deba@2017: /* -*- C++ -*-
deba@2017:  *
deba@2017:  * This file is a part of LEMON, a generic C++ optimization library
deba@2017:  *
deba@2017:  * Copyright (C) 2003-2006
deba@2017:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2017:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2017:  *
deba@2017:  * Permission to use, modify and distribute this software is granted
deba@2017:  * provided that this copyright notice appears in all copies. For
deba@2017:  * precise terms see the accompanying LICENSE file.
deba@2017:  *
deba@2017:  * This software is provided "AS IS" with no warranty of any kind,
deba@2017:  * express or implied, and with no claim as to its suitability for any
deba@2017:  * purpose.
deba@2017:  *
deba@2017:  */
deba@2017: 
deba@2017: #ifndef LEMON_MIN_COST_ARBORESCENCE_H
deba@2017: #define LEMON_MIN_COST_ARBORESCENCE_H
deba@2017: 
deba@2017: ///\ingroup spantree
deba@2017: ///\file
deba@2017: ///\brief Minimum Cost Arborescence algorithm.
deba@2017: 
deba@2017: #include <vector>
deba@2017: 
deba@2017: #include <lemon/list_graph.h>
deba@2017: 
deba@2017: namespace lemon {
deba@2017: 
deba@2017: 
deba@2017:   /// \brief Default traits class of MinCostArborescence class.
deba@2017:   /// 
deba@2017:   /// Default traits class of MinCostArborescence class.
deba@2017:   /// \param _Graph Graph type.
deba@2017:   /// \param _CostMap Type of cost map.
deba@2017:   template <class _Graph, class _CostMap>
deba@2017:   struct MinCostArborescenceDefaultTraits{
deba@2017: 
deba@2017:     /// \brief The graph type the algorithm runs on. 
deba@2017:     typedef _Graph Graph;
deba@2017: 
deba@2017:     /// \brief The type of the map that stores the edge costs.
deba@2017:     ///
deba@2017:     /// The type of the map that stores the edge costs.
deba@2017:     /// It must meet the \ref concept::ReadMap "ReadMap" concept.
deba@2017:     typedef _CostMap CostMap;
deba@2017: 
deba@2017:     /// \brief The value type of the costs.
deba@2017:     ///
deba@2017:     /// The value type of the costs.
deba@2017:     typedef typename CostMap::Value Value;
deba@2017: 
deba@2017:     /// \brief The type of the map that stores which edges are 
deba@2017:     /// in the arborescence.
deba@2017:     ///
deba@2017:     /// The type of the map that stores which edges are in the arborescence.
deba@2017:     /// It must meet the \ref concept::ReadWriteMap "ReadWriteMap" concept.
deba@2017:     /// Initially it will be setted to false on each edge. The algorithm
deba@2017:     /// may set each value one time to true and maybe after it to false again.
deba@2017:     /// Therefore you cannot use maps like BackInserteBoolMap with this
deba@2017:     /// algorithm.   
deba@2017:     typedef typename Graph::template EdgeMap<bool> ArborescenceMap; 
deba@2017: 
deba@2017:     /// \brief Instantiates a ArborescenceMap.
deba@2017:     ///
deba@2017:     /// This function instantiates a \ref ArborescenceMap. 
deba@2017:     /// \param _graph is the graph, to which we would like to define the 
deba@2017:     /// ArborescenceMap.
deba@2017:     static ArborescenceMap *createArborescenceMap(const Graph &_graph){
deba@2017:       return new ArborescenceMap(_graph);
deba@2017:     }
deba@2017: 
deba@2017:   };
deba@2017: 
deba@2017:   /// \ingroup spantree
deba@2017:   ///
deba@2017:   /// \brief %MinCostArborescence algorithm class.
deba@2017:   ///
deba@2017:   /// This class provides an efficient implementation of 
deba@2017:   /// %MinCostArborescence algorithm. The arborescence is a tree 
deba@2017:   /// which is directed from a given source node of the graph. One or
deba@2017:   /// more sources should be given for the algorithm and it will calculate
deba@2017:   /// the minimum cost subgraph which are union of arborescences with the
deba@2017:   /// given sources and spans all the nodes which are reachable from the
deba@2017:   /// sources. The time complexity of the algorithm is O(n^2 + e).
deba@2017:   ///
deba@2017:   /// \param _Graph The graph type the algorithm runs on. The default value
deba@2017:   /// is \ref ListGraph. The value of _Graph is not used directly by
deba@2017:   /// MinCostArborescence, it is only passed to 
deba@2017:   /// \ref MinCostArborescenceDefaultTraits.
deba@2017:   /// \param _CostMap This read-only EdgeMap determines the costs of the
deba@2017:   /// edges. It is read once for each edge, so the map may involve in
deba@2017:   /// relatively time consuming process to compute the edge cost if
deba@2017:   /// it is necessary. The default map type is \ref
deba@2017:   /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
deba@2017:   /// of _CostMap is not used directly by MinCostArborescence, 
deba@2017:   /// it is only passed to \ref MinCostArborescenceDefaultTraits.  
deba@2017:   /// \param _Traits Traits class to set various data types used 
deba@2017:   /// by the algorithm.  The default traits class is 
deba@2017:   /// \ref MinCostArborescenceDefaultTraits
deba@2017:   /// "MinCostArborescenceDefaultTraits<_Graph,_CostMap>".  See \ref
deba@2017:   /// MinCostArborescenceDefaultTraits for the documentation of a 
deba@2017:   /// MinCostArborescence traits class.
deba@2017:   ///
deba@2017:   /// \author Balazs Dezso
deba@2017: #ifndef DOXYGEN
deba@2017:   template <typename _Graph = ListGraph, 
deba@2017:             typename _CostMap = typename _Graph::template EdgeMap<int>,
deba@2017:             typename _Traits = 
deba@2017:             MinCostArborescenceDefaultTraits<_Graph, _CostMap> >
deba@2017: #else 
deba@2017:   template <typename _Graph, typename _CostMap, typedef _Traits>
deba@2017: #endif
deba@2017:   class MinCostArborescence {
deba@2017:   public:
deba@2017: 
deba@2017:     /// \brief \ref Exception for uninitialized parameters.
deba@2017:     ///
deba@2017:     /// This error represents problems in the initialization
deba@2017:     /// of the parameters of the algorithms.    
deba@2017:     class UninitializedParameter : public lemon::UninitializedParameter {
deba@2017:     public:
deba@2017:       virtual const char* exceptionName() const {
deba@2017: 	return "lemon::MinCostArborescence::UninitializedParameter";
deba@2017:       }
deba@2017:     };
deba@2017: 
deba@2017:     /// The traits.
deba@2017:     typedef _Traits Traits;
deba@2017:     /// The type of the underlying graph.
deba@2017:     typedef typename Traits::Graph Graph;
deba@2017:     /// The type of the map that stores the edge costs.
deba@2017:     typedef typename Traits::CostMap CostMap;
deba@2017:     ///The type of the costs of the edges.
deba@2017:     typedef typename Traits::Value Value;
deba@2017:     ///The type of the map that stores which edges are in the arborescence.
deba@2017:     typedef typename Traits::ArborescenceMap ArborescenceMap;
deba@2017: 
deba@2017:   protected:
deba@2017: 
deba@2017:     typedef typename Graph::Node Node;
deba@2017:     typedef typename Graph::Edge Edge;
deba@2017:     typedef typename Graph::NodeIt NodeIt;
deba@2017:     typedef typename Graph::EdgeIt EdgeIt;
deba@2017:     typedef typename Graph::InEdgeIt InEdgeIt;
deba@2017:     typedef typename Graph::OutEdgeIt OutEdgeIt;
deba@2017: 
deba@2017:     struct CostEdge {
deba@2017: 
deba@2017:       Edge edge;
deba@2017:       Value value;
deba@2017: 
deba@2017:       CostEdge() {}
deba@2017:       CostEdge(Edge _edge, Value _value) : edge(_edge), value(_value) {}
deba@2017: 
deba@2017:     };
deba@2017: 
deba@2017:     const Graph* graph;
deba@2017:     const CostMap* cost;
deba@2017: 
deba@2017:     ArborescenceMap* _arborescence_map;
deba@2017:     bool local_arborescence_map;
deba@2017: 
deba@2017:     typedef typename Graph::template NodeMap<int> LevelMap;
deba@2017:     LevelMap *_level;
deba@2017: 
deba@2017:     typedef typename Graph::template NodeMap<CostEdge> CostEdgeMap;
deba@2017:     CostEdgeMap *_cost_edges; 
deba@2017: 
deba@2017:     struct StackLevel {
deba@2017: 
deba@2017:       std::vector<CostEdge> edges;
deba@2017:       int node_level;
deba@2017: 
deba@2017:     };
deba@2017: 
deba@2017:     std::vector<StackLevel> level_stack;    
deba@2017:     std::vector<Node> queue;
deba@2017: 
deba@2017:     int node_counter;
deba@2017: 
deba@2017:   public:
deba@2017: 
deba@2017:     /// \name Named template parameters
deba@2017: 
deba@2017:     /// @{
deba@2017: 
deba@2017:     template <class T>
deba@2017:     struct DefArborescenceMapTraits : public Traits {
deba@2017:       typedef T ArborescenceMap;
deba@2017:       static ArborescenceMap *createArborescenceMap(const Graph &)
deba@2017:       {
deba@2017: 	throw UninitializedParameter();
deba@2017:       }
deba@2017:     };
deba@2017: 
deba@2017:     /// \brief \ref named-templ-param "Named parameter" for 
deba@2017:     /// setting ArborescenceMap type
deba@2017:     ///
deba@2017:     /// \ref named-templ-param "Named parameter" for setting 
deba@2017:     /// ArborescenceMap type
deba@2017:     template <class T>
deba@2017:     struct DefArborescenceMap 
deba@2017:       : public MinCostArborescence<Graph, CostMap,
deba@2017:                                    DefArborescenceMapTraits<T> > {
deba@2017:       typedef MinCostArborescence<Graph, CostMap, 
deba@2017:                                    DefArborescenceMapTraits<T> > Create;
deba@2017:     };
deba@2017:     
deba@2017:     /// @}
deba@2017: 
deba@2017:     /// \brief Constructor.
deba@2017:     ///
deba@2017:     /// \param _graph The graph the algorithm will run on.
deba@2017:     /// \param _cost The cost map used by the algorithm.
deba@2017:     MinCostArborescence(const Graph& _graph, const CostMap& _cost) 
deba@2017:       : graph(&_graph), cost(&_cost),
deba@2017:         _arborescence_map(0), local_arborescence_map(false), 
deba@2017:         _level(0), _cost_edges(0) {}
deba@2017: 
deba@2017:     /// \brief Destructor.
deba@2017:     ~MinCostArborescence() {
deba@2017:       destroyStructures();
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Sets the arborescence map.
deba@2017:     /// 
deba@2017:     /// Sets the arborescence map.
deba@2017:     /// \return \c (*this)
deba@2017:     MinCostArborescence& arborescenceMap(ArborescenceMap& m) {
deba@2017:       _arborescence_map = &m;
deba@2017:       return *this;
deba@2017:     }
deba@2017: 
deba@2017:     /// \name Query Functions
deba@2017:     /// The result of the %MinCostArborescence algorithm can be obtained 
deba@2017:     /// using these functions.\n
deba@2017:     /// Before the use of these functions,
deba@2017:     /// either run() or start() must be called.
deba@2017:     
deba@2017:     /// @{
deba@2017: 
deba@2017:     /// \brief Returns a reference to the arborescence map.
deba@2017:     ///
deba@2017:     /// Returns a reference to the arborescence map.
deba@2017:     const ArborescenceMap& arborescenceMap() const {
deba@2017:       return *_arborescence_map;
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Returns true if the edge is in the arborescence.
deba@2017:     ///
deba@2017:     /// Returns true if the edge is in the arborescence.
deba@2017:     /// \param edge The edge of the graph.
deba@2017:     /// \pre \ref run() must be called before using this function.
deba@2017:     bool arborescenceEdge(Edge edge) const {
deba@2017:       return (*_arborescence_map)[edge];
deba@2017:     }
deba@2017:  
deba@2017:     /// \brief Returns the cost of the arborescence.
deba@2017:     ///
deba@2017:     /// Returns the cost of the arborescence.
deba@2017:    Value arborescenceCost() const {
deba@2017:       Value sum = 0;
deba@2017:       for (EdgeIt it(*graph); it != INVALID; ++it) {
deba@2017:         if (arborescenceEdge(it)) {
deba@2017:           sum += (*cost)[it];
deba@2017:         }
deba@2017:       }
deba@2017:       return sum;
deba@2017:     }
deba@2017: 
deba@2017:     /// @}
deba@2017:     
deba@2017:     /// \name Execution control
deba@2017:     /// The simplest way to execute the algorithm is to use
deba@2017:     /// one of the member functions called \c run(...). \n
deba@2017:     /// If you need more control on the execution,
deba@2017:     /// first you must call \ref init(), then you can add several 
deba@2017:     /// source nodes with \ref addSource().
deba@2017:     /// Finally \ref start() will perform the actual path
deba@2017:     /// computation.
deba@2017: 
deba@2017:     ///@{
deba@2017: 
deba@2017:     /// \brief Initializes the internal data structures.
deba@2017:     ///
deba@2017:     /// Initializes the internal data structures.
deba@2017:     ///
deba@2017:     void init() {
deba@2017:       initStructures();
deba@2017:       for (NodeIt it(*graph); it != INVALID; ++it) {
deba@2017:         (*_cost_edges)[it].edge = INVALID;
deba@2017:         (*_level)[it] = -3; 
deba@2017:       }
deba@2017:       for (EdgeIt it(*graph); it != INVALID; ++it) {
deba@2017:         _arborescence_map->set(it, false);
deba@2017:       }
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Adds a new source node.
deba@2017:     ///
deba@2017:     /// Adds a new source node to the algorithm.
deba@2017:     void addSource(Node source) {
deba@2017:       std::vector<Node> nodes;
deba@2017:       nodes.push_back(source);
deba@2017:       while (!nodes.empty()) {
deba@2017:         Node node = nodes.back();
deba@2017:         nodes.pop_back();
deba@2017:         for (OutEdgeIt it(*graph, node); it != INVALID; ++it) {
deba@2017:           if ((*_level)[graph->target(it)] == -3) {
deba@2017:             (*_level)[graph->target(it)] = -2;
deba@2017:             nodes.push_back(graph->target(it));
deba@2017:             queue.push_back(graph->target(it));
deba@2017:           }
deba@2017:         }
deba@2017:       }
deba@2017:       (*_level)[source] = -1;
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Processes the next node in the priority queue.
deba@2017:     ///
deba@2017:     /// Processes the next node in the priority queue.
deba@2017:     ///
deba@2017:     /// \return The processed node.
deba@2017:     ///
deba@2017:     /// \warning The queue must not be empty!
deba@2017:     Node processNextNode() {
deba@2017:       node_counter = 0;
deba@2017:       Node node = queue.back();
deba@2017:       queue.pop_back();
deba@2017:       if ((*_level)[node] == -2) {
deba@2017:         Edge edge = prepare(node);
deba@2017:         while ((*_level)[graph->source(edge)] != -1) {
deba@2017:           if ((*_level)[graph->source(edge)] >= 0) {
deba@2017:             edge = contract(bottom((*_level)[graph->source(edge)]));
deba@2017:           } else {
deba@2017:             edge = prepare(graph->source(edge));
deba@2017:           }
deba@2017:         }
deba@2017:         finalize(graph->target(edge));
deba@2017:         level_stack.clear();        
deba@2017:       }
deba@2017:       return node;
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Returns the number of the nodes to be processed.
deba@2017:     ///
deba@2017:     /// Returns the number of the nodes to be processed.
deba@2017:     int queueSize() const {
deba@2017:       return queue.size();
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Returns \c false if there are nodes to be processed.
deba@2017:     ///
deba@2017:     /// Returns \c false if there are nodes to be processed.
deba@2017:     bool emptyQueue() const {
deba@2017:       return queue.empty();
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Executes the algorithm.
deba@2017:     ///
deba@2017:     /// Executes the algorithm.
deba@2017:     ///
deba@2017:     /// \pre init() must be called and at least one node should be added
deba@2017:     /// with addSource() before using this function.
deba@2017:     ///
deba@2017:     ///\note mca.start() is just a shortcut of the following code.
deba@2017:     ///\code
deba@2017:     ///while (!mca.emptyQueue()) {
deba@2017:     ///  mca.processNextNode();
deba@2017:     ///}
deba@2017:     ///\endcode
deba@2017:     void start() {
deba@2017:       while (!emptyQueue()) {
deba@2017:         processNextNode();
deba@2017:       }
deba@2017:     }
deba@2017: 
deba@2017:     /// \brief Runs %MinCostArborescence algorithm from node \c s.
deba@2017:     /// 
deba@2017:     /// This method runs the %MinCostArborescence algorithm from 
deba@2017:     /// a root node \c s.
deba@2017:     ///
deba@2017:     ///\note mca.run(s) is just a shortcut of the following code.
deba@2017:     ///\code
deba@2017:     ///mca.init();
deba@2017:     ///mca.addSource(s);
deba@2017:     ///mca.start();
deba@2017:     ///\endcode
deba@2017:     void run(Node node) {
deba@2017:       init();
deba@2017:       addSource(node);
deba@2017:       start();
deba@2017:     }
deba@2017: 
deba@2017:     ///@}
deba@2017: 
deba@2017:   protected:
deba@2017: 
deba@2017:     void initStructures() {
deba@2017:       if (!_arborescence_map) {
deba@2017:         local_arborescence_map = true;
deba@2017:         _arborescence_map = Traits::createArborescenceMap(*graph);
deba@2017:       }
deba@2017:       if (!_level) {
deba@2017:         _level = new LevelMap(*graph);
deba@2017:       }
deba@2017:       if (!_cost_edges) {
deba@2017:         _cost_edges = new CostEdgeMap(*graph);
deba@2017:       }
deba@2017:     }
deba@2017: 
deba@2017:     void destroyStructures() {
deba@2017:       if (_level) {
deba@2017:         delete _level;
deba@2017:       }
deba@2017:       if (!_cost_edges) {
deba@2017:         delete _cost_edges;
deba@2017:       }
deba@2017:       if (local_arborescence_map) {
deba@2017:         delete _arborescence_map;
deba@2017:       }
deba@2017:     }
deba@2017: 
deba@2017:     Edge prepare(Node node) {
deba@2017:       std::vector<Node> nodes;
deba@2017:       (*_level)[node] = node_counter;
deba@2017:       for (InEdgeIt it(*graph, node); it != INVALID; ++it) {
deba@2017:         Edge edge = it;
deba@2017:         Value value = (*cost)[it];
deba@2017:         if (graph->source(edge) == node || 
deba@2017:             (*_level)[graph->source(edge)] == -3) continue;
deba@2017:         if ((*_cost_edges)[graph->source(edge)].edge == INVALID) {
deba@2017:           (*_cost_edges)[graph->source(edge)].edge = edge;
deba@2017:           (*_cost_edges)[graph->source(edge)].value = value;
deba@2017:           nodes.push_back(graph->source(edge));
deba@2017:         } else {
deba@2017:           if ((*_cost_edges)[graph->source(edge)].value > value) {
deba@2017:             (*_cost_edges)[graph->source(edge)].edge = edge;
deba@2017:             (*_cost_edges)[graph->source(edge)].value = value;
deba@2017:           }
deba@2017:         }      
deba@2017:       }
deba@2017:       CostEdge minimum = (*_cost_edges)[nodes[0]]; 
deba@2017:       for (int i = 1; i < (int)nodes.size(); ++i) {
deba@2017:         if ((*_cost_edges)[nodes[i]].value < minimum.value) {
deba@2017:           minimum = (*_cost_edges)[nodes[i]];
deba@2017:         }
deba@2017:       }
deba@2017:       StackLevel level;
deba@2017:       level.node_level = node_counter;
deba@2017:       for (int i = 0; i < (int)nodes.size(); ++i) {
deba@2017:         (*_cost_edges)[nodes[i]].value -= minimum.value;
deba@2017:         level.edges.push_back((*_cost_edges)[nodes[i]]);
deba@2017:         (*_cost_edges)[nodes[i]].edge = INVALID;
deba@2017:       }
deba@2017:       level_stack.push_back(level);
deba@2017:       ++node_counter;
deba@2017:       _arborescence_map->set(minimum.edge, true);
deba@2017:       return minimum.edge;
deba@2017:     }
deba@2017:   
deba@2017:     Edge contract(int node_bottom) {
deba@2017:       std::vector<Node> nodes;
deba@2017:       while (!level_stack.empty() && 
deba@2017:              level_stack.back().node_level >= node_bottom) {
deba@2017:         for (int i = 0; i < (int)level_stack.back().edges.size(); ++i) {
deba@2017:           Edge edge = level_stack.back().edges[i].edge;
deba@2017:           Value value = level_stack.back().edges[i].value;
deba@2017:           if ((*_level)[graph->source(edge)] >= node_bottom) continue;
deba@2017:           if ((*_cost_edges)[graph->source(edge)].edge == INVALID) {
deba@2017:             (*_cost_edges)[graph->source(edge)].edge = edge;
deba@2017:             (*_cost_edges)[graph->source(edge)].value = value;
deba@2017:             nodes.push_back(graph->source(edge));
deba@2017:           } else {
deba@2017:             if ((*_cost_edges)[graph->source(edge)].value > value) {
deba@2017:               (*_cost_edges)[graph->source(edge)].edge = edge;
deba@2017:               (*_cost_edges)[graph->source(edge)].value = value;
deba@2017:             }
deba@2017:           }
deba@2017:         }
deba@2017:         level_stack.pop_back();
deba@2017:       }
deba@2017:       CostEdge minimum = (*_cost_edges)[nodes[0]]; 
deba@2017:       for (int i = 1; i < (int)nodes.size(); ++i) {
deba@2017:         if ((*_cost_edges)[nodes[i]].value < minimum.value) {
deba@2017:           minimum = (*_cost_edges)[nodes[i]];
deba@2017:         }
deba@2017:       }
deba@2017:       StackLevel level;
deba@2017:       level.node_level = node_bottom;
deba@2017:       for (int i = 0; i < (int)nodes.size(); ++i) {
deba@2017:         (*_cost_edges)[nodes[i]].value -= minimum.value;
deba@2017:         level.edges.push_back((*_cost_edges)[nodes[i]]);
deba@2017:         (*_cost_edges)[nodes[i]].edge = INVALID;
deba@2017:       }
deba@2017:       level_stack.push_back(level);
deba@2017:       _arborescence_map->set(minimum.edge, true);
deba@2017:       return minimum.edge;
deba@2017:     }
deba@2017: 
deba@2017:     int bottom(int level) {
deba@2017:       int k = level_stack.size() - 1;
deba@2017:       while (level_stack[k].node_level > level) {
deba@2017:         --k;
deba@2017:       }
deba@2017:       return level_stack[k].node_level;
deba@2017:     }
deba@2017: 
deba@2017:     void finalize(Node source) {
deba@2017:       std::vector<Node> nodes;
deba@2017:       nodes.push_back(source);
deba@2017:       while (!nodes.empty()) {
deba@2017:         Node node = nodes.back();
deba@2017:         nodes.pop_back();
deba@2017:         for (OutEdgeIt it(*graph, node); it != INVALID; ++it) {
deba@2017:           if ((*_level)[graph->target(it)] >= 0 && (*_arborescence_map)[it]) {
deba@2017:             (*_level)[graph->target(it)] = -1;
deba@2017:             nodes.push_back(graph->target(it));
deba@2017:           } else {
deba@2017:             _arborescence_map->set(it, false);
deba@2017:           }
deba@2017:         }
deba@2017:       }
deba@2017:       (*_level)[source] = -1;      
deba@2017:     }
deba@2017: 
deba@2017:   };
deba@2017: 
deba@2017:   /// \ingroup spantree
deba@2017:   ///
deba@2017:   /// \brief Function type interface for MinCostArborescence algorithm.
deba@2017:   ///
deba@2017:   /// Function type interface for MinCostArborescence algorithm.
deba@2017:   /// \param graph The Graph that the algorithm runs on.
deba@2017:   /// \param cost The CostMap of the edges.
deba@2017:   /// \param source The source of the arborescence.
deba@2017:   /// \retval arborescence The bool EdgeMap which stores the arborescence.
deba@2017:   /// \return The cost of the arborescence. 
deba@2017:   ///
deba@2017:   /// \sa MinCostArborescence
deba@2017:   template <typename Graph, typename CostMap, typename ArborescenceMap>
deba@2017:   typename CostMap::Value minCostArborescence(const Graph& graph, 
deba@2017:                                               const CostMap& cost,
deba@2017:                                               typename Graph::Node source,
deba@2017:                                               ArborescenceMap& arborescence) {
deba@2017:     typename MinCostArborescence<Graph, CostMap>
deba@2017:       ::template DefArborescenceMap<ArborescenceMap>
deba@2017:       ::Create mca(graph, cost);
deba@2017:     mca.arborescenceMap(arborescence);
deba@2017:     mca.run(source);
deba@2017:     return mca.arborescenceCost();
deba@2017:   }
deba@2017: 
deba@2017: }
deba@2017: 
deba@2017: #endif
deba@2017: 
deba@2017: // Hilbert - Huang