lemon/min_cost_arborescence.h
author Peter Kovacs <kpeter@inf.elte.hu>
Mon, 23 Mar 2009 23:54:42 +0100
changeset 603 425cc8328c0e
child 559 c5fd2d996909
permissions -rw-r--r--
Internal restructuring and renamings in NetworkSimplex (#234)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2008
     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_MIN_COST_ARBORESCENCE_H
    20 #define LEMON_MIN_COST_ARBORESCENCE_H
    21 
    22 ///\ingroup spantree
    23 ///\file
    24 ///\brief Minimum Cost Arborescence algorithm.
    25 
    26 #include <vector>
    27 
    28 #include <lemon/list_graph.h>
    29 #include <lemon/bin_heap.h>
    30 #include <lemon/assert.h>
    31 
    32 namespace lemon {
    33 
    34 
    35   /// \brief Default traits class for MinCostArborescence class.
    36   ///
    37   /// Default traits class for MinCostArborescence class.
    38   /// \param _Digraph Digraph type.
    39   /// \param _CostMap Type of cost map.
    40   template <class _Digraph, class _CostMap>
    41   struct MinCostArborescenceDefaultTraits{
    42 
    43     /// \brief The digraph type the algorithm runs on.
    44     typedef _Digraph Digraph;
    45 
    46     /// \brief The type of the map that stores the arc costs.
    47     ///
    48     /// The type of the map that stores the arc costs.
    49     /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
    50     typedef _CostMap CostMap;
    51 
    52     /// \brief The value type of the costs.
    53     ///
    54     /// The value type of the costs.
    55     typedef typename CostMap::Value Value;
    56 
    57     /// \brief The type of the map that stores which arcs are in the
    58     /// arborescence.
    59     ///
    60     /// The type of the map that stores which arcs are in the
    61     /// arborescence.  It must meet the \ref concepts::WriteMap
    62     /// "WriteMap" concept.  Initially it will be set to false on each
    63     /// arc. After it will set all arborescence arcs once.
    64     typedef typename Digraph::template ArcMap<bool> ArborescenceMap;
    65 
    66     /// \brief Instantiates a ArborescenceMap.
    67     ///
    68     /// This function instantiates a \ref ArborescenceMap.
    69     /// \param digraph is the graph, to which we would like to
    70     /// calculate the ArborescenceMap.
    71     static ArborescenceMap *createArborescenceMap(const Digraph &digraph){
    72       return new ArborescenceMap(digraph);
    73     }
    74 
    75     /// \brief The type of the PredMap
    76     ///
    77     /// The type of the PredMap. It is a node map with an arc value type.
    78     typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
    79 
    80     /// \brief Instantiates a PredMap.
    81     ///
    82     /// This function instantiates a \ref PredMap.
    83     /// \param _digraph is the digraph, to which we would like to define the
    84     /// PredMap.
    85     static PredMap *createPredMap(const Digraph &digraph){
    86       return new PredMap(digraph);
    87     }
    88 
    89   };
    90 
    91   /// \ingroup spantree
    92   ///
    93   /// \brief %MinCostArborescence algorithm class.
    94   ///
    95   /// This class provides an efficient implementation of
    96   /// %MinCostArborescence algorithm. The arborescence is a tree
    97   /// which is directed from a given source node of the digraph. One or
    98   /// more sources should be given for the algorithm and it will calculate
    99   /// the minimum cost subgraph which are union of arborescences with the
   100   /// given sources and spans all the nodes which are reachable from the
   101   /// sources. The time complexity of the algorithm is \f$ O(n^2+e) \f$.
   102   ///
   103   /// The algorithm provides also an optimal dual solution, therefore
   104   /// the optimality of the solution can be checked.
   105   ///
   106   /// \param _Digraph The digraph type the algorithm runs on. The default value
   107   /// is \ref ListDigraph.
   108   /// \param _CostMap This read-only ArcMap determines the costs of the
   109   /// arcs. It is read once for each arc, so the map may involve in
   110   /// relatively time consuming process to compute the arc cost if
   111   /// it is necessary. The default map type is \ref
   112   /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>".
   113   /// \param _Traits Traits class to set various data types used
   114   /// by the algorithm. The default traits class is
   115   /// \ref MinCostArborescenceDefaultTraits
   116   /// "MinCostArborescenceDefaultTraits<_Digraph, _CostMap>".  See \ref
   117   /// MinCostArborescenceDefaultTraits for the documentation of a
   118   /// MinCostArborescence traits class.
   119   ///
   120   /// \author Balazs Dezso
   121 #ifndef DOXYGEN
   122   template <typename _Digraph = ListDigraph,
   123             typename _CostMap = typename _Digraph::template ArcMap<int>,
   124             typename _Traits =
   125             MinCostArborescenceDefaultTraits<_Digraph, _CostMap> >
   126 #else
   127   template <typename _Digraph, typename _CostMap, typedef _Traits>
   128 #endif
   129   class MinCostArborescence {
   130   public:
   131 
   132     /// The traits.
   133     typedef _Traits Traits;
   134     /// The type of the underlying digraph.
   135     typedef typename Traits::Digraph Digraph;
   136     /// The type of the map that stores the arc costs.
   137     typedef typename Traits::CostMap CostMap;
   138     ///The type of the costs of the arcs.
   139     typedef typename Traits::Value Value;
   140     ///The type of the predecessor map.
   141     typedef typename Traits::PredMap PredMap;
   142     ///The type of the map that stores which arcs are in the arborescence.
   143     typedef typename Traits::ArborescenceMap ArborescenceMap;
   144 
   145     typedef MinCostArborescence Create;
   146 
   147   private:
   148 
   149     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
   150 
   151     struct CostArc {
   152 
   153       Arc arc;
   154       Value value;
   155 
   156       CostArc() {}
   157       CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {}
   158 
   159     };
   160 
   161     const Digraph *_digraph;
   162     const CostMap *_cost;
   163 
   164     PredMap *_pred;
   165     bool local_pred;
   166 
   167     ArborescenceMap *_arborescence;
   168     bool local_arborescence;
   169 
   170     typedef typename Digraph::template ArcMap<int> ArcOrder;
   171     ArcOrder *_arc_order;
   172 
   173     typedef typename Digraph::template NodeMap<int> NodeOrder;
   174     NodeOrder *_node_order;
   175 
   176     typedef typename Digraph::template NodeMap<CostArc> CostArcMap;
   177     CostArcMap *_cost_arcs;
   178 
   179     struct StackLevel {
   180 
   181       std::vector<CostArc> arcs;
   182       int node_level;
   183 
   184     };
   185 
   186     std::vector<StackLevel> level_stack;
   187     std::vector<Node> queue;
   188 
   189     typedef std::vector<typename Digraph::Node> DualNodeList;
   190 
   191     DualNodeList _dual_node_list;
   192 
   193     struct DualVariable {
   194       int begin, end;
   195       Value value;
   196 
   197       DualVariable(int _begin, int _end, Value _value)
   198         : begin(_begin), end(_end), value(_value) {}
   199 
   200     };
   201 
   202     typedef std::vector<DualVariable> DualVariables;
   203 
   204     DualVariables _dual_variables;
   205 
   206     typedef typename Digraph::template NodeMap<int> HeapCrossRef;
   207 
   208     HeapCrossRef *_heap_cross_ref;
   209 
   210     typedef BinHeap<int, HeapCrossRef> Heap;
   211 
   212     Heap *_heap;
   213 
   214   protected:
   215 
   216     MinCostArborescence() {}
   217 
   218   private:
   219 
   220     void createStructures() {
   221       if (!_pred) {
   222         local_pred = true;
   223         _pred = Traits::createPredMap(*_digraph);
   224       }
   225       if (!_arborescence) {
   226         local_arborescence = true;
   227         _arborescence = Traits::createArborescenceMap(*_digraph);
   228       }
   229       if (!_arc_order) {
   230         _arc_order = new ArcOrder(*_digraph);
   231       }
   232       if (!_node_order) {
   233         _node_order = new NodeOrder(*_digraph);
   234       }
   235       if (!_cost_arcs) {
   236         _cost_arcs = new CostArcMap(*_digraph);
   237       }
   238       if (!_heap_cross_ref) {
   239         _heap_cross_ref = new HeapCrossRef(*_digraph, -1);
   240       }
   241       if (!_heap) {
   242         _heap = new Heap(*_heap_cross_ref);
   243       }
   244     }
   245 
   246     void destroyStructures() {
   247       if (local_arborescence) {
   248         delete _arborescence;
   249       }
   250       if (local_pred) {
   251         delete _pred;
   252       }
   253       if (_arc_order) {
   254         delete _arc_order;
   255       }
   256       if (_node_order) {
   257         delete _node_order;
   258       }
   259       if (_cost_arcs) {
   260         delete _cost_arcs;
   261       }
   262       if (_heap) {
   263         delete _heap;
   264       }
   265       if (_heap_cross_ref) {
   266         delete _heap_cross_ref;
   267       }
   268     }
   269 
   270     Arc prepare(Node node) {
   271       std::vector<Node> nodes;
   272       (*_node_order)[node] = _dual_node_list.size();
   273       StackLevel level;
   274       level.node_level = _dual_node_list.size();
   275       _dual_node_list.push_back(node);
   276       for (InArcIt it(*_digraph, node); it != INVALID; ++it) {
   277         Arc arc = it;
   278         Node source = _digraph->source(arc);
   279         Value value = (*_cost)[it];
   280         if (source == node || (*_node_order)[source] == -3) continue;
   281         if ((*_cost_arcs)[source].arc == INVALID) {
   282           (*_cost_arcs)[source].arc = arc;
   283           (*_cost_arcs)[source].value = value;
   284           nodes.push_back(source);
   285         } else {
   286           if ((*_cost_arcs)[source].value > value) {
   287             (*_cost_arcs)[source].arc = arc;
   288             (*_cost_arcs)[source].value = value;
   289           }
   290         }
   291       }
   292       CostArc minimum = (*_cost_arcs)[nodes[0]];
   293       for (int i = 1; i < int(nodes.size()); ++i) {
   294         if ((*_cost_arcs)[nodes[i]].value < minimum.value) {
   295           minimum = (*_cost_arcs)[nodes[i]];
   296         }
   297       }
   298       _arc_order->set(minimum.arc, _dual_variables.size());
   299       DualVariable var(_dual_node_list.size() - 1,
   300                        _dual_node_list.size(), minimum.value);
   301       _dual_variables.push_back(var);
   302       for (int i = 0; i < int(nodes.size()); ++i) {
   303         (*_cost_arcs)[nodes[i]].value -= minimum.value;
   304         level.arcs.push_back((*_cost_arcs)[nodes[i]]);
   305         (*_cost_arcs)[nodes[i]].arc = INVALID;
   306       }
   307       level_stack.push_back(level);
   308       return minimum.arc;
   309     }
   310 
   311     Arc contract(Node node) {
   312       int node_bottom = bottom(node);
   313       std::vector<Node> nodes;
   314       while (!level_stack.empty() &&
   315              level_stack.back().node_level >= node_bottom) {
   316         for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) {
   317           Arc arc = level_stack.back().arcs[i].arc;
   318           Node source = _digraph->source(arc);
   319           Value value = level_stack.back().arcs[i].value;
   320           if ((*_node_order)[source] >= node_bottom) continue;
   321           if ((*_cost_arcs)[source].arc == INVALID) {
   322             (*_cost_arcs)[source].arc = arc;
   323             (*_cost_arcs)[source].value = value;
   324             nodes.push_back(source);
   325           } else {
   326             if ((*_cost_arcs)[source].value > value) {
   327               (*_cost_arcs)[source].arc = arc;
   328               (*_cost_arcs)[source].value = value;
   329             }
   330           }
   331         }
   332         level_stack.pop_back();
   333       }
   334       CostArc minimum = (*_cost_arcs)[nodes[0]];
   335       for (int i = 1; i < int(nodes.size()); ++i) {
   336         if ((*_cost_arcs)[nodes[i]].value < minimum.value) {
   337           minimum = (*_cost_arcs)[nodes[i]];
   338         }
   339       }
   340       _arc_order->set(minimum.arc, _dual_variables.size());
   341       DualVariable var(node_bottom, _dual_node_list.size(), minimum.value);
   342       _dual_variables.push_back(var);
   343       StackLevel level;
   344       level.node_level = node_bottom;
   345       for (int i = 0; i < int(nodes.size()); ++i) {
   346         (*_cost_arcs)[nodes[i]].value -= minimum.value;
   347         level.arcs.push_back((*_cost_arcs)[nodes[i]]);
   348         (*_cost_arcs)[nodes[i]].arc = INVALID;
   349       }
   350       level_stack.push_back(level);
   351       return minimum.arc;
   352     }
   353 
   354     int bottom(Node node) {
   355       int k = level_stack.size() - 1;
   356       while (level_stack[k].node_level > (*_node_order)[node]) {
   357         --k;
   358       }
   359       return level_stack[k].node_level;
   360     }
   361 
   362     void finalize(Arc arc) {
   363       Node node = _digraph->target(arc);
   364       _heap->push(node, (*_arc_order)[arc]);
   365       _pred->set(node, arc);
   366       while (!_heap->empty()) {
   367         Node source = _heap->top();
   368         _heap->pop();
   369         _node_order->set(source, -1);
   370         for (OutArcIt it(*_digraph, source); it != INVALID; ++it) {
   371           if ((*_arc_order)[it] < 0) continue;
   372           Node target = _digraph->target(it);
   373           switch(_heap->state(target)) {
   374           case Heap::PRE_HEAP:
   375             _heap->push(target, (*_arc_order)[it]);
   376             _pred->set(target, it);
   377             break;
   378           case Heap::IN_HEAP:
   379             if ((*_arc_order)[it] < (*_heap)[target]) {
   380               _heap->decrease(target, (*_arc_order)[it]);
   381               _pred->set(target, it);
   382             }
   383             break;
   384           case Heap::POST_HEAP:
   385             break;
   386           }
   387         }
   388         _arborescence->set((*_pred)[source], true);
   389       }
   390     }
   391 
   392 
   393   public:
   394 
   395     /// \name Named template parameters
   396 
   397     /// @{
   398 
   399     template <class T>
   400     struct DefArborescenceMapTraits : public Traits {
   401       typedef T ArborescenceMap;
   402       static ArborescenceMap *createArborescenceMap(const Digraph &)
   403       {
   404         LEMON_ASSERT(false, "ArborescenceMap is not initialized");
   405         return 0; // ignore warnings
   406       }
   407     };
   408 
   409     /// \brief \ref named-templ-param "Named parameter" for
   410     /// setting ArborescenceMap type
   411     ///
   412     /// \ref named-templ-param "Named parameter" for setting
   413     /// ArborescenceMap type
   414     template <class T>
   415     struct DefArborescenceMap
   416       : public MinCostArborescence<Digraph, CostMap,
   417                                    DefArborescenceMapTraits<T> > {
   418     };
   419 
   420     template <class T>
   421     struct DefPredMapTraits : public Traits {
   422       typedef T PredMap;
   423       static PredMap *createPredMap(const Digraph &)
   424       {
   425         LEMON_ASSERT(false, "PredMap is not initialized");
   426       }
   427     };
   428 
   429     /// \brief \ref named-templ-param "Named parameter" for
   430     /// setting PredMap type
   431     ///
   432     /// \ref named-templ-param "Named parameter" for setting
   433     /// PredMap type
   434     template <class T>
   435     struct DefPredMap
   436       : public MinCostArborescence<Digraph, CostMap, DefPredMapTraits<T> > {
   437     };
   438 
   439     /// @}
   440 
   441     /// \brief Constructor.
   442     ///
   443     /// \param _digraph The digraph the algorithm will run on.
   444     /// \param _cost The cost map used by the algorithm.
   445     MinCostArborescence(const Digraph& digraph, const CostMap& cost)
   446       : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false),
   447         _arborescence(0), local_arborescence(false),
   448         _arc_order(0), _node_order(0), _cost_arcs(0),
   449         _heap_cross_ref(0), _heap(0) {}
   450 
   451     /// \brief Destructor.
   452     ~MinCostArborescence() {
   453       destroyStructures();
   454     }
   455 
   456     /// \brief Sets the arborescence map.
   457     ///
   458     /// Sets the arborescence map.
   459     /// \return \c (*this)
   460     MinCostArborescence& arborescenceMap(ArborescenceMap& m) {
   461       if (local_arborescence) {
   462         delete _arborescence;
   463       }
   464       local_arborescence = false;
   465       _arborescence = &m;
   466       return *this;
   467     }
   468 
   469     /// \brief Sets the arborescence map.
   470     ///
   471     /// Sets the arborescence map.
   472     /// \return \c (*this)
   473     MinCostArborescence& predMap(PredMap& m) {
   474       if (local_pred) {
   475         delete _pred;
   476       }
   477       local_pred = false;
   478       _pred = &m;
   479       return *this;
   480     }
   481 
   482     /// \name Query Functions
   483     /// The result of the %MinCostArborescence algorithm can be obtained
   484     /// using these functions.\n
   485     /// Before the use of these functions,
   486     /// either run() or start() must be called.
   487 
   488     /// @{
   489 
   490     /// \brief Returns a reference to the arborescence map.
   491     ///
   492     /// Returns a reference to the arborescence map.
   493     const ArborescenceMap& arborescenceMap() const {
   494       return *_arborescence;
   495     }
   496 
   497     /// \brief Returns true if the arc is in the arborescence.
   498     ///
   499     /// Returns true if the arc is in the arborescence.
   500     /// \param arc The arc of the digraph.
   501     /// \pre \ref run() must be called before using this function.
   502     bool arborescence(Arc arc) const {
   503       return (*_pred)[_digraph->target(arc)] == arc;
   504     }
   505 
   506     /// \brief Returns a reference to the pred map.
   507     ///
   508     /// Returns a reference to the pred map.
   509     const PredMap& predMap() const {
   510       return *_pred;
   511     }
   512 
   513     /// \brief Returns the predecessor arc of the given node.
   514     ///
   515     /// Returns the predecessor arc of the given node.
   516     Arc pred(Node node) const {
   517       return (*_pred)[node];
   518     }
   519 
   520     /// \brief Returns the cost of the arborescence.
   521     ///
   522     /// Returns the cost of the arborescence.
   523     Value arborescenceValue() const {
   524       Value sum = 0;
   525       for (ArcIt it(*_digraph); it != INVALID; ++it) {
   526         if (arborescence(it)) {
   527           sum += (*_cost)[it];
   528         }
   529       }
   530       return sum;
   531     }
   532 
   533     /// \brief Indicates that a node is reachable from the sources.
   534     ///
   535     /// Indicates that a node is reachable from the sources.
   536     bool reached(Node node) const {
   537       return (*_node_order)[node] != -3;
   538     }
   539 
   540     /// \brief Indicates that a node is processed.
   541     ///
   542     /// Indicates that a node is processed. The arborescence path exists
   543     /// from the source to the given node.
   544     bool processed(Node node) const {
   545       return (*_node_order)[node] == -1;
   546     }
   547 
   548     /// \brief Returns the number of the dual variables in basis.
   549     ///
   550     /// Returns the number of the dual variables in basis.
   551     int dualNum() const {
   552       return _dual_variables.size();
   553     }
   554 
   555     /// \brief Returns the value of the dual solution.
   556     ///
   557     /// Returns the value of the dual solution. It should be
   558     /// equal to the arborescence value.
   559     Value dualValue() const {
   560       Value sum = 0;
   561       for (int i = 0; i < int(_dual_variables.size()); ++i) {
   562         sum += _dual_variables[i].value;
   563       }
   564       return sum;
   565     }
   566 
   567     /// \brief Returns the number of the nodes in the dual variable.
   568     ///
   569     /// Returns the number of the nodes in the dual variable.
   570     int dualSize(int k) const {
   571       return _dual_variables[k].end - _dual_variables[k].begin;
   572     }
   573 
   574     /// \brief Returns the value of the dual variable.
   575     ///
   576     /// Returns the the value of the dual variable.
   577     const Value& dualValue(int k) const {
   578       return _dual_variables[k].value;
   579     }
   580 
   581     /// \brief Lemon iterator for get a dual variable.
   582     ///
   583     /// Lemon iterator for get a dual variable. This class provides
   584     /// a common style lemon iterator which gives back a subset of
   585     /// the nodes.
   586     class DualIt {
   587     public:
   588 
   589       /// \brief Constructor.
   590       ///
   591       /// Constructor for get the nodeset of the variable.
   592       DualIt(const MinCostArborescence& algorithm, int variable)
   593         : _algorithm(&algorithm)
   594       {
   595         _index = _algorithm->_dual_variables[variable].begin;
   596         _last = _algorithm->_dual_variables[variable].end;
   597       }
   598 
   599       /// \brief Conversion to node.
   600       ///
   601       /// Conversion to node.
   602       operator Node() const {
   603         return _algorithm->_dual_node_list[_index];
   604       }
   605 
   606       /// \brief Increment operator.
   607       ///
   608       /// Increment operator.
   609       DualIt& operator++() {
   610         ++_index;
   611         return *this;
   612       }
   613 
   614       /// \brief Validity checking
   615       ///
   616       /// Checks whether the iterator is invalid.
   617       bool operator==(Invalid) const {
   618         return _index == _last;
   619       }
   620 
   621       /// \brief Validity checking
   622       ///
   623       /// Checks whether the iterator is valid.
   624       bool operator!=(Invalid) const {
   625         return _index != _last;
   626       }
   627 
   628     private:
   629       const MinCostArborescence* _algorithm;
   630       int _index, _last;
   631     };
   632 
   633     /// @}
   634 
   635     /// \name Execution control
   636     /// The simplest way to execute the algorithm is to use
   637     /// one of the member functions called \c run(...). \n
   638     /// If you need more control on the execution,
   639     /// first you must call \ref init(), then you can add several
   640     /// source nodes with \ref addSource().
   641     /// Finally \ref start() will perform the arborescence
   642     /// computation.
   643 
   644     ///@{
   645 
   646     /// \brief Initializes the internal data structures.
   647     ///
   648     /// Initializes the internal data structures.
   649     ///
   650     void init() {
   651       createStructures();
   652       _heap->clear();
   653       for (NodeIt it(*_digraph); it != INVALID; ++it) {
   654         (*_cost_arcs)[it].arc = INVALID;
   655         _node_order->set(it, -3);
   656         _heap_cross_ref->set(it, Heap::PRE_HEAP);
   657         _pred->set(it, INVALID);
   658       }
   659       for (ArcIt it(*_digraph); it != INVALID; ++it) {
   660         _arborescence->set(it, false);
   661         _arc_order->set(it, -1);
   662       }
   663       _dual_node_list.clear();
   664       _dual_variables.clear();
   665     }
   666 
   667     /// \brief Adds a new source node.
   668     ///
   669     /// Adds a new source node to the algorithm.
   670     void addSource(Node source) {
   671       std::vector<Node> nodes;
   672       nodes.push_back(source);
   673       while (!nodes.empty()) {
   674         Node node = nodes.back();
   675         nodes.pop_back();
   676         for (OutArcIt it(*_digraph, node); it != INVALID; ++it) {
   677           Node target = _digraph->target(it);
   678           if ((*_node_order)[target] == -3) {
   679             (*_node_order)[target] = -2;
   680             nodes.push_back(target);
   681             queue.push_back(target);
   682           }
   683         }
   684       }
   685       (*_node_order)[source] = -1;
   686     }
   687 
   688     /// \brief Processes the next node in the priority queue.
   689     ///
   690     /// Processes the next node in the priority queue.
   691     ///
   692     /// \return The processed node.
   693     ///
   694     /// \warning The queue must not be empty!
   695     Node processNextNode() {
   696       Node node = queue.back();
   697       queue.pop_back();
   698       if ((*_node_order)[node] == -2) {
   699         Arc arc = prepare(node);
   700         Node source = _digraph->source(arc);
   701         while ((*_node_order)[source] != -1) {
   702           if ((*_node_order)[source] >= 0) {
   703             arc = contract(source);
   704           } else {
   705             arc = prepare(source);
   706           }
   707           source = _digraph->source(arc);
   708         }
   709         finalize(arc);
   710         level_stack.clear();
   711       }
   712       return node;
   713     }
   714 
   715     /// \brief Returns the number of the nodes to be processed.
   716     ///
   717     /// Returns the number of the nodes to be processed.
   718     int queueSize() const {
   719       return queue.size();
   720     }
   721 
   722     /// \brief Returns \c false if there are nodes to be processed.
   723     ///
   724     /// Returns \c false if there are nodes to be processed.
   725     bool emptyQueue() const {
   726       return queue.empty();
   727     }
   728 
   729     /// \brief Executes the algorithm.
   730     ///
   731     /// Executes the algorithm.
   732     ///
   733     /// \pre init() must be called and at least one node should be added
   734     /// with addSource() before using this function.
   735     ///
   736     ///\note mca.start() is just a shortcut of the following code.
   737     ///\code
   738     ///while (!mca.emptyQueue()) {
   739     ///  mca.processNextNode();
   740     ///}
   741     ///\endcode
   742     void start() {
   743       while (!emptyQueue()) {
   744         processNextNode();
   745       }
   746     }
   747 
   748     /// \brief Runs %MinCostArborescence algorithm from node \c s.
   749     ///
   750     /// This method runs the %MinCostArborescence algorithm from
   751     /// a root node \c s.
   752     ///
   753     /// \note mca.run(s) is just a shortcut of the following code.
   754     /// \code
   755     /// mca.init();
   756     /// mca.addSource(s);
   757     /// mca.start();
   758     /// \endcode
   759     void run(Node node) {
   760       init();
   761       addSource(node);
   762       start();
   763     }
   764 
   765     ///@}
   766 
   767   };
   768 
   769   /// \ingroup spantree
   770   ///
   771   /// \brief Function type interface for MinCostArborescence algorithm.
   772   ///
   773   /// Function type interface for MinCostArborescence algorithm.
   774   /// \param digraph The Digraph that the algorithm runs on.
   775   /// \param cost The CostMap of the arcs.
   776   /// \param source The source of the arborescence.
   777   /// \retval arborescence The bool ArcMap which stores the arborescence.
   778   /// \return The cost of the arborescence.
   779   ///
   780   /// \sa MinCostArborescence
   781   template <typename Digraph, typename CostMap, typename ArborescenceMap>
   782   typename CostMap::Value minCostArborescence(const Digraph& digraph,
   783                                               const CostMap& cost,
   784                                               typename Digraph::Node source,
   785                                               ArborescenceMap& arborescence) {
   786     typename MinCostArborescence<Digraph, CostMap>
   787       ::template DefArborescenceMap<ArborescenceMap>
   788       ::Create mca(digraph, cost);
   789     mca.arborescenceMap(arborescence);
   790     mca.run(source);
   791     return mca.arborescenceValue();
   792   }
   793 
   794 }
   795 
   796 #endif