COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/floyd_warshall.h @ 2334:c1e936e6a46b

Last change on this file since 2334:c1e936e6a46b was 2260:4274224f8a7d, checked in by Alpar Juttner, 13 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) 2003-2006
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_FLOYD_WARSHALL_H
20#define LEMON_FLOYD_WARSHALL_H
21
22///\ingroup flowalgs
23/// \file
24/// \brief FloydWarshall algorithm.
25///
26
27#include <lemon/list_graph.h>
28#include <lemon/graph_utils.h>
29#include <lemon/bits/invalid.h>
30#include <lemon/error.h>
31#include <lemon/matrix_maps.h>
32#include <lemon/maps.h>
33
34#include <limits>
35
36namespace lemon {
37
38  /// \brief Default OperationTraits for the FloydWarshall algorithm class.
39  /// 
40  /// It defines all computational operations and constants which are
41  /// used in the Floyd-Warshall algorithm. The default implementation
42  /// is based on the numeric_limits class. If the numeric type does not
43  /// have infinity value then the maximum value is used as extremal
44  /// infinity value.
45  template <
46    typename Value,
47    bool has_infinity = std::numeric_limits<Value>::has_infinity>
48  struct FloydWarshallDefaultOperationTraits {
49    /// \brief Gives back the zero value of the type.
50    static Value zero() {
51      return static_cast<Value>(0);
52    }
53    /// \brief Gives back the positive infinity value of the type.
54    static Value infinity() {
55      return std::numeric_limits<Value>::infinity();
56    }
57    /// \brief Gives back the sum of the given two elements.
58    static Value plus(const Value& left, const Value& right) {
59      return left + right;
60    }
61    /// \brief Gives back true only if the first value less than the second.
62    static bool less(const Value& left, const Value& right) {
63      return left < right;
64    }
65  };
66
67  template <typename Value>
68  struct FloydWarshallDefaultOperationTraits<Value, false> {
69    static Value zero() {
70      return static_cast<Value>(0);
71    }
72    static Value infinity() {
73      return std::numeric_limits<Value>::max();
74    }
75    static Value plus(const Value& left, const Value& right) {
76      if (left == infinity() || right == infinity()) return infinity();
77      return left + right;
78    }
79    static bool less(const Value& left, const Value& right) {
80      return left < right;
81    }
82  };
83 
84  /// \brief Default traits class of FloydWarshall class.
85  ///
86  /// Default traits class of FloydWarshall class.
87  /// \param _Graph Graph type.
88  /// \param _LegthMap Type of length map.
89  template<class _Graph, class _LengthMap>
90  struct FloydWarshallDefaultTraits {
91    /// The graph type the algorithm runs on.
92    typedef _Graph Graph;
93
94    /// \brief The type of the map that stores the edge lengths.
95    ///
96    /// The type of the map that stores the edge lengths.
97    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
98    typedef _LengthMap LengthMap;
99
100    // The type of the length of the edges.
101    typedef typename _LengthMap::Value Value;
102
103    /// \brief Operation traits for floyd-warshall algorithm.
104    ///
105    /// It defines the infinity type on the given Value type
106    /// and the used operation.
107    /// \see FloydWarshallDefaultOperationTraits
108    typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;
109 
110    /// \brief The type of the matrix map that stores the last edges of the
111    /// shortest paths.
112    ///
113    /// The type of the map that stores the last edges of the shortest paths.
114    /// It must be a matrix map with \c Graph::Edge value type.
115    ///
116    typedef DynamicMatrixMap<Graph, typename Graph::Node,
117                             typename Graph::Edge> PredMap;
118
119    /// \brief Instantiates a PredMap.
120    ///
121    /// This function instantiates a \ref PredMap.
122    /// \param graph is the graph,
123    /// to which we would like to define the PredMap.
124    /// \todo The graph alone may be insufficient for the initialization
125    static PredMap *createPredMap(const _Graph& graph) {
126      return new PredMap(graph);
127    }
128
129    /// \brief The type of the map that stores the dists of the nodes.
130    ///
131    /// The type of the map that stores the dists of the nodes.
132    /// It must meet the \ref concepts::WriteMatrixMap "WriteMatrixMap" concept.
133    ///
134    typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
135
136    /// \brief Instantiates a DistMap.
137    ///
138    /// This function instantiates a \ref DistMap.
139    /// \param graph is the graph, to which we would like to define the
140    /// \ref DistMap
141    static DistMap *createDistMap(const _Graph& graph) {
142      return new DistMap(graph);
143    }
144
145  };
146 
147  /// \brief %FloydWarshall algorithm class.
148  ///
149  /// \ingroup flowalgs
150  /// This class provides an efficient implementation of \c Floyd-Warshall
151  /// algorithm. The edge lengths are passed to the algorithm using a
152  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any
153  /// kind of length.
154  ///
155  /// The algorithm solves the shortest path problem for each pair
156  /// of node when the edges can have negative length but the graph should
157  /// not contain cycles with negative sum of length. If we can assume
158  /// that all edge is non-negative in the graph then the dijkstra algorithm
159  /// should be used from each node rather and if the graph is sparse and
160  /// there are negative circles then the johnson algorithm.
161  ///
162  /// The complexity of this algorithm is \f$ O(n^3+e) \f$.
163  ///
164  /// The type of the length is determined by the
165  /// \ref concepts::ReadMap::Value "Value" of the length map.
166  ///
167  /// \param _Graph The graph type the algorithm runs on. The default value
168  /// is \ref ListGraph. The value of _Graph is not used directly by
169  /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
170  /// \param _LengthMap This read-only EdgeMap determines the lengths of the
171  /// edges. It is read once for each edge, so the map may involve in
172  /// relatively time consuming process to compute the edge length if
173  /// it is necessary. The default map type is \ref
174  /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>".  The value
175  /// of _LengthMap is not used directly by FloydWarshall, it is only passed
176  /// to \ref FloydWarshallDefaultTraits.  \param _Traits Traits class to set
177  /// various data types used by the algorithm.  The default traits
178  /// class is \ref FloydWarshallDefaultTraits
179  /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>".  See \ref
180  /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall
181  /// traits class.
182  ///
183  /// \author Balazs Dezso
184  /// \todo A function type interface would be nice.
185  /// \todo Implement \c nextNode() and \c nextEdge()
186#ifdef DOXYGEN
187  template <typename _Graph, typename _LengthMap, typename _Traits >
188#else
189  template <typename _Graph=ListGraph,
190            typename _LengthMap=typename _Graph::template EdgeMap<int>,
191            typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
192#endif
193  class FloydWarshall {
194  public:
195   
196    /// \brief \ref Exception for uninitialized parameters.
197    ///
198    /// This error represents problems in the initialization
199    /// of the parameters of the algorithms.
200
201    class UninitializedParameter : public lemon::UninitializedParameter {
202    public:
203      virtual const char* what() const throw() {
204        return "lemon::FloydWarshall::UninitializedParameter";
205      }
206    };
207
208    typedef _Traits Traits;
209    ///The type of the underlying graph.
210    typedef typename _Traits::Graph Graph;
211
212    typedef typename Graph::Node Node;
213    typedef typename Graph::NodeIt NodeIt;
214    typedef typename Graph::Edge Edge;
215    typedef typename Graph::EdgeIt EdgeIt;
216   
217    /// \brief The type of the length of the edges.
218    typedef typename _Traits::LengthMap::Value Value;
219    /// \brief The type of the map that stores the edge lengths.
220    typedef typename _Traits::LengthMap LengthMap;
221    /// \brief The type of the map that stores the last
222    /// edges of the shortest paths. The type of the PredMap
223    /// is a matrix map for Edges
224    typedef typename _Traits::PredMap PredMap;
225    /// \brief The type of the map that stores the dists of the nodes.
226    /// The type of the DistMap is a matrix map for Values
227    ///
228    /// \todo It should rather be
229    /// called \c DistMatrix
230    typedef typename _Traits::DistMap DistMap;
231    /// \brief The operation traits.
232    typedef typename _Traits::OperationTraits OperationTraits;
233  private:
234    /// Pointer to the underlying graph.
235    const Graph *graph;
236    /// Pointer to the length map
237    const LengthMap *length;
238    ///Pointer to the map of predecessors edges.
239    PredMap *_pred;
240    ///Indicates if \ref _pred is locally allocated (\c true) or not.
241    bool local_pred;
242    ///Pointer to the map of distances.
243    DistMap *_dist;
244    ///Indicates if \ref _dist is locally allocated (\c true) or not.
245    bool local_dist;
246
247    /// Creates the maps if necessary.
248    void create_maps() {
249      if(!_pred) {
250        local_pred = true;
251        _pred = Traits::createPredMap(*graph);
252      }
253      if(!_dist) {
254        local_dist = true;
255        _dist = Traits::createDistMap(*graph);
256      }
257    }
258   
259  public :
260 
261    /// \name Named template parameters
262
263    ///@{
264
265    template <class T>
266    struct DefPredMapTraits : public Traits {
267      typedef T PredMap;
268      static PredMap *createPredMap(const Graph& graph) {
269        throw UninitializedParameter();
270      }
271    };
272
273    /// \brief \ref named-templ-param "Named parameter" for setting PredMap
274    /// type
275    /// \ref named-templ-param "Named parameter" for setting PredMap type
276    ///
277    template <class T>
278    struct DefPredMap
279      : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
280      typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;
281    };
282   
283    template <class T>
284    struct DefDistMapTraits : public Traits {
285      typedef T DistMap;
286      static DistMap *createDistMap(const Graph& graph) {
287        throw UninitializedParameter();
288      }
289    };
290    /// \brief \ref named-templ-param "Named parameter" for setting DistMap
291    /// type
292    ///
293    /// \ref named-templ-param "Named parameter" for setting DistMap type
294    ///
295    template <class T>
296    struct DefDistMap
297      : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
298      typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;
299    };
300   
301    template <class T>
302    struct DefOperationTraitsTraits : public Traits {
303      typedef T OperationTraits;
304    };
305   
306    /// \brief \ref named-templ-param "Named parameter" for setting
307    /// OperationTraits type
308    ///
309    /// \ref named-templ-param "Named parameter" for setting PredMap type
310    template <class T>
311    struct DefOperationTraits
312      : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
313      typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
314      Create;
315    };
316   
317    ///@}
318
319  protected:
320
321    FloydWarshall() {}
322
323  public:     
324
325    typedef FloydWarshall Create;
326   
327    /// \brief Constructor.
328    ///
329    /// \param _graph the graph the algorithm will run on.
330    /// \param _length the length map used by the algorithm.
331    FloydWarshall(const Graph& _graph, const LengthMap& _length) :
332      graph(&_graph), length(&_length),
333      _pred(0), local_pred(false),
334      _dist(0), local_dist(false) {}
335   
336    ///Destructor.
337    ~FloydWarshall() {
338      if(local_pred) delete _pred;
339      if(local_dist) delete _dist;
340    }
341
342    /// \brief Sets the length map.
343    ///
344    /// Sets the length map.
345    /// \return \c (*this)
346    FloydWarshall &lengthMap(const LengthMap &m) {
347      length = &m;
348      return *this;
349    }
350
351    /// \brief Sets the map storing the predecessor edges.
352    ///
353    /// Sets the map storing the predecessor edges.
354    /// If you don't use this function before calling \ref run(),
355    /// it will allocate one. The destuctor deallocates this
356    /// automatically allocated map, of course.
357    /// \return \c (*this)
358    FloydWarshall &predMap(PredMap &m) {
359      if(local_pred) {
360        delete _pred;
361        local_pred=false;
362      }
363      _pred = &m;
364      return *this;
365    }
366
367    /// \brief Sets the map storing the distances calculated by the algorithm.
368    ///
369    /// Sets the map storing the distances calculated by the algorithm.
370    /// If you don't use this function before calling \ref run(),
371    /// it will allocate one. The destuctor deallocates this
372    /// automatically allocated map, of course.
373    /// \return \c (*this)
374    FloydWarshall &distMap(DistMap &m) {
375      if(local_dist) {
376        delete _dist;
377        local_dist=false;
378      }
379      _dist = &m;
380      return *this;
381    }
382
383    ///\name Execution control
384    /// The simplest way to execute the algorithm is to use
385    /// one of the member functions called \c run(...).
386    /// \n
387    /// If you need more control on the execution,
388    /// Finally \ref start() will perform the actual path
389    /// computation.
390
391    ///@{
392
393    /// \brief Initializes the internal data structures.
394    ///
395    /// Initializes the internal data structures.
396    void init() {
397      create_maps();
398      for (NodeIt it(*graph); it != INVALID; ++it) {
399        for (NodeIt jt(*graph); jt != INVALID; ++jt) {
400          _pred->set(it, jt, INVALID);
401          _dist->set(it, jt, OperationTraits::infinity());
402        }
403        _dist->set(it, it, OperationTraits::zero());
404      }
405      for (EdgeIt it(*graph); it != INVALID; ++it) {
406        Node source = graph->source(it);
407        Node target = graph->target(it);       
408        if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
409          _dist->set(source, target, (*length)[it]);
410          _pred->set(source, target, it);
411        }
412      }
413    }
414   
415    /// \brief Executes the algorithm.
416    ///
417    /// This method runs the %FloydWarshall algorithm in order to compute
418    /// the shortest path to each node pairs. The algorithm
419    /// computes
420    /// - The shortest path tree for each node.
421    /// - The distance between each node pairs.
422    void start() {
423      for (NodeIt kt(*graph); kt != INVALID; ++kt) {
424        for (NodeIt it(*graph); it != INVALID; ++it) {
425          for (NodeIt jt(*graph); jt != INVALID; ++jt) {
426            Value relaxed = OperationTraits::plus((*_dist)(it, kt),
427                                                  (*_dist)(kt, jt));
428            if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
429              _dist->set(it, jt, relaxed);
430              _pred->set(it, jt, (*_pred)(kt, jt));
431            }
432          }
433        }
434      }
435    }
436
437    /// \brief Executes the algorithm and checks the negative cycles.
438    ///
439    /// This method runs the %FloydWarshall algorithm in order to compute
440    /// the shortest path to each node pairs. If there is a negative cycle
441    /// in the graph it gives back false.
442    /// The algorithm computes
443    /// - The shortest path tree for each node.
444    /// - The distance between each node pairs.
445    bool checkedStart() {
446      start();
447      for (NodeIt it(*graph); it != INVALID; ++it) {
448        if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
449          return false;
450        }
451      }
452      return true;
453    }
454   
455    /// \brief Runs %FloydWarshall algorithm.
456    ///   
457    /// This method runs the %FloydWarshall algorithm from a each node
458    /// in order to compute the shortest path to each node pairs.
459    /// The algorithm computes
460    /// - The shortest path tree for each node.
461    /// - The distance between each node pairs.
462    ///
463    /// \note d.run(s) is just a shortcut of the following code.
464    ///\code
465    ///  d.init();
466    ///  d.start();
467    ///\endcode
468    void run() {
469      init();
470      start();
471    }
472   
473    ///@}
474
475    /// \name Query Functions
476    /// The result of the %FloydWarshall algorithm can be obtained using these
477    /// functions.\n
478    /// Before the use of these functions,
479    /// either run() or start() must be called.
480   
481    ///@{
482
483    /// \brief Copies the shortest path to \c t into \c p
484    ///   
485    /// This function copies the shortest path to \c t into \c p.
486    /// If it \c t is a source itself or unreachable, then it does not
487    /// alter \c p.
488    /// \return Returns \c true if a path to \c t was actually copied to \c p,
489    /// \c false otherwise.
490    /// \sa DirPath
491    template <typename Path>
492    bool getPath(Path &p, Node source, Node target) {
493      if (connected(source, target)) {
494        p.clear();
495        typename Path::Builder b(target);
496        for(b.setStartNode(target); predEdge(source, target) != INVALID;
497            target = predNode(target)) {
498          b.pushFront(predEdge(source, target));
499        }
500        b.commit();
501        return true;
502      }
503      return false;
504    }
505         
506    /// \brief The distance between two nodes.
507    ///
508    /// Returns the distance between two nodes.
509    /// \pre \ref run() must be called before using this function.
510    /// \warning If node \c v in unreachable from the root the return value
511    /// of this funcion is undefined.
512    Value dist(Node source, Node target) const {
513      return (*_dist)(source, target);
514    }
515
516    /// \brief Returns the 'previous edge' of the shortest path tree.
517    ///
518    /// For the node \c node it returns the 'previous edge' of the shortest
519    /// path tree to direction of the node \c root
520    /// i.e. it returns the last edge of a shortest path from the node \c root
521    /// to \c node. It is \ref INVALID if \c node is unreachable from the root
522    /// or if \c node=root. The shortest path tree used here is equal to the
523    /// shortest path tree used in \ref predNode().
524    /// \pre \ref run() must be called before using this function.
525    Edge predEdge(Node root, Node node) const {
526      return (*_pred)(root, node);
527    }
528
529    /// \brief Returns the 'previous node' of the shortest path tree.
530    ///
531    /// For a node \c node it returns the 'previous node' of the shortest path
532    /// tree to direction of the node \c root, i.e. it returns the last but
533    /// one node from a shortest path from the \c root to \c node. It is
534    /// INVALID if \c node is unreachable from the root or if \c node=root.
535    /// The shortest path tree used here is equal to the
536    /// shortest path tree used in \ref predEdge(). 
537    /// \pre \ref run() must be called before using this function.
538    Node predNode(Node root, Node node) const {
539      return (*_pred)(root, node) == INVALID ?
540      INVALID : graph->source((*_pred)(root, node));
541    }
542   
543    /// \brief Returns a reference to the matrix node map of distances.
544    ///
545    /// Returns a reference to the matrix node map of distances.
546    ///
547    /// \pre \ref run() must be called before using this function.
548    const DistMap &distMap() const { return *_dist;}
549 
550    /// \brief Returns a reference to the shortest path tree map.
551    ///
552    /// Returns a reference to the matrix node map of the edges of the
553    /// shortest path tree.
554    /// \pre \ref run() must be called before using this function.
555    const PredMap &predMap() const { return *_pred;}
556 
557    /// \brief Checks if a node is reachable from the root.
558    ///
559    /// Returns \c true if \c v is reachable from the root.
560    /// \pre \ref run() must be called before using this function.
561    ///
562    bool connected(Node source, Node target) {
563      return (*_dist)(source, target) != OperationTraits::infinity();
564    }
565   
566    ///@}
567  };
568 
569} //END OF NAMESPACE LEMON
570
571#endif
572
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