lemon/suurballe.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 15 Nov 2009 19:57:02 +0100
changeset 787 c2230649a493
parent 584 33c6b6e755cd
child 851 c67e235c832f
permissions -rw-r--r--
Various doc improvements (#331)

- Add notes to the graph classes about the time of
item counting.
- Clarify the doc for run() in BFS and DFS.
- Other improvements.
alpar@440
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@345
     2
 *
alpar@440
     3
 * This file is a part of LEMON, a generic C++ optimization library.
alpar@345
     4
 *
alpar@440
     5
 * Copyright (C) 2003-2009
alpar@345
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@345
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@345
     8
 *
alpar@345
     9
 * Permission to use, modify and distribute this software is granted
alpar@345
    10
 * provided that this copyright notice appears in all copies. For
alpar@345
    11
 * precise terms see the accompanying LICENSE file.
alpar@345
    12
 *
alpar@345
    13
 * This software is provided "AS IS" with no warranty of any kind,
alpar@345
    14
 * express or implied, and with no claim as to its suitability for any
alpar@345
    15
 * purpose.
alpar@345
    16
 *
alpar@345
    17
 */
alpar@345
    18
alpar@345
    19
#ifndef LEMON_SUURBALLE_H
alpar@345
    20
#define LEMON_SUURBALLE_H
alpar@345
    21
alpar@345
    22
///\ingroup shortest_path
alpar@345
    23
///\file
alpar@345
    24
///\brief An algorithm for finding arc-disjoint paths between two
alpar@345
    25
/// nodes having minimum total length.
alpar@345
    26
alpar@345
    27
#include <vector>
kpeter@623
    28
#include <limits>
alpar@345
    29
#include <lemon/bin_heap.h>
alpar@345
    30
#include <lemon/path.h>
deba@519
    31
#include <lemon/list_graph.h>
deba@519
    32
#include <lemon/maps.h>
alpar@345
    33
alpar@345
    34
namespace lemon {
alpar@345
    35
alpar@345
    36
  /// \addtogroup shortest_path
alpar@345
    37
  /// @{
alpar@345
    38
kpeter@346
    39
  /// \brief Algorithm for finding arc-disjoint paths between two nodes
kpeter@346
    40
  /// having minimum total length.
alpar@345
    41
  ///
alpar@345
    42
  /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
alpar@345
    43
  /// finding arc-disjoint paths having minimum total length (cost)
kpeter@346
    44
  /// from a given source node to a given target node in a digraph.
alpar@345
    45
  ///
kpeter@623
    46
  /// Note that this problem is a special case of the \ref min_cost_flow
kpeter@623
    47
  /// "minimum cost flow problem". This implementation is actually an
kpeter@623
    48
  /// efficient specialized version of the \ref CapacityScaling
kpeter@623
    49
  /// "Successive Shortest Path" algorithm directly for this problem.
kpeter@623
    50
  /// Therefore this class provides query functions for flow values and
kpeter@623
    51
  /// node potentials (the dual solution) just like the minimum cost flow
kpeter@623
    52
  /// algorithms.
alpar@345
    53
  ///
kpeter@559
    54
  /// \tparam GR The digraph type the algorithm runs on.
kpeter@623
    55
  /// \tparam LEN The type of the length map.
kpeter@623
    56
  /// The default value is <tt>GR::ArcMap<int></tt>.
alpar@345
    57
  ///
alpar@345
    58
  /// \warning Length values should be \e non-negative \e integers.
alpar@345
    59
  ///
alpar@345
    60
  /// \note For finding node-disjoint paths this algorithm can be used
kpeter@623
    61
  /// along with the \ref SplitNodes adaptor.
kpeter@346
    62
#ifdef DOXYGEN
kpeter@559
    63
  template <typename GR, typename LEN>
kpeter@346
    64
#else
kpeter@623
    65
  template < typename GR,
kpeter@559
    66
             typename LEN = typename GR::template ArcMap<int> >
kpeter@346
    67
#endif
alpar@345
    68
  class Suurballe
alpar@345
    69
  {
kpeter@559
    70
    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
alpar@345
    71
alpar@345
    72
    typedef ConstMap<Arc, int> ConstArcMap;
kpeter@559
    73
    typedef typename GR::template NodeMap<Arc> PredMap;
alpar@345
    74
alpar@345
    75
  public:
alpar@345
    76
kpeter@559
    77
    /// The type of the digraph the algorithm runs on.
kpeter@559
    78
    typedef GR Digraph;
kpeter@559
    79
    /// The type of the length map.
kpeter@559
    80
    typedef LEN LengthMap;
kpeter@559
    81
    /// The type of the lengths.
kpeter@559
    82
    typedef typename LengthMap::Value Length;
kpeter@623
    83
#ifdef DOXYGEN
kpeter@623
    84
    /// The type of the flow map.
kpeter@623
    85
    typedef GR::ArcMap<int> FlowMap;
kpeter@623
    86
    /// The type of the potential map.
kpeter@623
    87
    typedef GR::NodeMap<Length> PotentialMap;
kpeter@623
    88
#else
alpar@345
    89
    /// The type of the flow map.
alpar@345
    90
    typedef typename Digraph::template ArcMap<int> FlowMap;
alpar@345
    91
    /// The type of the potential map.
alpar@345
    92
    typedef typename Digraph::template NodeMap<Length> PotentialMap;
kpeter@623
    93
#endif
kpeter@623
    94
alpar@345
    95
    /// The type of the path structures.
kpeter@623
    96
    typedef SimplePath<GR> Path;
alpar@345
    97
alpar@345
    98
  private:
alpar@440
    99
kpeter@623
   100
    // ResidualDijkstra is a special implementation of the
kpeter@623
   101
    // Dijkstra algorithm for finding shortest paths in the
kpeter@623
   102
    // residual network with respect to the reduced arc lengths
kpeter@623
   103
    // and modifying the node potentials according to the
kpeter@623
   104
    // distance of the nodes.
alpar@345
   105
    class ResidualDijkstra
alpar@345
   106
    {
alpar@345
   107
      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
alpar@345
   108
      typedef BinHeap<Length, HeapCrossRef> Heap;
alpar@345
   109
alpar@345
   110
    private:
alpar@345
   111
kpeter@346
   112
      // The digraph the algorithm runs on
alpar@345
   113
      const Digraph &_graph;
alpar@345
   114
alpar@345
   115
      // The main maps
alpar@345
   116
      const FlowMap &_flow;
alpar@345
   117
      const LengthMap &_length;
alpar@345
   118
      PotentialMap &_potential;
alpar@345
   119
alpar@345
   120
      // The distance map
alpar@345
   121
      PotentialMap _dist;
alpar@345
   122
      // The pred arc map
alpar@345
   123
      PredMap &_pred;
alpar@345
   124
      // The processed (i.e. permanently labeled) nodes
alpar@345
   125
      std::vector<Node> _proc_nodes;
alpar@440
   126
alpar@345
   127
      Node _s;
alpar@345
   128
      Node _t;
alpar@345
   129
alpar@345
   130
    public:
alpar@345
   131
alpar@345
   132
      /// Constructor.
kpeter@623
   133
      ResidualDijkstra( const Digraph &graph,
alpar@345
   134
                        const FlowMap &flow,
alpar@345
   135
                        const LengthMap &length,
alpar@345
   136
                        PotentialMap &potential,
alpar@345
   137
                        PredMap &pred,
alpar@345
   138
                        Node s, Node t ) :
kpeter@623
   139
        _graph(graph), _flow(flow), _length(length), _potential(potential),
kpeter@623
   140
        _dist(graph), _pred(pred), _s(s), _t(t) {}
alpar@345
   141
kpeter@346
   142
      /// \brief Run the algorithm. It returns \c true if a path is found
alpar@345
   143
      /// from the source node to the target node.
alpar@345
   144
      bool run() {
alpar@345
   145
        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
alpar@345
   146
        Heap heap(heap_cross_ref);
alpar@345
   147
        heap.push(_s, 0);
alpar@345
   148
        _pred[_s] = INVALID;
alpar@345
   149
        _proc_nodes.clear();
alpar@345
   150
kpeter@346
   151
        // Process nodes
alpar@345
   152
        while (!heap.empty() && heap.top() != _t) {
alpar@345
   153
          Node u = heap.top(), v;
alpar@345
   154
          Length d = heap.prio() + _potential[u], nd;
alpar@345
   155
          _dist[u] = heap.prio();
alpar@345
   156
          heap.pop();
alpar@345
   157
          _proc_nodes.push_back(u);
alpar@345
   158
kpeter@346
   159
          // Traverse outgoing arcs
alpar@345
   160
          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
alpar@345
   161
            if (_flow[e] == 0) {
alpar@345
   162
              v = _graph.target(e);
alpar@345
   163
              switch(heap.state(v)) {
alpar@345
   164
              case Heap::PRE_HEAP:
alpar@345
   165
                heap.push(v, d + _length[e] - _potential[v]);
alpar@345
   166
                _pred[v] = e;
alpar@345
   167
                break;
alpar@345
   168
              case Heap::IN_HEAP:
alpar@345
   169
                nd = d + _length[e] - _potential[v];
alpar@345
   170
                if (nd < heap[v]) {
alpar@345
   171
                  heap.decrease(v, nd);
alpar@345
   172
                  _pred[v] = e;
alpar@345
   173
                }
alpar@345
   174
                break;
alpar@345
   175
              case Heap::POST_HEAP:
alpar@345
   176
                break;
alpar@345
   177
              }
alpar@345
   178
            }
alpar@345
   179
          }
alpar@345
   180
kpeter@346
   181
          // Traverse incoming arcs
alpar@345
   182
          for (InArcIt e(_graph, u); e != INVALID; ++e) {
alpar@345
   183
            if (_flow[e] == 1) {
alpar@345
   184
              v = _graph.source(e);
alpar@345
   185
              switch(heap.state(v)) {
alpar@345
   186
              case Heap::PRE_HEAP:
alpar@345
   187
                heap.push(v, d - _length[e] - _potential[v]);
alpar@345
   188
                _pred[v] = e;
alpar@345
   189
                break;
alpar@345
   190
              case Heap::IN_HEAP:
alpar@345
   191
                nd = d - _length[e] - _potential[v];
alpar@345
   192
                if (nd < heap[v]) {
alpar@345
   193
                  heap.decrease(v, nd);
alpar@345
   194
                  _pred[v] = e;
alpar@345
   195
                }
alpar@345
   196
                break;
alpar@345
   197
              case Heap::POST_HEAP:
alpar@345
   198
                break;
alpar@345
   199
              }
alpar@345
   200
            }
alpar@345
   201
          }
alpar@345
   202
        }
alpar@345
   203
        if (heap.empty()) return false;
alpar@345
   204
kpeter@346
   205
        // Update potentials of processed nodes
alpar@345
   206
        Length t_dist = heap.prio();
alpar@345
   207
        for (int i = 0; i < int(_proc_nodes.size()); ++i)
alpar@345
   208
          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
alpar@345
   209
        return true;
alpar@345
   210
      }
alpar@345
   211
alpar@345
   212
    }; //class ResidualDijkstra
alpar@345
   213
alpar@345
   214
  private:
alpar@345
   215
kpeter@346
   216
    // The digraph the algorithm runs on
alpar@345
   217
    const Digraph &_graph;
alpar@345
   218
    // The length map
alpar@345
   219
    const LengthMap &_length;
alpar@440
   220
alpar@345
   221
    // Arc map of the current flow
alpar@345
   222
    FlowMap *_flow;
alpar@345
   223
    bool _local_flow;
alpar@345
   224
    // Node map of the current potentials
alpar@345
   225
    PotentialMap *_potential;
alpar@345
   226
    bool _local_potential;
alpar@345
   227
alpar@345
   228
    // The source node
alpar@345
   229
    Node _source;
alpar@345
   230
    // The target node
alpar@345
   231
    Node _target;
alpar@345
   232
alpar@345
   233
    // Container to store the found paths
alpar@345
   234
    std::vector< SimplePath<Digraph> > paths;
alpar@345
   235
    int _path_num;
alpar@345
   236
alpar@345
   237
    // The pred arc map
alpar@345
   238
    PredMap _pred;
alpar@345
   239
    // Implementation of the Dijkstra algorithm for finding augmenting
alpar@345
   240
    // shortest paths in the residual network
alpar@345
   241
    ResidualDijkstra *_dijkstra;
alpar@345
   242
alpar@345
   243
  public:
alpar@345
   244
alpar@345
   245
    /// \brief Constructor.
alpar@345
   246
    ///
alpar@345
   247
    /// Constructor.
alpar@345
   248
    ///
kpeter@623
   249
    /// \param graph The digraph the algorithm runs on.
alpar@345
   250
    /// \param length The length (cost) values of the arcs.
kpeter@623
   251
    Suurballe( const Digraph &graph,
kpeter@623
   252
               const LengthMap &length ) :
kpeter@623
   253
      _graph(graph), _length(length), _flow(0), _local_flow(false),
kpeter@623
   254
      _potential(0), _local_potential(false), _pred(graph)
kpeter@623
   255
    {
kpeter@623
   256
      LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
kpeter@623
   257
        "The length type of Suurballe must be integer");
kpeter@623
   258
    }
alpar@345
   259
alpar@345
   260
    /// Destructor.
alpar@345
   261
    ~Suurballe() {
alpar@345
   262
      if (_local_flow) delete _flow;
alpar@345
   263
      if (_local_potential) delete _potential;
alpar@345
   264
      delete _dijkstra;
alpar@345
   265
    }
alpar@345
   266
kpeter@346
   267
    /// \brief Set the flow map.
alpar@345
   268
    ///
kpeter@346
   269
    /// This function sets the flow map.
kpeter@623
   270
    /// If it is not used before calling \ref run() or \ref init(),
kpeter@623
   271
    /// an instance will be allocated automatically. The destructor
kpeter@623
   272
    /// deallocates this automatically allocated map, of course.
alpar@345
   273
    ///
kpeter@623
   274
    /// The found flow contains only 0 and 1 values, since it is the
kpeter@623
   275
    /// union of the found arc-disjoint paths.
alpar@345
   276
    ///
kpeter@559
   277
    /// \return <tt>(*this)</tt>
alpar@345
   278
    Suurballe& flowMap(FlowMap &map) {
alpar@345
   279
      if (_local_flow) {
alpar@345
   280
        delete _flow;
alpar@345
   281
        _local_flow = false;
alpar@345
   282
      }
alpar@345
   283
      _flow = &map;
alpar@345
   284
      return *this;
alpar@345
   285
    }
alpar@345
   286
kpeter@346
   287
    /// \brief Set the potential map.
alpar@345
   288
    ///
kpeter@346
   289
    /// This function sets the potential map.
kpeter@623
   290
    /// If it is not used before calling \ref run() or \ref init(),
kpeter@623
   291
    /// an instance will be allocated automatically. The destructor
kpeter@623
   292
    /// deallocates this automatically allocated map, of course.
alpar@345
   293
    ///
kpeter@623
   294
    /// The node potentials provide the dual solution of the underlying
kpeter@623
   295
    /// \ref min_cost_flow "minimum cost flow problem".
alpar@345
   296
    ///
kpeter@559
   297
    /// \return <tt>(*this)</tt>
alpar@345
   298
    Suurballe& potentialMap(PotentialMap &map) {
alpar@345
   299
      if (_local_potential) {
alpar@345
   300
        delete _potential;
alpar@345
   301
        _local_potential = false;
alpar@345
   302
      }
alpar@345
   303
      _potential = &map;
alpar@345
   304
      return *this;
alpar@345
   305
    }
alpar@345
   306
kpeter@584
   307
    /// \name Execution Control
alpar@345
   308
    /// The simplest way to execute the algorithm is to call the run()
alpar@345
   309
    /// function.
alpar@345
   310
    /// \n
alpar@345
   311
    /// If you only need the flow that is the union of the found
alpar@345
   312
    /// arc-disjoint paths, you may call init() and findFlow().
alpar@345
   313
alpar@345
   314
    /// @{
alpar@345
   315
kpeter@346
   316
    /// \brief Run the algorithm.
alpar@345
   317
    ///
kpeter@346
   318
    /// This function runs the algorithm.
alpar@345
   319
    ///
kpeter@623
   320
    /// \param s The source node.
kpeter@623
   321
    /// \param t The target node.
alpar@345
   322
    /// \param k The number of paths to be found.
alpar@345
   323
    ///
kpeter@346
   324
    /// \return \c k if there are at least \c k arc-disjoint paths from
kpeter@346
   325
    /// \c s to \c t in the digraph. Otherwise it returns the number of
alpar@345
   326
    /// arc-disjoint paths found.
alpar@345
   327
    ///
kpeter@623
   328
    /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
kpeter@623
   329
    /// just a shortcut of the following code.
alpar@345
   330
    /// \code
kpeter@623
   331
    ///   s.init(s);
kpeter@623
   332
    ///   s.findFlow(t, k);
alpar@345
   333
    ///   s.findPaths();
alpar@345
   334
    /// \endcode
kpeter@623
   335
    int run(const Node& s, const Node& t, int k = 2) {
kpeter@623
   336
      init(s);
kpeter@623
   337
      findFlow(t, k);
alpar@345
   338
      findPaths();
alpar@345
   339
      return _path_num;
alpar@345
   340
    }
alpar@345
   341
kpeter@346
   342
    /// \brief Initialize the algorithm.
alpar@345
   343
    ///
kpeter@346
   344
    /// This function initializes the algorithm.
kpeter@623
   345
    ///
kpeter@623
   346
    /// \param s The source node.
kpeter@623
   347
    void init(const Node& s) {
kpeter@623
   348
      _source = s;
kpeter@623
   349
kpeter@346
   350
      // Initialize maps
alpar@345
   351
      if (!_flow) {
alpar@345
   352
        _flow = new FlowMap(_graph);
alpar@345
   353
        _local_flow = true;
alpar@345
   354
      }
alpar@345
   355
      if (!_potential) {
alpar@345
   356
        _potential = new PotentialMap(_graph);
alpar@345
   357
        _local_potential = true;
alpar@345
   358
      }
alpar@345
   359
      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
alpar@345
   360
      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
alpar@345
   361
    }
alpar@345
   362
kpeter@623
   363
    /// \brief Execute the algorithm to find an optimal flow.
alpar@345
   364
    ///
kpeter@346
   365
    /// This function executes the successive shortest path algorithm to
kpeter@623
   366
    /// find a minimum cost flow, which is the union of \c k (or less)
alpar@345
   367
    /// arc-disjoint paths.
alpar@345
   368
    ///
kpeter@623
   369
    /// \param t The target node.
kpeter@623
   370
    /// \param k The number of paths to be found.
kpeter@623
   371
    ///
kpeter@346
   372
    /// \return \c k if there are at least \c k arc-disjoint paths from
kpeter@623
   373
    /// the source node to the given node \c t in the digraph.
kpeter@623
   374
    /// Otherwise it returns the number of arc-disjoint paths found.
alpar@345
   375
    ///
alpar@345
   376
    /// \pre \ref init() must be called before using this function.
kpeter@623
   377
    int findFlow(const Node& t, int k = 2) {
kpeter@623
   378
      _target = t;
kpeter@623
   379
      _dijkstra =
kpeter@623
   380
        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
kpeter@623
   381
                              _source, _target );
kpeter@623
   382
kpeter@346
   383
      // Find shortest paths
alpar@345
   384
      _path_num = 0;
alpar@345
   385
      while (_path_num < k) {
kpeter@346
   386
        // Run Dijkstra
alpar@345
   387
        if (!_dijkstra->run()) break;
alpar@345
   388
        ++_path_num;
alpar@345
   389
kpeter@346
   390
        // Set the flow along the found shortest path
alpar@345
   391
        Node u = _target;
alpar@345
   392
        Arc e;
alpar@345
   393
        while ((e = _pred[u]) != INVALID) {
alpar@345
   394
          if (u == _graph.target(e)) {
alpar@345
   395
            (*_flow)[e] = 1;
alpar@345
   396
            u = _graph.source(e);
alpar@345
   397
          } else {
alpar@345
   398
            (*_flow)[e] = 0;
alpar@345
   399
            u = _graph.target(e);
alpar@345
   400
          }
alpar@345
   401
        }
alpar@345
   402
      }
alpar@345
   403
      return _path_num;
alpar@345
   404
    }
alpar@440
   405
kpeter@346
   406
    /// \brief Compute the paths from the flow.
alpar@345
   407
    ///
kpeter@623
   408
    /// This function computes the paths from the found minimum cost flow,
kpeter@623
   409
    /// which is the union of some arc-disjoint paths.
alpar@345
   410
    ///
alpar@345
   411
    /// \pre \ref init() and \ref findFlow() must be called before using
alpar@345
   412
    /// this function.
alpar@345
   413
    void findPaths() {
alpar@345
   414
      FlowMap res_flow(_graph);
kpeter@346
   415
      for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
alpar@345
   416
alpar@345
   417
      paths.clear();
alpar@345
   418
      paths.resize(_path_num);
alpar@345
   419
      for (int i = 0; i < _path_num; ++i) {
alpar@345
   420
        Node n = _source;
alpar@345
   421
        while (n != _target) {
alpar@345
   422
          OutArcIt e(_graph, n);
alpar@345
   423
          for ( ; res_flow[e] == 0; ++e) ;
alpar@345
   424
          n = _graph.target(e);
alpar@345
   425
          paths[i].addBack(e);
alpar@345
   426
          res_flow[e] = 0;
alpar@345
   427
        }
alpar@345
   428
      }
alpar@345
   429
    }
alpar@345
   430
alpar@345
   431
    /// @}
alpar@345
   432
alpar@345
   433
    /// \name Query Functions
kpeter@346
   434
    /// The results of the algorithm can be obtained using these
alpar@345
   435
    /// functions.
alpar@345
   436
    /// \n The algorithm should be executed before using them.
alpar@345
   437
alpar@345
   438
    /// @{
alpar@345
   439
kpeter@623
   440
    /// \brief Return the total length of the found paths.
kpeter@623
   441
    ///
kpeter@623
   442
    /// This function returns the total length of the found paths, i.e.
kpeter@623
   443
    /// the total cost of the found flow.
kpeter@623
   444
    /// The complexity of the function is O(e).
kpeter@623
   445
    ///
kpeter@623
   446
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@623
   447
    /// this function.
kpeter@623
   448
    Length totalLength() const {
kpeter@623
   449
      Length c = 0;
kpeter@623
   450
      for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@623
   451
        c += (*_flow)[e] * _length[e];
kpeter@623
   452
      return c;
kpeter@623
   453
    }
kpeter@623
   454
kpeter@623
   455
    /// \brief Return the flow value on the given arc.
kpeter@623
   456
    ///
kpeter@623
   457
    /// This function returns the flow value on the given arc.
kpeter@623
   458
    /// It is \c 1 if the arc is involved in one of the found arc-disjoint
kpeter@623
   459
    /// paths, otherwise it is \c 0.
kpeter@623
   460
    ///
kpeter@623
   461
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@623
   462
    /// this function.
kpeter@623
   463
    int flow(const Arc& arc) const {
kpeter@623
   464
      return (*_flow)[arc];
kpeter@623
   465
    }
kpeter@623
   466
kpeter@623
   467
    /// \brief Return a const reference to an arc map storing the
alpar@345
   468
    /// found flow.
alpar@345
   469
    ///
kpeter@623
   470
    /// This function returns a const reference to an arc map storing
kpeter@346
   471
    /// the flow that is the union of the found arc-disjoint paths.
alpar@345
   472
    ///
kpeter@346
   473
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@346
   474
    /// this function.
alpar@345
   475
    const FlowMap& flowMap() const {
alpar@345
   476
      return *_flow;
alpar@345
   477
    }
alpar@345
   478
kpeter@346
   479
    /// \brief Return the potential of the given node.
alpar@345
   480
    ///
kpeter@346
   481
    /// This function returns the potential of the given node.
kpeter@623
   482
    /// The node potentials provide the dual solution of the
kpeter@623
   483
    /// underlying \ref min_cost_flow "minimum cost flow problem".
alpar@345
   484
    ///
kpeter@346
   485
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@346
   486
    /// this function.
alpar@345
   487
    Length potential(const Node& node) const {
alpar@345
   488
      return (*_potential)[node];
alpar@345
   489
    }
alpar@345
   490
kpeter@623
   491
    /// \brief Return a const reference to a node map storing the
kpeter@623
   492
    /// found potentials (the dual solution).
alpar@345
   493
    ///
kpeter@623
   494
    /// This function returns a const reference to a node map storing
kpeter@623
   495
    /// the found potentials that provide the dual solution of the
kpeter@623
   496
    /// underlying \ref min_cost_flow "minimum cost flow problem".
alpar@345
   497
    ///
kpeter@346
   498
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@346
   499
    /// this function.
kpeter@623
   500
    const PotentialMap& potentialMap() const {
kpeter@623
   501
      return *_potential;
alpar@345
   502
    }
alpar@345
   503
kpeter@346
   504
    /// \brief Return the number of the found paths.
alpar@345
   505
    ///
kpeter@346
   506
    /// This function returns the number of the found paths.
alpar@345
   507
    ///
kpeter@346
   508
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@346
   509
    /// this function.
alpar@345
   510
    int pathNum() const {
alpar@345
   511
      return _path_num;
alpar@345
   512
    }
alpar@345
   513
kpeter@346
   514
    /// \brief Return a const reference to the specified path.
alpar@345
   515
    ///
kpeter@346
   516
    /// This function returns a const reference to the specified path.
alpar@345
   517
    ///
kpeter@623
   518
    /// \param i The function returns the <tt>i</tt>-th path.
alpar@345
   519
    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
alpar@345
   520
    ///
kpeter@346
   521
    /// \pre \ref run() or \ref findPaths() must be called before using
kpeter@346
   522
    /// this function.
alpar@345
   523
    Path path(int i) const {
alpar@345
   524
      return paths[i];
alpar@345
   525
    }
alpar@345
   526
alpar@345
   527
    /// @}
alpar@345
   528
alpar@345
   529
  }; //class Suurballe
alpar@345
   530
alpar@345
   531
  ///@}
alpar@345
   532
alpar@345
   533
} //namespace lemon
alpar@345
   534
alpar@345
   535
#endif //LEMON_SUURBALLE_H