COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/dijkstra.h @ 2391:14a343be7a5a

Last change on this file since 2391:14a343be7a5a was 2391:14a343be7a5a, checked in by Alpar Juttner, 12 years ago

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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///\todo dijkstraZero() solution should be revised.
27
28#include <lemon/list_graph.h>
29#include <lemon/bin_heap.h>
30#include <lemon/bits/path_dump.h>
31#include <lemon/bits/invalid.h>
32#include <lemon/error.h>
33#include <lemon/maps.h>
34
35
36namespace lemon {
37
38  template<class T> T dijkstraZero() {return 0;}
39 
40  ///Default traits class of Dijkstra class.
41
42  ///Default traits class of Dijkstra class.
43  ///\param GR Graph type.
44  ///\param LM Type of length map.
45  template<class GR, class LM>
46  struct DijkstraDefaultTraits
47  {
48    ///The graph type the algorithm runs on.
49    typedef GR Graph;
50    ///The type of the map that stores the edge lengths.
51
52    ///The type of the map that stores the edge lengths.
53    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
54    typedef LM LengthMap;
55    //The type of the length of the edges.
56    typedef typename LM::Value Value;
57    /// The cross reference type used by heap.
58
59    /// The cross reference type used by heap.
60    /// Usually it is \c Graph::NodeMap<int>.
61    typedef typename Graph::template NodeMap<int> HeapCrossRef;
62    ///Instantiates a HeapCrossRef.
63
64    ///This function instantiates a \ref HeapCrossRef.
65    /// \param G is the graph, to which we would like to define the
66    /// HeapCrossRef.
67    static HeapCrossRef *createHeapCrossRef(const GR &G)
68    {
69      return new HeapCrossRef(G);
70    }
71   
72    ///The heap type used by Dijkstra algorithm.
73
74    ///The heap type used by Dijkstra algorithm.
75    ///
76    ///\sa BinHeap
77    ///\sa Dijkstra
78    typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;
79
80    static Heap *createHeap(HeapCrossRef& R)
81    {
82      return new Heap(R);
83    }
84
85    ///\brief The type of the map that stores the last
86    ///edges of the shortest paths.
87    ///
88    ///The type of the map that stores the last
89    ///edges of the shortest paths.
90    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
91    ///
92    typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;
93    ///Instantiates a PredMap.
94 
95    ///This function instantiates a \ref PredMap.
96    ///\param G is the graph, to which we would like to define the PredMap.
97    ///\todo The graph alone may be insufficient for the initialization
98    static PredMap *createPredMap(const GR &G)
99    {
100      return new PredMap(G);
101    }
102
103    ///The type of the map that stores whether a nodes is processed.
104 
105    ///The type of the map that stores whether a nodes is processed.
106    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
107    ///By default it is a NullMap.
108    ///\todo If it is set to a real map,
109    ///Dijkstra::processed() should read this.
110    ///\todo named parameter to set this type, function to read and write.
111    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
112    ///Instantiates a ProcessedMap.
113 
114    ///This function instantiates a \ref ProcessedMap.
115    ///\param g is the graph, to which
116    ///we would like to define the \ref ProcessedMap
117#ifdef DOXYGEN
118    static ProcessedMap *createProcessedMap(const GR &g)
119#else
120    static ProcessedMap *createProcessedMap(const GR &)
121#endif
122    {
123      return new ProcessedMap();
124    }
125    ///The type of the map that stores the dists of the nodes.
126 
127    ///The type of the map that stores the dists of the nodes.
128    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
129    ///
130    typedef typename Graph::template NodeMap<typename LM::Value> DistMap;
131    ///Instantiates a DistMap.
132 
133    ///This function instantiates a \ref DistMap.
134    ///\param G is the graph, to which we would like to define the \ref DistMap
135    static DistMap *createDistMap(const GR &G)
136    {
137      return new DistMap(G);
138    }
139  };
140 
141  ///%Dijkstra algorithm class.
142 
143  /// \ingroup shortest_path
144  ///This class provides an efficient implementation of %Dijkstra algorithm.
145  ///The edge lengths are passed to the algorithm using a
146  ///\ref concepts::ReadMap "ReadMap",
147  ///so it is easy to change it to any kind of length.
148  ///
149  ///The type of the length is determined by the
150  ///\ref concepts::ReadMap::Value "Value" of the length map.
151  ///
152  ///It is also possible to change the underlying priority heap.
153  ///
154  ///\param GR The graph type the algorithm runs on. The default value
155  ///is \ref ListGraph. The value of GR is not used directly by
156  ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits.
157  ///\param LM This read-only EdgeMap determines the lengths of the
158  ///edges. It is read once for each edge, so the map may involve in
159  ///relatively time consuming process to compute the edge length if
160  ///it is necessary. The default map type is \ref
161  ///concepts::Graph::EdgeMap "Graph::EdgeMap<int>".  The value
162  ///of LM is not used directly by Dijkstra, it is only passed to \ref
163  ///DijkstraDefaultTraits.  \param TR Traits class to set
164  ///various data types used by the algorithm.  The default traits
165  ///class is \ref DijkstraDefaultTraits
166  ///"DijkstraDefaultTraits<GR,LM>".  See \ref
167  ///DijkstraDefaultTraits for the documentation of a Dijkstra traits
168  ///class.
169  ///
170  ///\author Jacint Szabo and Alpar Juttner
171
172#ifdef DOXYGEN
173  template <typename GR,
174            typename LM,
175            typename TR>
176#else
177  template <typename GR=ListGraph,
178            typename LM=typename GR::template EdgeMap<int>,
179            typename TR=DijkstraDefaultTraits<GR,LM> >
180#endif
181  class Dijkstra {
182  public:
183    /**
184     * \brief \ref Exception for uninitialized parameters.
185     *
186     * This error represents problems in the initialization
187     * of the parameters of the algorithms.
188     */
189    class UninitializedParameter : public lemon::UninitializedParameter {
190    public:
191      virtual const char* what() const throw() {
192        return "lemon::Dijkstra::UninitializedParameter";
193      }
194    };
195
196    typedef TR Traits;
197    ///The type of the underlying graph.
198    typedef typename TR::Graph Graph;
199    ///\e
200    typedef typename Graph::Node Node;
201    ///\e
202    typedef typename Graph::NodeIt NodeIt;
203    ///\e
204    typedef typename Graph::Edge Edge;
205    ///\e
206    typedef typename Graph::OutEdgeIt OutEdgeIt;
207   
208    ///The type of the length of the edges.
209    typedef typename TR::LengthMap::Value Value;
210    ///The type of the map that stores the edge lengths.
211    typedef typename TR::LengthMap LengthMap;
212    ///\brief The type of the map that stores the last
213    ///edges of the shortest paths.
214    typedef typename TR::PredMap PredMap;
215    ///The type of the map indicating if a node is processed.
216    typedef typename TR::ProcessedMap ProcessedMap;
217    ///The type of the map that stores the dists of the nodes.
218    typedef typename TR::DistMap DistMap;
219    ///The cross reference type used for the current heap.
220    typedef typename TR::HeapCrossRef HeapCrossRef;
221    ///The heap type used by the dijkstra algorithm.
222    typedef typename TR::Heap Heap;
223  private:
224    /// Pointer to the underlying graph.
225    const Graph *G;
226    /// Pointer to the length map
227    const LengthMap *length;
228    ///Pointer to the map of predecessors edges.
229    PredMap *_pred;
230    ///Indicates if \ref _pred is locally allocated (\c true) or not.
231    bool local_pred;
232    ///Pointer to the map of distances.
233    DistMap *_dist;
234    ///Indicates if \ref _dist is locally allocated (\c true) or not.
235    bool local_dist;
236    ///Pointer to the map of processed status of the nodes.
237    ProcessedMap *_processed;
238    ///Indicates if \ref _processed is locally allocated (\c true) or not.
239    bool local_processed;
240    ///Pointer to the heap cross references.
241    HeapCrossRef *_heap_cross_ref;
242    ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.
243    bool local_heap_cross_ref;
244    ///Pointer to the heap.
245    Heap *_heap;
246    ///Indicates if \ref _heap is locally allocated (\c true) or not.
247    bool local_heap;
248
249    ///Creates the maps if necessary.
250   
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 &)
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 &)
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    ///\brief \ref named-templ-param "Named parameter" for setting
370    ///heap and cross 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    ///\brief \ref named-templ-param "Named parameter" for setting
394    ///heap and cross 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 heap and cross reference, of course.
489    ///\return <tt> (*this) </tt>
490    Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
491    {
492      if(local_heap_cross_ref) {
493        delete _heap_cross_ref;
494        local_heap_cross_ref=false;
495      }
496      _heap_cross_ref = &cr;
497      if(local_heap) {
498        delete _heap;
499        local_heap=false;
500      }
501      _heap = &hp;
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
514    typedef PredMapPath<Graph, PredMap> Path;
515
516    ///\name Execution control
517    ///The simplest way to execute the algorithm is to use
518    ///one of the member functions called \c run(...).
519    ///\n
520    ///If you need more control on the execution,
521    ///first you must call \ref init(), then you can add several source nodes
522    ///with \ref addSource().
523    ///Finally \ref start() will perform the actual path
524    ///computation.
525
526    ///@{
527
528    ///Initializes the internal data structures.
529
530    ///Initializes the internal data structures.
531    ///
532    void init()
533    {
534      create_maps();
535      _heap->clear();
536      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
537        _pred->set(u,INVALID);
538        _processed->set(u,false);
539        _heap_cross_ref->set(u,Heap::PRE_HEAP);
540      }
541    }
542   
543    ///Adds a new source node.
544
545    ///Adds a new source node to the priority heap.
546    ///
547    ///The optional second parameter is the initial distance of the node.
548    ///
549    ///It checks if the node has already been added to the heap and
550    ///it is pushed to the heap only if either it was not in the heap
551    ///or the shortest path found till then is shorter than \c dst.
552    void addSource(Node s,Value dst=dijkstraZero<Value>())
553    {
554      if(_heap->state(s) != Heap::IN_HEAP) {
555        _heap->push(s,dst);
556      } else if((*_heap)[s]<dst) {
557        _heap->set(s,dst);
558        _pred->set(s,INVALID);
559      }
560    }
561   
562    ///Processes the next node in the priority heap
563
564    ///Processes the next node in the priority heap.
565    ///
566    ///\return The processed node.
567    ///
568    ///\warning The priority heap must not be empty!
569    Node processNextNode()
570    {
571      Node v=_heap->top();
572      Value oldvalue=_heap->prio();
573      _heap->pop();
574      finalizeNodeData(v,oldvalue);
575     
576      for(OutEdgeIt e(*G,v); e!=INVALID; ++e) {
577        Node w=G->target(e);
578        switch(_heap->state(w)) {
579        case Heap::PRE_HEAP:
580          _heap->push(w,oldvalue+(*length)[e]);
581          _pred->set(w,e);
582          break;
583        case Heap::IN_HEAP:
584          if ( oldvalue+(*length)[e] < (*_heap)[w] ) {
585            _heap->decrease(w, oldvalue+(*length)[e]);
586            _pred->set(w,e);
587          }
588          break;
589        case Heap::POST_HEAP:
590          break;
591        }
592      }
593      return v;
594    }
595
596    ///Next node to be processed.
597   
598    ///Next node to be processed.
599    ///
600    ///\return The next node to be processed or INVALID if the priority heap
601    /// is empty.
602    Node nextNode()
603    {
604      return _heap->empty()?_heap->top():INVALID;
605    }
606 
607    ///\brief Returns \c false if there are nodes
608    ///to be processed in the priority heap
609    ///
610    ///Returns \c false if there are nodes
611    ///to be processed in the priority heap
612    bool emptyQueue() { return _heap->empty(); }
613    ///Returns the number of the nodes to be processed in the priority heap
614
615    ///Returns the number of the nodes to be processed in the priority heap
616    ///
617    int queueSize() { return _heap->size(); }
618   
619    ///Executes the algorithm.
620
621    ///Executes the algorithm.
622    ///
623    ///\pre init() must be called and at least one node should be added
624    ///with addSource() before using this function.
625    ///
626    ///This method runs the %Dijkstra algorithm from the root node(s)
627    ///in order to
628    ///compute the
629    ///shortest path to each node. The algorithm computes
630    ///- The shortest path tree.
631    ///- The distance of each node from the root(s).
632    ///
633    void start()
634    {
635      while ( !_heap->empty() ) processNextNode();
636    }
637   
638    ///Executes the algorithm until \c dest is reached.
639
640    ///Executes the algorithm until \c dest is reached.
641    ///
642    ///\pre init() must be called and at least one node should be added
643    ///with addSource() before using this function.
644    ///
645    ///This method runs the %Dijkstra algorithm from the root node(s)
646    ///in order to
647    ///compute the
648    ///shortest path to \c dest. The algorithm computes
649    ///- The shortest path to \c  dest.
650    ///- The distance of \c dest from the root(s).
651    ///
652    void start(Node dest)
653    {
654      while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();
655      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
656    }
657   
658    ///Executes the algorithm until a condition is met.
659
660    ///Executes the algorithm until a condition is met.
661    ///
662    ///\pre init() must be called and at least one node should be added
663    ///with addSource() before using this function.
664    ///
665    ///\param nm must be a bool (or convertible) node map. The algorithm
666    ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>.
667    template<class NodeBoolMap>
668    void start(const NodeBoolMap &nm)
669    {
670      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
671      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
672    }
673   
674    ///Runs %Dijkstra algorithm from node \c s.
675   
676    ///This method runs the %Dijkstra algorithm from a root node \c s
677    ///in order to
678    ///compute the
679    ///shortest path to each node. The algorithm computes
680    ///- The shortest path tree.
681    ///- The distance of each node from the root.
682    ///
683    ///\note d.run(s) is just a shortcut of the following code.
684    ///\code
685    ///  d.init();
686    ///  d.addSource(s);
687    ///  d.start();
688    ///\endcode
689    void run(Node s) {
690      init();
691      addSource(s);
692      start();
693    }
694   
695    ///Finds the shortest path between \c s and \c t.
696   
697    ///Finds the shortest path between \c s and \c t.
698    ///
699    ///\return The length of the shortest s---t path if there exists one,
700    ///0 otherwise.
701    ///\note Apart from the return value, d.run(s) is
702    ///just a shortcut of the following code.
703    ///\code
704    ///  d.init();
705    ///  d.addSource(s);
706    ///  d.start(t);
707    ///\endcode
708    Value run(Node s,Node t) {
709      init();
710      addSource(s);
711      start(t);
712      return (*_pred)[t]==INVALID?dijkstraZero<Value>():(*_dist)[t];
713    }
714   
715    ///@}
716
717    ///\name Query Functions
718    ///The result of the %Dijkstra algorithm can be obtained using these
719    ///functions.\n
720    ///Before the use of these functions,
721    ///either run() or start() must be called.
722   
723    ///@{
724
725    ///Gives back the shortest path.
726   
727    ///Gives back the shortest path.
728    ///\pre The \c t should be reachable from the source.
729    Path path(Node t)
730    {
731      return Path(*G, *_pred, t);
732    }
733
734    ///The distance of a node from the root.
735
736    ///Returns the distance of a node from the root.
737    ///\pre \ref run() must be called before using this function.
738    ///\warning If node \c v in unreachable from the root the return value
739    ///of this funcion is undefined.
740    Value dist(Node v) const { return (*_dist)[v]; }
741
742    ///The current distance of a node from the root.
743
744    ///Returns the current distance of a node from the root.
745    ///It may be decreased in the following processes.
746    ///\pre \c node should be reached but not processed
747    Value currentDist(Node v) const { return (*_heap)[v]; }
748
749    ///Returns the 'previous edge' of the shortest path tree.
750
751    ///For a node \c v it returns the 'previous edge' of the shortest path tree,
752    ///i.e. it returns the last edge of a shortest path from the root to \c
753    ///v. It is \ref INVALID
754    ///if \c v is unreachable from the root or if \c v=s. The
755    ///shortest path tree used here is equal to the shortest path tree used in
756    ///\ref predNode().  \pre \ref run() must be called before using
757    ///this function.
758    Edge predEdge(Node v) const { return (*_pred)[v]; }
759
760    ///Returns the 'previous node' of the shortest path tree.
761
762    ///For a node \c v it returns the 'previous node' of the shortest path tree,
763    ///i.e. it returns the last but one node from a shortest path from the
764    ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
765    ///\c v=s. The shortest path tree used here is equal to the shortest path
766    ///tree used in \ref predEdge().  \pre \ref run() must be called before
767    ///using this function.
768    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
769                                  G->source((*_pred)[v]); }
770   
771    ///Returns a reference to the NodeMap of distances.
772
773    ///Returns a reference to the NodeMap of distances. \pre \ref run() must
774    ///be called before using this function.
775    const DistMap &distMap() const { return *_dist;}
776 
777    ///Returns a reference to the shortest path tree map.
778
779    ///Returns a reference to the NodeMap of the edges of the
780    ///shortest path tree.
781    ///\pre \ref run() must be called before using this function.
782    const PredMap &predMap() const { return *_pred;}
783 
784    ///Checks if a node is reachable from the root.
785
786    ///Returns \c true if \c v is reachable from the root.
787    ///\warning The source nodes are inditated as unreached.
788    ///\pre \ref run() must be called before using this function.
789    ///
790    bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }
791
792    ///Checks if a node is processed.
793
794    ///Returns \c true if \c v is processed, i.e. the shortest
795    ///path to \c v has already found.
796    ///\pre \ref run() must be called before using this function.
797    ///
798    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }
799   
800    ///@}
801  };
802
803
804
805
806 
807  ///Default traits class of Dijkstra function.
808
809  ///Default traits class of Dijkstra function.
810  ///\param GR Graph type.
811  ///\param LM Type of length map.
812  template<class GR, class LM>
813  struct DijkstraWizardDefaultTraits
814  {
815    ///The graph type the algorithm runs on.
816    typedef GR Graph;
817    ///The type of the map that stores the edge lengths.
818
819    ///The type of the map that stores the edge lengths.
820    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
821    typedef LM LengthMap;
822    //The type of the length of the edges.
823    typedef typename LM::Value Value;
824    ///The heap type used by Dijkstra algorithm.
825
826    /// The cross reference type used by heap.
827
828    /// The cross reference type used by heap.
829    /// Usually it is \c Graph::NodeMap<int>.
830    typedef typename Graph::template NodeMap<int> HeapCrossRef;
831    ///Instantiates a HeapCrossRef.
832
833    ///This function instantiates a \ref HeapCrossRef.
834    /// \param G is the graph, to which we would like to define the
835    /// HeapCrossRef.
836    /// \todo The graph alone may be insufficient for the initialization
837    static HeapCrossRef *createHeapCrossRef(const GR &G)
838    {
839      return new HeapCrossRef(G);
840    }
841   
842    ///The heap type used by Dijkstra algorithm.
843
844    ///The heap type used by Dijkstra algorithm.
845    ///
846    ///\sa BinHeap
847    ///\sa Dijkstra
848    typedef BinHeap<typename LM::Value, typename GR::template NodeMap<int>,
849                    std::less<Value> > Heap;
850
851    static Heap *createHeap(HeapCrossRef& R)
852    {
853      return new Heap(R);
854    }
855
856    ///\brief The type of the map that stores the last
857    ///edges of the shortest paths.
858    ///
859    ///The type of the map that stores the last
860    ///edges of the shortest paths.
861    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
862    ///
863    typedef NullMap <typename GR::Node,typename GR::Edge> PredMap;
864    ///Instantiates a PredMap.
865 
866    ///This function instantiates a \ref PredMap.
867    ///\param g is the graph, to which we would like to define the PredMap.
868    ///\todo The graph alone may be insufficient for the initialization
869#ifdef DOXYGEN
870    static PredMap *createPredMap(const GR &g)
871#else
872    static PredMap *createPredMap(const GR &)
873#endif
874    {
875      return new PredMap();
876    }
877    ///The type of the map that stores whether a nodes is processed.
878 
879    ///The type of the map that stores whether a nodes is processed.
880    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
881    ///By default it is a NullMap.
882    ///\todo If it is set to a real map,
883    ///Dijkstra::processed() should read this.
884    ///\todo named parameter to set this type, function to read and write.
885    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
886    ///Instantiates a ProcessedMap.
887 
888    ///This function instantiates a \ref ProcessedMap.
889    ///\param g is the graph, to which
890    ///we would like to define the \ref ProcessedMap
891#ifdef DOXYGEN
892    static ProcessedMap *createProcessedMap(const GR &g)
893#else
894    static ProcessedMap *createProcessedMap(const GR &)
895#endif
896    {
897      return new ProcessedMap();
898    }
899    ///The type of the map that stores the dists of the nodes.
900 
901    ///The type of the map that stores the dists of the nodes.
902    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
903    ///
904    typedef NullMap<typename Graph::Node,typename LM::Value> DistMap;
905    ///Instantiates a DistMap.
906 
907    ///This function instantiates a \ref DistMap.
908    ///\param g is the graph, to which we would like to define the \ref DistMap
909#ifdef DOXYGEN
910    static DistMap *createDistMap(const GR &g)
911#else
912    static DistMap *createDistMap(const GR &)
913#endif
914    {
915      return new DistMap();
916    }
917  };
918 
919  /// Default traits used by \ref DijkstraWizard
920
921  /// To make it easier to use Dijkstra algorithm
922  ///we have created a wizard class.
923  /// This \ref DijkstraWizard class needs default traits,
924  ///as well as the \ref Dijkstra class.
925  /// The \ref DijkstraWizardBase is a class to be the default traits of the
926  /// \ref DijkstraWizard class.
927  /// \todo More named parameters are required...
928  template<class GR,class LM>
929  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
930  {
931
932    typedef DijkstraWizardDefaultTraits<GR,LM> Base;
933  protected:
934    /// Type of the nodes in the graph.
935    typedef typename Base::Graph::Node Node;
936
937    /// Pointer to the underlying graph.
938    void *_g;
939    /// Pointer to the length map
940    void *_length;
941    ///Pointer to the map of predecessors edges.
942    void *_pred;
943    ///Pointer to the map of distances.
944    void *_dist;
945    ///Pointer to the source node.
946    Node _source;
947
948    public:
949    /// Constructor.
950   
951    /// This constructor does not require parameters, therefore it initiates
952    /// all of the attributes to default values (0, INVALID).
953    DijkstraWizardBase() : _g(0), _length(0), _pred(0),
954                           _dist(0), _source(INVALID) {}
955
956    /// Constructor.
957   
958    /// This constructor requires some parameters,
959    /// listed in the parameters list.
960    /// Others are initiated to 0.
961    /// \param g is the initial value of  \ref _g
962    /// \param l is the initial value of  \ref _length
963    /// \param s is the initial value of  \ref _source
964    DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
965      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
966      _length(reinterpret_cast<void*>(const_cast<LM*>(&l))),
967      _pred(0), _dist(0), _source(s) {}
968
969  };
970 
971  /// A class to make the usage of Dijkstra algorithm easier
972
973  /// This class is created to make it easier to use Dijkstra algorithm.
974  /// It uses the functions and features of the plain \ref Dijkstra,
975  /// but it is much simpler to use it.
976  ///
977  /// Simplicity means that the way to change the types defined
978  /// in the traits class is based on functions that returns the new class
979  /// and not on templatable built-in classes.
980  /// When using the plain \ref Dijkstra
981  /// the new class with the modified type comes from
982  /// the original class by using the ::
983  /// operator. In the case of \ref DijkstraWizard only
984  /// a function have to be called and it will
985  /// return the needed class.
986  ///
987  /// It does not have own \ref run method. When its \ref run method is called
988  /// it initiates a plain \ref Dijkstra class, and calls the \ref
989  /// Dijkstra::run method of it.
990  template<class TR>
991  class DijkstraWizard : public TR
992  {
993    typedef TR Base;
994
995    ///The type of the underlying graph.
996    typedef typename TR::Graph Graph;
997    //\e
998    typedef typename Graph::Node Node;
999    //\e
1000    typedef typename Graph::NodeIt NodeIt;
1001    //\e
1002    typedef typename Graph::Edge Edge;
1003    //\e
1004    typedef typename Graph::OutEdgeIt OutEdgeIt;
1005   
1006    ///The type of the map that stores the edge lengths.
1007    typedef typename TR::LengthMap LengthMap;
1008    ///The type of the length of the edges.
1009    typedef typename LengthMap::Value Value;
1010    ///\brief The type of the map that stores the last
1011    ///edges of the shortest paths.
1012    typedef typename TR::PredMap PredMap;
1013    ///The type of the map that stores the dists of the nodes.
1014    typedef typename TR::DistMap DistMap;
1015    ///The heap type used by the dijkstra algorithm.
1016    typedef typename TR::Heap Heap;
1017  public:
1018    /// Constructor.
1019    DijkstraWizard() : TR() {}
1020
1021    /// Constructor that requires parameters.
1022
1023    /// Constructor that requires parameters.
1024    /// These parameters will be the default values for the traits class.
1025    DijkstraWizard(const Graph &g,const LengthMap &l, Node s=INVALID) :
1026      TR(g,l,s) {}
1027
1028    ///Copy constructor
1029    DijkstraWizard(const TR &b) : TR(b) {}
1030
1031    ~DijkstraWizard() {}
1032
1033    ///Runs Dijkstra algorithm from a given node.
1034   
1035    ///Runs Dijkstra algorithm from a given node.
1036    ///The node can be given by the \ref source function.
1037    void run()
1038    {
1039      if(Base::_source==INVALID) throw UninitializedParameter();
1040      Dijkstra<Graph,LengthMap,TR>
1041        dij(*reinterpret_cast<const Graph*>(Base::_g),
1042            *reinterpret_cast<const LengthMap*>(Base::_length));
1043      if(Base::_pred) dij.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
1044      if(Base::_dist) dij.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
1045      dij.run(Base::_source);
1046    }
1047
1048    ///Runs Dijkstra algorithm from the given node.
1049
1050    ///Runs Dijkstra algorithm from the given node.
1051    ///\param s is the given source.
1052    void run(Node s)
1053    {
1054      Base::_source=s;
1055      run();
1056    }
1057
1058    template<class T>
1059    struct DefPredMapBase : public Base {
1060      typedef T PredMap;
1061      static PredMap *createPredMap(const Graph &) { return 0; };
1062      DefPredMapBase(const TR &b) : TR(b) {}
1063    };
1064   
1065    ///\brief \ref named-templ-param "Named parameter"
1066    ///function for setting PredMap type
1067    ///
1068    /// \ref named-templ-param "Named parameter"
1069    ///function for setting PredMap type
1070    ///
1071    template<class T>
1072    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t)
1073    {
1074      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
1075      return DijkstraWizard<DefPredMapBase<T> >(*this);
1076    }
1077   
1078    template<class T>
1079    struct DefDistMapBase : public Base {
1080      typedef T DistMap;
1081      static DistMap *createDistMap(const Graph &) { return 0; };
1082      DefDistMapBase(const TR &b) : TR(b) {}
1083    };
1084   
1085    ///\brief \ref named-templ-param "Named parameter"
1086    ///function for setting DistMap type
1087    ///
1088    /// \ref named-templ-param "Named parameter"
1089    ///function for setting DistMap type
1090    ///
1091    template<class T>
1092    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t)
1093    {
1094      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
1095      return DijkstraWizard<DefDistMapBase<T> >(*this);
1096    }
1097   
1098    /// Sets the source node, from which the Dijkstra algorithm runs.
1099
1100    /// Sets the source node, from which the Dijkstra algorithm runs.
1101    /// \param s is the source node.
1102    DijkstraWizard<TR> &source(Node s)
1103    {
1104      Base::_source=s;
1105      return *this;
1106    }
1107   
1108  };
1109 
1110  ///Function type interface for Dijkstra algorithm.
1111
1112  /// \ingroup shortest_path
1113  ///Function type interface for Dijkstra algorithm.
1114  ///
1115  ///This function also has several
1116  ///\ref named-templ-func-param "named parameters",
1117  ///they are declared as the members of class \ref DijkstraWizard.
1118  ///The following
1119  ///example shows how to use these parameters.
1120  ///\code
1121  ///  dijkstra(g,length,source).predMap(preds).run();
1122  ///\endcode
1123  ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
1124  ///to the end of the parameter list.
1125  ///\sa DijkstraWizard
1126  ///\sa Dijkstra
1127  template<class GR, class LM>
1128  DijkstraWizard<DijkstraWizardBase<GR,LM> >
1129  dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
1130  {
1131    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
1132  }
1133
1134} //END OF NAMESPACE LEMON
1135
1136#endif
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