COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/dijkstra.h @ 2335:27aa03cd3121

Last change on this file since 2335:27aa03cd3121 was 2335:27aa03cd3121, checked in by Balazs Dezso, 13 years ago

New path concept and path structures

TODO: BellmanFord::negativeCycle()

File size: 35.0 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
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 flowalgs
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 flowalgs
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& 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 shorter than \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->set(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    typedef PredMapPath<Graph, PredMap> Path;
723
724    ///Gives back the shortest path.
725   
726    ///Gives back the shortest path.
727    ///\pre The \c t should be reachable from the source.
728    Path path(Node t)
729    {
730      return Path(*G, *_pred, t);
731    }
732
733    ///The distance of a node from the root.
734
735    ///Returns the distance of a node from the root.
736    ///\pre \ref run() must be called before using this function.
737    ///\warning If node \c v in unreachable from the root the return value
738    ///of this funcion is undefined.
739    Value dist(Node v) const { return (*_dist)[v]; }
740
741    ///Returns the 'previous edge' of the shortest path tree.
742
743    ///For a node \c v it returns the 'previous edge' of the shortest path tree,
744    ///i.e. it returns the last edge of a shortest path from the root to \c
745    ///v. It is \ref INVALID
746    ///if \c v is unreachable from the root or if \c v=s. The
747    ///shortest path tree used here is equal to the shortest path tree used in
748    ///\ref predNode().  \pre \ref run() must be called before using
749    ///this function.
750    Edge predEdge(Node v) const { return (*_pred)[v]; }
751
752    ///Returns the 'previous node' of the shortest path tree.
753
754    ///For a node \c v it returns the 'previous node' of the shortest path tree,
755    ///i.e. it returns the last but one node from a shortest path from the
756    ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
757    ///\c v=s. The shortest path tree used here is equal to the shortest path
758    ///tree used in \ref predEdge().  \pre \ref run() must be called before
759    ///using this function.
760    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
761                                  G->source((*_pred)[v]); }
762   
763    ///Returns a reference to the NodeMap of distances.
764
765    ///Returns a reference to the NodeMap of distances. \pre \ref run() must
766    ///be called before using this function.
767    const DistMap &distMap() const { return *_dist;}
768 
769    ///Returns a reference to the shortest path tree map.
770
771    ///Returns a reference to the NodeMap of the edges of the
772    ///shortest path tree.
773    ///\pre \ref run() must be called before using this function.
774    const PredMap &predMap() const { return *_pred;}
775 
776    ///Checks if a node is reachable from the root.
777
778    ///Returns \c true if \c v is reachable from the root.
779    ///\warning The source nodes are inditated as unreached.
780    ///\pre \ref run() must be called before using this function.
781    ///
782    bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; }
783
784    ///Checks if a node is processed.
785
786    ///Returns \c true if \c v is processed, i.e. the shortest
787    ///path to \c v has already found.
788    ///\pre \ref run() must be called before using this function.
789    ///
790    bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; }
791   
792    ///@}
793  };
794
795
796
797
798 
799  ///Default traits class of Dijkstra function.
800
801  ///Default traits class of Dijkstra function.
802  ///\param GR Graph type.
803  ///\param LM Type of length map.
804  template<class GR, class LM>
805  struct DijkstraWizardDefaultTraits
806  {
807    ///The graph type the algorithm runs on.
808    typedef GR Graph;
809    ///The type of the map that stores the edge lengths.
810
811    ///The type of the map that stores the edge lengths.
812    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
813    typedef LM LengthMap;
814    //The type of the length of the edges.
815    typedef typename LM::Value Value;
816    ///The heap type used by Dijkstra algorithm.
817
818    /// The cross reference type used by heap.
819
820    /// The cross reference type used by heap.
821    /// Usually it is \c Graph::NodeMap<int>.
822    typedef typename Graph::template NodeMap<int> HeapCrossRef;
823    ///Instantiates a HeapCrossRef.
824
825    ///This function instantiates a \ref HeapCrossRef.
826    /// \param G is the graph, to which we would like to define the
827    /// HeapCrossRef.
828    /// \todo The graph alone may be insufficient for the initialization
829    static HeapCrossRef *createHeapCrossRef(const GR &G)
830    {
831      return new HeapCrossRef(G);
832    }
833   
834    ///The heap type used by Dijkstra algorithm.
835
836    ///The heap type used by Dijkstra algorithm.
837    ///
838    ///\sa BinHeap
839    ///\sa Dijkstra
840    typedef BinHeap<typename LM::Value, typename GR::template NodeMap<int>,
841                    std::less<Value> > Heap;
842
843    static Heap *createHeap(HeapCrossRef& R)
844    {
845      return new Heap(R);
846    }
847
848    ///\brief The type of the map that stores the last
849    ///edges of the shortest paths.
850    ///
851    ///The type of the map that stores the last
852    ///edges of the shortest paths.
853    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
854    ///
855    typedef NullMap <typename GR::Node,typename GR::Edge> PredMap;
856    ///Instantiates a PredMap.
857 
858    ///This function instantiates a \ref PredMap.
859    ///\param g is the graph, to which we would like to define the PredMap.
860    ///\todo The graph alone may be insufficient for the initialization
861#ifdef DOXYGEN
862    static PredMap *createPredMap(const GR &g)
863#else
864    static PredMap *createPredMap(const GR &)
865#endif
866    {
867      return new PredMap();
868    }
869    ///The type of the map that stores whether a nodes is processed.
870 
871    ///The type of the map that stores whether a nodes is processed.
872    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
873    ///By default it is a NullMap.
874    ///\todo If it is set to a real map,
875    ///Dijkstra::processed() should read this.
876    ///\todo named parameter to set this type, function to read and write.
877    typedef NullMap<typename Graph::Node,bool> ProcessedMap;
878    ///Instantiates a ProcessedMap.
879 
880    ///This function instantiates a \ref ProcessedMap.
881    ///\param g is the graph, to which
882    ///we would like to define the \ref ProcessedMap
883#ifdef DOXYGEN
884    static ProcessedMap *createProcessedMap(const GR &g)
885#else
886    static ProcessedMap *createProcessedMap(const GR &)
887#endif
888    {
889      return new ProcessedMap();
890    }
891    ///The type of the map that stores the dists of the nodes.
892 
893    ///The type of the map that stores the dists of the nodes.
894    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.
895    ///
896    typedef NullMap<typename Graph::Node,typename LM::Value> DistMap;
897    ///Instantiates a DistMap.
898 
899    ///This function instantiates a \ref DistMap.
900    ///\param g is the graph, to which we would like to define the \ref DistMap
901#ifdef DOXYGEN
902    static DistMap *createDistMap(const GR &g)
903#else
904    static DistMap *createDistMap(const GR &)
905#endif
906    {
907      return new DistMap();
908    }
909  };
910 
911  /// Default traits used by \ref DijkstraWizard
912
913  /// To make it easier to use Dijkstra algorithm
914  ///we have created a wizard class.
915  /// This \ref DijkstraWizard class needs default traits,
916  ///as well as the \ref Dijkstra class.
917  /// The \ref DijkstraWizardBase is a class to be the default traits of the
918  /// \ref DijkstraWizard class.
919  /// \todo More named parameters are required...
920  template<class GR,class LM>
921  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM>
922  {
923
924    typedef DijkstraWizardDefaultTraits<GR,LM> Base;
925  protected:
926    /// Type of the nodes in the graph.
927    typedef typename Base::Graph::Node Node;
928
929    /// Pointer to the underlying graph.
930    void *_g;
931    /// Pointer to the length map
932    void *_length;
933    ///Pointer to the map of predecessors edges.
934    void *_pred;
935    ///Pointer to the map of distances.
936    void *_dist;
937    ///Pointer to the source node.
938    Node _source;
939
940    public:
941    /// Constructor.
942   
943    /// This constructor does not require parameters, therefore it initiates
944    /// all of the attributes to default values (0, INVALID).
945    DijkstraWizardBase() : _g(0), _length(0), _pred(0),
946                           _dist(0), _source(INVALID) {}
947
948    /// Constructor.
949   
950    /// This constructor requires some parameters,
951    /// listed in the parameters list.
952    /// Others are initiated to 0.
953    /// \param g is the initial value of  \ref _g
954    /// \param l is the initial value of  \ref _length
955    /// \param s is the initial value of  \ref _source
956    DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
957      _g((void *)&g), _length((void *)&l), _pred(0),
958      _dist(0), _source(s) {}
959
960  };
961 
962  /// A class to make the usage of Dijkstra algorithm easier
963
964  /// This class is created to make it easier to use Dijkstra algorithm.
965  /// It uses the functions and features of the plain \ref Dijkstra,
966  /// but it is much simpler to use it.
967  ///
968  /// Simplicity means that the way to change the types defined
969  /// in the traits class is based on functions that returns the new class
970  /// and not on templatable built-in classes.
971  /// When using the plain \ref Dijkstra
972  /// the new class with the modified type comes from
973  /// the original class by using the ::
974  /// operator. In the case of \ref DijkstraWizard only
975  /// a function have to be called and it will
976  /// return the needed class.
977  ///
978  /// It does not have own \ref run method. When its \ref run method is called
979  /// it initiates a plain \ref Dijkstra class, and calls the \ref
980  /// Dijkstra::run method of it.
981  template<class TR>
982  class DijkstraWizard : public TR
983  {
984    typedef TR Base;
985
986    ///The type of the underlying graph.
987    typedef typename TR::Graph Graph;
988    //\e
989    typedef typename Graph::Node Node;
990    //\e
991    typedef typename Graph::NodeIt NodeIt;
992    //\e
993    typedef typename Graph::Edge Edge;
994    //\e
995    typedef typename Graph::OutEdgeIt OutEdgeIt;
996   
997    ///The type of the map that stores the edge lengths.
998    typedef typename TR::LengthMap LengthMap;
999    ///The type of the length of the edges.
1000    typedef typename LengthMap::Value Value;
1001    ///\brief The type of the map that stores the last
1002    ///edges of the shortest paths.
1003    typedef typename TR::PredMap PredMap;
1004    ///The type of the map that stores the dists of the nodes.
1005    typedef typename TR::DistMap DistMap;
1006    ///The heap type used by the dijkstra algorithm.
1007    typedef typename TR::Heap Heap;
1008  public:
1009    /// Constructor.
1010    DijkstraWizard() : TR() {}
1011
1012    /// Constructor that requires parameters.
1013
1014    /// Constructor that requires parameters.
1015    /// These parameters will be the default values for the traits class.
1016    DijkstraWizard(const Graph &g,const LengthMap &l, Node s=INVALID) :
1017      TR(g,l,s) {}
1018
1019    ///Copy constructor
1020    DijkstraWizard(const TR &b) : TR(b) {}
1021
1022    ~DijkstraWizard() {}
1023
1024    ///Runs Dijkstra algorithm from a given node.
1025   
1026    ///Runs Dijkstra algorithm from a given node.
1027    ///The node can be given by the \ref source function.
1028    void run()
1029    {
1030      if(Base::_source==INVALID) throw UninitializedParameter();
1031      Dijkstra<Graph,LengthMap,TR>
1032        dij(*(Graph*)Base::_g,*(LengthMap*)Base::_length);
1033      if(Base::_pred) dij.predMap(*(PredMap*)Base::_pred);
1034      if(Base::_dist) dij.distMap(*(DistMap*)Base::_dist);
1035      dij.run(Base::_source);
1036    }
1037
1038    ///Runs Dijkstra algorithm from the given node.
1039
1040    ///Runs Dijkstra algorithm from the given node.
1041    ///\param s is the given source.
1042    void run(Node s)
1043    {
1044      Base::_source=s;
1045      run();
1046    }
1047
1048    template<class T>
1049    struct DefPredMapBase : public Base {
1050      typedef T PredMap;
1051      static PredMap *createPredMap(const Graph &) { return 0; };
1052      DefPredMapBase(const TR &b) : TR(b) {}
1053    };
1054   
1055    ///\brief \ref named-templ-param "Named parameter"
1056    ///function for setting PredMap type
1057    ///
1058    /// \ref named-templ-param "Named parameter"
1059    ///function for setting PredMap type
1060    ///
1061    template<class T>
1062    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t)
1063    {
1064      Base::_pred=(void *)&t;
1065      return DijkstraWizard<DefPredMapBase<T> >(*this);
1066    }
1067   
1068    template<class T>
1069    struct DefDistMapBase : public Base {
1070      typedef T DistMap;
1071      static DistMap *createDistMap(const Graph &) { return 0; };
1072      DefDistMapBase(const TR &b) : TR(b) {}
1073    };
1074   
1075    ///\brief \ref named-templ-param "Named parameter"
1076    ///function for setting DistMap type
1077    ///
1078    /// \ref named-templ-param "Named parameter"
1079    ///function for setting DistMap type
1080    ///
1081    template<class T>
1082    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t)
1083    {
1084      Base::_dist=(void *)&t;
1085      return DijkstraWizard<DefDistMapBase<T> >(*this);
1086    }
1087   
1088    /// Sets the source node, from which the Dijkstra algorithm runs.
1089
1090    /// Sets the source node, from which the Dijkstra algorithm runs.
1091    /// \param s is the source node.
1092    DijkstraWizard<TR> &source(Node s)
1093    {
1094      Base::_source=s;
1095      return *this;
1096    }
1097   
1098  };
1099 
1100  ///Function type interface for Dijkstra algorithm.
1101
1102  /// \ingroup flowalgs
1103  ///Function type interface for Dijkstra algorithm.
1104  ///
1105  ///This function also has several
1106  ///\ref named-templ-func-param "named parameters",
1107  ///they are declared as the members of class \ref DijkstraWizard.
1108  ///The following
1109  ///example shows how to use these parameters.
1110  ///\code
1111  ///  dijkstra(g,length,source).predMap(preds).run();
1112  ///\endcode
1113  ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()"
1114  ///to the end of the parameter list.
1115  ///\sa DijkstraWizard
1116  ///\sa Dijkstra
1117  template<class GR, class LM>
1118  DijkstraWizard<DijkstraWizardBase<GR,LM> >
1119  dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
1120  {
1121    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
1122  }
1123
1124} //END OF NAMESPACE LEMON
1125
1126#endif
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