COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/johnson.h @ 1993:2115143eceea

Last change on this file since 1993:2115143eceea was 1993:2115143eceea, checked in by Balazs Dezso, 14 years ago

utility, invalid and traits moved to bits

File size: 23.8 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_JOHNSON_H
20#define LEMON_JOHNSON_H
21
22///\ingroup flowalgs
23/// \file
24/// \brief Johnson algorithm.
25///
26
27#include <lemon/list_graph.h>
28#include <lemon/graph_utils.h>
29#include <lemon/dijkstra.h>
30#include <lemon/bellman_ford.h>
31#include <lemon/bits/invalid.h>
32#include <lemon/error.h>
33#include <lemon/maps.h>
34#include <lemon/matrix_maps.h>
35
36#include <limits>
37
38namespace lemon {
39
40  /// \brief Default OperationTraits for the Johnson algorithm class.
41  /// 
42  /// It defines all computational operations and constants which are
43  /// used in the Floyd-Warshall algorithm. The default implementation
44  /// is based on the numeric_limits class. If the numeric type does not
45  /// have infinity value then the maximum value is used as extremal
46  /// infinity value.
47  template <
48    typename Value,
49    bool has_infinity = std::numeric_limits<Value>::has_infinity>
50  struct JohnsonDefaultOperationTraits {
51    /// \brief Gives back the zero value of the type.
52    static Value zero() {
53      return static_cast<Value>(0);
54    }
55    /// \brief Gives back the positive infinity value of the type.
56    static Value infinity() {
57      return std::numeric_limits<Value>::infinity();
58    }
59    /// \brief Gives back the sum of the given two elements.
60    static Value plus(const Value& left, const Value& right) {
61      return left + right;
62    }
63    /// \brief Gives back true only if the first value less than the second.
64    static bool less(const Value& left, const Value& right) {
65      return left < right;
66    }
67  };
68
69  template <typename Value>
70  struct JohnsonDefaultOperationTraits<Value, false> {
71    static Value zero() {
72      return static_cast<Value>(0);
73    }
74    static Value infinity() {
75      return std::numeric_limits<Value>::max();
76    }
77    static Value plus(const Value& left, const Value& right) {
78      if (left == infinity() || right == infinity()) return infinity();
79      return left + right;
80    }
81    static bool less(const Value& left, const Value& right) {
82      return left < right;
83    }
84  };
85 
86  /// \brief Default traits class of Johnson class.
87  ///
88  /// Default traits class of Johnson class.
89  /// \param _Graph Graph type.
90  /// \param _LegthMap Type of length map.
91  template<class _Graph, class _LengthMap>
92  struct JohnsonDefaultTraits {
93    /// The graph type the algorithm runs on.
94    typedef _Graph Graph;
95
96    /// \brief The type of the map that stores the edge lengths.
97    ///
98    /// The type of the map that stores the edge lengths.
99    /// It must meet the \ref concept::ReadMap "ReadMap" concept.
100    typedef _LengthMap LengthMap;
101
102    // The type of the length of the edges.
103    typedef typename _LengthMap::Value Value;
104
105    /// \brief Operation traits for bellman-ford algorithm.
106    ///
107    /// It defines the infinity type on the given Value type
108    /// and the used operation.
109    /// \see JohnsonDefaultOperationTraits
110    typedef JohnsonDefaultOperationTraits<Value> OperationTraits;
111
112    /// The cross reference type used by heap.
113
114    /// The cross reference type used by heap.
115    /// Usually it is \c Graph::NodeMap<int>.
116    typedef typename Graph::template NodeMap<int> HeapCrossRef;
117
118    ///Instantiates a HeapCrossRef.
119
120    ///This function instantiates a \ref HeapCrossRef.
121    /// \param graph is the graph, to which we would like to define the
122    /// HeapCrossRef.
123    static HeapCrossRef *createHeapCrossRef(const Graph& graph) {
124      return new HeapCrossRef(graph);
125    }
126   
127    ///The heap type used by Dijkstra algorithm.
128
129    ///The heap type used by Dijkstra algorithm.
130    ///
131    ///\sa BinHeap
132    ///\sa Dijkstra
133    typedef BinHeap<typename Graph::Node, typename LengthMap::Value,
134                    HeapCrossRef, std::less<Value> > Heap;
135
136    ///Instantiates a Heap.
137
138    ///This function instantiates a \ref Heap.
139    /// \param crossRef The cross reference for the heap.
140    static Heap *createHeap(HeapCrossRef& crossRef) {
141      return new Heap(crossRef);
142    }
143 
144    /// \brief The type of the matrix map that stores the last edges of the
145    /// shortest paths.
146    ///
147    /// The type of the map that stores the last edges of the shortest paths.
148    /// It must be a matrix map with \c Graph::Edge value type.
149    ///
150    typedef DynamicMatrixMap<Graph, typename Graph::Node,
151                             typename Graph::Edge> PredMap;
152
153    /// \brief Instantiates a PredMap.
154    ///
155    /// This function instantiates a \ref PredMap.
156    /// \param graph is the graph, to which we would like to define the PredMap.
157    /// \todo The graph alone may be insufficient for the initialization
158    static PredMap *createPredMap(const Graph& graph) {
159      return new PredMap(graph);
160    }
161
162    /// \brief The type of the matrix map that stores the dists of the nodes.
163    ///
164    /// The type of the matrix map that stores the dists of the nodes.
165    /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept.
166    ///
167    typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
168   
169    /// \brief Instantiates a DistMap.
170    ///
171    /// This function instantiates a \ref DistMap.
172    /// \param graph is the graph, to which we would like to define the
173    /// \ref DistMap
174    static DistMap *createDistMap(const _Graph& graph) {
175      return new DistMap(graph);
176    }
177
178  };
179
180  /// \brief %Johnson algorithm class.
181  ///
182  /// \ingroup flowalgs
183  /// This class provides an efficient implementation of \c %Johnson
184  /// algorithm. The edge lengths are passed to the algorithm using a
185  /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any
186  /// kind of length.
187  ///
188  /// The algorithm solves the shortest path problem for each pair
189  /// of node when the edges can have negative length but the graph should
190  /// not contain cycles with negative sum of length. If we can assume
191  /// that all edge is non-negative in the graph then the dijkstra algorithm
192  /// should be used from each node.
193  ///
194  /// The complexity of this algorithm is $O(n^2 * log(n) + n * log(n) * e)$ or
195  /// with fibonacci heap O(n^2 * log(n) + n * e). Usually the fibonacci heap
196  /// implementation is slower than either binary heap implementation or the
197  /// Floyd-Warshall algorithm.
198  ///
199  /// The type of the length is determined by the
200  /// \ref concept::ReadMap::Value "Value" of the length map.
201  ///
202  /// \param _Graph The graph type the algorithm runs on. The default value
203  /// is \ref ListGraph. The value of _Graph is not used directly by
204  /// Johnson, it is only passed to \ref JohnsonDefaultTraits.
205  /// \param _LengthMap This read-only EdgeMap determines the lengths of the
206  /// edges. It is read once for each edge, so the map may involve in
207  /// relatively time consuming process to compute the edge length if
208  /// it is necessary. The default map type is \ref
209  /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
210  /// of _LengthMap is not used directly by Johnson, it is only passed
211  /// to \ref JohnsonDefaultTraits.  \param _Traits Traits class to set
212  /// various data types used by the algorithm.  The default traits
213  /// class is \ref JohnsonDefaultTraits
214  /// "JohnsonDefaultTraits<_Graph,_LengthMap>".  See \ref
215  /// JohnsonDefaultTraits for the documentation of a Johnson traits
216  /// class.
217  ///
218  /// \author Balazs Dezso
219
220#ifdef DOXYGEN
221  template <typename _Graph, typename _LengthMap, typename _Traits>
222#else
223  template <typename _Graph=ListGraph,
224            typename _LengthMap=typename _Graph::template EdgeMap<int>,
225            typename _Traits=JohnsonDefaultTraits<_Graph,_LengthMap> >
226#endif
227  class Johnson {
228  public:
229   
230    /// \brief \ref Exception for uninitialized parameters.
231    ///
232    /// This error represents problems in the initialization
233    /// of the parameters of the algorithms.
234
235    class UninitializedParameter : public lemon::UninitializedParameter {
236    public:
237      virtual const char* exceptionName() const {
238        return "lemon::Johnson::UninitializedParameter";
239      }
240    };
241
242    typedef _Traits Traits;
243    ///The type of the underlying graph.
244    typedef typename _Traits::Graph Graph;
245
246    typedef typename Graph::Node Node;
247    typedef typename Graph::NodeIt NodeIt;
248    typedef typename Graph::Edge Edge;
249    typedef typename Graph::EdgeIt EdgeIt;
250   
251    /// \brief The type of the length of the edges.
252    typedef typename _Traits::LengthMap::Value Value;
253    /// \brief The type of the map that stores the edge lengths.
254    typedef typename _Traits::LengthMap LengthMap;
255    /// \brief The type of the map that stores the last
256    /// edges of the shortest paths. The type of the PredMap
257    /// is a matrix map for Edges
258    typedef typename _Traits::PredMap PredMap;
259    /// \brief The type of the map that stores the dists of the nodes.
260    /// The type of the DistMap is a matrix map for Values
261    typedef typename _Traits::DistMap DistMap;
262    /// \brief The operation traits.
263    typedef typename _Traits::OperationTraits OperationTraits;
264    ///The cross reference type used for the current heap.
265    typedef typename _Traits::HeapCrossRef HeapCrossRef;
266    ///The heap type used by the dijkstra algorithm.
267    typedef typename _Traits::Heap Heap;
268  private:
269    /// Pointer to the underlying graph.
270    const Graph *graph;
271    /// Pointer to the length map
272    const LengthMap *length;
273    ///Pointer to the map of predecessors edges.
274    PredMap *_pred;
275    ///Indicates if \ref _pred is locally allocated (\c true) or not.
276    bool local_pred;
277    ///Pointer to the map of distances.
278    DistMap *_dist;
279    ///Indicates if \ref _dist is locally allocated (\c true) or not.
280    bool local_dist;
281    ///Pointer to the heap cross references.
282    HeapCrossRef *_heap_cross_ref;
283    ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not.
284    bool local_heap_cross_ref;
285    ///Pointer to the heap.
286    Heap *_heap;
287    ///Indicates if \ref _heap is locally allocated (\c true) or not.
288    bool local_heap;
289
290    /// Creates the maps if necessary.
291    void create_maps() {
292      if(!_pred) {
293        local_pred = true;
294        _pred = Traits::createPredMap(*graph);
295      }
296      if(!_dist) {
297        local_dist = true;
298        _dist = Traits::createDistMap(*graph);
299      }
300      if (!_heap_cross_ref) {
301        local_heap_cross_ref = true;
302        _heap_cross_ref = Traits::createHeapCrossRef(*graph);
303      }
304      if (!_heap) {
305        local_heap = true;
306        _heap = Traits::createHeap(*_heap_cross_ref);
307      }
308    }
309
310  public :
311
312    /// \name Named template parameters
313
314    ///@{
315
316    template <class T>
317    struct DefPredMapTraits : public Traits {
318      typedef T PredMap;
319      static PredMap *createPredMap(const Graph& graph) {
320        throw UninitializedParameter();
321      }
322    };
323
324    /// \brief \ref named-templ-param "Named parameter" for setting PredMap
325    /// type
326    /// \ref named-templ-param "Named parameter" for setting PredMap type
327    ///
328    template <class T>
329    struct DefPredMap
330      : public Johnson< Graph, LengthMap, DefPredMapTraits<T> > {
331      typedef Johnson< Graph, LengthMap, DefPredMapTraits<T> > Create;
332    };
333   
334    template <class T>
335    struct DefDistMapTraits : public Traits {
336      typedef T DistMap;
337      static DistMap *createDistMap(const Graph& graph) {
338        throw UninitializedParameter();
339      }
340    };
341    /// \brief \ref named-templ-param "Named parameter" for setting DistMap
342    /// type
343    ///
344    /// \ref named-templ-param "Named parameter" for setting DistMap type
345    ///
346    template <class T>
347    struct DefDistMap
348      : public Johnson< Graph, LengthMap, DefDistMapTraits<T> > {
349      typedef Johnson< Graph, LengthMap, DefDistMapTraits<T> > Create;
350    };
351   
352    template <class T>
353    struct DefOperationTraitsTraits : public Traits {
354      typedef T OperationTraits;
355    };
356   
357    /// \brief \ref named-templ-param "Named parameter" for setting
358    /// OperationTraits type
359    ///
360    /// \ref named-templ-param "Named parameter" for setting
361    /// OperationTraits type
362    template <class T>
363    struct DefOperationTraits
364      : public Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > {
365      typedef Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > Create;
366    };
367
368    template <class H, class CR>
369    struct DefHeapTraits : public Traits {
370      typedef CR HeapCrossRef;
371      typedef H Heap;
372      static HeapCrossRef *createHeapCrossRef(const Graph &) {
373        throw UninitializedParameter();
374      }
375      static Heap *createHeap(HeapCrossRef &)
376      {
377        throw UninitializedParameter();
378      }
379    };
380    ///\brief \ref named-templ-param "Named parameter" for setting heap and
381    ///cross reference type
382
383    ///\ref named-templ-param "Named parameter" for setting heap and cross
384    ///reference type
385    ///
386    template <class H, class CR = typename Graph::template NodeMap<int> >
387    struct DefHeap
388      : public Johnson< Graph, LengthMap, DefHeapTraits<H, CR> > {
389      typedef Johnson< Graph, LengthMap, DefHeapTraits<H, CR> > Create;
390    };
391
392    template <class H, class CR>
393    struct DefStandardHeapTraits : public Traits {
394      typedef CR HeapCrossRef;
395      typedef H Heap;
396      static HeapCrossRef *createHeapCrossRef(const Graph &G) {
397        return new HeapCrossRef(G);
398      }
399      static Heap *createHeap(HeapCrossRef &R)
400      {
401        return new Heap(R);
402      }
403    };
404    ///\ref named-templ-param "Named parameter" for setting heap and cross
405    ///reference type with automatic allocation
406
407    ///\ref named-templ-param "Named parameter" for setting heap and cross
408    ///reference type. It can allocate the heap and the cross reference
409    ///object if the cross reference's constructor waits for the graph as
410    ///parameter and the heap's constructor waits for the cross reference.
411    template <class H, class CR = typename Graph::template NodeMap<int> >
412    struct DefStandardHeap
413      : public Johnson< Graph, LengthMap, DefStandardHeapTraits<H, CR> > {
414      typedef Johnson< Graph, LengthMap, DefStandardHeapTraits<H, CR> >
415      Create;
416    };
417   
418    ///@}
419
420  protected:
421
422    Johnson() {}
423
424  public:     
425
426    typedef Johnson Create;
427   
428    /// \brief Constructor.
429    ///
430    /// \param _graph the graph the algorithm will run on.
431    /// \param _length the length map used by the algorithm.
432    Johnson(const Graph& _graph, const LengthMap& _length) :
433      graph(&_graph), length(&_length),
434      _pred(0), local_pred(false),
435      _dist(0), local_dist(false),
436      _heap_cross_ref(0), local_heap_cross_ref(false),
437      _heap(0), local_heap(false) {}
438   
439    ///Destructor.
440    ~Johnson() {
441      if (local_pred) delete _pred;
442      if (local_dist) delete _dist;
443      if (local_heap_cross_ref) delete _heap_cross_ref;
444      if (local_heap) delete _heap;
445    }
446
447    /// \brief Sets the length map.
448    ///
449    /// Sets the length map.
450    /// \return \c (*this)
451    Johnson &lengthMap(const LengthMap &m) {
452      length = &m;
453      return *this;
454    }
455
456    /// \brief Sets the map storing the predecessor edges.
457    ///
458    /// Sets the map storing the predecessor edges.
459    /// If you don't use this function before calling \ref run(),
460    /// it will allocate one. The destuctor deallocates this
461    /// automatically allocated map, of course.
462    /// \return \c (*this)
463    Johnson &predMap(PredMap &m) {
464      if(local_pred) {
465        delete _pred;
466        local_pred=false;
467      }
468      _pred = &m;
469      return *this;
470    }
471
472    /// \brief Sets the map storing the distances calculated by the algorithm.
473    ///
474    /// Sets the map storing the distances calculated by the algorithm.
475    /// If you don't use this function before calling \ref run(),
476    /// it will allocate one. The destuctor deallocates this
477    /// automatically allocated map, of course.
478    /// \return \c (*this)
479    Johnson &distMap(DistMap &m) {
480      if(local_dist) {
481        delete _dist;
482        local_dist=false;
483      }
484      _dist = &m;
485      return *this;
486    }
487
488  public:   
489
490    ///\name Execution control
491    /// The simplest way to execute the algorithm is to use
492    /// one of the member functions called \c run(...).
493    /// \n
494    /// If you need more control on the execution,
495    /// Finally \ref start() will perform the actual path
496    /// computation.
497
498    ///@{
499
500    /// \brief Initializes the internal data structures.
501    ///
502    /// Initializes the internal data structures.
503    void init() {
504      create_maps();
505    }
506
507    /// \brief Executes the algorithm with own potential map.
508    ///
509    /// This method runs the %Johnson algorithm in order to compute
510    /// the shortest path to each node pairs. The potential map
511    /// can be given for this algorithm which usually calculated
512    /// by the Bellman-Ford algorithm. If the graph does not have
513    /// negative length edge then this start function can be used
514    /// with constMap<Node, int>(0) parameter to omit the running time of
515    /// the Bellman-Ford.
516    /// The algorithm computes
517    /// - The shortest path tree for each node.
518    /// - The distance between each node pairs.
519    template <typename PotentialMap>
520    void shiftedStart(const PotentialMap& potential) {     
521      typename Graph::template EdgeMap<Value> shiftlen(*graph);
522      for (EdgeIt it(*graph);  it != INVALID; ++it) {
523        shiftlen[it] = (*length)[it]
524          + potential[graph->source(it)]
525          - potential[graph->target(it)];
526      }
527     
528      typename Dijkstra<Graph, typename Graph::template EdgeMap<Value> >::
529        template DefHeap<Heap, HeapCrossRef>::
530        Create dijkstra(*graph, shiftlen);
531
532      dijkstra.heap(*_heap, *_heap_cross_ref);
533     
534      for (NodeIt it(*graph); it != INVALID; ++it) {
535        dijkstra.run(it);
536        for (NodeIt jt(*graph); jt != INVALID; ++jt) {
537          if (dijkstra.reached(jt)) {
538            _dist->set(it, jt, dijkstra.dist(jt) +
539                       potential[jt] - potential[it]);
540            _pred->set(it, jt, dijkstra.predEdge(jt));
541          } else {
542            _dist->set(it, jt, OperationTraits::infinity());
543            _pred->set(it, jt, INVALID);
544          }
545        }
546      }
547    }
548
549    /// \brief Executes the algorithm.
550    ///
551    /// This method runs the %Johnson algorithm in order to compute
552    /// the shortest path to each node pairs. The algorithm
553    /// computes
554    /// - The shortest path tree for each node.
555    /// - The distance between each node pairs.
556    void start() {
557
558      typedef typename BellmanFord<Graph, LengthMap>::
559      template DefOperationTraits<OperationTraits>::
560      template DefPredMap<NullMap<Node, Edge> >::
561      Create BellmanFordType;
562     
563      BellmanFordType bellmanford(*graph, *length);
564
565      NullMap<Node, Edge> predMap;
566
567      bellmanford.predMap(predMap);
568     
569      bellmanford.init(OperationTraits::zero());
570      bellmanford.start();
571
572      shiftedStart(bellmanford.distMap());
573    }
574
575    /// \brief Executes the algorithm and checks the negatvie cycles.
576    ///
577    /// This method runs the %Johnson algorithm in order to compute
578    /// the shortest path to each node pairs. If the graph contains
579    /// negative cycle it gives back false. The algorithm
580    /// computes
581    /// - The shortest path tree for each node.
582    /// - The distance between each node pairs.
583    bool checkedStart() {
584     
585      typedef typename BellmanFord<Graph, LengthMap>::
586      template DefOperationTraits<OperationTraits>::
587      template DefPredMap<NullMap<Node, Edge> >::
588      Create BellmanFordType;
589
590      BellmanFordType bellmanford(*graph, *length);
591
592      NullMap<Node, Edge> predMap;
593
594      bellmanford.predMap(predMap);
595     
596      bellmanford.init(OperationTraits::zero());
597      if (!bellmanford.checkedStart()) return false;
598
599      shiftedStart(bellmanford.distMap());
600      return true;
601    }
602
603   
604    /// \brief Runs %Johnson algorithm.
605    ///   
606    /// This method runs the %Johnson algorithm from a each node
607    /// in order to compute the shortest path to each node pairs.
608    /// The algorithm computes
609    /// - The shortest path tree for each node.
610    /// - The distance between each node pairs.
611    ///
612    /// \note d.run(s) is just a shortcut of the following code.
613    ///\code
614    ///  d.init();
615    ///  d.start();
616    ///\endcode
617    void run() {
618      init();
619      start();
620    }
621   
622    ///@}
623
624    /// \name Query Functions
625    /// The result of the %Johnson algorithm can be obtained using these
626    /// functions.\n
627    /// Before the use of these functions,
628    /// either run() or start() must be called.
629   
630    ///@{
631
632    /// \brief Copies the shortest path to \c t into \c p
633    ///   
634    /// This function copies the shortest path to \c t into \c p.
635    /// If it \c t is a source itself or unreachable, then it does not
636    /// alter \c p.
637    /// \return Returns \c true if a path to \c t was actually copied to \c p,
638    /// \c false otherwise.
639    /// \sa DirPath
640    template <typename Path>
641    bool getPath(Path &p, Node source, Node target) {
642      if (connected(source, target)) {
643        p.clear();
644        typename Path::Builder b(target);
645        for(b.setStartNode(target); predEdge(source, target) != INVALID;
646            target = predNode(target)) {
647          b.pushFront(predEdge(source, target));
648        }
649        b.commit();
650        return true;
651      }
652      return false;
653    }
654         
655    /// \brief The distance between two nodes.
656    ///
657    /// Returns the distance between two nodes.
658    /// \pre \ref run() must be called before using this function.
659    /// \warning If node \c v in unreachable from the root the return value
660    /// of this funcion is undefined.
661    Value dist(Node source, Node target) const {
662      return (*_dist)(source, target);
663    }
664
665    /// \brief Returns the 'previous edge' of the shortest path tree.
666    ///
667    /// For the node \c node it returns the 'previous edge' of the shortest
668    /// path tree to direction of the node \c root
669    /// i.e. it returns the last edge of a shortest path from the node \c root
670    /// to \c node. It is \ref INVALID if \c node is unreachable from the root
671    /// or if \c node=root. The shortest path tree used here is equal to the
672    /// shortest path tree used in \ref predNode().
673    /// \pre \ref run() must be called before using this function.
674    Edge predEdge(Node root, Node node) const {
675      return (*_pred)(root, node);
676    }
677
678    /// \brief Returns the 'previous node' of the shortest path tree.
679    ///
680    /// For a node \c node it returns the 'previous node' of the shortest path
681    /// tree to direction of the node \c root, i.e. it returns the last but
682    /// one node from a shortest path from the \c root to \c node. It is
683    /// INVALID if \c node is unreachable from the root or if \c node=root.
684    /// The shortest path tree used here is equal to the
685    /// shortest path tree used in \ref predEdge(). 
686    /// \pre \ref run() must be called before using this function.
687    Node predNode(Node root, Node node) const {
688      return (*_pred)(root, node) == INVALID ?
689      INVALID : graph->source((*_pred)(root, node));
690    }
691   
692    /// \brief Returns a reference to the matrix node map of distances.
693    ///
694    /// Returns a reference to the matrix node map of distances.
695    ///
696    /// \pre \ref run() must be called before using this function.
697    const DistMap &distMap() const { return *_dist;}
698 
699    /// \brief Returns a reference to the shortest path tree map.
700    ///
701    /// Returns a reference to the matrix node map of the edges of the
702    /// shortest path tree.
703    /// \pre \ref run() must be called before using this function.
704    const PredMap &predMap() const { return *_pred;}
705 
706    /// \brief Checks if a node is reachable from the root.
707    ///
708    /// Returns \c true if \c v is reachable from the root.
709    /// \pre \ref run() must be called before using this function.
710    ///
711    bool connected(Node source, Node target) {
712      return (*_dist)(source, target) != OperationTraits::infinity();
713    }
714   
715    ///@}
716  };
717 
718} //END OF NAMESPACE LEMON
719
720#endif
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