lemon/floyd_warshall.h
author hegyi
Mon, 09 Jan 2006 12:41:06 +0000
changeset 1887 22fdc00894aa
parent 1865 dcefd1d1377f
child 1946 17eb3eaad9f8
permissions -rw-r--r--
The tree that is created for evaluation of expression string at new map creation is deleted after usage.
deba@1699
     1
/* -*- C++ -*-
deba@1699
     2
 * lemon/floyd_warshall.h - Part of LEMON, a generic C++ optimization library
deba@1699
     3
 *
alpar@1875
     4
 * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@1699
     5
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@1699
     6
 *
deba@1699
     7
 * Permission to use, modify and distribute this software is granted
deba@1699
     8
 * provided that this copyright notice appears in all copies. For
deba@1699
     9
 * precise terms see the accompanying LICENSE file.
deba@1699
    10
 *
deba@1699
    11
 * This software is provided "AS IS" with no warranty of any kind,
deba@1699
    12
 * express or implied, and with no claim as to its suitability for any
deba@1699
    13
 * purpose.
deba@1699
    14
 *
deba@1699
    15
 */
deba@1699
    16
deba@1699
    17
#ifndef LEMON_FLOYD_WARSHALL_H
deba@1699
    18
#define LEMON_FLOYD_WARSHALL_H
deba@1699
    19
deba@1699
    20
///\ingroup flowalgs
deba@1699
    21
/// \file
deba@1699
    22
/// \brief FloydWarshall algorithm.
deba@1699
    23
///
deba@1699
    24
deba@1699
    25
#include <lemon/list_graph.h>
deba@1699
    26
#include <lemon/graph_utils.h>
deba@1699
    27
#include <lemon/invalid.h>
deba@1699
    28
#include <lemon/error.h>
deba@1723
    29
#include <lemon/matrix_maps.h>
deba@1699
    30
#include <lemon/maps.h>
deba@1699
    31
deba@1699
    32
#include <limits>
deba@1699
    33
deba@1699
    34
namespace lemon {
deba@1699
    35
deba@1699
    36
  /// \brief Default OperationTraits for the FloydWarshall algorithm class.
deba@1699
    37
  ///  
deba@1699
    38
  /// It defines all computational operations and constants which are
deba@1699
    39
  /// used in the Floyd-Warshall algorithm. The default implementation
deba@1699
    40
  /// is based on the numeric_limits class. If the numeric type does not
deba@1699
    41
  /// have infinity value then the maximum value is used as extremal
deba@1699
    42
  /// infinity value.
deba@1699
    43
  template <
deba@1699
    44
    typename Value, 
deba@1699
    45
    bool has_infinity = std::numeric_limits<Value>::has_infinity>
deba@1699
    46
  struct FloydWarshallDefaultOperationTraits {
deba@1699
    47
    /// \brief Gives back the zero value of the type.
deba@1699
    48
    static Value zero() {
deba@1699
    49
      return static_cast<Value>(0);
deba@1699
    50
    }
deba@1699
    51
    /// \brief Gives back the positive infinity value of the type.
deba@1699
    52
    static Value infinity() {
deba@1699
    53
      return std::numeric_limits<Value>::infinity();
deba@1699
    54
    }
deba@1699
    55
    /// \brief Gives back the sum of the given two elements.
deba@1699
    56
    static Value plus(const Value& left, const Value& right) {
deba@1699
    57
      return left + right;
deba@1699
    58
    }
deba@1699
    59
    /// \brief Gives back true only if the first value less than the second.
deba@1699
    60
    static bool less(const Value& left, const Value& right) {
deba@1699
    61
      return left < right;
deba@1699
    62
    }
deba@1699
    63
  };
deba@1699
    64
deba@1699
    65
  template <typename Value>
deba@1699
    66
  struct FloydWarshallDefaultOperationTraits<Value, false> {
deba@1699
    67
    static Value zero() {
deba@1699
    68
      return static_cast<Value>(0);
deba@1699
    69
    }
deba@1699
    70
    static Value infinity() {
deba@1699
    71
      return std::numeric_limits<Value>::max();
deba@1699
    72
    }
deba@1699
    73
    static Value plus(const Value& left, const Value& right) {
deba@1699
    74
      if (left == infinity() || right == infinity()) return infinity();
deba@1699
    75
      return left + right;
deba@1699
    76
    }
deba@1699
    77
    static bool less(const Value& left, const Value& right) {
deba@1699
    78
      return left < right;
deba@1699
    79
    }
deba@1699
    80
  };
deba@1699
    81
  
deba@1699
    82
  /// \brief Default traits class of FloydWarshall class.
deba@1699
    83
  ///
deba@1699
    84
  /// Default traits class of FloydWarshall class.
deba@1699
    85
  /// \param _Graph Graph type.
deba@1699
    86
  /// \param _LegthMap Type of length map.
deba@1699
    87
  template<class _Graph, class _LengthMap>
deba@1699
    88
  struct FloydWarshallDefaultTraits {
deba@1699
    89
    /// The graph type the algorithm runs on. 
deba@1699
    90
    typedef _Graph Graph;
deba@1699
    91
deba@1699
    92
    /// \brief The type of the map that stores the edge lengths.
deba@1699
    93
    ///
deba@1699
    94
    /// The type of the map that stores the edge lengths.
deba@1699
    95
    /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@1699
    96
    typedef _LengthMap LengthMap;
deba@1699
    97
deba@1699
    98
    // The type of the length of the edges.
deba@1699
    99
    typedef typename _LengthMap::Value Value;
deba@1699
   100
deba@1865
   101
    /// \brief Operation traits for floyd-warshall algorithm.
deba@1699
   102
    ///
deba@1699
   103
    /// It defines the infinity type on the given Value type
deba@1699
   104
    /// and the used operation.
deba@1699
   105
    /// \see FloydWarshallDefaultOperationTraits
deba@1699
   106
    typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;
deba@1699
   107
 
deba@1723
   108
    /// \brief The type of the matrix map that stores the last edges of the 
deba@1699
   109
    /// shortest paths.
deba@1699
   110
    /// 
deba@1723
   111
    /// The type of the map that stores the last edges of the shortest paths.
deba@1699
   112
    /// It must be a matrix map with \c Graph::Edge value type.
deba@1699
   113
    ///
deba@1723
   114
    typedef DynamicMatrixMap<Graph, typename Graph::Node, 
deba@1723
   115
			     typename Graph::Edge> PredMap;
deba@1699
   116
deba@1699
   117
    /// \brief Instantiates a PredMap.
deba@1699
   118
    /// 
deba@1699
   119
    /// This function instantiates a \ref PredMap. 
deba@1699
   120
    /// \param G is the graph, to which we would like to define the PredMap.
deba@1699
   121
    /// \todo The graph alone may be insufficient for the initialization
deba@1699
   122
    static PredMap *createPredMap(const _Graph& graph) {
deba@1699
   123
      return new PredMap(graph);
deba@1699
   124
    }
deba@1699
   125
deba@1699
   126
    /// \brief The type of the map that stores the dists of the nodes.
deba@1699
   127
    ///
deba@1699
   128
    /// The type of the map that stores the dists of the nodes.
deba@1723
   129
    /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept.
deba@1699
   130
    ///
deba@1723
   131
    typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
deba@1699
   132
deba@1699
   133
    /// \brief Instantiates a DistMap.
deba@1699
   134
    ///
deba@1699
   135
    /// This function instantiates a \ref DistMap. 
deba@1699
   136
    /// \param G is the graph, to which we would like to define the 
deba@1699
   137
    /// \ref DistMap
deba@1699
   138
    static DistMap *createDistMap(const _Graph& graph) {
deba@1699
   139
      return new DistMap(graph);
deba@1699
   140
    }
deba@1699
   141
deba@1699
   142
  };
deba@1699
   143
  
deba@1754
   144
  /// \brief %FloydWarshall algorithm class.
deba@1699
   145
  ///
deba@1699
   146
  /// \ingroup flowalgs
deba@1754
   147
  /// This class provides an efficient implementation of \c Floyd-Warshall 
deba@1699
   148
  /// algorithm. The edge lengths are passed to the algorithm using a
deba@1699
   149
  /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any 
deba@1699
   150
  /// kind of length.
deba@1699
   151
  ///
alpar@1757
   152
  /// The algorithm solves the shortest path problem for each pair
deba@1723
   153
  /// of node when the edges can have negative length but the graph should
deba@1754
   154
  /// not contain cycles with negative sum of length. If we can assume
deba@1723
   155
  /// that all edge is non-negative in the graph then the dijkstra algorithm
deba@1723
   156
  /// should be used from each node rather and if the graph is sparse and
deba@1754
   157
  /// there are negative circles then the johnson algorithm.
deba@1723
   158
  ///
deba@1723
   159
  /// The complexity of this algorithm is O(n^3 + e).
deba@1723
   160
  ///
deba@1699
   161
  /// The type of the length is determined by the
deba@1699
   162
  /// \ref concept::ReadMap::Value "Value" of the length map.
deba@1699
   163
  ///
deba@1699
   164
  /// \param _Graph The graph type the algorithm runs on. The default value
deba@1699
   165
  /// is \ref ListGraph. The value of _Graph is not used directly by
deba@1699
   166
  /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
deba@1699
   167
  /// \param _LengthMap This read-only EdgeMap determines the lengths of the
deba@1699
   168
  /// edges. It is read once for each edge, so the map may involve in
deba@1699
   169
  /// relatively time consuming process to compute the edge length if
deba@1699
   170
  /// it is necessary. The default map type is \ref
deba@1699
   171
  /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
deba@1699
   172
  /// of _LengthMap is not used directly by FloydWarshall, it is only passed 
deba@1699
   173
  /// to \ref FloydWarshallDefaultTraits.  \param _Traits Traits class to set
deba@1699
   174
  /// various data types used by the algorithm.  The default traits
deba@1699
   175
  /// class is \ref FloydWarshallDefaultTraits
deba@1699
   176
  /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>".  See \ref
deba@1699
   177
  /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall 
deba@1699
   178
  /// traits class.
deba@1699
   179
  ///
deba@1699
   180
  /// \author Balazs Dezso
deba@1699
   181
deba@1710
   182
#ifdef DOXYGEN
deba@1710
   183
  template <typename _Graph, typename _LengthMap typename _Traits >
deba@1710
   184
#else
deba@1699
   185
  template <typename _Graph=ListGraph,
deba@1699
   186
	    typename _LengthMap=typename _Graph::template EdgeMap<int>,
deba@1699
   187
	    typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
deba@1710
   188
#endif
deba@1699
   189
  class FloydWarshall {
deba@1699
   190
  public:
deba@1699
   191
    
deba@1699
   192
    /// \brief \ref Exception for uninitialized parameters.
deba@1699
   193
    ///
deba@1699
   194
    /// This error represents problems in the initialization
deba@1699
   195
    /// of the parameters of the algorithms.
deba@1699
   196
deba@1699
   197
    class UninitializedParameter : public lemon::UninitializedParameter {
deba@1699
   198
    public:
deba@1699
   199
      virtual const char* exceptionName() const {
deba@1699
   200
	return "lemon::FloydWarshall::UninitializedParameter";
deba@1699
   201
      }
deba@1699
   202
    };
deba@1699
   203
deba@1699
   204
    typedef _Traits Traits;
deba@1699
   205
    ///The type of the underlying graph.
deba@1699
   206
    typedef typename _Traits::Graph Graph;
deba@1699
   207
deba@1699
   208
    typedef typename Graph::Node Node;
deba@1699
   209
    typedef typename Graph::NodeIt NodeIt;
deba@1699
   210
    typedef typename Graph::Edge Edge;
deba@1699
   211
    typedef typename Graph::EdgeIt EdgeIt;
deba@1699
   212
    
deba@1699
   213
    /// \brief The type of the length of the edges.
deba@1699
   214
    typedef typename _Traits::LengthMap::Value Value;
deba@1699
   215
    /// \brief The type of the map that stores the edge lengths.
deba@1699
   216
    typedef typename _Traits::LengthMap LengthMap;
deba@1699
   217
    /// \brief The type of the map that stores the last
deba@1699
   218
    /// edges of the shortest paths. The type of the PredMap
deba@1699
   219
    /// is a matrix map for Edges
deba@1699
   220
    typedef typename _Traits::PredMap PredMap;
deba@1699
   221
    /// \brief The type of the map that stores the dists of the nodes.
deba@1699
   222
    /// The type of the DistMap is a matrix map for Values
deba@1699
   223
    typedef typename _Traits::DistMap DistMap;
deba@1699
   224
    /// \brief The operation traits.
deba@1699
   225
    typedef typename _Traits::OperationTraits OperationTraits;
deba@1699
   226
  private:
deba@1699
   227
    /// Pointer to the underlying graph.
deba@1699
   228
    const Graph *graph;
deba@1699
   229
    /// Pointer to the length map
deba@1699
   230
    const LengthMap *length;
deba@1699
   231
    ///Pointer to the map of predecessors edges.
deba@1699
   232
    PredMap *_pred;
deba@1699
   233
    ///Indicates if \ref _pred is locally allocated (\c true) or not.
deba@1699
   234
    bool local_pred;
deba@1699
   235
    ///Pointer to the map of distances.
deba@1699
   236
    DistMap *_dist;
deba@1699
   237
    ///Indicates if \ref _dist is locally allocated (\c true) or not.
deba@1699
   238
    bool local_dist;
deba@1699
   239
deba@1699
   240
    /// Creates the maps if necessary.
deba@1699
   241
    void create_maps() {
deba@1699
   242
      if(!_pred) {
deba@1699
   243
	local_pred = true;
deba@1699
   244
	_pred = Traits::createPredMap(*graph);
deba@1699
   245
      }
deba@1699
   246
      if(!_dist) {
deba@1699
   247
	local_dist = true;
deba@1699
   248
	_dist = Traits::createDistMap(*graph);
deba@1699
   249
      }
deba@1699
   250
    }
deba@1699
   251
    
deba@1699
   252
  public :
deba@1699
   253
 
deba@1699
   254
    /// \name Named template parameters
deba@1699
   255
deba@1699
   256
    ///@{
deba@1699
   257
deba@1699
   258
    template <class T>
deba@1699
   259
    struct DefPredMapTraits : public Traits {
deba@1699
   260
      typedef T PredMap;
deba@1699
   261
      static PredMap *createPredMap(const Graph& graph) {
deba@1699
   262
	throw UninitializedParameter();
deba@1699
   263
      }
deba@1699
   264
    };
deba@1699
   265
deba@1699
   266
    /// \brief \ref named-templ-param "Named parameter" for setting PredMap 
deba@1699
   267
    /// type
deba@1699
   268
    /// \ref named-templ-param "Named parameter" for setting PredMap type
deba@1699
   269
    ///
deba@1699
   270
    template <class T>
deba@1710
   271
    struct DefPredMap 
deba@1710
   272
      : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
deba@1710
   273
      typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;
deba@1710
   274
    };
deba@1699
   275
    
deba@1699
   276
    template <class T>
deba@1699
   277
    struct DefDistMapTraits : public Traits {
deba@1699
   278
      typedef T DistMap;
deba@1699
   279
      static DistMap *createDistMap(const Graph& graph) {
deba@1699
   280
	throw UninitializedParameter();
deba@1699
   281
      }
deba@1699
   282
    };
deba@1699
   283
    /// \brief \ref named-templ-param "Named parameter" for setting DistMap 
deba@1699
   284
    /// type
deba@1699
   285
    ///
deba@1699
   286
    /// \ref named-templ-param "Named parameter" for setting DistMap type
deba@1699
   287
    ///
deba@1699
   288
    template <class T>
deba@1710
   289
    struct DefDistMap 
deba@1710
   290
      : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
deba@1710
   291
      typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;
deba@1710
   292
    };
deba@1699
   293
    
deba@1699
   294
    template <class T>
deba@1699
   295
    struct DefOperationTraitsTraits : public Traits {
deba@1699
   296
      typedef T OperationTraits;
deba@1699
   297
    };
deba@1699
   298
    
deba@1699
   299
    /// \brief \ref named-templ-param "Named parameter" for setting 
deba@1699
   300
    /// OperationTraits type
deba@1699
   301
    ///
deba@1699
   302
    /// \ref named-templ-param "Named parameter" for setting PredMap type
deba@1699
   303
    template <class T>
deba@1710
   304
    struct DefOperationTraits
deba@1699
   305
      : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
deba@1710
   306
      typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
deba@1710
   307
      Create;
deba@1699
   308
    };
deba@1699
   309
    
deba@1699
   310
    ///@}
deba@1699
   311
deba@1710
   312
  protected:
deba@1710
   313
deba@1710
   314
    FloydWarshall() {}
deba@1710
   315
deba@1699
   316
  public:      
deba@1710
   317
deba@1710
   318
    typedef FloydWarshall Create;
deba@1699
   319
    
deba@1699
   320
    /// \brief Constructor.
deba@1699
   321
    ///
deba@1699
   322
    /// \param _graph the graph the algorithm will run on.
deba@1699
   323
    /// \param _length the length map used by the algorithm.
deba@1699
   324
    FloydWarshall(const Graph& _graph, const LengthMap& _length) :
deba@1699
   325
      graph(&_graph), length(&_length),
deba@1699
   326
      _pred(0), local_pred(false),
deba@1699
   327
      _dist(0), local_dist(false) {}
deba@1699
   328
    
deba@1699
   329
    ///Destructor.
deba@1699
   330
    ~FloydWarshall() {
deba@1699
   331
      if(local_pred) delete _pred;
deba@1699
   332
      if(local_dist) delete _dist;
deba@1699
   333
    }
deba@1699
   334
deba@1699
   335
    /// \brief Sets the length map.
deba@1699
   336
    ///
deba@1699
   337
    /// Sets the length map.
deba@1699
   338
    /// \return \c (*this)
deba@1699
   339
    FloydWarshall &lengthMap(const LengthMap &m) {
deba@1699
   340
      length = &m;
deba@1699
   341
      return *this;
deba@1699
   342
    }
deba@1699
   343
deba@1699
   344
    /// \brief Sets the map storing the predecessor edges.
deba@1699
   345
    ///
deba@1699
   346
    /// Sets the map storing the predecessor edges.
deba@1699
   347
    /// If you don't use this function before calling \ref run(),
deba@1699
   348
    /// it will allocate one. The destuctor deallocates this
deba@1699
   349
    /// automatically allocated map, of course.
deba@1699
   350
    /// \return \c (*this)
deba@1699
   351
    FloydWarshall &predMap(PredMap &m) {
deba@1699
   352
      if(local_pred) {
deba@1699
   353
	delete _pred;
deba@1699
   354
	local_pred=false;
deba@1699
   355
      }
deba@1699
   356
      _pred = &m;
deba@1699
   357
      return *this;
deba@1699
   358
    }
deba@1699
   359
deba@1699
   360
    /// \brief Sets the map storing the distances calculated by the algorithm.
deba@1699
   361
    ///
deba@1699
   362
    /// Sets the map storing the distances calculated by the algorithm.
deba@1699
   363
    /// If you don't use this function before calling \ref run(),
deba@1699
   364
    /// it will allocate one. The destuctor deallocates this
deba@1699
   365
    /// automatically allocated map, of course.
deba@1699
   366
    /// \return \c (*this)
deba@1699
   367
    FloydWarshall &distMap(DistMap &m) {
deba@1699
   368
      if(local_dist) {
deba@1699
   369
	delete _dist;
deba@1699
   370
	local_dist=false;
deba@1699
   371
      }
deba@1699
   372
      _dist = &m;
deba@1699
   373
      return *this;
deba@1699
   374
    }
deba@1699
   375
deba@1699
   376
    ///\name Execution control
deba@1699
   377
    /// The simplest way to execute the algorithm is to use
deba@1699
   378
    /// one of the member functions called \c run(...).
deba@1699
   379
    /// \n
deba@1699
   380
    /// If you need more control on the execution,
deba@1699
   381
    /// Finally \ref start() will perform the actual path
deba@1699
   382
    /// computation.
deba@1699
   383
deba@1699
   384
    ///@{
deba@1699
   385
deba@1699
   386
    /// \brief Initializes the internal data structures.
deba@1699
   387
    /// 
deba@1699
   388
    /// Initializes the internal data structures.
deba@1699
   389
    void init() {
deba@1699
   390
      create_maps();
deba@1699
   391
      for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699
   392
	for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699
   393
	  _pred->set(it, jt, INVALID);
deba@1741
   394
	  _dist->set(it, jt, OperationTraits::infinity());
deba@1699
   395
	}
deba@1741
   396
	_dist->set(it, it, OperationTraits::zero());
deba@1699
   397
      }
deba@1699
   398
      for (EdgeIt it(*graph); it != INVALID; ++it) {
deba@1699
   399
	Node source = graph->source(it);
deba@1699
   400
	Node target = graph->target(it);	
deba@1699
   401
	if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
deba@1699
   402
	  _dist->set(source, target, (*length)[it]);
deba@1699
   403
	  _pred->set(source, target, it);
deba@1699
   404
	}
deba@1699
   405
      }
deba@1699
   406
    }
deba@1699
   407
    
deba@1699
   408
    /// \brief Executes the algorithm.
deba@1699
   409
    ///
deba@1699
   410
    /// This method runs the %FloydWarshall algorithm in order to compute 
deba@1699
   411
    /// the shortest path to each node pairs. The algorithm 
deba@1699
   412
    /// computes 
deba@1699
   413
    /// - The shortest path tree for each node.
deba@1699
   414
    /// - The distance between each node pairs.
deba@1699
   415
    void start() {
deba@1699
   416
      for (NodeIt kt(*graph); kt != INVALID; ++kt) {
deba@1699
   417
	for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699
   418
	  for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699
   419
	    Value relaxed = OperationTraits::plus((*_dist)(it, kt),
deba@1699
   420
						  (*_dist)(kt, jt));
deba@1699
   421
	    if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
deba@1699
   422
	      _dist->set(it, jt, relaxed);
deba@1699
   423
	      _pred->set(it, jt, (*_pred)(kt, jt));
deba@1699
   424
	    }
deba@1699
   425
	  }
deba@1699
   426
	}
deba@1699
   427
      }
deba@1699
   428
    }
deba@1741
   429
deba@1754
   430
    /// \brief Executes the algorithm and checks the negative cycles.
deba@1741
   431
    ///
deba@1741
   432
    /// This method runs the %FloydWarshall algorithm in order to compute 
deba@1754
   433
    /// the shortest path to each node pairs. If there is a negative cycle 
deba@1741
   434
    /// in the graph it gives back false. 
deba@1741
   435
    /// The algorithm computes 
deba@1741
   436
    /// - The shortest path tree for each node.
deba@1741
   437
    /// - The distance between each node pairs.
deba@1741
   438
    bool checkedStart() {
deba@1741
   439
      start();
deba@1741
   440
      for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1741
   441
	if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
deba@1741
   442
	  return false;
deba@1741
   443
	}
deba@1741
   444
      }
deba@1741
   445
      return true;
deba@1741
   446
    }
deba@1699
   447
    
deba@1699
   448
    /// \brief Runs %FloydWarshall algorithm.
deba@1699
   449
    ///    
deba@1699
   450
    /// This method runs the %FloydWarshall algorithm from a each node
deba@1699
   451
    /// in order to compute the shortest path to each node pairs. 
deba@1699
   452
    /// The algorithm computes
deba@1699
   453
    /// - The shortest path tree for each node.
deba@1699
   454
    /// - The distance between each node pairs.
deba@1699
   455
    ///
deba@1699
   456
    /// \note d.run(s) is just a shortcut of the following code.
deba@1699
   457
    /// \code
deba@1699
   458
    ///  d.init();
deba@1699
   459
    ///  d.start();
deba@1699
   460
    /// \endcode
deba@1699
   461
    void run() {
deba@1699
   462
      init();
deba@1699
   463
      start();
deba@1699
   464
    }
deba@1699
   465
    
deba@1699
   466
    ///@}
deba@1699
   467
deba@1699
   468
    /// \name Query Functions
deba@1699
   469
    /// The result of the %FloydWarshall algorithm can be obtained using these
deba@1699
   470
    /// functions.\n
deba@1699
   471
    /// Before the use of these functions,
deba@1699
   472
    /// either run() or start() must be called.
deba@1699
   473
    
deba@1699
   474
    ///@{
deba@1699
   475
deba@1699
   476
    /// \brief Copies the shortest path to \c t into \c p
deba@1699
   477
    ///    
deba@1699
   478
    /// This function copies the shortest path to \c t into \c p.
deba@1699
   479
    /// If it \c t is a source itself or unreachable, then it does not
deba@1699
   480
    /// alter \c p.
deba@1699
   481
    /// \return Returns \c true if a path to \c t was actually copied to \c p,
deba@1699
   482
    /// \c false otherwise.
deba@1699
   483
    /// \sa DirPath
deba@1699
   484
    template <typename Path>
deba@1699
   485
    bool getPath(Path &p, Node source, Node target) {
deba@1699
   486
      if (connected(source, target)) {
deba@1699
   487
	p.clear();
deba@1699
   488
	typename Path::Builder b(target);
deba@1763
   489
	for(b.setStartNode(target); predEdge(source, target) != INVALID;
deba@1699
   490
	    target = predNode(target)) {
deba@1763
   491
	  b.pushFront(predEdge(source, target));
deba@1699
   492
	}
deba@1699
   493
	b.commit();
deba@1699
   494
	return true;
deba@1699
   495
      }
deba@1699
   496
      return false;
deba@1699
   497
    }
deba@1699
   498
	  
deba@1699
   499
    /// \brief The distance between two nodes.
deba@1699
   500
    ///
deba@1699
   501
    /// Returns the distance between two nodes.
deba@1699
   502
    /// \pre \ref run() must be called before using this function.
deba@1699
   503
    /// \warning If node \c v in unreachable from the root the return value
deba@1699
   504
    /// of this funcion is undefined.
deba@1699
   505
    Value dist(Node source, Node target) const { 
deba@1699
   506
      return (*_dist)(source, target); 
deba@1699
   507
    }
deba@1699
   508
deba@1699
   509
    /// \brief Returns the 'previous edge' of the shortest path tree.
deba@1699
   510
    ///
deba@1699
   511
    /// For the node \c node it returns the 'previous edge' of the shortest 
deba@1699
   512
    /// path tree to direction of the node \c root 
deba@1699
   513
    /// i.e. it returns the last edge of a shortest path from the node \c root 
deba@1699
   514
    /// to \c node. It is \ref INVALID if \c node is unreachable from the root
deba@1699
   515
    /// or if \c node=root. The shortest path tree used here is equal to the 
deba@1699
   516
    /// shortest path tree used in \ref predNode(). 
deba@1699
   517
    /// \pre \ref run() must be called before using this function.
deba@1763
   518
    Edge predEdge(Node root, Node node) const { 
deba@1699
   519
      return (*_pred)(root, node); 
deba@1699
   520
    }
deba@1699
   521
deba@1699
   522
    /// \brief Returns the 'previous node' of the shortest path tree.
deba@1699
   523
    ///
deba@1699
   524
    /// For a node \c node it returns the 'previous node' of the shortest path 
deba@1699
   525
    /// tree to direction of the node \c root, i.e. it returns the last but 
deba@1699
   526
    /// one node from a shortest path from the \c root to \c node. It is 
deba@1699
   527
    /// INVALID if \c node is unreachable from the root or if \c node=root. 
deba@1699
   528
    /// The shortest path tree used here is equal to the 
deba@1763
   529
    /// shortest path tree used in \ref predEdge().  
deba@1699
   530
    /// \pre \ref run() must be called before using this function.
deba@1699
   531
    Node predNode(Node root, Node node) const { 
deba@1699
   532
      return (*_pred)(root, node) == INVALID ? 
deba@1699
   533
      INVALID : graph->source((*_pred)(root, node)); 
deba@1699
   534
    }
deba@1699
   535
    
deba@1699
   536
    /// \brief Returns a reference to the matrix node map of distances.
deba@1699
   537
    ///
deba@1699
   538
    /// Returns a reference to the matrix node map of distances. 
deba@1699
   539
    ///
deba@1699
   540
    /// \pre \ref run() must be called before using this function.
deba@1699
   541
    const DistMap &distMap() const { return *_dist;}
deba@1699
   542
 
deba@1699
   543
    /// \brief Returns a reference to the shortest path tree map.
deba@1699
   544
    ///
deba@1699
   545
    /// Returns a reference to the matrix node map of the edges of the
deba@1699
   546
    /// shortest path tree.
deba@1699
   547
    /// \pre \ref run() must be called before using this function.
deba@1699
   548
    const PredMap &predMap() const { return *_pred;}
deba@1699
   549
 
deba@1699
   550
    /// \brief Checks if a node is reachable from the root.
deba@1699
   551
    ///
deba@1699
   552
    /// Returns \c true if \c v is reachable from the root.
deba@1699
   553
    /// \pre \ref run() must be called before using this function.
deba@1699
   554
    ///
deba@1699
   555
    bool connected(Node source, Node target) { 
deba@1699
   556
      return (*_dist)(source, target) != OperationTraits::infinity(); 
deba@1699
   557
    }
deba@1699
   558
    
deba@1699
   559
    ///@}
deba@1699
   560
  };
deba@1699
   561
 
deba@1699
   562
} //END OF NAMESPACE LEMON
deba@1699
   563
deba@1699
   564
#endif
deba@1699
   565