lemon/edmonds_karp.h
changeset 1145 1de908281369
parent 1074 97d978243703
equal deleted inserted replaced
6:22cb54844c63 7:e45ba503f89b
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     4  *
     5  * Copyright (C) 2003-2010
     5  * Copyright (C) 2003-2013
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     8  *
     9  * Permission to use, modify and distribute this software is granted
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    10  * provided that this copyright notice appears in all copies. For
    34   /// \param GR Digraph type.
    34   /// \param GR Digraph type.
    35   /// \param CAP Type of capacity map.
    35   /// \param CAP Type of capacity map.
    36   template <typename GR, typename CAP>
    36   template <typename GR, typename CAP>
    37   struct EdmondsKarpDefaultTraits {
    37   struct EdmondsKarpDefaultTraits {
    38 
    38 
    39     /// \brief The digraph type the algorithm runs on. 
    39     /// \brief The digraph type the algorithm runs on.
    40     typedef GR Digraph;
    40     typedef GR Digraph;
    41 
    41 
    42     /// \brief The type of the map that stores the arc capacities.
    42     /// \brief The type of the map that stores the arc capacities.
    43     ///
    43     ///
    44     /// The type of the map that stores the arc capacities.
    44     /// The type of the map that stores the arc capacities.
    58     typedef typename Digraph::template ArcMap<Value> FlowMap;
    58     typedef typename Digraph::template ArcMap<Value> FlowMap;
    59 #endif
    59 #endif
    60 
    60 
    61     /// \brief Instantiates a FlowMap.
    61     /// \brief Instantiates a FlowMap.
    62     ///
    62     ///
    63     /// This function instantiates a \ref FlowMap. 
    63     /// This function instantiates a \ref FlowMap.
    64     /// \param digraph The digraph for which we would like to define
    64     /// \param digraph The digraph for which we would like to define
    65     /// the flow map.
    65     /// the flow map.
    66     static FlowMap* createFlowMap(const Digraph& digraph) {
    66     static FlowMap* createFlowMap(const Digraph& digraph) {
    67       return new FlowMap(digraph);
    67       return new FlowMap(digraph);
    68     }
    68     }
    93   /// worst case. Always try the Preflow algorithm instead of this if
    93   /// worst case. Always try the Preflow algorithm instead of this if
    94   /// you just want to compute the optimal flow.
    94   /// you just want to compute the optimal flow.
    95   ///
    95   ///
    96   /// \tparam GR The type of the digraph the algorithm runs on.
    96   /// \tparam GR The type of the digraph the algorithm runs on.
    97   /// \tparam CAP The type of the capacity map. The default map
    97   /// \tparam CAP The type of the capacity map. The default map
    98   /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". 
    98   /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
    99   /// \tparam TR The traits class that defines various types used by the
    99   /// \tparam TR The traits class that defines various types used by the
   100   /// algorithm. By default, it is \ref EdmondsKarpDefaultTraits
   100   /// algorithm. By default, it is \ref EdmondsKarpDefaultTraits
   101   /// "EdmondsKarpDefaultTraits<GR, CAP>".
   101   /// "EdmondsKarpDefaultTraits<GR, CAP>".
   102   /// In most cases, this parameter should not be set directly,
   102   /// In most cases, this parameter should not be set directly,
   103   /// consider to use the named template parameters instead.
   103   /// consider to use the named template parameters instead.
   104 
   104 
   105 #ifdef DOXYGEN
   105 #ifdef DOXYGEN
   106   template <typename GR, typename CAP, typename TR>
   106   template <typename GR, typename CAP, typename TR>
   107 #else 
   107 #else
   108   template <typename GR,
   108   template <typename GR,
   109 	    typename CAP = typename GR::template ArcMap<int>,
   109             typename CAP = typename GR::template ArcMap<int>,
   110             typename TR = EdmondsKarpDefaultTraits<GR, CAP> >
   110             typename TR = EdmondsKarpDefaultTraits<GR, CAP> >
   111 #endif
   111 #endif
   112   class EdmondsKarp {
   112   class EdmondsKarp {
   113   public:
   113   public:
   114 
   114 
   118     /// The type of the digraph the algorithm runs on.
   118     /// The type of the digraph the algorithm runs on.
   119     typedef typename Traits::Digraph Digraph;
   119     typedef typename Traits::Digraph Digraph;
   120     /// The type of the capacity map.
   120     /// The type of the capacity map.
   121     typedef typename Traits::CapacityMap CapacityMap;
   121     typedef typename Traits::CapacityMap CapacityMap;
   122     /// The type of the flow values.
   122     /// The type of the flow values.
   123     typedef typename Traits::Value Value; 
   123     typedef typename Traits::Value Value;
   124 
   124 
   125     /// The type of the flow map.
   125     /// The type of the flow map.
   126     typedef typename Traits::FlowMap FlowMap;
   126     typedef typename Traits::FlowMap FlowMap;
   127     /// The type of the tolerance.
   127     /// The type of the tolerance.
   128     typedef typename Traits::Tolerance Tolerance;
   128     typedef typename Traits::Tolerance Tolerance;
   129 
   129 
   130   private:
   130   private:
   131 
   131 
   132     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
   132     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
   133     typedef typename Digraph::template NodeMap<Arc> PredMap;
   133     typedef typename Digraph::template NodeMap<Arc> PredMap;
   134     
   134 
   135     const Digraph& _graph;
   135     const Digraph& _graph;
   136     const CapacityMap* _capacity;
   136     const CapacityMap* _capacity;
   137 
   137 
   138     Node _source, _target;
   138     Node _source, _target;
   139 
   139 
   140     FlowMap* _flow;
   140     FlowMap* _flow;
   141     bool _local_flow;
   141     bool _local_flow;
   142 
   142 
   143     PredMap* _pred;
   143     PredMap* _pred;
   144     std::vector<Node> _queue;
   144     std::vector<Node> _queue;
   145     
   145 
   146     Tolerance _tolerance;
   146     Tolerance _tolerance;
   147     Value _flow_value;
   147     Value _flow_value;
   148 
   148 
   149     void createStructures() {
   149     void createStructures() {
   150       if (!_flow) {
   150       if (!_flow) {
   151 	_flow = Traits::createFlowMap(_graph);
   151         _flow = Traits::createFlowMap(_graph);
   152 	_local_flow = true;
   152         _local_flow = true;
   153       }
   153       }
   154       if (!_pred) {
   154       if (!_pred) {
   155 	_pred = new PredMap(_graph);
   155         _pred = new PredMap(_graph);
   156       }
   156       }
   157       _queue.resize(countNodes(_graph));
   157       _queue.resize(countNodes(_graph));
   158     }
   158     }
   159 
   159 
   160     void destroyStructures() {
   160     void destroyStructures() {
   161       if (_local_flow) {
   161       if (_local_flow) {
   162 	delete _flow;
   162         delete _flow;
   163       }
   163       }
   164       if (_pred) {
   164       if (_pred) {
   165 	delete _pred;
   165         delete _pred;
   166       }
   166       }
   167     }
   167     }
   168     
   168 
   169   public:
   169   public:
   170 
   170 
   171     typedef EdmondsKarp Create;
   171     typedef EdmondsKarp Create;
   172 
   172 
   173     ///\name Named template parameters
   173     ///\name Named template parameters
   176 
   176 
   177     template <typename T>
   177     template <typename T>
   178     struct SetFlowMapTraits : public Traits {
   178     struct SetFlowMapTraits : public Traits {
   179       typedef T FlowMap;
   179       typedef T FlowMap;
   180       static FlowMap *createFlowMap(const Digraph&) {
   180       static FlowMap *createFlowMap(const Digraph&) {
   181 	LEMON_ASSERT(false, "FlowMap is not initialized");
   181         LEMON_ASSERT(false, "FlowMap is not initialized");
   182         return 0;
   182         return 0;
   183       }
   183       }
   184     };
   184     };
   185 
   185 
   186     /// \brief \ref named-templ-param "Named parameter" for setting
   186     /// \brief \ref named-templ-param "Named parameter" for setting
   187     /// FlowMap type
   187     /// FlowMap type
   188     ///
   188     ///
   189     /// \ref named-templ-param "Named parameter" for setting FlowMap
   189     /// \ref named-templ-param "Named parameter" for setting FlowMap
   190     /// type
   190     /// type
   191     template <typename T>
   191     template <typename T>
   192     struct SetFlowMap 
   192     struct SetFlowMap
   193       : public EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > {
   193       : public EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > {
   194       typedef EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > Create;
   194       typedef EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > Create;
   195     };
   195     };
   196 
   196 
   197     /// @}
   197     /// @}
   198 
   198 
   199   protected:
   199   protected:
   200     
   200 
   201     EdmondsKarp() {}
   201     EdmondsKarp() {}
   202 
   202 
   203   public:
   203   public:
   204 
   204 
   205     /// \brief The constructor of the class.
   205     /// \brief The constructor of the class.
   206     ///
   206     ///
   207     /// The constructor of the class. 
   207     /// The constructor of the class.
   208     /// \param digraph The digraph the algorithm runs on. 
   208     /// \param digraph The digraph the algorithm runs on.
   209     /// \param capacity The capacity of the arcs. 
   209     /// \param capacity The capacity of the arcs.
   210     /// \param source The source node.
   210     /// \param source The source node.
   211     /// \param target The target node.
   211     /// \param target The target node.
   212     EdmondsKarp(const Digraph& digraph, const CapacityMap& capacity,
   212     EdmondsKarp(const Digraph& digraph, const CapacityMap& capacity,
   213 		Node source, Node target)
   213                 Node source, Node target)
   214       : _graph(digraph), _capacity(&capacity), _source(source), _target(target),
   214       : _graph(digraph), _capacity(&capacity), _source(source), _target(target),
   215 	_flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()
   215         _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()
   216     {
   216     {
   217       LEMON_ASSERT(_source != _target,
   217       LEMON_ASSERT(_source != _target,
   218                    "Flow source and target are the same nodes.");
   218                    "Flow source and target are the same nodes.");
   219     }
   219     }
   220 
   220 
   242     /// The destructor deallocates this automatically allocated map,
   242     /// The destructor deallocates this automatically allocated map,
   243     /// of course.
   243     /// of course.
   244     /// \return <tt>(*this)</tt>
   244     /// \return <tt>(*this)</tt>
   245     EdmondsKarp& flowMap(FlowMap& map) {
   245     EdmondsKarp& flowMap(FlowMap& map) {
   246       if (_local_flow) {
   246       if (_local_flow) {
   247 	delete _flow;
   247         delete _flow;
   248 	_local_flow = false;
   248         _local_flow = false;
   249       }
   249       }
   250       _flow = &map;
   250       _flow = &map;
   251       return *this;
   251       return *this;
   252     }
   252     }
   253 
   253 
   274     /// Sets the tolerance used by algorithm.
   274     /// Sets the tolerance used by algorithm.
   275     /// \return <tt>(*this)</tt>
   275     /// \return <tt>(*this)</tt>
   276     EdmondsKarp& tolerance(const Tolerance& tolerance) {
   276     EdmondsKarp& tolerance(const Tolerance& tolerance) {
   277       _tolerance = tolerance;
   277       _tolerance = tolerance;
   278       return *this;
   278       return *this;
   279     } 
   279     }
   280 
   280 
   281     /// \brief Returns a const reference to the tolerance.
   281     /// \brief Returns a const reference to the tolerance.
   282     ///
   282     ///
   283     /// Returns a const reference to the tolerance object used by
   283     /// Returns a const reference to the tolerance object used by
   284     /// the algorithm.
   284     /// the algorithm.
   285     const Tolerance& tolerance() const {
   285     const Tolerance& tolerance() const {
   286       return _tolerance;
   286       return _tolerance;
   287     } 
   287     }
   288 
   288 
   289     /// \name Execution control
   289     /// \name Execution control
   290     /// The simplest way to execute the algorithm is to use \ref run().\n
   290     /// The simplest way to execute the algorithm is to use \ref run().\n
   291     /// If you need better control on the initial solution or the execution,
   291     /// If you need better control on the initial solution or the execution,
   292     /// you have to call one of the \ref init() functions first, then
   292     /// you have to call one of the \ref init() functions first, then
   293     /// \ref start() or multiple times the \ref augment() function.
   293     /// \ref start() or multiple times the \ref augment() function.
   294     
   294 
   295     ///@{
   295     ///@{
   296 
   296 
   297     /// \brief Initializes the algorithm.
   297     /// \brief Initializes the algorithm.
   298     ///
   298     ///
   299     /// Initializes the internal data structures and sets the initial
   299     /// Initializes the internal data structures and sets the initial
   303       for (ArcIt it(_graph); it != INVALID; ++it) {
   303       for (ArcIt it(_graph); it != INVALID; ++it) {
   304         _flow->set(it, 0);
   304         _flow->set(it, 0);
   305       }
   305       }
   306       _flow_value = 0;
   306       _flow_value = 0;
   307     }
   307     }
   308     
   308 
   309     /// \brief Initializes the algorithm using the given flow map.
   309     /// \brief Initializes the algorithm using the given flow map.
   310     ///
   310     ///
   311     /// Initializes the internal data structures and sets the initial
   311     /// Initializes the internal data structures and sets the initial
   312     /// flow to the given \c flowMap. The \c flowMap should
   312     /// flow to the given \c flowMap. The \c flowMap should
   313     /// contain a feasible flow, i.e. at each node excluding the source
   313     /// contain a feasible flow, i.e. at each node excluding the source
   315     /// outgoing flow.
   315     /// outgoing flow.
   316     template <typename FlowMap>
   316     template <typename FlowMap>
   317     void init(const FlowMap& flowMap) {
   317     void init(const FlowMap& flowMap) {
   318       createStructures();
   318       createStructures();
   319       for (ArcIt e(_graph); e != INVALID; ++e) {
   319       for (ArcIt e(_graph); e != INVALID; ++e) {
   320 	_flow->set(e, flowMap[e]);
   320         _flow->set(e, flowMap[e]);
   321       }
   321       }
   322       _flow_value = 0;
   322       _flow_value = 0;
   323       for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
   323       for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
   324         _flow_value += (*_flow)[jt];
   324         _flow_value += (*_flow)[jt];
   325       }
   325       }
   332     ///
   332     ///
   333     /// Initializes the internal data structures and sets the initial
   333     /// Initializes the internal data structures and sets the initial
   334     /// flow to the given \c flowMap. The \c flowMap should
   334     /// flow to the given \c flowMap. The \c flowMap should
   335     /// contain a feasible flow, i.e. at each node excluding the source
   335     /// contain a feasible flow, i.e. at each node excluding the source
   336     /// and the target, the incoming flow should be equal to the
   336     /// and the target, the incoming flow should be equal to the
   337     /// outgoing flow. 
   337     /// outgoing flow.
   338     /// \return \c false when the given \c flowMap does not contain a
   338     /// \return \c false when the given \c flowMap does not contain a
   339     /// feasible flow.
   339     /// feasible flow.
   340     template <typename FlowMap>
   340     template <typename FlowMap>
   341     bool checkedInit(const FlowMap& flowMap) {
   341     bool checkedInit(const FlowMap& flowMap) {
   342       createStructures();
   342       createStructures();
   343       for (ArcIt e(_graph); e != INVALID; ++e) {
   343       for (ArcIt e(_graph); e != INVALID; ++e) {
   344 	_flow->set(e, flowMap[e]);
   344         _flow->set(e, flowMap[e]);
   345       }
   345       }
   346       for (NodeIt it(_graph); it != INVALID; ++it) {
   346       for (NodeIt it(_graph); it != INVALID; ++it) {
   347         if (it == _source || it == _target) continue;
   347         if (it == _source || it == _target) continue;
   348         Value outFlow = 0;
   348         Value outFlow = 0;
   349         for (OutArcIt jt(_graph, it); jt != INVALID; ++jt) {
   349         for (OutArcIt jt(_graph, it); jt != INVALID; ++jt) {
   370       }
   370       }
   371       return true;
   371       return true;
   372     }
   372     }
   373 
   373 
   374     /// \brief Augments the solution along a shortest path.
   374     /// \brief Augments the solution along a shortest path.
   375     /// 
   375     ///
   376     /// Augments the solution along a shortest path. This function searches a
   376     /// Augments the solution along a shortest path. This function searches a
   377     /// shortest path between the source and the target
   377     /// shortest path between the source and the target
   378     /// in the residual digraph by the Bfs algoritm.
   378     /// in the residual digraph by the Bfs algoritm.
   379     /// Then it increases the flow on this path with the minimal residual
   379     /// Then it increases the flow on this path with the minimal residual
   380     /// capacity on the path. If there is no such path, it gives back
   380     /// capacity on the path. If there is no such path, it gives back
   381     /// false.
   381     /// false.
   382     /// \return \c false when the augmenting did not success, i.e. the
   382     /// \return \c false when the augmenting did not success, i.e. the
   383     /// current flow is a feasible and optimal solution.
   383     /// current flow is a feasible and optimal solution.
   384     bool augment() {
   384     bool augment() {
   385       for (NodeIt n(_graph); n != INVALID; ++n) {
   385       for (NodeIt n(_graph); n != INVALID; ++n) {
   386 	_pred->set(n, INVALID);
   386         _pred->set(n, INVALID);
   387       }
   387       }
   388       
   388 
   389       int first = 0, last = 1;
   389       int first = 0, last = 1;
   390       
   390 
   391       _queue[0] = _source;
   391       _queue[0] = _source;
   392       _pred->set(_source, OutArcIt(_graph, _source));
   392       _pred->set(_source, OutArcIt(_graph, _source));
   393 
   393 
   394       while (first != last && (*_pred)[_target] == INVALID) {
   394       while (first != last && (*_pred)[_target] == INVALID) {
   395 	Node n = _queue[first++];
   395         Node n = _queue[first++];
   396 	
   396 
   397 	for (OutArcIt e(_graph, n); e != INVALID; ++e) {
   397         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
   398 	  Value rem = (*_capacity)[e] - (*_flow)[e];
   398           Value rem = (*_capacity)[e] - (*_flow)[e];
   399 	  Node t = _graph.target(e);
   399           Node t = _graph.target(e);
   400 	  if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
   400           if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
   401 	    _pred->set(t, e);
   401             _pred->set(t, e);
   402 	    _queue[last++] = t;
   402             _queue[last++] = t;
   403 	  }
   403           }
   404 	}
   404         }
   405 	for (InArcIt e(_graph, n); e != INVALID; ++e) {
   405         for (InArcIt e(_graph, n); e != INVALID; ++e) {
   406 	  Value rem = (*_flow)[e];
   406           Value rem = (*_flow)[e];
   407 	  Node t = _graph.source(e);
   407           Node t = _graph.source(e);
   408 	  if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
   408           if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
   409 	    _pred->set(t, e);
   409             _pred->set(t, e);
   410 	    _queue[last++] = t;
   410             _queue[last++] = t;
   411 	  }
   411           }
   412 	}
   412         }
   413       }
   413       }
   414 
   414 
   415       if ((*_pred)[_target] != INVALID) {
   415       if ((*_pred)[_target] != INVALID) {
   416 	Node n = _target;
   416         Node n = _target;
   417 	Arc e = (*_pred)[n];
   417         Arc e = (*_pred)[n];
   418 
   418 
   419 	Value prem = (*_capacity)[e] - (*_flow)[e];
   419         Value prem = (*_capacity)[e] - (*_flow)[e];
   420 	n = _graph.source(e);
   420         n = _graph.source(e);
   421 	while (n != _source) {
   421         while (n != _source) {
   422 	  e = (*_pred)[n];
   422           e = (*_pred)[n];
   423 	  if (_graph.target(e) == n) {
   423           if (_graph.target(e) == n) {
   424 	    Value rem = (*_capacity)[e] - (*_flow)[e];
   424             Value rem = (*_capacity)[e] - (*_flow)[e];
   425 	    if (rem < prem) prem = rem;
   425             if (rem < prem) prem = rem;
   426 	    n = _graph.source(e);
   426             n = _graph.source(e);
   427 	  } else {
   427           } else {
   428 	    Value rem = (*_flow)[e];
   428             Value rem = (*_flow)[e];
   429 	    if (rem < prem) prem = rem;
   429             if (rem < prem) prem = rem;
   430 	    n = _graph.target(e);   
   430             n = _graph.target(e);
   431 	  } 
   431           }
   432 	}
   432         }
   433 
   433 
   434 	n = _target;
   434         n = _target;
   435 	e = (*_pred)[n];
   435         e = (*_pred)[n];
   436 
   436 
   437 	_flow->set(e, (*_flow)[e] + prem);
   437         _flow->set(e, (*_flow)[e] + prem);
   438 	n = _graph.source(e);
   438         n = _graph.source(e);
   439 	while (n != _source) {
   439         while (n != _source) {
   440 	  e = (*_pred)[n];
   440           e = (*_pred)[n];
   441 	  if (_graph.target(e) == n) {
   441           if (_graph.target(e) == n) {
   442 	    _flow->set(e, (*_flow)[e] + prem);
   442             _flow->set(e, (*_flow)[e] + prem);
   443 	    n = _graph.source(e);
   443             n = _graph.source(e);
   444 	  } else {
   444           } else {
   445 	    _flow->set(e, (*_flow)[e] - prem);
   445             _flow->set(e, (*_flow)[e] - prem);
   446 	    n = _graph.target(e);   
   446             n = _graph.target(e);
   447 	  } 
   447           }
   448 	}
   448         }
   449 
   449 
   450 	_flow_value += prem;	
   450         _flow_value += prem;
   451 	return true;
   451         return true;
   452       } else {
   452       } else {
   453 	return false;
   453         return false;
   454       }
   454       }
   455     }
   455     }
   456 
   456 
   457     /// \brief Executes the algorithm
   457     /// \brief Executes the algorithm
   458     ///
   458     ///
   459     /// Executes the algorithm by performing augmenting phases until the
   459     /// Executes the algorithm by performing augmenting phases until the
   460     /// optimal solution is reached. 
   460     /// optimal solution is reached.
   461     /// \pre One of the \ref init() functions must be called before
   461     /// \pre One of the \ref init() functions must be called before
   462     /// using this function.
   462     /// using this function.
   463     void start() {
   463     void start() {
   464       while (augment()) {}
   464       while (augment()) {}
   465     }
   465     }
   466 
   466 
   467     /// \brief Runs the algorithm.
   467     /// \brief Runs the algorithm.
   468     /// 
   468     ///
   469     /// Runs the Edmonds-Karp algorithm.
   469     /// Runs the Edmonds-Karp algorithm.
   470     /// \note ek.run() is just a shortcut of the following code.
   470     /// \note ek.run() is just a shortcut of the following code.
   471     ///\code 
   471     ///\code
   472     /// ek.init();
   472     /// ek.init();
   473     /// ek.start();
   473     /// ek.start();
   474     ///\endcode
   474     ///\endcode
   475     void run() {
   475     void run() {
   476       init();
   476       init();
   481 
   481 
   482     /// \name Query Functions
   482     /// \name Query Functions
   483     /// The result of the Edmonds-Karp algorithm can be obtained using these
   483     /// The result of the Edmonds-Karp algorithm can be obtained using these
   484     /// functions.\n
   484     /// functions.\n
   485     /// Either \ref run() or \ref start() should be called before using them.
   485     /// Either \ref run() or \ref start() should be called before using them.
   486     
   486 
   487     ///@{
   487     ///@{
   488 
   488 
   489     /// \brief Returns the value of the maximum flow.
   489     /// \brief Returns the value of the maximum flow.
   490     ///
   490     ///
   491     /// Returns the value of the maximum flow found by the algorithm.
   491     /// Returns the value of the maximum flow found by the algorithm.
   540     /// \pre Either \ref run() or \ref init() must be called before
   540     /// \pre Either \ref run() or \ref init() must be called before
   541     /// using this function.
   541     /// using this function.
   542     template <typename CutMap>
   542     template <typename CutMap>
   543     void minCutMap(CutMap& cutMap) const {
   543     void minCutMap(CutMap& cutMap) const {
   544       for (NodeIt n(_graph); n != INVALID; ++n) {
   544       for (NodeIt n(_graph); n != INVALID; ++n) {
   545 	cutMap.set(n, (*_pred)[n] != INVALID);
   545         cutMap.set(n, (*_pred)[n] != INVALID);
   546       }
   546       }
   547       cutMap.set(_source, true);
   547       cutMap.set(_source, true);
   548     }    
   548     }
   549 
   549 
   550     /// @}
   550     /// @}
   551 
   551 
   552   };
   552   };
   553 
   553