///\ref named-templ-param "Named parameter" for setting heap and cross
397    ///reference type. It can allocate the heap and the cross reference
398    ///object if the cross reference's constructor waits for the graph as
399    ///parameter and the heap's constructor waits for the cross reference.
400    template <class H, class CR = typename Graph::template NodeMap<int> >
401    struct DefStandardHeap
402      : public Dijkstra< Graph, LengthMap, DefStandardHeapTraits<H, CR> > {
403      typedef Dijkstra< Graph,  LengthMap, DefStandardHeapTraits<H, CR> >
404      Create;
405    };
406   
407    ///@}
408
409
410  protected:
411
412    Dijkstra() {}
413
414  public:     
415   
416    ///Constructor.
417   
418    ///\param _G the graph the algorithm will run on.
419    ///\param _length the length map used by the algorithm.
420    Dijkstra(const Graph& _G, const LengthMap& _length) :
421      G(&_G), length(&_length),
422      _pred(NULL), local_pred(false),
423      _dist(NULL), local_dist(false),
424      _processed(NULL), local_processed(false),
425      _heap_cross_ref(NULL), local_heap_cross_ref(false),
426      _heap(NULL), local_heap(false)
427    { }
428   
429    ///Destructor.
430    ~Dijkstra()
431    {
432      if(local_pred) delete _pred;
433      if(local_dist) delete _dist;
434      if(local_processed) delete _processed;
435      if(local_heap_cross_ref) delete _heap_cross_ref;
436      if(local_heap) delete _heap;
437    }
438
439    ///Sets the length map.
440
441    ///Sets the length map.
442    ///\return <tt> (*this) </tt>
443    Dijkstra &lengthMap(const LengthMap &m)
444    {
445      length = &m;
446      return *this;
447    }
448
449    ///Sets the map storing the predecessor edges.
450
451    ///Sets the map storing the predecessor edges.
452    ///If you don't use this function before calling \ref run(),
453    ///it will allocate one. The destuctor deallocates this
454    ///automatically allocated map, of course.
455    ///\return <tt> (*this) </tt>
456    Dijkstra &predMap(PredMap &m)
457    {
458      if(local_pred) {
459        delete _pred;
460        local_pred=false;
461      }
462      _pred = &m;
463      return *this;
464    }
465
466    ///Sets the map storing the distances calculated by the algorithm.
467
468    ///Sets the map storing the distances calculated by the algorithm.
469    ///If you don't use this function before calling \ref run(),
470    ///it will allocate one. The destuctor deallocates this
471    ///automatically allocated map, of course.
472    ///\return <tt> (*this) </tt>
473    Dijkstra &distMap(DistMap &m)
474    {
475      if(local_dist) {
476        delete _dist;
477        local_dist=false;
478      }
479      _dist = &m;
480      return *this;
481    }
482
483    ///Sets the heap and the cross reference used by algorithm.
484
485    ///Sets the heap and the cross reference used by algorithm.
486    ///If you don't use this function before calling \ref run(),
487    ///it will allocate one. The destuctor deallocates this
488    ///automatically allocated map, of course.
489    ///\return <tt> (*this) </tt>
490    Dijkstra &heap(Heap& heap, HeapCrossRef &crossRef)
491    {
492      if(local_heap_cross_ref) {
493        delete _heap_cross_ref;
494        local_heap_cross_ref=false;
495      }
496      _heap_cross_ref = &crossRef;
497      if(local_heap) {
498        delete _heap;
499        local_heap=false;
500      }
501      _heap = &heap;
502      return *this;
503    }
504
505  private:
506    void finalizeNodeData(Node v,Value dst)
507    {
508      _processed->set(v,true);
509      _dist->set(v, dst);
510    }
511
512  public:
513    ///\name Execution control
514    ///The simplest way to execute the algorithm is to use
515    ///one of the member functions called \c run(...).
516    ///\n
517    ///If you need more control on the execution,
518    ///first you must call \ref init(), then you can add several source nodes
519    ///with \ref addSource().
520    ///Finally \ref start() will perform the actual path
521    ///computation.
522
523    ///@{
524
525    ///Initializes the internal data structures.
526
527    ///Initializes the internal data structures.
528    ///
529    void init()
530    {
531      create_maps();
532      _heap->clear();
533      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
534        _pred->set(u,INVALID);
535        _processed->set(u,false);
536        _heap_cross_ref->set(u,Heap::PRE_HEAP);
537      }
538    }
539   
540    ///Adds a new source node.
541
542    ///Adds a new source node to the priority heap.
543    ///
544    ///The optional second parameter is the initial distance of the node.
545    ///
546    ///It checks if the node has already been added to the heap and
547    ///It is pushed to the heap only if either it was not in the heap
548    ///or the shortest path found till then is longer then \c dst.
549    void addSource(Node s,Value dst=dijkstraZero<Value>())
550    {
551      if(_heap->state(s) != Heap::IN_HEAP) {
552        _heap->push(s,dst);
553      } else if((*_heap)[s]<dst) {
554        _heap->push(s,dst);
555        _pred->set(s,INVALID);
556      }
557    }
558   
559    ///Processes the next node in the priority heap
560
561    ///Processes the next node in the priority heap.
562    ///
563    ///\return The processed node.
564    ///
565    ///\warning The priority heap must not be empty!
566    Node processNextNode()
567    {
568      Node v=_heap->top();
569      Value oldvalue=_heap->prio();
570      _heap->pop();
571      finalizeNodeData(v,oldvalue);
572     
573      for(OutEdgeIt e(*G,v); e!=INVALID; ++e) {
574        Node w=G->target(e);
575        switch(_heap->state(w)) {
576        case Heap::PRE_HEAP:
577          _heap->push(w,oldvalue+(*length)[e]);
578          _pred->set(w,e);
579          break;
580        case Heap::IN_HEAP:
581          if ( oldvalue+(*length)[e] < (*_heap)[w] ) {
582            _heap->decrease(w, oldvalue+(*length)[e]);
583            _pred->set(w,e);
584          }
585          break;
586        case Heap::POST_HEAP:
587          break;
588        }
589      }
590      return v;
591    }
592
593    ///Next node to be processed.
594   
595    ///Next node to be processed.
596    ///
597    ///\return The next node to be processed or INVALID if the priority heap
598    /// is empty.
599    Node nextNode()
600    {
601      return _heap->empty()?_heap->top():INVALID;
602    }
603 
604    ///\brief Returns \c false if there are nodes
605    ///to be processed in the priority heap
606    ///
607    ///Returns \c false if there are nodes
608    ///to be processed in the priority heap
609    bool emptyQueue() { return _heap->empty(); }
610    ///Returns the number of the nodes to be processed in the priority heap
611
612    ///Returns the number of the nodes to be processed in the priority heap
613    ///
614    int queueSize() { return _heap->size(); }
615   
616    ///Executes the algorithm.
617
618    ///Executes the algorithm.
619    ///
620    ///\pre init() must be called and at least one node should be added
621    ///with addSource() before using this function.
622    ///
623    ///This method runs the %Dijkstra algorithm from the root node(s)
624    ///in order to
625    ///compute the
626    ///shortest path to each node. The algorithm computes
627    ///- The shortest path tree.
628    ///- The distance of each node from the root(s).
629    ///
630    void start()
631    {
632      while ( !_heap->empty() ) processNextNode();
633    }
634   
635    ///Executes the algorithm until \c dest is reached.
636
637    ///Executes the algorithm until \c dest is reached.
638    ///
639    ///\pre init() must be called and at least one node should be added
640    ///with addSource() before using this function.
641    ///
642    ///This method runs the %Dijkstra algorithm from the root node(s)
643    ///in order to
644    ///compute the
645    ///shortest path to \c dest. The algorithm computes
646    ///- The shortest path to \c  dest.
647    ///- The distance of \c dest from the root(s).
648    ///
649    void start(Node dest)
650    {
651      while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();
652      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
653    }
654   
655    ///Executes the algorithm until a condition is met.
656
657    ///Executes the algorithm until a condition is met.
658    ///
659    ///\pre init() must be called and at least one node should be added
660    ///with addSource() before using this function.
661    ///
662    ///\param nm must be a bool (or convertible) node map. The algorithm
663    ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.
664    template<class NodeBoolMap>
665    void start(const NodeBoolMap &nm)
666    {
667      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
668      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
669    }
670   
671    ///Runs %Dijkstra algorithm from node \c s.
672   
673    ///This method runs the %Dijkstra algorithm from a root node \c s
674    ///in order to
675    ///compute the
676    ///shortest path to each node. The algorithm computes
677    ///- The shortest path tree.
678    ///- The distance of each node from the root.
679    ///
680    ///\note d.run(s) is just a shortcut of the following code.
681    ///\code
682    ///  d.init();
683    ///  d.addSource(s);
684    ///  d.start();
685    ///\endcode
686    void run(Node s) {
687      init();
688      addSource(s);
689      start();
690    }
691   
692    ///Finds the shortest path between \c s and \c t.
693   
694    ///Finds the shortest path between \c s and \c t.
695    ///
696    ///\return The length of the shortest s---t path if there exists one,
697    ///0 otherwise.
698    ///\note Apart from the return value, d.run(s) is
699    ///just a shortcut of the following code.
700    ///\code
701    ///  d.init();
702    ///  d.addSource(s);
703    ///  d.start(t);
704    ///\endcode
705    Value run(Node s,Node t) {
706      init();
707      addSource(s);
708      start(t);
709      return (*_pred)[t]==INVALID?dijkstraZero<Value>():(*_dist)[t];
710    }
711   
712    ///@}
713
714    ///\name Query Functions
715    ///The result of the %Dijkstra algorithm can be obtained using these
716    ///functions.\n
717    ///Before the use of these functions,
718    ///either run() or start() must be called.
719   
720    ///@{
721
722    ///Copies the shortest path to \c t into \c p
723   
724    ///This function copies the shortest path to \c t into \c p.
725    ///If it \c t is a source itself or unreachable, then it does not
726    ///alter \c p.
727    ///\todo Is it the right way to handle unreachable nodes?
728    ///\return Returns \c true if a path to \c t was actually copied to \c p,
729    ///\c false otherwise.
730    ///\sa DirPath
731    template<class P>
732    bool getPath(P &p,Node t)
733    {
734      if(reached(t)) {
735        p.clear();
736        typename P::Builder b(p);
737        for(b.setStartNode(t);pred(t)!=INVALID;t=predNode(t))
738          b.pushFront(pred(t));
739        b.commit();
740        return true;
741      }
742      return false;
743    }
744         
745    ///The distance of a node from the root.
746
747    ///Returns the distance of a node from the root.
748    ///\pre \ref run() must be called before using this function.
749    ///\warning If node \c v in unreachable from the root the return value
750    ///of this funcion is undefined.
751    Value dist(Node v) const { return (*_dist)[v]; }
752
753    ///Returns the 'previous edge' of the shortest path tree.
754
755    ///For a node \c v it returns the 'previous edge' of the shortest path tree,
756    ///i.e. it returns the last edge of a shortest path from the root to \c
757    ///v. It is \ref INVALID
758    ///if \c v is unreachable from the root or if \c v=s. The
759    ///shortest path tree used here is equal to the shortest path tree used in
760    ///\ref predNode().  \pre \ref run() must be called before using
761    ///this function.
762    ///\todo predEdge could be a better name.
763    Edge pred(Node v) const { return (*_pred)[v]; }
764
765    ///Returns the 'previous node' of the shortest path tree.
766
767    ///For a node \c v it returns the 'previous node' of the shortest path tree,
768    ///i.e. it returns the last but one node from a shortest path from the
769    ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
770    ///\c v=s. The shortest path tree used here is equal to the shortest path
771    ///tree used in \ref pred().  \pre \ref run() must be called before
772    ///using this function.
773    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
774                                  G->source((*_pred)[v]); }
775   
776    ///Returns a reference to the NodeMap of distances.
777
778    ///Returns a reference to the NodeMap of distances. \pre \ref run() must
779    ///be called before using this function.
780    const DistMap &distMap() const { return *_dist;}
781 
782    ///Returns a reference to the shortest path tree map.
783
784    ///Returns a reference to the NodeMap of the edges of the
785    ///shortest path tree.
786    ///\pre \ref run() must be called before using this function.
787    const PredMap &predMap() const { return *_pred;}
788 
789    ///Checks if a node is reachable from the root.
790
791    ///Returns \c true if \c v is reachable from the root.
792    ///\warning The source nodes are inditated as unreached.
793    ///\pre \ref run() must be called before using this function.
794    ///
795    bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }
796
797    ///Checks if a node is processed.
798
799    ///Returns \c true if \c v is processed, i.e. the shortest
800    ///path to \c v has already found.
801    ///\pre \ref run() must be called before using this function.
802    ///
803    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }
804   
805    ///@}
806  };
807
808
809
810
811 
812  ///Default traits class of Dijkstra function.
813
814  ///Default traits class of Dijkstra function.
815  ///\param GR Graph type.
816  ///\param LM Type of length map.
817  template<class GR, class LM>
818  struct DijkstraWizardDefaultTraits
819  {
820    ///The graph type the algorithm runs on.
821    typedef GR Graph;
822    ///The type of the map that stores the edge lengths.
823
824    ///The type of the map that stores the edge lengths.
825    ///It must meet the \ref concept::ReadMap "ReadMap" concept.
826    typedef LM LengthMap;
827    //The type of the length of the edges.
828    typedef typename LM::Value Value;
829    ///The heap type used by Dijkstra algorithm.
830
831    /// The cross reference type used by heap.
832
833    /// The cross reference type used by heap.
834    /// Usually it is \c Graph::NodeMap<int>.
835    typedef typename Graph::template NodeMap<int> HeapCrossRef;
836    ///Instantiates a HeapCrossRef.
837
838    ///This function instantiates a \ref HeapCrossRef.
839    /// \param G is the graph, to which we would like to define the
840    /// HeapCrossRef.
841    /// \todo The graph alone may be insufficient for the initialization
842    static HeapCrossRef *createHeapCrossRef(const GR &G)
843    {
844      return new HeapCrossRef(G);
845    }
846   
847    ///The heap type used by Dijkstra algorithm.
848
849    ///The heap type used by Dijkstra algorithm.
850    ///
851    ///\sa BinHeap
852    ///\sa Dijkstra
853    typedef BinHeap<typename Graph::Node, typename LM::Value,
854                    typename GR::template NodeMap<int>,
855                    std::less<Value> > Heap;
856
857    static Heap *createHeap(HeapCrossRef& R)
858    {
859      return new Heap(R);
860    }
861
862    ///\brief The type of the map that stores the last
863    ///edges of the shortest paths.
864    ///
865    ///The type of the map that stores the last
866    ///edges of the shortest paths.
867    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
868    ///
869    typedef NullMap <typename GR::Node,typename GR::Edge> PredMap;
870    ///Instantiates a PredMap.
871 
872    ///This function instantiates a \ref PredMap.
873    ///\param g is the graph, to which we would like to define the PredMap.
874    ///\todo The graph alone may be insufficient for the initialization
875#ifdef DOXYGEN
876    static PredMap *createPredMap(const GR &g)
877#else
878    static PredMap *createPredMap(const GR &)
879#endif
880    {
881      return new PredMap();
882    }
883    ///The type of the map that stores whether a nodes is processed.
884 
885    ///The type of the map that stores whether a nodes is processed.
886    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
887    ///By default it is a NullMap.
888    ///\todo If it is set to a real map,
889    ///Dijkstra::processed() should read this.
890    ///\todo named parameter to set this type, function to read and write.
891    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
892    ///Instantiates a ProcessedMap.
893 
894    ///This function instantiates a \ref ProcessedMap.
895    ///\param g is the graph, to which
896    ///we would like to define the \ref ProcessedMap
897#ifdef DOXYGEN
898    static ProcessedMap *createProcessedMap(const GR &g)
899#else
900    static ProcessedMap *createProcessedMap(const GR &)
901#endif
902    {
903      return new ProcessedMap();
904    }
905    ///The type of the map that stores the dists of the nodes.
906 
907    ///The type of the map that stores the dists of the nodes.
908    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
909    ///
910    typedef NullMap<typename Graph::Node,typename LM::Value> DistMap;
911    ///Instantiates a DistMap.
912 
913    ///This function instantiates a \ref DistMap.
914    ///\param g is the graph, to which we would like to define the \ref DistMap
915#ifdef DOXYGEN
916    static DistMap *createDistMap(const GR &g)
917#else
918    static DistMap *createDistMap(const GR &)
919#endif
920    {
921      return new DistMap();
922    }
923  };
924 
925  /// Default traits used by \ref DijkstraWizard
926
927  /// To make it easier to use Dijkstra algorithm
928  ///we have created a wizard class.
929  /// This \ref DijkstraWizard class needs default traits,
930  ///as well as the \ref Dijkstra class.
931  /// The \ref DijkstraWizardBase is a class to be the default traits of the
932  /// \ref DijkstraWizard class.
933  /// \todo More named parameters are required...
934  template<class GR,class LM>
935  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
936  {
937
938    typedef DijkstraWizardDefaultTraits<GR,LM> Base;
939  protected:
940    /// Type of the nodes in the graph.
941    typedef typename Base::Graph::Node Node;
942
943    /// Pointer to the underlying graph.
944    void *_g;
945    /// Pointer to the length map
946    void *_length;
947    ///Pointer to the map of predecessors edges.
948    void *_pred;
949    ///Pointer to the map of distances.
950    void *_dist;
951    ///Pointer to the source node.
952    Node _source;
953
954    public:
955    /// Constructor.
956   
957    /// This constructor does not require parameters, therefore it initiates
958    /// all of the attributes to default values (0, INVALID).
959    DijkstraWizardBase() : _g(0), _length(0), _pred(0),
960                           _dist(0), _source(INVALID) {}
961
962    /// Constructor.
963   
964    /// This constructor requires some parameters,
965    /// listed in the parameters list.
966    /// Others are initiated to 0.
967    /// \param g is the initial value of  \ref _g
968    /// \param l is the initial value of  \ref _length
969    /// \param s is the initial value of  \ref _source
970    DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
971      _g((void *)&g), _length((void *)&l), _pred(0),
972      _dist(0), _source(s) {}
973
974  };
975 
976  /// A class to make the usage of Dijkstra algorithm easier
977
978  /// This class is created to make it easier to use Dijkstra algorithm.
979  /// It uses the functions and features of the plain \ref Dijkstra,
980  /// but it is much simpler to use it.
981  ///
982  /// Simplicity means that the way to change the types defined
983  /// in the traits class is based on functions that returns the new class
984  /// and not on templatable built-in classes.
985  /// When using the plain \ref Dijkstra
986  /// the new class with the modified type comes from
987  /// the original class by using the ::
988  /// operator. In the case of \ref DijkstraWizard only
989  /// a function have to be called and it will
990  /// return the needed class.
991  ///
992  /// It does not have own \ref run method. When its \ref run method is called
993  /// it initiates a plain \ref Dijkstra class, and calls the \ref
994  /// Dijkstra::run method of it.
995  template<class TR>
996  class DijkstraWizard : public TR
997  {
998    typedef TR Base;
999
1000    ///The type of the underlying graph.
1001    typedef typename TR::Graph Graph;
1002    //\e
1003    typedef typename Graph::Node Node;
1004    //\e
1005    typedef typename Graph::NodeIt NodeIt;
1006    //\e
1007    typedef typename Graph::Edge Edge;
1008    //\e
1009    typedef typename Graph::OutEdgeIt OutEdgeIt;
1010   
1011    ///The type of the map that stores the edge lengths.
1012    typedef typename TR::LengthMap LengthMap;
1013    ///The type of the length of the edges.
1014    typedef typename LengthMap::Value Value;
1015    ///\brief The type of the map that stores the last
1016    ///edges of the shortest paths.
1017    typedef typename TR::PredMap PredMap;
1018    ///The type of the map that stores the dists of the nodes.
1019    typedef typename TR::DistMap DistMap;
1020    ///The heap type used by the dijkstra algorithm.
1021    typedef typename TR::Heap Heap;
1022public:
1023    /// Constructor.
1024    DijkstraWizard() : TR() {}
1025
1026    /// Constructor that requires parameters.
1027
1028    /// Constructor that requires parameters.
1029    /// These parameters will be the default values for the traits class.
1030    DijkstraWizard(const Graph &g,const LengthMap &l, Node s=INVALID) :
1031      TR(g,l,s) {}
1032
1033    ///Copy constructor
1034    DijkstraWizard(const TR &b) : TR(b) {}
1035
1036    ~DijkstraWizard() {}
1037
1038    ///Runs Dijkstra algorithm from a given node.
1039   
1040    ///Runs Dijkstra algorithm from a given node.
1041    ///The node can be given by the \ref source function.
1042    void run()
1043    {
1044      if(Base::_source==INVALID) throw UninitializedParameter();
1045      Dijkstra<Graph,LengthMap,TR>
1046        dij(*(Graph*)Base::_g,*(LengthMap*)Base::_length);
1047      if(Base::_pred) dij.predMap(*(PredMap*)Base::_pred);
1048      if(Base::_dist) dij.distMap(*(DistMap*)Base::_dist);
1049      dij.run(Base::_source);
1050    }
1051
1052    ///Runs Dijkstra algorithm from the given node.
1053
1054    ///Runs Dijkstra algorithm from the given node.
1055    ///\param s is the given source.
1056    void run(Node s)
1057    {
1058      Base::_source=s;
1059      run();
1060    }
1061
1062    template<class T>
1063    struct DefPredMapBase : public Base {
1064      typedef T PredMap;
1065      static PredMap *createPredMap(const Graph &) { return 0; };
1066      DefPredMapBase(const TR &b) : TR(b) {}
1067    };
1068   
1069    ///\brief \ref named-templ-param "Named parameter"
1070    ///function for setting PredMap type
1071    ///
1072    /// \ref named-templ-param "Named parameter"
1073    ///function for setting PredMap type
1074    ///
1075    template<class T>
1076    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t)
1077    {
1078      Base::_pred=(void *)&t;
1079      return DijkstraWizard<DefPredMapBase<T> >(*this);
1080    }
1081   
1082    template<class T>
1083    struct DefDistMapBase : public Base {
1084      typedef T DistMap;
1085      static DistMap *createDistMap(const Graph &) { return 0; };
1086      DefDistMapBase(const TR &b) : TR(b) {}
1087    };
1088   
1089    ///\brief \ref named-templ-param "Named parameter"
1090    ///function for setting DistMap type
1091    ///
1092    /// \ref named-templ-param "Named parameter"
1093    ///function for setting DistMap type
1094    ///
1095    template<class T>
1096    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t)
1097    {
1098      Base::_dist=(void *)&t;
1099      return DijkstraWizard<DefDistMapBase<T> >(*this);
1100    }
1101   
1102    /// Sets the source node, from which the Dijkstra algorithm runs.
1103
1104    /// Sets the source node, from which the Dijkstra algorithm runs.
1105    /// \param s is the source node.
1106    DijkstraWizard<TR> &source(Node s)
1107    {
1108      Base::_source=s;
1109      return *this;
1110    }
1111   
1112  };
1113 
1114  ///Function type interface for Dijkstra algorithm.
1115
1116  /// \ingroup flowalgs
1117  ///Function type interface for Dijkstra algorithm.
1118  ///
1119  ///This function also has several
1120  ///\ref named-templ-func-param "named parameters",
1121  ///they are declared as the members of class \ref DijkstraWizard.
1122  ///The following
1123  ///example shows how to use these parameters.
1124  ///\code
1125  ///  dijkstra(g,length,source).predMap(preds).run();
1126  ///\endcode
1127  ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
1128  ///to the end of the parameter list.
1129  ///\sa DijkstraWizard
1130  ///\sa Dijkstra
1131  template<class GR, class LM>
1132  DijkstraWizard<DijkstraWizardBase<GR,LM> >
1133  dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
1134  {
1135    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
1136  }
1137
1138} //END OF NAMESPACE LEMON
1139
1140#endif
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