COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/floyd_warshall.h @ 1866:c2de2ed28e59

Last change on this file since 1866:c2de2ed28e59 was 1865:dcefd1d1377f, checked in by Balazs Dezso, 14 years ago

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1/* -*- C++ -*-
2 * lemon/floyd_warshall.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_FLOYD_WARSHALL_H
18#define LEMON_FLOYD_WARSHALL_H
19
20///\ingroup flowalgs
21/// \file
22/// \brief FloydWarshall algorithm.
23///
24
25#include <lemon/list_graph.h>
26#include <lemon/graph_utils.h>
27#include <lemon/invalid.h>
28#include <lemon/error.h>
29#include <lemon/matrix_maps.h>
30#include <lemon/maps.h>
31
32#include <limits>
33
34namespace lemon {
35
36  /// \brief Default OperationTraits for the FloydWarshall algorithm class.
37  /// 
38  /// It defines all computational operations and constants which are
39  /// used in the Floyd-Warshall algorithm. The default implementation
40  /// is based on the numeric_limits class. If the numeric type does not
41  /// have infinity value then the maximum value is used as extremal
42  /// infinity value.
43  template <
44    typename Value,
45    bool has_infinity = std::numeric_limits<Value>::has_infinity>
46  struct FloydWarshallDefaultOperationTraits {
47    /// \brief Gives back the zero value of the type.
48    static Value zero() {
49      return static_cast<Value>(0);
50    }
51    /// \brief Gives back the positive infinity value of the type.
52    static Value infinity() {
53      return std::numeric_limits<Value>::infinity();
54    }
55    /// \brief Gives back the sum of the given two elements.
56    static Value plus(const Value& left, const Value& right) {
57      return left + right;
58    }
59    /// \brief Gives back true only if the first value less than the second.
60    static bool less(const Value& left, const Value& right) {
61      return left < right;
62    }
63  };
64
65  template <typename Value>
66  struct FloydWarshallDefaultOperationTraits<Value, false> {
67    static Value zero() {
68      return static_cast<Value>(0);
69    }
70    static Value infinity() {
71      return std::numeric_limits<Value>::max();
72    }
73    static Value plus(const Value& left, const Value& right) {
74      if (left == infinity() || right == infinity()) return infinity();
75      return left + right;
76    }
77    static bool less(const Value& left, const Value& right) {
78      return left < right;
79    }
80  };
81 
82  /// \brief Default traits class of FloydWarshall class.
83  ///
84  /// Default traits class of FloydWarshall class.
85  /// \param _Graph Graph type.
86  /// \param _LegthMap Type of length map.
87  template<class _Graph, class _LengthMap>
88  struct FloydWarshallDefaultTraits {
89    /// The graph type the algorithm runs on.
90    typedef _Graph Graph;
91
92    /// \brief The type of the map that stores the edge lengths.
93    ///
94    /// The type of the map that stores the edge lengths.
95    /// It must meet the \ref concept::ReadMap "ReadMap" concept.
96    typedef _LengthMap LengthMap;
97
98    // The type of the length of the edges.
99    typedef typename _LengthMap::Value Value;
100
101    /// \brief Operation traits for floyd-warshall algorithm.
102    ///
103    /// It defines the infinity type on the given Value type
104    /// and the used operation.
105    /// \see FloydWarshallDefaultOperationTraits
106    typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;
107 
108    /// \brief The type of the matrix map that stores the last edges of the
109    /// shortest paths.
110    ///
111    /// The type of the map that stores the last edges of the shortest paths.
112    /// It must be a matrix map with \c Graph::Edge value type.
113    ///
114    typedef DynamicMatrixMap<Graph, typename Graph::Node,
115                             typename Graph::Edge> PredMap;
116
117    /// \brief Instantiates a PredMap.
118    ///
119    /// This function instantiates a \ref PredMap.
120    /// \param G is the graph, to which we would like to define the PredMap.
121    /// \todo The graph alone may be insufficient for the initialization
122    static PredMap *createPredMap(const _Graph& graph) {
123      return new PredMap(graph);
124    }
125
126    /// \brief The type of the map that stores the dists of the nodes.
127    ///
128    /// The type of the map that stores the dists of the nodes.
129    /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept.
130    ///
131    typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
132
133    /// \brief Instantiates a DistMap.
134    ///
135    /// This function instantiates a \ref DistMap.
136    /// \param G is the graph, to which we would like to define the
137    /// \ref DistMap
138    static DistMap *createDistMap(const _Graph& graph) {
139      return new DistMap(graph);
140    }
141
142  };
143 
144  /// \brief %FloydWarshall algorithm class.
145  ///
146  /// \ingroup flowalgs
147  /// This class provides an efficient implementation of \c Floyd-Warshall
148  /// algorithm. The edge lengths are passed to the algorithm using a
149  /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any
150  /// kind of length.
151  ///
152  /// The algorithm solves the shortest path problem for each pair
153  /// of node when the edges can have negative length but the graph should
154  /// not contain cycles with negative sum of length. If we can assume
155  /// that all edge is non-negative in the graph then the dijkstra algorithm
156  /// should be used from each node rather and if the graph is sparse and
157  /// there are negative circles then the johnson algorithm.
158  ///
159  /// The complexity of this algorithm is O(n^3 + e).
160  ///
161  /// The type of the length is determined by the
162  /// \ref concept::ReadMap::Value "Value" of the length map.
163  ///
164  /// \param _Graph The graph type the algorithm runs on. The default value
165  /// is \ref ListGraph. The value of _Graph is not used directly by
166  /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
167  /// \param _LengthMap This read-only EdgeMap determines the lengths of the
168  /// edges. It is read once for each edge, so the map may involve in
169  /// relatively time consuming process to compute the edge length if
170  /// it is necessary. The default map type is \ref
171  /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
172  /// of _LengthMap is not used directly by FloydWarshall, it is only passed
173  /// to \ref FloydWarshallDefaultTraits.  \param _Traits Traits class to set
174  /// various data types used by the algorithm.  The default traits
175  /// class is \ref FloydWarshallDefaultTraits
176  /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>".  See \ref
177  /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall
178  /// traits class.
179  ///
180  /// \author Balazs Dezso
181
182#ifdef DOXYGEN
183  template <typename _Graph, typename _LengthMap typename _Traits >
184#else
185  template <typename _Graph=ListGraph,
186            typename _LengthMap=typename _Graph::template EdgeMap<int>,
187            typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
188#endif
189  class FloydWarshall {
190  public:
191   
192    /// \brief \ref Exception for uninitialized parameters.
193    ///
194    /// This error represents problems in the initialization
195    /// of the parameters of the algorithms.
196
197    class UninitializedParameter : public lemon::UninitializedParameter {
198    public:
199      virtual const char* exceptionName() const {
200        return "lemon::FloydWarshall::UninitializedParameter";
201      }
202    };
203
204    typedef _Traits Traits;
205    ///The type of the underlying graph.
206    typedef typename _Traits::Graph Graph;
207
208    typedef typename Graph::Node Node;
209    typedef typename Graph::NodeIt NodeIt;
210    typedef typename Graph::Edge Edge;
211    typedef typename Graph::EdgeIt EdgeIt;
212   
213    /// \brief The type of the length of the edges.
214    typedef typename _Traits::LengthMap::Value Value;
215    /// \brief The type of the map that stores the edge lengths.
216    typedef typename _Traits::LengthMap LengthMap;
217    /// \brief The type of the map that stores the last
218    /// edges of the shortest paths. The type of the PredMap
219    /// is a matrix map for Edges
220    typedef typename _Traits::PredMap PredMap;
221    /// \brief The type of the map that stores the dists of the nodes.
222    /// The type of the DistMap is a matrix map for Values
223    typedef typename _Traits::DistMap DistMap;
224    /// \brief The operation traits.
225    typedef typename _Traits::OperationTraits OperationTraits;
226  private:
227    /// Pointer to the underlying graph.
228    const Graph *graph;
229    /// Pointer to the length map
230    const LengthMap *length;
231    ///Pointer to the map of predecessors edges.
232    PredMap *_pred;
233    ///Indicates if \ref _pred is locally allocated (\c true) or not.
234    bool local_pred;
235    ///Pointer to the map of distances.
236    DistMap *_dist;
237    ///Indicates if \ref _dist is locally allocated (\c true) or not.
238    bool local_dist;
239
240    /// Creates the maps if necessary.
241    void create_maps() {
242      if(!_pred) {
243        local_pred = true;
244        _pred = Traits::createPredMap(*graph);
245      }
246      if(!_dist) {
247        local_dist = true;
248        _dist = Traits::createDistMap(*graph);
249      }
250    }
251   
252  public :
253 
254    /// \name Named template parameters
255
256    ///@{
257
258    template <class T>
259    struct DefPredMapTraits : public Traits {
260      typedef T PredMap;
261      static PredMap *createPredMap(const Graph& graph) {
262        throw UninitializedParameter();
263      }
264    };
265
266    /// \brief \ref named-templ-param "Named parameter" for setting PredMap
267    /// type
268    /// \ref named-templ-param "Named parameter" for setting PredMap type
269    ///
270    template <class T>
271    struct DefPredMap
272      : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
273      typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;
274    };
275   
276    template <class T>
277    struct DefDistMapTraits : public Traits {
278      typedef T DistMap;
279      static DistMap *createDistMap(const Graph& graph) {
280        throw UninitializedParameter();
281      }
282    };
283    /// \brief \ref named-templ-param "Named parameter" for setting DistMap
284    /// type
285    ///
286    /// \ref named-templ-param "Named parameter" for setting DistMap type
287    ///
288    template <class T>
289    struct DefDistMap
290      : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
291      typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;
292    };
293   
294    template <class T>
295    struct DefOperationTraitsTraits : public Traits {
296      typedef T OperationTraits;
297    };
298   
299    /// \brief \ref named-templ-param "Named parameter" for setting
300    /// OperationTraits type
301    ///
302    /// \ref named-templ-param "Named parameter" for setting PredMap type
303    template <class T>
304    struct DefOperationTraits
305      : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
306      typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
307      Create;
308    };
309   
310    ///@}
311
312  protected:
313
314    FloydWarshall() {}
315
316  public:     
317
318    typedef FloydWarshall Create;
319   
320    /// \brief Constructor.
321    ///
322    /// \param _graph the graph the algorithm will run on.
323    /// \param _length the length map used by the algorithm.
324    FloydWarshall(const Graph& _graph, const LengthMap& _length) :
325      graph(&_graph), length(&_length),
326      _pred(0), local_pred(false),
327      _dist(0), local_dist(false) {}
328   
329    ///Destructor.
330    ~FloydWarshall() {
331      if(local_pred) delete _pred;
332      if(local_dist) delete _dist;
333    }
334
335    /// \brief Sets the length map.
336    ///
337    /// Sets the length map.
338    /// \return \c (*this)
339    FloydWarshall &lengthMap(const LengthMap &m) {
340      length = &m;
341      return *this;
342    }
343
344    /// \brief Sets the map storing the predecessor edges.
345    ///
346    /// Sets the map storing the predecessor edges.
347    /// If you don't use this function before calling \ref run(),
348    /// it will allocate one. The destuctor deallocates this
349    /// automatically allocated map, of course.
350    /// \return \c (*this)
351    FloydWarshall &predMap(PredMap &m) {
352      if(local_pred) {
353        delete _pred;
354        local_pred=false;
355      }
356      _pred = &m;
357      return *this;
358    }
359
360    /// \brief Sets the map storing the distances calculated by the algorithm.
361    ///
362    /// Sets the map storing the distances calculated by the algorithm.
363    /// If you don't use this function before calling \ref run(),
364    /// it will allocate one. The destuctor deallocates this
365    /// automatically allocated map, of course.
366    /// \return \c (*this)
367    FloydWarshall &distMap(DistMap &m) {
368      if(local_dist) {
369        delete _dist;
370        local_dist=false;
371      }
372      _dist = &m;
373      return *this;
374    }
375
376    ///\name Execution control
377    /// The simplest way to execute the algorithm is to use
378    /// one of the member functions called \c run(...).
379    /// \n
380    /// If you need more control on the execution,
381    /// Finally \ref start() will perform the actual path
382    /// computation.
383
384    ///@{
385
386    /// \brief Initializes the internal data structures.
387    ///
388    /// Initializes the internal data structures.
389    void init() {
390      create_maps();
391      for (NodeIt it(*graph); it != INVALID; ++it) {
392        for (NodeIt jt(*graph); jt != INVALID; ++jt) {
393          _pred->set(it, jt, INVALID);
394          _dist->set(it, jt, OperationTraits::infinity());
395        }
396        _dist->set(it, it, OperationTraits::zero());
397      }
398      for (EdgeIt it(*graph); it != INVALID; ++it) {
399        Node source = graph->source(it);
400        Node target = graph->target(it);       
401        if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
402          _dist->set(source, target, (*length)[it]);
403          _pred->set(source, target, it);
404        }
405      }
406    }
407   
408    /// \brief Executes the algorithm.
409    ///
410    /// This method runs the %FloydWarshall algorithm in order to compute
411    /// the shortest path to each node pairs. The algorithm
412    /// computes
413    /// - The shortest path tree for each node.
414    /// - The distance between each node pairs.
415    void start() {
416      for (NodeIt kt(*graph); kt != INVALID; ++kt) {
417        for (NodeIt it(*graph); it != INVALID; ++it) {
418          for (NodeIt jt(*graph); jt != INVALID; ++jt) {
419            Value relaxed = OperationTraits::plus((*_dist)(it, kt),
420                                                  (*_dist)(kt, jt));
421            if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
422              _dist->set(it, jt, relaxed);
423              _pred->set(it, jt, (*_pred)(kt, jt));
424            }
425          }
426        }
427      }
428    }
429
430    /// \brief Executes the algorithm and checks the negative cycles.
431    ///
432    /// This method runs the %FloydWarshall algorithm in order to compute
433    /// the shortest path to each node pairs. If there is a negative cycle
434    /// in the graph it gives back false.
435    /// The algorithm computes
436    /// - The shortest path tree for each node.
437    /// - The distance between each node pairs.
438    bool checkedStart() {
439      start();
440      for (NodeIt it(*graph); it != INVALID; ++it) {
441        if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
442          return false;
443        }
444      }
445      return true;
446    }
447   
448    /// \brief Runs %FloydWarshall algorithm.
449    ///   
450    /// This method runs the %FloydWarshall algorithm from a each node
451    /// in order to compute the shortest path to each node pairs.
452    /// The algorithm computes
453    /// - The shortest path tree for each node.
454    /// - The distance between each node pairs.
455    ///
456    /// \note d.run(s) is just a shortcut of the following code.
457    /// \code
458    ///  d.init();
459    ///  d.start();
460    /// \endcode
461    void run() {
462      init();
463      start();
464    }
465   
466    ///@}
467
468    /// \name Query Functions
469    /// The result of the %FloydWarshall algorithm can be obtained using these
470    /// functions.\n
471    /// Before the use of these functions,
472    /// either run() or start() must be called.
473   
474    ///@{
475
476    /// \brief Copies the shortest path to \c t into \c p
477    ///   
478    /// This function copies the shortest path to \c t into \c p.
479    /// If it \c t is a source itself or unreachable, then it does not
480    /// alter \c p.
481    /// \return Returns \c true if a path to \c t was actually copied to \c p,
482    /// \c false otherwise.
483    /// \sa DirPath
484    template <typename Path>
485    bool getPath(Path &p, Node source, Node target) {
486      if (connected(source, target)) {
487        p.clear();
488        typename Path::Builder b(target);
489        for(b.setStartNode(target); predEdge(source, target) != INVALID;
490            target = predNode(target)) {
491          b.pushFront(predEdge(source, target));
492        }
493        b.commit();
494        return true;
495      }
496      return false;
497    }
498         
499    /// \brief The distance between two nodes.
500    ///
501    /// Returns the distance between two nodes.
502    /// \pre \ref run() must be called before using this function.
503    /// \warning If node \c v in unreachable from the root the return value
504    /// of this funcion is undefined.
505    Value dist(Node source, Node target) const {
506      return (*_dist)(source, target);
507    }
508
509    /// \brief Returns the 'previous edge' of the shortest path tree.
510    ///
511    /// For the node \c node it returns the 'previous edge' of the shortest
512    /// path tree to direction of the node \c root
513    /// i.e. it returns the last edge of a shortest path from the node \c root
514    /// to \c node. It is \ref INVALID if \c node is unreachable from the root
515    /// or if \c node=root. The shortest path tree used here is equal to the
516    /// shortest path tree used in \ref predNode().
517    /// \pre \ref run() must be called before using this function.
518    Edge predEdge(Node root, Node node) const {
519      return (*_pred)(root, node);
520    }
521
522    /// \brief Returns the 'previous node' of the shortest path tree.
523    ///
524    /// For a node \c node it returns the 'previous node' of the shortest path
525    /// tree to direction of the node \c root, i.e. it returns the last but
526    /// one node from a shortest path from the \c root to \c node. It is
527    /// INVALID if \c node is unreachable from the root or if \c node=root.
528    /// The shortest path tree used here is equal to the
529    /// shortest path tree used in \ref predEdge(). 
530    /// \pre \ref run() must be called before using this function.
531    Node predNode(Node root, Node node) const {
532      return (*_pred)(root, node) == INVALID ?
533      INVALID : graph->source((*_pred)(root, node));
534    }
535   
536    /// \brief Returns a reference to the matrix node map of distances.
537    ///
538    /// Returns a reference to the matrix node map of distances.
539    ///
540    /// \pre \ref run() must be called before using this function.
541    const DistMap &distMap() const { return *_dist;}
542 
543    /// \brief Returns a reference to the shortest path tree map.
544    ///
545    /// Returns a reference to the matrix node map of the edges of the
546    /// shortest path tree.
547    /// \pre \ref run() must be called before using this function.
548    const PredMap &predMap() const { return *_pred;}
549 
550    /// \brief Checks if a node is reachable from the root.
551    ///
552    /// Returns \c true if \c v is reachable from the root.
553    /// \pre \ref run() must be called before using this function.
554    ///
555    bool connected(Node source, Node target) {
556      return (*_dist)(source, target) != OperationTraits::infinity();
557    }
558   
559    ///@}
560  };
561 
562} //END OF NAMESPACE LEMON
563
564#endif
565
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