source: lemon-1.2/lemon/max_matching.h @ 449:91fcb8ed4cdc

/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2008
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_MAX_MATCHING_H
#define LEMON_MAX_MATCHING_H

#include <vector>
#include <queue>
#include <set>
#include <limits>

#include <lemon/core.h>
#include <lemon/unionfind.h>
#include <lemon/bin_heap.h>
#include <lemon/maps.h>

///\ingroup matching
///\file
///\brief Maximum matching algorithms in general graphs.

namespace lemon {

  /// \ingroup matching
  ///
  /// \brief Edmonds' alternating forest maximum matching algorithm.
  ///
  /// This class implements Edmonds' alternating forest matching
  /// algorithm. The algorithm can be started from an arbitrary initial
  /// matching (the default is the empty one)
  ///
  /// The dual solution of the problem is a map of the nodes to
  /// MaxMatching::Status, having values \c EVEN/D, \c ODD/A and \c
  /// MATCHED/C showing the Gallai-Edmonds decomposition of the
  /// graph. The nodes in \c EVEN/D induce a graph with
  /// factor-critical components, the nodes in \c ODD/A form the
  /// barrier, and the nodes in \c MATCHED/C induce a graph having a
  /// perfect matching. The number of the factor-critical components
  /// minus the number of barrier nodes is a lower bound on the
  /// unmatched nodes, and the matching is optimal if and only if this bound is
  /// tight. This decomposition can be attained by calling \c
  /// decomposition() after running the algorithm.
  ///
  /// \param _Graph The graph type the algorithm runs on.
  template <typename _Graph>
  class MaxMatching {
  public:

    typedef _Graph Graph;
    typedef typename Graph::template NodeMap<typename Graph::Arc>
    MatchingMap;

    ///\brief Indicates the Gallai-Edmonds decomposition of the graph.
    ///
    ///Indicates the Gallai-Edmonds decomposition of the graph. The
    ///nodes with Status \c EVEN/D induce a graph with factor-critical
    ///components, the nodes in \c ODD/A form the canonical barrier,
    ///and the nodes in \c MATCHED/C induce a graph having a perfect
    ///matching.
    enum Status {
      EVEN = 1, D = 1, MATCHED = 0, C = 0, ODD = -1, A = -1, UNMATCHED = -2
    };

    typedef typename Graph::template NodeMap<Status> StatusMap;

  private:

    TEMPLATE_GRAPH_TYPEDEFS(Graph);

    typedef UnionFindEnum<IntNodeMap> BlossomSet;
    typedef ExtendFindEnum<IntNodeMap> TreeSet;
    typedef RangeMap<Node> NodeIntMap;
    typedef MatchingMap EarMap;
    typedef std::vector<Node> NodeQueue;

    const Graph& _graph;
    MatchingMap* _matching;
    StatusMap* _status;

    EarMap* _ear;

    IntNodeMap* _blossom_set_index;
    BlossomSet* _blossom_set;
    NodeIntMap* _blossom_rep;

    IntNodeMap* _tree_set_index;
    TreeSet* _tree_set;

    NodeQueue _node_queue;
    int _process, _postpone, _last;

    int _node_num;

  private:

    void createStructures() {
      _node_num = countNodes(_graph);
      if (!_matching) {
        _matching = new MatchingMap(_graph);
      }
      if (!_status) {
        _status = new StatusMap(_graph);
      }
      if (!_ear) {
        _ear = new EarMap(_graph);
      }
      if (!_blossom_set) {
        _blossom_set_index = new IntNodeMap(_graph);
        _blossom_set = new BlossomSet(*_blossom_set_index);
      }
      if (!_blossom_rep) {
        _blossom_rep = new NodeIntMap(_node_num);
      }
      if (!_tree_set) {
        _tree_set_index = new IntNodeMap(_graph);
        _tree_set = new TreeSet(*_tree_set_index);
      }
      _node_queue.resize(_node_num);
    }

    void destroyStructures() {
      if (_matching) {
        delete _matching;
      }
      if (_status) {
        delete _status;
      }
      if (_ear) {
        delete _ear;
      }
      if (_blossom_set) {
        delete _blossom_set;
        delete _blossom_set_index;
      }
      if (_blossom_rep) {
        delete _blossom_rep;
      }
      if (_tree_set) {
        delete _tree_set_index;
        delete _tree_set;
      }
    }

    void processDense(const Node& n) {
      _process = _postpone = _last = 0;
      _node_queue[_last++] = n;

      while (_process != _last) {
        Node u = _node_queue[_process++];
        for (OutArcIt a(_graph, u); a != INVALID; ++a) {
          Node v = _graph.target(a);
          if ((*_status)[v] == MATCHED) {
            extendOnArc(a);
          } else if ((*_status)[v] == UNMATCHED) {
            augmentOnArc(a);
            return;
          }
        }
      }

      while (_postpone != _last) {
        Node u = _node_queue[_postpone++];

        for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
          Node v = _graph.target(a);

          if ((*_status)[v] == EVEN) {
            if (_blossom_set->find(u) != _blossom_set->find(v)) {
              shrinkOnEdge(a);
            }
          }

          while (_process != _last) {
            Node w = _node_queue[_process++];
            for (OutArcIt b(_graph, w); b != INVALID; ++b) {
              Node x = _graph.target(b);
              if ((*_status)[x] == MATCHED) {
                extendOnArc(b);
              } else if ((*_status)[x] == UNMATCHED) {
                augmentOnArc(b);
                return;
              }
            }
          }
        }
      }
    }

    void processSparse(const Node& n) {
      _process = _last = 0;
      _node_queue[_last++] = n;
      while (_process != _last) {
        Node u = _node_queue[_process++];
        for (OutArcIt a(_graph, u); a != INVALID; ++a) {
          Node v = _graph.target(a);

          if ((*_status)[v] == EVEN) {
            if (_blossom_set->find(u) != _blossom_set->find(v)) {
              shrinkOnEdge(a);
            }
          } else if ((*_status)[v] == MATCHED) {
            extendOnArc(a);
          } else if ((*_status)[v] == UNMATCHED) {
            augmentOnArc(a);
            return;
          }
        }
      }
    }

    void shrinkOnEdge(const Edge& e) {
      Node nca = INVALID;

      {
        std::set<Node> left_set, right_set;

        Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
        left_set.insert(left);

        Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
        right_set.insert(right);

        while (true) {
          if ((*_matching)[left] == INVALID) break;
          left = _graph.target((*_matching)[left]);
          left = (*_blossom_rep)[_blossom_set->
                                 find(_graph.target((*_ear)[left]))];
          if (right_set.find(left) != right_set.end()) {
            nca = left;
            break;
          }
          left_set.insert(left);

          if ((*_matching)[right] == INVALID) break;
          right = _graph.target((*_matching)[right]);
          right = (*_blossom_rep)[_blossom_set->
                                  find(_graph.target((*_ear)[right]))];
          if (left_set.find(right) != left_set.end()) {
            nca = right;
            break;
          }
          right_set.insert(right);
        }

        if (nca == INVALID) {
          if ((*_matching)[left] == INVALID) {
            nca = right;
            while (left_set.find(nca) == left_set.end()) {
              nca = _graph.target((*_matching)[nca]);
              nca =(*_blossom_rep)[_blossom_set->
                                   find(_graph.target((*_ear)[nca]))];
            }
          } else {
            nca = left;
            while (right_set.find(nca) == right_set.end()) {
              nca = _graph.target((*_matching)[nca]);
              nca = (*_blossom_rep)[_blossom_set->
                                   find(_graph.target((*_ear)[nca]))];
            }
          }
        }
      }

      {

        Node node = _graph.u(e);
        Arc arc = _graph.direct(e, true);
        Node base = (*_blossom_rep)[_blossom_set->find(node)];

        while (base != nca) {
          _ear->set(node, arc);

          Node n = node;
          while (n != base) {
            n = _graph.target((*_matching)[n]);
            Arc a = (*_ear)[n];
            n = _graph.target(a);
            _ear->set(n, _graph.oppositeArc(a));
          }
          node = _graph.target((*_matching)[base]);
          _tree_set->erase(base);
          _tree_set->erase(node);
          _blossom_set->insert(node, _blossom_set->find(base));
          _status->set(node, EVEN);
          _node_queue[_last++] = node;
          arc = _graph.oppositeArc((*_ear)[node]);
          node = _graph.target((*_ear)[node]);
          base = (*_blossom_rep)[_blossom_set->find(node)];
          _blossom_set->join(_graph.target(arc), base);
        }
      }

      _blossom_rep->set(_blossom_set->find(nca), nca);

      {

        Node node = _graph.v(e);
        Arc arc = _graph.direct(e, false);
        Node base = (*_blossom_rep)[_blossom_set->find(node)];

        while (base != nca) {
          _ear->set(node, arc);

          Node n = node;
          while (n != base) {
            n = _graph.target((*_matching)[n]);
            Arc a = (*_ear)[n];
            n = _graph.target(a);
            _ear->set(n, _graph.oppositeArc(a));
          }
          node = _graph.target((*_matching)[base]);
          _tree_set->erase(base);
          _tree_set->erase(node);
          _blossom_set->insert(node, _blossom_set->find(base));
          _status->set(node, EVEN);
          _node_queue[_last++] = node;
          arc = _graph.oppositeArc((*_ear)[node]);
          node = _graph.target((*_ear)[node]);
          base = (*_blossom_rep)[_blossom_set->find(node)];
          _blossom_set->join(_graph.target(arc), base);
        }
      }

      _blossom_rep->set(_blossom_set->find(nca), nca);
    }



    void extendOnArc(const Arc& a) {
      Node base = _graph.source(a);
      Node odd = _graph.target(a);

      _ear->set(odd, _graph.oppositeArc(a));
      Node even = _graph.target((*_matching)[odd]);
      _blossom_rep->set(_blossom_set->insert(even), even);
      _status->set(odd, ODD);
      _status->set(even, EVEN);
      int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
      _tree_set->insert(odd, tree);
      _tree_set->insert(even, tree);
      _node_queue[_last++] = even;

    }

    void augmentOnArc(const Arc& a) {
      Node even = _graph.source(a);
      Node odd = _graph.target(a);

      int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);

      _matching->set(odd, _graph.oppositeArc(a));
      _status->set(odd, MATCHED);

      Arc arc = (*_matching)[even];
      _matching->set(even, a);

      while (arc != INVALID) {
        odd = _graph.target(arc);
        arc = (*_ear)[odd];
        even = _graph.target(arc);
        _matching->set(odd, arc);
        arc = (*_matching)[even];
        _matching->set(even, _graph.oppositeArc((*_matching)[odd]));
      }

      for (typename TreeSet::ItemIt it(*_tree_set, tree);
           it != INVALID; ++it) {
        if ((*_status)[it] == ODD) {
          _status->set(it, MATCHED);
        } else {
          int blossom = _blossom_set->find(it);
          for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
               jt != INVALID; ++jt) {
            _status->set(jt, MATCHED);
          }
          _blossom_set->eraseClass(blossom);
        }
      }
      _tree_set->eraseClass(tree);

    }

  public:

    /// \brief Constructor
    ///
    /// Constructor.
    MaxMatching(const Graph& graph)
      : _graph(graph), _matching(0), _status(0), _ear(0),
        _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
        _tree_set_index(0), _tree_set(0) {}

    ~MaxMatching() {
      destroyStructures();
    }

    /// \name Execution control
    /// The simplest way to execute the algorithm is to use the
    /// \c run() member function.
    /// \n

    /// If you need better control on the execution, you must call
    /// \ref init(), \ref greedyInit() or \ref matchingInit()
    /// functions first, then you can start the algorithm with the \ref
    /// startParse() or startDense() functions.

    ///@{

    /// \brief Sets the actual matching to the empty matching.
    ///
    /// Sets the actual matching to the empty matching.
    ///
    void init() {
      createStructures();
      for(NodeIt n(_graph); n != INVALID; ++n) {
        _matching->set(n, INVALID);
        _status->set(n, UNMATCHED);
      }
    }

    ///\brief Finds an initial matching in a greedy way
    ///
    ///It finds an initial matching in a greedy way.
    void greedyInit() {
      createStructures();
      for (NodeIt n(_graph); n != INVALID; ++n) {
        _matching->set(n, INVALID);
        _status->set(n, UNMATCHED);
      }
      for (NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_matching)[n] == INVALID) {
          for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
            Node v = _graph.target(a);
            if ((*_matching)[v] == INVALID && v != n) {
              _matching->set(n, a);
              _status->set(n, MATCHED);
              _matching->set(v, _graph.oppositeArc(a));
              _status->set(v, MATCHED);
              break;
            }
          }
        }
      }
    }


    /// \brief Initialize the matching from a map containing.
    ///
    /// Initialize the matching from a \c bool valued \c Edge map. This
    /// map must have the property that there are no two incident edges
    /// with true value, ie. it contains a matching.
    /// \return %True if the map contains a matching.
    template <typename MatchingMap>
    bool matchingInit(const MatchingMap& matching) {
      createStructures();

      for (NodeIt n(_graph); n != INVALID; ++n) {
        _matching->set(n, INVALID);
        _status->set(n, UNMATCHED);
      }
      for(EdgeIt e(_graph); e!=INVALID; ++e) {
        if (matching[e]) {

          Node u = _graph.u(e);
          if ((*_matching)[u] != INVALID) return false;
          _matching->set(u, _graph.direct(e, true));
          _status->set(u, MATCHED);

          Node v = _graph.v(e);
          if ((*_matching)[v] != INVALID) return false;
          _matching->set(v, _graph.direct(e, false));
          _status->set(v, MATCHED);
        }
      }
      return true;
    }

    /// \brief Starts Edmonds' algorithm
    ///
    /// If runs the original Edmonds' algorithm.
    void startSparse() {
      for(NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_status)[n] == UNMATCHED) {
          (*_blossom_rep)[_blossom_set->insert(n)] = n;
          _tree_set->insert(n);
          _status->set(n, EVEN);
          processSparse(n);
        }
      }
    }

    /// \brief Starts Edmonds' algorithm.
    ///
    /// It runs Edmonds' algorithm with a heuristic of postponing
    /// shrinks, therefore resulting in a faster algorithm for dense graphs.
    void startDense() {
      for(NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_status)[n] == UNMATCHED) {
          (*_blossom_rep)[_blossom_set->insert(n)] = n;
          _tree_set->insert(n);
          _status->set(n, EVEN);
          processDense(n);
        }
      }
    }


    /// \brief Runs Edmonds' algorithm
    ///
    /// Runs Edmonds' algorithm for sparse graphs (<tt>m<2*n</tt>)
    /// or Edmonds' algorithm with a heuristic of
    /// postponing shrinks for dense graphs.
    void run() {
      if (countEdges(_graph) < 2 * countNodes(_graph)) {
        greedyInit();
        startSparse();
      } else {
        init();
        startDense();
      }
    }

    /// @}

    /// \name Primal solution
    /// Functions to get the primal solution, ie. the matching.

    /// @{

    ///\brief Returns the size of the current matching.
    ///
    ///Returns the size of the current matching. After \ref
    ///run() it returns the size of the maximum matching in the graph.
    int matchingSize() const {
      int size = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_matching)[n] != INVALID) {
          ++size;
        }
      }
      return size / 2;
    }

    /// \brief Returns true when the edge is in the matching.
    ///
    /// Returns true when the edge is in the matching.
    bool matching(const Edge& edge) const {
      return edge == (*_matching)[_graph.u(edge)];
    }

    /// \brief Returns the matching edge incident to the given node.
    ///
    /// Returns the matching edge of a \c node in the actual matching or
    /// INVALID if the \c node is not covered by the actual matching.
    Arc matching(const Node& n) const {
      return (*_matching)[n];
    }

    ///\brief Returns the mate of a node in the actual matching.
    ///
    ///Returns the mate of a \c node in the actual matching or
    ///INVALID if the \c node is not covered by the actual matching.
    Node mate(const Node& n) const {
      return (*_matching)[n] != INVALID ?
        _graph.target((*_matching)[n]) : INVALID;
    }

    /// @}

    /// \name Dual solution
    /// Functions to get the dual solution, ie. the decomposition.

    /// @{

    /// \brief Returns the class of the node in the Edmonds-Gallai
    /// decomposition.
    ///
    /// Returns the class of the node in the Edmonds-Gallai
    /// decomposition.
    Status decomposition(const Node& n) const {
      return (*_status)[n];
    }

    /// \brief Returns true when the node is in the barrier.
    ///
    /// Returns true when the node is in the barrier.
    bool barrier(const Node& n) const {
      return (*_status)[n] == ODD;
    }

    /// @}

  };

  /// \ingroup matching
  ///
  /// \brief Weighted matching in general graphs
  ///
  /// This class provides an efficient implementation of Edmond's
  /// maximum weighted matching algorithm. The implementation is based
  /// on extensive use of priority queues and provides
  /// \f$O(nm\log(n))\f$ time complexity.
  ///
  /// The maximum weighted matching problem is to find undirected
  /// edges in the graph with maximum overall weight and no two of
  /// them shares their ends. The problem can be formulated with the
  /// following linear program.
  /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
  /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
      \quad \forall B\in\mathcal{O}\f] */
  /// \f[x_e \ge 0\quad \forall e\in E\f]
  /// \f[\max \sum_{e\in E}x_ew_e\f]
  /// where \f$\delta(X)\f$ is the set of edges incident to a node in
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
  /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
  /// subsets of the nodes.
  ///
  /// The algorithm calculates an optimal matching and a proof of the
  /// optimality. The solution of the dual problem can be used to check
  /// the result of the algorithm. The dual linear problem is the
  /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
      z_B \ge w_{uv} \quad \forall uv\in E\f] */
  /// \f[y_u \ge 0 \quad \forall u \in V\f]
  /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
  /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
      \frac{\vert B \vert - 1}{2}z_B\f] */
  ///
  /// The algorithm can be executed with \c run() or the \c init() and
  /// then the \c start() member functions. After it the matching can
  /// be asked with \c matching() or mate() functions. The dual
  /// solution can be get with \c nodeValue(), \c blossomNum() and \c
  /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
  /// "BlossomIt" nested class, which is able to iterate on the nodes
  /// of a blossom. If the value type is integral then the dual
  /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
  template <typename _Graph,
            typename _WeightMap = typename _Graph::template EdgeMap<int> >
  class MaxWeightedMatching {
  public:

    typedef _Graph Graph;
    typedef _WeightMap WeightMap;
    typedef typename WeightMap::Value Value;

    /// \brief Scaling factor for dual solution
    ///
    /// Scaling factor for dual solution, it is equal to 4 or 1
    /// according to the value type.
    static const int dualScale =
      std::numeric_limits<Value>::is_integer ? 4 : 1;

    typedef typename Graph::template NodeMap<typename Graph::Arc>
    MatchingMap;

  private:

    TEMPLATE_GRAPH_TYPEDEFS(Graph);

    typedef typename Graph::template NodeMap<Value> NodePotential;
    typedef std::vector<Node> BlossomNodeList;

    struct BlossomVariable {
      int begin, end;
      Value value;

      BlossomVariable(int _begin, int _end, Value _value)
        : begin(_begin), end(_end), value(_value) {}

    };

    typedef std::vector<BlossomVariable> BlossomPotential;

    const Graph& _graph;
    const WeightMap& _weight;

    MatchingMap* _matching;

    NodePotential* _node_potential;

    BlossomPotential _blossom_potential;
    BlossomNodeList _blossom_node_list;

    int _node_num;
    int _blossom_num;

    typedef RangeMap<int> IntIntMap;

    enum Status {
      EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
    };

    typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
    struct BlossomData {
      int tree;
      Status status;
      Arc pred, next;
      Value pot, offset;
      Node base;
    };

    IntNodeMap *_blossom_index;
    BlossomSet *_blossom_set;
    RangeMap<BlossomData>* _blossom_data;

    IntNodeMap *_node_index;
    IntArcMap *_node_heap_index;

    struct NodeData {

      NodeData(IntArcMap& node_heap_index)
        : heap(node_heap_index) {}

      int blossom;
      Value pot;
      BinHeap<Value, IntArcMap> heap;
      std::map<int, Arc> heap_index;

      int tree;
    };

    RangeMap<NodeData>* _node_data;

    typedef ExtendFindEnum<IntIntMap> TreeSet;

    IntIntMap *_tree_set_index;
    TreeSet *_tree_set;

    IntNodeMap *_delta1_index;
    BinHeap<Value, IntNodeMap> *_delta1;

    IntIntMap *_delta2_index;
    BinHeap<Value, IntIntMap> *_delta2;

    IntEdgeMap *_delta3_index;
    BinHeap<Value, IntEdgeMap> *_delta3;

    IntIntMap *_delta4_index;
    BinHeap<Value, IntIntMap> *_delta4;

    Value _delta_sum;

    void createStructures() {
      _node_num = countNodes(_graph);
      _blossom_num = _node_num * 3 / 2;

      if (!_matching) {
        _matching = new MatchingMap(_graph);
      }
      if (!_node_potential) {
        _node_potential = new NodePotential(_graph);
      }
      if (!_blossom_set) {
        _blossom_index = new IntNodeMap(_graph);
        _blossom_set = new BlossomSet(*_blossom_index);
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
      }

      if (!_node_index) {
        _node_index = new IntNodeMap(_graph);
        _node_heap_index = new IntArcMap(_graph);
        _node_data = new RangeMap<NodeData>(_node_num,
                                              NodeData(*_node_heap_index));
      }

      if (!_tree_set) {
        _tree_set_index = new IntIntMap(_blossom_num);
        _tree_set = new TreeSet(*_tree_set_index);
      }
      if (!_delta1) {
        _delta1_index = new IntNodeMap(_graph);
        _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
      }
      if (!_delta2) {
        _delta2_index = new IntIntMap(_blossom_num);
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
      }
      if (!_delta3) {
        _delta3_index = new IntEdgeMap(_graph);
        _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
      }
      if (!_delta4) {
        _delta4_index = new IntIntMap(_blossom_num);
        _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
      }
    }

    void destroyStructures() {
      _node_num = countNodes(_graph);
      _blossom_num = _node_num * 3 / 2;

      if (_matching) {
        delete _matching;
      }
      if (_node_potential) {
        delete _node_potential;
      }
      if (_blossom_set) {
        delete _blossom_index;
        delete _blossom_set;
        delete _blossom_data;
      }

      if (_node_index) {
        delete _node_index;
        delete _node_heap_index;
        delete _node_data;
      }

      if (_tree_set) {
        delete _tree_set_index;
        delete _tree_set;
      }
      if (_delta1) {
        delete _delta1_index;
        delete _delta1;
      }
      if (_delta2) {
        delete _delta2_index;
        delete _delta2;
      }
      if (_delta3) {
        delete _delta3_index;
        delete _delta3;
      }
      if (_delta4) {
        delete _delta4_index;
        delete _delta4;
      }
    }

    void matchedToEven(int blossom, int tree) {
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }

      if (!_blossom_set->trivial(blossom)) {
        (*_blossom_data)[blossom].pot -=
          2 * (_delta_sum - (*_blossom_data)[blossom].offset);
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {

        _blossom_set->increase(n, std::numeric_limits<Value>::max());
        int ni = (*_node_index)[n];

        (*_node_data)[ni].heap.clear();
        (*_node_data)[ni].heap_index.clear();

        (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;

        _delta1->push(n, (*_node_data)[ni].pot);

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if ((*_blossom_data)[vb].status == EVEN) {
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
              _delta3->push(e, rw / 2);
            }
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
            if (_delta3->state(e) != _delta3->IN_HEAP) {
              _delta3->push(e, rw);
            }
          } else {
            typename std::map<int, Arc>::iterator it =
              (*_node_data)[vi].heap_index.find(tree);

            if (it != (*_node_data)[vi].heap_index.end()) {
              if ((*_node_data)[vi].heap[it->second] > rw) {
                (*_node_data)[vi].heap.replace(it->second, e);
                (*_node_data)[vi].heap.decrease(e, rw);
                it->second = e;
              }
            } else {
              (*_node_data)[vi].heap.push(e, rw);
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
            }

            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());

              if ((*_blossom_data)[vb].status == MATCHED) {
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
                               (*_blossom_data)[vb].offset);
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
                           (*_blossom_data)[vb].offset){
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
                                   (*_blossom_data)[vb].offset);
                }
              }
            }
          }
        }
      }
      (*_blossom_data)[blossom].offset = 0;
    }

    void matchedToOdd(int blossom) {
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }
      (*_blossom_data)[blossom].offset += _delta_sum;
      if (!_blossom_set->trivial(blossom)) {
        _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
                     (*_blossom_data)[blossom].offset);
      }
    }

    void evenToMatched(int blossom, int tree) {
      if (!_blossom_set->trivial(blossom)) {
        (*_blossom_data)[blossom].pot += 2 * _delta_sum;
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {
        int ni = (*_node_index)[n];
        (*_node_data)[ni].pot -= _delta_sum;

        _delta1->erase(n);

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if (vb == blossom) {
            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }
          } else if ((*_blossom_data)[vb].status == EVEN) {

            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }

            int vt = _tree_set->find(vb);

            if (vt != tree) {

              Arc r = _graph.oppositeArc(e);

              typename std::map<int, Arc>::iterator it =
                (*_node_data)[ni].heap_index.find(vt);

              if (it != (*_node_data)[ni].heap_index.end()) {
                if ((*_node_data)[ni].heap[it->second] > rw) {
                  (*_node_data)[ni].heap.replace(it->second, r);
                  (*_node_data)[ni].heap.decrease(r, rw);
                  it->second = r;
                }
              } else {
                (*_node_data)[ni].heap.push(r, rw);
                (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
              }

              if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
                _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());

                if (_delta2->state(blossom) != _delta2->IN_HEAP) {
                  _delta2->push(blossom, _blossom_set->classPrio(blossom) -
                               (*_blossom_data)[blossom].offset);
                } else if ((*_delta2)[blossom] >
                           _blossom_set->classPrio(blossom) -
                           (*_blossom_data)[blossom].offset){
                  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
                                   (*_blossom_data)[blossom].offset);
                }
              }
            }

          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }
          } else {

            typename std::map<int, Arc>::iterator it =
              (*_node_data)[vi].heap_index.find(tree);

            if (it != (*_node_data)[vi].heap_index.end()) {
              (*_node_data)[vi].heap.erase(it->second);
              (*_node_data)[vi].heap_index.erase(it);
              if ((*_node_data)[vi].heap.empty()) {
                _blossom_set->increase(v, std::numeric_limits<Value>::max());
              } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
                _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
              }

              if ((*_blossom_data)[vb].status == MATCHED) {
                if (_blossom_set->classPrio(vb) ==
                    std::numeric_limits<Value>::max()) {
                  _delta2->erase(vb);
                } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
                           (*_blossom_data)[vb].offset) {
                  _delta2->increase(vb, _blossom_set->classPrio(vb) -
                                   (*_blossom_data)[vb].offset);
                }
              }
            }
          }
        }
      }
    }

    void oddToMatched(int blossom) {
      (*_blossom_data)[blossom].offset -= _delta_sum;

      if (_blossom_set->classPrio(blossom) !=
          std::numeric_limits<Value>::max()) {
        _delta2->push(blossom, _blossom_set->classPrio(blossom) -
                       (*_blossom_data)[blossom].offset);
      }

      if (!_blossom_set->trivial(blossom)) {
        _delta4->erase(blossom);
      }
    }

    void oddToEven(int blossom, int tree) {
      if (!_blossom_set->trivial(blossom)) {
        _delta4->erase(blossom);
        (*_blossom_data)[blossom].pot -=
          2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {
        int ni = (*_node_index)[n];

        _blossom_set->increase(n, std::numeric_limits<Value>::max());

        (*_node_data)[ni].heap.clear();
        (*_node_data)[ni].heap_index.clear();
        (*_node_data)[ni].pot +=
          2 * _delta_sum - (*_blossom_data)[blossom].offset;

        _delta1->push(n, (*_node_data)[ni].pot);

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if ((*_blossom_data)[vb].status == EVEN) {
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
              _delta3->push(e, rw / 2);
            }
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
            if (_delta3->state(e) != _delta3->IN_HEAP) {
              _delta3->push(e, rw);
            }
          } else {

            typename std::map<int, Arc>::iterator it =
              (*_node_data)[vi].heap_index.find(tree);

            if (it != (*_node_data)[vi].heap_index.end()) {
              if ((*_node_data)[vi].heap[it->second] > rw) {
                (*_node_data)[vi].heap.replace(it->second, e);
                (*_node_data)[vi].heap.decrease(e, rw);
                it->second = e;
              }
            } else {
              (*_node_data)[vi].heap.push(e, rw);
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
            }

            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());

              if ((*_blossom_data)[vb].status == MATCHED) {
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
                               (*_blossom_data)[vb].offset);
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
                           (*_blossom_data)[vb].offset) {
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
                                   (*_blossom_data)[vb].offset);
                }
              }
            }
          }
        }
      }
      (*_blossom_data)[blossom].offset = 0;
    }


    void matchedToUnmatched(int blossom) {
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {
        int ni = (*_node_index)[n];

        _blossom_set->increase(n, std::numeric_limits<Value>::max());

        (*_node_data)[ni].heap.clear();
        (*_node_data)[ni].heap_index.clear();

        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.target(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if ((*_blossom_data)[vb].status == EVEN) {
            if (_delta3->state(e) != _delta3->IN_HEAP) {
              _delta3->push(e, rw);
            }
          }
        }
      }
    }

    void unmatchedToMatched(int blossom) {
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {
        int ni = (*_node_index)[n];

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if (vb == blossom) {
            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }
          } else if ((*_blossom_data)[vb].status == EVEN) {

            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }

            int vt = _tree_set->find(vb);

            Arc r = _graph.oppositeArc(e);

            typename std::map<int, Arc>::iterator it =
              (*_node_data)[ni].heap_index.find(vt);

            if (it != (*_node_data)[ni].heap_index.end()) {
              if ((*_node_data)[ni].heap[it->second] > rw) {
                (*_node_data)[ni].heap.replace(it->second, r);
                (*_node_data)[ni].heap.decrease(r, rw);
                it->second = r;
              }
            } else {
              (*_node_data)[ni].heap.push(r, rw);
              (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
            }

            if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
              _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());

              if (_delta2->state(blossom) != _delta2->IN_HEAP) {
                _delta2->push(blossom, _blossom_set->classPrio(blossom) -
                             (*_blossom_data)[blossom].offset);
              } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
                         (*_blossom_data)[blossom].offset){
                _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
                                 (*_blossom_data)[blossom].offset);
              }
            }

          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }
          }
        }
      }
    }

    void alternatePath(int even, int tree) {
      int odd;

      evenToMatched(even, tree);
      (*_blossom_data)[even].status = MATCHED;

      while ((*_blossom_data)[even].pred != INVALID) {
        odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
        (*_blossom_data)[odd].status = MATCHED;
        oddToMatched(odd);
        (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;

        even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
        (*_blossom_data)[even].status = MATCHED;
        evenToMatched(even, tree);
        (*_blossom_data)[even].next =
          _graph.oppositeArc((*_blossom_data)[odd].pred);
      }

    }

    void destroyTree(int tree) {
      for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
        if ((*_blossom_data)[b].status == EVEN) {
          (*_blossom_data)[b].status = MATCHED;
          evenToMatched(b, tree);
        } else if ((*_blossom_data)[b].status == ODD) {
          (*_blossom_data)[b].status = MATCHED;
          oddToMatched(b);
        }
      }
      _tree_set->eraseClass(tree);
    }


    void unmatchNode(const Node& node) {
      int blossom = _blossom_set->find(node);
      int tree = _tree_set->find(blossom);

      alternatePath(blossom, tree);
      destroyTree(tree);

      (*_blossom_data)[blossom].status = UNMATCHED;
      (*_blossom_data)[blossom].base = node;
      matchedToUnmatched(blossom);
    }


    void augmentOnEdge(const Edge& edge) {

      int left = _blossom_set->find(_graph.u(edge));
      int right = _blossom_set->find(_graph.v(edge));

      if ((*_blossom_data)[left].status == EVEN) {
        int left_tree = _tree_set->find(left);
        alternatePath(left, left_tree);
        destroyTree(left_tree);
      } else {
        (*_blossom_data)[left].status = MATCHED;
        unmatchedToMatched(left);
      }

      if ((*_blossom_data)[right].status == EVEN) {
        int right_tree = _tree_set->find(right);
        alternatePath(right, right_tree);
        destroyTree(right_tree);
      } else {
        (*_blossom_data)[right].status = MATCHED;
        unmatchedToMatched(right);
      }

      (*_blossom_data)[left].next = _graph.direct(edge, true);
      (*_blossom_data)[right].next = _graph.direct(edge, false);
    }

    void extendOnArc(const Arc& arc) {
      int base = _blossom_set->find(_graph.target(arc));
      int tree = _tree_set->find(base);

      int odd = _blossom_set->find(_graph.source(arc));
      _tree_set->insert(odd, tree);
      (*_blossom_data)[odd].status = ODD;
      matchedToOdd(odd);
      (*_blossom_data)[odd].pred = arc;

      int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
      (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
      _tree_set->insert(even, tree);
      (*_blossom_data)[even].status = EVEN;
      matchedToEven(even, tree);
    }

    void shrinkOnEdge(const Edge& edge, int tree) {
      int nca = -1;
      std::vector<int> left_path, right_path;

      {
        std::set<int> left_set, right_set;
        int left = _blossom_set->find(_graph.u(edge));
        left_path.push_back(left);
        left_set.insert(left);

        int right = _blossom_set->find(_graph.v(edge));
        right_path.push_back(right);
        right_set.insert(right);

        while (true) {

          if ((*_blossom_data)[left].pred == INVALID) break;

          left =
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
          left_path.push_back(left);
          left =
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
          left_path.push_back(left);

          left_set.insert(left);

          if (right_set.find(left) != right_set.end()) {
            nca = left;
            break;
          }

          if ((*_blossom_data)[right].pred == INVALID) break;

          right =
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
          right_path.push_back(right);
          right =
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
          right_path.push_back(right);

          right_set.insert(right);

          if (left_set.find(right) != left_set.end()) {
            nca = right;
            break;
          }

        }

        if (nca == -1) {
          if ((*_blossom_data)[left].pred == INVALID) {
            nca = right;
            while (left_set.find(nca) == left_set.end()) {
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              right_path.push_back(nca);
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              right_path.push_back(nca);
            }
          } else {
            nca = left;
            while (right_set.find(nca) == right_set.end()) {
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              left_path.push_back(nca);
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              left_path.push_back(nca);
            }
          }
        }
      }

      std::vector<int> subblossoms;
      Arc prev;

      prev = _graph.direct(edge, true);
      for (int i = 0; left_path[i] != nca; i += 2) {
        subblossoms.push_back(left_path[i]);
        (*_blossom_data)[left_path[i]].next = prev;
        _tree_set->erase(left_path[i]);

        subblossoms.push_back(left_path[i + 1]);
        (*_blossom_data)[left_path[i + 1]].status = EVEN;
        oddToEven(left_path[i + 1], tree);
        _tree_set->erase(left_path[i + 1]);
        prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
      }

      int k = 0;
      while (right_path[k] != nca) ++k;

      subblossoms.push_back(nca);
      (*_blossom_data)[nca].next = prev;

      for (int i = k - 2; i >= 0; i -= 2) {
        subblossoms.push_back(right_path[i + 1]);
        (*_blossom_data)[right_path[i + 1]].status = EVEN;
        oddToEven(right_path[i + 1], tree);
        _tree_set->erase(right_path[i + 1]);

        (*_blossom_data)[right_path[i + 1]].next =
          (*_blossom_data)[right_path[i + 1]].pred;

        subblossoms.push_back(right_path[i]);
        _tree_set->erase(right_path[i]);
      }

      int surface =
        _blossom_set->join(subblossoms.begin(), subblossoms.end());

      for (int i = 0; i < int(subblossoms.size()); ++i) {
        if (!_blossom_set->trivial(subblossoms[i])) {
          (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
        }
        (*_blossom_data)[subblossoms[i]].status = MATCHED;
      }

      (*_blossom_data)[surface].pot = -2 * _delta_sum;
      (*_blossom_data)[surface].offset = 0;
      (*_blossom_data)[surface].status = EVEN;
      (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
      (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;

      _tree_set->insert(surface, tree);
      _tree_set->erase(nca);
    }

    void splitBlossom(int blossom) {
      Arc next = (*_blossom_data)[blossom].next;
      Arc pred = (*_blossom_data)[blossom].pred;

      int tree = _tree_set->find(blossom);

      (*_blossom_data)[blossom].status = MATCHED;
      oddToMatched(blossom);
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }

      std::vector<int> subblossoms;
      _blossom_set->split(blossom, std::back_inserter(subblossoms));

      Value offset = (*_blossom_data)[blossom].offset;
      int b = _blossom_set->find(_graph.source(pred));
      int d = _blossom_set->find(_graph.source(next));

      int ib = -1, id = -1;
      for (int i = 0; i < int(subblossoms.size()); ++i) {
        if (subblossoms[i] == b) ib = i;
        if (subblossoms[i] == d) id = i;

        (*_blossom_data)[subblossoms[i]].offset = offset;
        if (!_blossom_set->trivial(subblossoms[i])) {
          (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
        }
        if (_blossom_set->classPrio(subblossoms[i]) !=
            std::numeric_limits<Value>::max()) {
          _delta2->push(subblossoms[i],
                        _blossom_set->classPrio(subblossoms[i]) -
                        (*_blossom_data)[subblossoms[i]].offset);
        }
      }

      if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
        for (int i = (id + 1) % subblossoms.size();
             i != ib; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          (*_blossom_data)[sb].next =
            _graph.oppositeArc((*_blossom_data)[tb].next);
        }

        for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          int ub = subblossoms[(i + 2) % subblossoms.size()];

          (*_blossom_data)[sb].status = ODD;
          matchedToOdd(sb);
          _tree_set->insert(sb, tree);
          (*_blossom_data)[sb].pred = pred;
          (*_blossom_data)[sb].next =
                           _graph.oppositeArc((*_blossom_data)[tb].next);

          pred = (*_blossom_data)[ub].next;

          (*_blossom_data)[tb].status = EVEN;
          matchedToEven(tb, tree);
          _tree_set->insert(tb, tree);
          (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
        }

        (*_blossom_data)[subblossoms[id]].status = ODD;
        matchedToOdd(subblossoms[id]);
        _tree_set->insert(subblossoms[id], tree);
        (*_blossom_data)[subblossoms[id]].next = next;
        (*_blossom_data)[subblossoms[id]].pred = pred;

      } else {

        for (int i = (ib + 1) % subblossoms.size();
             i != id; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          (*_blossom_data)[sb].next =
            _graph.oppositeArc((*_blossom_data)[tb].next);
        }

        for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          int ub = subblossoms[(i + 2) % subblossoms.size()];

          (*_blossom_data)[sb].status = ODD;
          matchedToOdd(sb);
          _tree_set->insert(sb, tree);
          (*_blossom_data)[sb].next = next;
          (*_blossom_data)[sb].pred =
            _graph.oppositeArc((*_blossom_data)[tb].next);

          (*_blossom_data)[tb].status = EVEN;
          matchedToEven(tb, tree);
          _tree_set->insert(tb, tree);
          (*_blossom_data)[tb].pred =
            (*_blossom_data)[tb].next =
            _graph.oppositeArc((*_blossom_data)[ub].next);
          next = (*_blossom_data)[ub].next;
        }

        (*_blossom_data)[subblossoms[ib]].status = ODD;
        matchedToOdd(subblossoms[ib]);
        _tree_set->insert(subblossoms[ib], tree);
        (*_blossom_data)[subblossoms[ib]].next = next;
        (*_blossom_data)[subblossoms[ib]].pred = pred;
      }
      _tree_set->erase(blossom);
    }

    void extractBlossom(int blossom, const Node& base, const Arc& matching) {
      if (_blossom_set->trivial(blossom)) {
        int bi = (*_node_index)[base];
        Value pot = (*_node_data)[bi].pot;

        _matching->set(base, matching);
        _blossom_node_list.push_back(base);
        _node_potential->set(base, pot);
      } else {

        Value pot = (*_blossom_data)[blossom].pot;
        int bn = _blossom_node_list.size();

        std::vector<int> subblossoms;
        _blossom_set->split(blossom, std::back_inserter(subblossoms));
        int b = _blossom_set->find(base);
        int ib = -1;
        for (int i = 0; i < int(subblossoms.size()); ++i) {
          if (subblossoms[i] == b) { ib = i; break; }
        }

        for (int i = 1; i < int(subblossoms.size()); i += 2) {
          int sb = subblossoms[(ib + i) % subblossoms.size()];
          int tb = subblossoms[(ib + i + 1) % subblossoms.size()];

          Arc m = (*_blossom_data)[tb].next;
          extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
          extractBlossom(tb, _graph.source(m), m);
        }
        extractBlossom(subblossoms[ib], base, matching);

        int en = _blossom_node_list.size();

        _blossom_potential.push_back(BlossomVariable(bn, en, pot));
      }
    }

    void extractMatching() {
      std::vector<int> blossoms;
      for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
        blossoms.push_back(c);
      }

      for (int i = 0; i < int(blossoms.size()); ++i) {
        if ((*_blossom_data)[blossoms[i]].status == MATCHED) {

          Value offset = (*_blossom_data)[blossoms[i]].offset;
          (*_blossom_data)[blossoms[i]].pot += 2 * offset;
          for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
               n != INVALID; ++n) {
            (*_node_data)[(*_node_index)[n]].pot -= offset;
          }

          Arc matching = (*_blossom_data)[blossoms[i]].next;
          Node base = _graph.source(matching);
          extractBlossom(blossoms[i], base, matching);
        } else {
          Node base = (*_blossom_data)[blossoms[i]].base;
          extractBlossom(blossoms[i], base, INVALID);
        }
      }
    }

  public:

    /// \brief Constructor
    ///
    /// Constructor.
    MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
      : _graph(graph), _weight(weight), _matching(0),
        _node_potential(0), _blossom_potential(), _blossom_node_list(),
        _node_num(0), _blossom_num(0),

        _blossom_index(0), _blossom_set(0), _blossom_data(0),
        _node_index(0), _node_heap_index(0), _node_data(0),
        _tree_set_index(0), _tree_set(0),

        _delta1_index(0), _delta1(0),
        _delta2_index(0), _delta2(0),
        _delta3_index(0), _delta3(0),
        _delta4_index(0), _delta4(0),

        _delta_sum() {}

    ~MaxWeightedMatching() {
      destroyStructures();
    }

    /// \name Execution control
    /// The simplest way to execute the algorithm is to use the
    /// \c run() member function.

    ///@{

    /// \brief Initialize the algorithm
    ///
    /// Initialize the algorithm
    void init() {
      createStructures();

      for (ArcIt e(_graph); e != INVALID; ++e) {
        _node_heap_index->set(e, BinHeap<Value, IntArcMap>::PRE_HEAP);
      }
      for (NodeIt n(_graph); n != INVALID; ++n) {
        _delta1_index->set(n, _delta1->PRE_HEAP);
      }
      for (EdgeIt e(_graph); e != INVALID; ++e) {
        _delta3_index->set(e, _delta3->PRE_HEAP);
      }
      for (int i = 0; i < _blossom_num; ++i) {
        _delta2_index->set(i, _delta2->PRE_HEAP);
        _delta4_index->set(i, _delta4->PRE_HEAP);
      }

      int index = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        Value max = 0;
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
          if (_graph.target(e) == n) continue;
          if ((dualScale * _weight[e]) / 2 > max) {
            max = (dualScale * _weight[e]) / 2;
          }
        }
        _node_index->set(n, index);
        (*_node_data)[index].pot = max;
        _delta1->push(n, max);
        int blossom =
          _blossom_set->insert(n, std::numeric_limits<Value>::max());

        _tree_set->insert(blossom);

        (*_blossom_data)[blossom].status = EVEN;
        (*_blossom_data)[blossom].pred = INVALID;
        (*_blossom_data)[blossom].next = INVALID;
        (*_blossom_data)[blossom].pot = 0;
        (*_blossom_data)[blossom].offset = 0;
        ++index;
      }
      for (EdgeIt e(_graph); e != INVALID; ++e) {
        int si = (*_node_index)[_graph.u(e)];
        int ti = (*_node_index)[_graph.v(e)];
        if (_graph.u(e) != _graph.v(e)) {
          _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
                            dualScale * _weight[e]) / 2);
        }
      }
    }

    /// \brief Starts the algorithm
    ///
    /// Starts the algorithm
    void start() {
      enum OpType {
        D1, D2, D3, D4
      };

      int unmatched = _node_num;
      while (unmatched > 0) {
        Value d1 = !_delta1->empty() ?
          _delta1->prio() : std::numeric_limits<Value>::max();

        Value d2 = !_delta2->empty() ?
          _delta2->prio() : std::numeric_limits<Value>::max();

        Value d3 = !_delta3->empty() ?
          _delta3->prio() : std::numeric_limits<Value>::max();

        Value d4 = !_delta4->empty() ?
          _delta4->prio() : std::numeric_limits<Value>::max();

        _delta_sum = d1; OpType ot = D1;
        if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
        if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
        if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }


        switch (ot) {
        case D1:
          {
            Node n = _delta1->top();
            unmatchNode(n);
            --unmatched;
          }
          break;
        case D2:
          {
            int blossom = _delta2->top();
            Node n = _blossom_set->classTop(blossom);
            Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
            extendOnArc(e);
          }
          break;
        case D3:
          {
            Edge e = _delta3->top();

            int left_blossom = _blossom_set->find(_graph.u(e));
            int right_blossom = _blossom_set->find(_graph.v(e));

            if (left_blossom == right_blossom) {
              _delta3->pop();
            } else {
              int left_tree;
              if ((*_blossom_data)[left_blossom].status == EVEN) {
                left_tree = _tree_set->find(left_blossom);
              } else {
                left_tree = -1;
                ++unmatched;
              }
              int right_tree;
              if ((*_blossom_data)[right_blossom].status == EVEN) {
                right_tree = _tree_set->find(right_blossom);
              } else {
                right_tree = -1;
                ++unmatched;
              }

              if (left_tree == right_tree) {
                shrinkOnEdge(e, left_tree);
              } else {
                augmentOnEdge(e);
                unmatched -= 2;
              }
            }
          } break;
        case D4:
          splitBlossom(_delta4->top());
          break;
        }
      }
      extractMatching();
    }

    /// \brief Runs %MaxWeightedMatching algorithm.
    ///
    /// This method runs the %MaxWeightedMatching algorithm.
    ///
    /// \note mwm.run() is just a shortcut of the following code.
    /// \code
    ///   mwm.init();
    ///   mwm.start();
    /// \endcode
    void run() {
      init();
      start();
    }

    /// @}

    /// \name Primal solution
    /// Functions to get the primal solution, ie. the matching.

    /// @{

    /// \brief Returns the weight of the matching.
    ///
    /// Returns the weight of the matching.
    Value matchingValue() const {
      Value sum = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_matching)[n] != INVALID) {
          sum += _weight[(*_matching)[n]];
        }
      }
      return sum /= 2;
    }

    /// \brief Returns the cardinality of the matching.
    ///
    /// Returns the cardinality of the matching.
    int matchingSize() const {
      int num = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_matching)[n] != INVALID) {
          ++num;
        }
      }
      return num /= 2;
    }

    /// \brief Returns true when the edge is in the matching.
    ///
    /// Returns true when the edge is in the matching.
    bool matching(const Edge& edge) const {
      return edge == (*_matching)[_graph.u(edge)];
    }

    /// \brief Returns the incident matching arc.
    ///
    /// Returns the incident matching arc from given node. If the
    /// node is not matched then it gives back \c INVALID.
    Arc matching(const Node& node) const {
      return (*_matching)[node];
    }

    /// \brief Returns the mate of the node.
    ///
    /// Returns the adjancent node in a mathcing arc. If the node is
    /// not matched then it gives back \c INVALID.
    Node mate(const Node& node) const {
      return (*_matching)[node] != INVALID ?
        _graph.target((*_matching)[node]) : INVALID;
    }

    /// @}

    /// \name Dual solution
    /// Functions to get the dual solution.

    /// @{

    /// \brief Returns the value of the dual solution.
    ///
    /// Returns the value of the dual solution. It should be equal to
    /// the primal value scaled by \ref dualScale "dual scale".
    Value dualValue() const {
      Value sum = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        sum += nodeValue(n);
      }
      for (int i = 0; i < blossomNum(); ++i) {
        sum += blossomValue(i) * (blossomSize(i) / 2);
      }
      return sum;
    }

    /// \brief Returns the value of the node.
    ///
    /// Returns the the value of the node.
    Value nodeValue(const Node& n) const {
      return (*_node_potential)[n];
    }

    /// \brief Returns the number of the blossoms in the basis.
    ///
    /// Returns the number of the blossoms in the basis.
    /// \see BlossomIt
    int blossomNum() const {
      return _blossom_potential.size();
    }


    /// \brief Returns the number of the nodes in the blossom.
    ///
    /// Returns the number of the nodes in the blossom.
    int blossomSize(int k) const {
      return _blossom_potential[k].end - _blossom_potential[k].begin;
    }

    /// \brief Returns the value of the blossom.
    ///
    /// Returns the the value of the blossom.
    /// \see BlossomIt
    Value blossomValue(int k) const {
      return _blossom_potential[k].value;
    }

    /// \brief Iterator for obtaining the nodes of the blossom.
    ///
    /// Iterator for obtaining the nodes of the blossom. This class
    /// provides a common lemon style iterator for listing a
    /// subset of the nodes.
    class BlossomIt {
    public:

      /// \brief Constructor.
      ///
      /// Constructor to get the nodes of the variable.
      BlossomIt(const MaxWeightedMatching& algorithm, int variable)
        : _algorithm(&algorithm)
      {
        _index = _algorithm->_blossom_potential[variable].begin;
        _last = _algorithm->_blossom_potential[variable].end;
      }

      /// \brief Conversion to node.
      ///
      /// Conversion to node.
      operator Node() const {
        return _algorithm->_blossom_node_list[_index];
      }

      /// \brief Increment operator.
      ///
      /// Increment operator.
      BlossomIt& operator++() {
        ++_index;
        return *this;
      }

      /// \brief Validity checking
      ///
      /// Checks whether the iterator is invalid.
      bool operator==(Invalid) const { return _index == _last; }

      /// \brief Validity checking
      ///
      /// Checks whether the iterator is valid.
      bool operator!=(Invalid) const { return _index != _last; }

    private:
      const MaxWeightedMatching* _algorithm;
      int _last;
      int _index;
    };

    /// @}

  };

  /// \ingroup matching
  ///
  /// \brief Weighted perfect matching in general graphs
  ///
  /// This class provides an efficient implementation of Edmond's
  /// maximum weighted perfect matching algorithm. The implementation
  /// is based on extensive use of priority queues and provides
  /// \f$O(nm\log(n))\f$ time complexity.
  ///
  /// The maximum weighted matching problem is to find undirected
  /// edges in the graph with maximum overall weight and no two of
  /// them shares their ends and covers all nodes. The problem can be
  /// formulated with the following linear program.
  /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
  /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
      \quad \forall B\in\mathcal{O}\f] */
  /// \f[x_e \ge 0\quad \forall e\in E\f]
  /// \f[\max \sum_{e\in E}x_ew_e\f]
  /// where \f$\delta(X)\f$ is the set of edges incident to a node in
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
  /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
  /// subsets of the nodes.
  ///
  /// The algorithm calculates an optimal matching and a proof of the
  /// optimality. The solution of the dual problem can be used to check
  /// the result of the algorithm. The dual linear problem is the
  /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
      w_{uv} \quad \forall uv\in E\f] */
  /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
  /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
      \frac{\vert B \vert - 1}{2}z_B\f] */
  ///
  /// The algorithm can be executed with \c run() or the \c init() and
  /// then the \c start() member functions. After it the matching can
  /// be asked with \c matching() or mate() functions. The dual
  /// solution can be get with \c nodeValue(), \c blossomNum() and \c
  /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
  /// "BlossomIt" nested class which is able to iterate on the nodes
  /// of a blossom. If the value type is integral then the dual
  /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
  template <typename _Graph,
            typename _WeightMap = typename _Graph::template EdgeMap<int> >
  class MaxWeightedPerfectMatching {
  public:

    typedef _Graph Graph;
    typedef _WeightMap WeightMap;
    typedef typename WeightMap::Value Value;

    /// \brief Scaling factor for dual solution
    ///
    /// Scaling factor for dual solution, it is equal to 4 or 1
    /// according to the value type.
    static const int dualScale =
      std::numeric_limits<Value>::is_integer ? 4 : 1;

    typedef typename Graph::template NodeMap<typename Graph::Arc>
    MatchingMap;

  private:

    TEMPLATE_GRAPH_TYPEDEFS(Graph);

    typedef typename Graph::template NodeMap<Value> NodePotential;
    typedef std::vector<Node> BlossomNodeList;

    struct BlossomVariable {
      int begin, end;
      Value value;

      BlossomVariable(int _begin, int _end, Value _value)
        : begin(_begin), end(_end), value(_value) {}

    };

    typedef std::vector<BlossomVariable> BlossomPotential;

    const Graph& _graph;
    const WeightMap& _weight;

    MatchingMap* _matching;

    NodePotential* _node_potential;

    BlossomPotential _blossom_potential;
    BlossomNodeList _blossom_node_list;

    int _node_num;
    int _blossom_num;

    typedef RangeMap<int> IntIntMap;

    enum Status {
      EVEN = -1, MATCHED = 0, ODD = 1
    };

    typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
    struct BlossomData {
      int tree;
      Status status;
      Arc pred, next;
      Value pot, offset;
    };

    IntNodeMap *_blossom_index;
    BlossomSet *_blossom_set;
    RangeMap<BlossomData>* _blossom_data;

    IntNodeMap *_node_index;
    IntArcMap *_node_heap_index;

    struct NodeData {

      NodeData(IntArcMap& node_heap_index)
        : heap(node_heap_index) {}

      int blossom;
      Value pot;
      BinHeap<Value, IntArcMap> heap;
      std::map<int, Arc> heap_index;

      int tree;
    };

    RangeMap<NodeData>* _node_data;

    typedef ExtendFindEnum<IntIntMap> TreeSet;

    IntIntMap *_tree_set_index;
    TreeSet *_tree_set;

    IntIntMap *_delta2_index;
    BinHeap<Value, IntIntMap> *_delta2;

    IntEdgeMap *_delta3_index;
    BinHeap<Value, IntEdgeMap> *_delta3;

    IntIntMap *_delta4_index;
    BinHeap<Value, IntIntMap> *_delta4;

    Value _delta_sum;

    void createStructures() {
      _node_num = countNodes(_graph);
      _blossom_num = _node_num * 3 / 2;

      if (!_matching) {
        _matching = new MatchingMap(_graph);
      }
      if (!_node_potential) {
        _node_potential = new NodePotential(_graph);
      }
      if (!_blossom_set) {
        _blossom_index = new IntNodeMap(_graph);
        _blossom_set = new BlossomSet(*_blossom_index);
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
      }

      if (!_node_index) {
        _node_index = new IntNodeMap(_graph);
        _node_heap_index = new IntArcMap(_graph);
        _node_data = new RangeMap<NodeData>(_node_num,
                                            NodeData(*_node_heap_index));
      }

      if (!_tree_set) {
        _tree_set_index = new IntIntMap(_blossom_num);
        _tree_set = new TreeSet(*_tree_set_index);
      }
      if (!_delta2) {
        _delta2_index = new IntIntMap(_blossom_num);
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
      }
      if (!_delta3) {
        _delta3_index = new IntEdgeMap(_graph);
        _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
      }
      if (!_delta4) {
        _delta4_index = new IntIntMap(_blossom_num);
        _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
      }
    }

    void destroyStructures() {
      _node_num = countNodes(_graph);
      _blossom_num = _node_num * 3 / 2;

      if (_matching) {
        delete _matching;
      }
      if (_node_potential) {
        delete _node_potential;
      }
      if (_blossom_set) {
        delete _blossom_index;
        delete _blossom_set;
        delete _blossom_data;
      }

      if (_node_index) {
        delete _node_index;
        delete _node_heap_index;
        delete _node_data;
      }

      if (_tree_set) {
        delete _tree_set_index;
        delete _tree_set;
      }
      if (_delta2) {
        delete _delta2_index;
        delete _delta2;
      }
      if (_delta3) {
        delete _delta3_index;
        delete _delta3;
      }
      if (_delta4) {
        delete _delta4_index;
        delete _delta4;
      }
    }

    void matchedToEven(int blossom, int tree) {
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }

      if (!_blossom_set->trivial(blossom)) {
        (*_blossom_data)[blossom].pot -=
          2 * (_delta_sum - (*_blossom_data)[blossom].offset);
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {

        _blossom_set->increase(n, std::numeric_limits<Value>::max());
        int ni = (*_node_index)[n];

        (*_node_data)[ni].heap.clear();
        (*_node_data)[ni].heap_index.clear();

        (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if ((*_blossom_data)[vb].status == EVEN) {
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
              _delta3->push(e, rw / 2);
            }
          } else {
            typename std::map<int, Arc>::iterator it =
              (*_node_data)[vi].heap_index.find(tree);

            if (it != (*_node_data)[vi].heap_index.end()) {
              if ((*_node_data)[vi].heap[it->second] > rw) {
                (*_node_data)[vi].heap.replace(it->second, e);
                (*_node_data)[vi].heap.decrease(e, rw);
                it->second = e;
              }
            } else {
              (*_node_data)[vi].heap.push(e, rw);
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
            }

            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());

              if ((*_blossom_data)[vb].status == MATCHED) {
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
                               (*_blossom_data)[vb].offset);
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
                           (*_blossom_data)[vb].offset){
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
                                   (*_blossom_data)[vb].offset);
                }
              }
            }
          }
        }
      }
      (*_blossom_data)[blossom].offset = 0;
    }

    void matchedToOdd(int blossom) {
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }
      (*_blossom_data)[blossom].offset += _delta_sum;
      if (!_blossom_set->trivial(blossom)) {
        _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
                     (*_blossom_data)[blossom].offset);
      }
    }

    void evenToMatched(int blossom, int tree) {
      if (!_blossom_set->trivial(blossom)) {
        (*_blossom_data)[blossom].pot += 2 * _delta_sum;
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {
        int ni = (*_node_index)[n];
        (*_node_data)[ni].pot -= _delta_sum;

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if (vb == blossom) {
            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }
          } else if ((*_blossom_data)[vb].status == EVEN) {

            if (_delta3->state(e) == _delta3->IN_HEAP) {
              _delta3->erase(e);
            }

            int vt = _tree_set->find(vb);

            if (vt != tree) {

              Arc r = _graph.oppositeArc(e);

              typename std::map<int, Arc>::iterator it =
                (*_node_data)[ni].heap_index.find(vt);

              if (it != (*_node_data)[ni].heap_index.end()) {
                if ((*_node_data)[ni].heap[it->second] > rw) {
                  (*_node_data)[ni].heap.replace(it->second, r);
                  (*_node_data)[ni].heap.decrease(r, rw);
                  it->second = r;
                }
              } else {
                (*_node_data)[ni].heap.push(r, rw);
                (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
              }

              if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
                _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());

                if (_delta2->state(blossom) != _delta2->IN_HEAP) {
                  _delta2->push(blossom, _blossom_set->classPrio(blossom) -
                               (*_blossom_data)[blossom].offset);
                } else if ((*_delta2)[blossom] >
                           _blossom_set->classPrio(blossom) -
                           (*_blossom_data)[blossom].offset){
                  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
                                   (*_blossom_data)[blossom].offset);
                }
              }
            }
          } else {

            typename std::map<int, Arc>::iterator it =
              (*_node_data)[vi].heap_index.find(tree);

            if (it != (*_node_data)[vi].heap_index.end()) {
              (*_node_data)[vi].heap.erase(it->second);
              (*_node_data)[vi].heap_index.erase(it);
              if ((*_node_data)[vi].heap.empty()) {
                _blossom_set->increase(v, std::numeric_limits<Value>::max());
              } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
                _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
              }

              if ((*_blossom_data)[vb].status == MATCHED) {
                if (_blossom_set->classPrio(vb) ==
                    std::numeric_limits<Value>::max()) {
                  _delta2->erase(vb);
                } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
                           (*_blossom_data)[vb].offset) {
                  _delta2->increase(vb, _blossom_set->classPrio(vb) -
                                   (*_blossom_data)[vb].offset);
                }
              }
            }
          }
        }
      }
    }

    void oddToMatched(int blossom) {
      (*_blossom_data)[blossom].offset -= _delta_sum;

      if (_blossom_set->classPrio(blossom) !=
          std::numeric_limits<Value>::max()) {
        _delta2->push(blossom, _blossom_set->classPrio(blossom) -
                       (*_blossom_data)[blossom].offset);
      }

      if (!_blossom_set->trivial(blossom)) {
        _delta4->erase(blossom);
      }
    }

    void oddToEven(int blossom, int tree) {
      if (!_blossom_set->trivial(blossom)) {
        _delta4->erase(blossom);
        (*_blossom_data)[blossom].pot -=
          2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
      }

      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
           n != INVALID; ++n) {
        int ni = (*_node_index)[n];

        _blossom_set->increase(n, std::numeric_limits<Value>::max());

        (*_node_data)[ni].heap.clear();
        (*_node_data)[ni].heap_index.clear();
        (*_node_data)[ni].pot +=
          2 * _delta_sum - (*_blossom_data)[blossom].offset;

        for (InArcIt e(_graph, n); e != INVALID; ++e) {
          Node v = _graph.source(e);
          int vb = _blossom_set->find(v);
          int vi = (*_node_index)[v];

          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
            dualScale * _weight[e];

          if ((*_blossom_data)[vb].status == EVEN) {
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
              _delta3->push(e, rw / 2);
            }
          } else {

            typename std::map<int, Arc>::iterator it =
              (*_node_data)[vi].heap_index.find(tree);

            if (it != (*_node_data)[vi].heap_index.end()) {
              if ((*_node_data)[vi].heap[it->second] > rw) {
                (*_node_data)[vi].heap.replace(it->second, e);
                (*_node_data)[vi].heap.decrease(e, rw);
                it->second = e;
              }
            } else {
              (*_node_data)[vi].heap.push(e, rw);
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
            }

            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());

              if ((*_blossom_data)[vb].status == MATCHED) {
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
                               (*_blossom_data)[vb].offset);
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
                           (*_blossom_data)[vb].offset) {
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
                                   (*_blossom_data)[vb].offset);
                }
              }
            }
          }
        }
      }
      (*_blossom_data)[blossom].offset = 0;
    }

    void alternatePath(int even, int tree) {
      int odd;

      evenToMatched(even, tree);
      (*_blossom_data)[even].status = MATCHED;

      while ((*_blossom_data)[even].pred != INVALID) {
        odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
        (*_blossom_data)[odd].status = MATCHED;
        oddToMatched(odd);
        (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;

        even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
        (*_blossom_data)[even].status = MATCHED;
        evenToMatched(even, tree);
        (*_blossom_data)[even].next =
          _graph.oppositeArc((*_blossom_data)[odd].pred);
      }

    }

    void destroyTree(int tree) {
      for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
        if ((*_blossom_data)[b].status == EVEN) {
          (*_blossom_data)[b].status = MATCHED;
          evenToMatched(b, tree);
        } else if ((*_blossom_data)[b].status == ODD) {
          (*_blossom_data)[b].status = MATCHED;
          oddToMatched(b);
        }
      }
      _tree_set->eraseClass(tree);
    }

    void augmentOnEdge(const Edge& edge) {

      int left = _blossom_set->find(_graph.u(edge));
      int right = _blossom_set->find(_graph.v(edge));

      int left_tree = _tree_set->find(left);
      alternatePath(left, left_tree);
      destroyTree(left_tree);

      int right_tree = _tree_set->find(right);
      alternatePath(right, right_tree);
      destroyTree(right_tree);

      (*_blossom_data)[left].next = _graph.direct(edge, true);
      (*_blossom_data)[right].next = _graph.direct(edge, false);
    }

    void extendOnArc(const Arc& arc) {
      int base = _blossom_set->find(_graph.target(arc));
      int tree = _tree_set->find(base);

      int odd = _blossom_set->find(_graph.source(arc));
      _tree_set->insert(odd, tree);
      (*_blossom_data)[odd].status = ODD;
      matchedToOdd(odd);
      (*_blossom_data)[odd].pred = arc;

      int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
      (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
      _tree_set->insert(even, tree);
      (*_blossom_data)[even].status = EVEN;
      matchedToEven(even, tree);
    }

    void shrinkOnEdge(const Edge& edge, int tree) {
      int nca = -1;
      std::vector<int> left_path, right_path;

      {
        std::set<int> left_set, right_set;
        int left = _blossom_set->find(_graph.u(edge));
        left_path.push_back(left);
        left_set.insert(left);

        int right = _blossom_set->find(_graph.v(edge));
        right_path.push_back(right);
        right_set.insert(right);

        while (true) {

          if ((*_blossom_data)[left].pred == INVALID) break;

          left =
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
          left_path.push_back(left);
          left =
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
          left_path.push_back(left);

          left_set.insert(left);

          if (right_set.find(left) != right_set.end()) {
            nca = left;
            break;
          }

          if ((*_blossom_data)[right].pred == INVALID) break;

          right =
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
          right_path.push_back(right);
          right =
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
          right_path.push_back(right);

          right_set.insert(right);

          if (left_set.find(right) != left_set.end()) {
            nca = right;
            break;
          }

        }

        if (nca == -1) {
          if ((*_blossom_data)[left].pred == INVALID) {
            nca = right;
            while (left_set.find(nca) == left_set.end()) {
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              right_path.push_back(nca);
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              right_path.push_back(nca);
            }
          } else {
            nca = left;
            while (right_set.find(nca) == right_set.end()) {
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              left_path.push_back(nca);
              nca =
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
              left_path.push_back(nca);
            }
          }
        }
      }

      std::vector<int> subblossoms;
      Arc prev;

      prev = _graph.direct(edge, true);
      for (int i = 0; left_path[i] != nca; i += 2) {
        subblossoms.push_back(left_path[i]);
        (*_blossom_data)[left_path[i]].next = prev;
        _tree_set->erase(left_path[i]);

        subblossoms.push_back(left_path[i + 1]);
        (*_blossom_data)[left_path[i + 1]].status = EVEN;
        oddToEven(left_path[i + 1], tree);
        _tree_set->erase(left_path[i + 1]);
        prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
      }

      int k = 0;
      while (right_path[k] != nca) ++k;

      subblossoms.push_back(nca);
      (*_blossom_data)[nca].next = prev;

      for (int i = k - 2; i >= 0; i -= 2) {
        subblossoms.push_back(right_path[i + 1]);
        (*_blossom_data)[right_path[i + 1]].status = EVEN;
        oddToEven(right_path[i + 1], tree);
        _tree_set->erase(right_path[i + 1]);

        (*_blossom_data)[right_path[i + 1]].next =
          (*_blossom_data)[right_path[i + 1]].pred;

        subblossoms.push_back(right_path[i]);
        _tree_set->erase(right_path[i]);
      }

      int surface =
        _blossom_set->join(subblossoms.begin(), subblossoms.end());

      for (int i = 0; i < int(subblossoms.size()); ++i) {
        if (!_blossom_set->trivial(subblossoms[i])) {
          (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
        }
        (*_blossom_data)[subblossoms[i]].status = MATCHED;
      }

      (*_blossom_data)[surface].pot = -2 * _delta_sum;
      (*_blossom_data)[surface].offset = 0;
      (*_blossom_data)[surface].status = EVEN;
      (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
      (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;

      _tree_set->insert(surface, tree);
      _tree_set->erase(nca);
    }

    void splitBlossom(int blossom) {
      Arc next = (*_blossom_data)[blossom].next;
      Arc pred = (*_blossom_data)[blossom].pred;

      int tree = _tree_set->find(blossom);

      (*_blossom_data)[blossom].status = MATCHED;
      oddToMatched(blossom);
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
        _delta2->erase(blossom);
      }

      std::vector<int> subblossoms;
      _blossom_set->split(blossom, std::back_inserter(subblossoms));

      Value offset = (*_blossom_data)[blossom].offset;
      int b = _blossom_set->find(_graph.source(pred));
      int d = _blossom_set->find(_graph.source(next));

      int ib = -1, id = -1;
      for (int i = 0; i < int(subblossoms.size()); ++i) {
        if (subblossoms[i] == b) ib = i;
        if (subblossoms[i] == d) id = i;

        (*_blossom_data)[subblossoms[i]].offset = offset;
        if (!_blossom_set->trivial(subblossoms[i])) {
          (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
        }
        if (_blossom_set->classPrio(subblossoms[i]) !=
            std::numeric_limits<Value>::max()) {
          _delta2->push(subblossoms[i],
                        _blossom_set->classPrio(subblossoms[i]) -
                        (*_blossom_data)[subblossoms[i]].offset);
        }
      }

      if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
        for (int i = (id + 1) % subblossoms.size();
             i != ib; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          (*_blossom_data)[sb].next =
            _graph.oppositeArc((*_blossom_data)[tb].next);
        }

        for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          int ub = subblossoms[(i + 2) % subblossoms.size()];

          (*_blossom_data)[sb].status = ODD;
          matchedToOdd(sb);
          _tree_set->insert(sb, tree);
          (*_blossom_data)[sb].pred = pred;
          (*_blossom_data)[sb].next =
                           _graph.oppositeArc((*_blossom_data)[tb].next);

          pred = (*_blossom_data)[ub].next;

          (*_blossom_data)[tb].status = EVEN;
          matchedToEven(tb, tree);
          _tree_set->insert(tb, tree);
          (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
        }

        (*_blossom_data)[subblossoms[id]].status = ODD;
        matchedToOdd(subblossoms[id]);
        _tree_set->insert(subblossoms[id], tree);
        (*_blossom_data)[subblossoms[id]].next = next;
        (*_blossom_data)[subblossoms[id]].pred = pred;

      } else {

        for (int i = (ib + 1) % subblossoms.size();
             i != id; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          (*_blossom_data)[sb].next =
            _graph.oppositeArc((*_blossom_data)[tb].next);
        }

        for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
          int sb = subblossoms[i];
          int tb = subblossoms[(i + 1) % subblossoms.size()];
          int ub = subblossoms[(i + 2) % subblossoms.size()];

          (*_blossom_data)[sb].status = ODD;
          matchedToOdd(sb);
          _tree_set->insert(sb, tree);
          (*_blossom_data)[sb].next = next;
          (*_blossom_data)[sb].pred =
            _graph.oppositeArc((*_blossom_data)[tb].next);

          (*_blossom_data)[tb].status = EVEN;
          matchedToEven(tb, tree);
          _tree_set->insert(tb, tree);
          (*_blossom_data)[tb].pred =
            (*_blossom_data)[tb].next =
            _graph.oppositeArc((*_blossom_data)[ub].next);
          next = (*_blossom_data)[ub].next;
        }

        (*_blossom_data)[subblossoms[ib]].status = ODD;
        matchedToOdd(subblossoms[ib]);
        _tree_set->insert(subblossoms[ib], tree);
        (*_blossom_data)[subblossoms[ib]].next = next;
        (*_blossom_data)[subblossoms[ib]].pred = pred;
      }
      _tree_set->erase(blossom);
    }

    void extractBlossom(int blossom, const Node& base, const Arc& matching) {
      if (_blossom_set->trivial(blossom)) {
        int bi = (*_node_index)[base];
        Value pot = (*_node_data)[bi].pot;

        _matching->set(base, matching);
        _blossom_node_list.push_back(base);
        _node_potential->set(base, pot);
      } else {

        Value pot = (*_blossom_data)[blossom].pot;
        int bn = _blossom_node_list.size();

        std::vector<int> subblossoms;
        _blossom_set->split(blossom, std::back_inserter(subblossoms));
        int b = _blossom_set->find(base);
        int ib = -1;
        for (int i = 0; i < int(subblossoms.size()); ++i) {
          if (subblossoms[i] == b) { ib = i; break; }
        }

        for (int i = 1; i < int(subblossoms.size()); i += 2) {
          int sb = subblossoms[(ib + i) % subblossoms.size()];
          int tb = subblossoms[(ib + i + 1) % subblossoms.size()];

          Arc m = (*_blossom_data)[tb].next;
          extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
          extractBlossom(tb, _graph.source(m), m);
        }
        extractBlossom(subblossoms[ib], base, matching);

        int en = _blossom_node_list.size();

        _blossom_potential.push_back(BlossomVariable(bn, en, pot));
      }
    }

    void extractMatching() {
      std::vector<int> blossoms;
      for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
        blossoms.push_back(c);
      }

      for (int i = 0; i < int(blossoms.size()); ++i) {

        Value offset = (*_blossom_data)[blossoms[i]].offset;
        (*_blossom_data)[blossoms[i]].pot += 2 * offset;
        for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
             n != INVALID; ++n) {
          (*_node_data)[(*_node_index)[n]].pot -= offset;
        }

        Arc matching = (*_blossom_data)[blossoms[i]].next;
        Node base = _graph.source(matching);
        extractBlossom(blossoms[i], base, matching);
      }
    }

  public:

    /// \brief Constructor
    ///
    /// Constructor.
    MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
      : _graph(graph), _weight(weight), _matching(0),
        _node_potential(0), _blossom_potential(), _blossom_node_list(),
        _node_num(0), _blossom_num(0),

        _blossom_index(0), _blossom_set(0), _blossom_data(0),
        _node_index(0), _node_heap_index(0), _node_data(0),
        _tree_set_index(0), _tree_set(0),

        _delta2_index(0), _delta2(0),
        _delta3_index(0), _delta3(0),
        _delta4_index(0), _delta4(0),

        _delta_sum() {}

    ~MaxWeightedPerfectMatching() {
      destroyStructures();
    }

    /// \name Execution control
    /// The simplest way to execute the algorithm is to use the
    /// \c run() member function.

    ///@{

    /// \brief Initialize the algorithm
    ///
    /// Initialize the algorithm
    void init() {
      createStructures();

      for (ArcIt e(_graph); e != INVALID; ++e) {
        _node_heap_index->set(e, BinHeap<Value, IntArcMap>::PRE_HEAP);
      }
      for (EdgeIt e(_graph); e != INVALID; ++e) {
        _delta3_index->set(e, _delta3->PRE_HEAP);
      }
      for (int i = 0; i < _blossom_num; ++i) {
        _delta2_index->set(i, _delta2->PRE_HEAP);
        _delta4_index->set(i, _delta4->PRE_HEAP);
      }

      int index = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        Value max = - std::numeric_limits<Value>::max();
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
          if (_graph.target(e) == n) continue;
          if ((dualScale * _weight[e]) / 2 > max) {
            max = (dualScale * _weight[e]) / 2;
          }
        }
        _node_index->set(n, index);
        (*_node_data)[index].pot = max;
        int blossom =
          _blossom_set->insert(n, std::numeric_limits<Value>::max());

        _tree_set->insert(blossom);

        (*_blossom_data)[blossom].status = EVEN;
        (*_blossom_data)[blossom].pred = INVALID;
        (*_blossom_data)[blossom].next = INVALID;
        (*_blossom_data)[blossom].pot = 0;
        (*_blossom_data)[blossom].offset = 0;
        ++index;
      }
      for (EdgeIt e(_graph); e != INVALID; ++e) {
        int si = (*_node_index)[_graph.u(e)];
        int ti = (*_node_index)[_graph.v(e)];
        if (_graph.u(e) != _graph.v(e)) {
          _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
                            dualScale * _weight[e]) / 2);
        }
      }
    }

    /// \brief Starts the algorithm
    ///
    /// Starts the algorithm
    bool start() {
      enum OpType {
        D2, D3, D4
      };

      int unmatched = _node_num;
      while (unmatched > 0) {
        Value d2 = !_delta2->empty() ?
          _delta2->prio() : std::numeric_limits<Value>::max();

        Value d3 = !_delta3->empty() ?
          _delta3->prio() : std::numeric_limits<Value>::max();

        Value d4 = !_delta4->empty() ?
          _delta4->prio() : std::numeric_limits<Value>::max();

        _delta_sum = d2; OpType ot = D2;
        if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
        if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }

        if (_delta_sum == std::numeric_limits<Value>::max()) {
          return false;
        }

        switch (ot) {
        case D2:
          {
            int blossom = _delta2->top();
            Node n = _blossom_set->classTop(blossom);
            Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
            extendOnArc(e);
          }
          break;
        case D3:
          {
            Edge e = _delta3->top();

            int left_blossom = _blossom_set->find(_graph.u(e));
            int right_blossom = _blossom_set->find(_graph.v(e));

            if (left_blossom == right_blossom) {
              _delta3->pop();
            } else {
              int left_tree = _tree_set->find(left_blossom);
              int right_tree = _tree_set->find(right_blossom);

              if (left_tree == right_tree) {
                shrinkOnEdge(e, left_tree);
              } else {
                augmentOnEdge(e);
                unmatched -= 2;
              }
            }
          } break;
        case D4:
          splitBlossom(_delta4->top());
          break;
        }
      }
      extractMatching();
      return true;
    }

    /// \brief Runs %MaxWeightedPerfectMatching algorithm.
    ///
    /// This method runs the %MaxWeightedPerfectMatching algorithm.
    ///
    /// \note mwm.run() is just a shortcut of the following code.
    /// \code
    ///   mwm.init();
    ///   mwm.start();
    /// \endcode
    bool run() {
      init();
      return start();
    }

    /// @}

    /// \name Primal solution
    /// Functions to get the primal solution, ie. the matching.

    /// @{

    /// \brief Returns the matching value.
    ///
    /// Returns the matching value.
    Value matchingValue() const {
      Value sum = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        if ((*_matching)[n] != INVALID) {
          sum += _weight[(*_matching)[n]];
        }
      }
      return sum /= 2;
    }

    /// \brief Returns true when the edge is in the matching.
    ///
    /// Returns true when the edge is in the matching.
    bool matching(const Edge& edge) const {
      return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
    }

    /// \brief Returns the incident matching edge.
    ///
    /// Returns the incident matching arc from given edge.
    Arc matching(const Node& node) const {
      return (*_matching)[node];
    }

    /// \brief Returns the mate of the node.
    ///
    /// Returns the adjancent node in a mathcing arc.
    Node mate(const Node& node) const {
      return _graph.target((*_matching)[node]);
    }

    /// @}

    /// \name Dual solution
    /// Functions to get the dual solution.

    /// @{

    /// \brief Returns the value of the dual solution.
    ///
    /// Returns the value of the dual solution. It should be equal to
    /// the primal value scaled by \ref dualScale "dual scale".
    Value dualValue() const {
      Value sum = 0;
      for (NodeIt n(_graph); n != INVALID; ++n) {
        sum += nodeValue(n);
      }
      for (int i = 0; i < blossomNum(); ++i) {
        sum += blossomValue(i) * (blossomSize(i) / 2);
      }
      return sum;
    }

    /// \brief Returns the value of the node.
    ///
    /// Returns the the value of the node.
    Value nodeValue(const Node& n) const {
      return (*_node_potential)[n];
    }

    /// \brief Returns the number of the blossoms in the basis.
    ///
    /// Returns the number of the blossoms in the basis.
    /// \see BlossomIt
    int blossomNum() const {
      return _blossom_potential.size();
    }


    /// \brief Returns the number of the nodes in the blossom.
    ///
    /// Returns the number of the nodes in the blossom.
    int blossomSize(int k) const {
      return _blossom_potential[k].end - _blossom_potential[k].begin;
    }

    /// \brief Returns the value of the blossom.
    ///
    /// Returns the the value of the blossom.
    /// \see BlossomIt
    Value blossomValue(int k) const {
      return _blossom_potential[k].value;
    }

    /// \brief Iterator for obtaining the nodes of the blossom.
    ///
    /// Iterator for obtaining the nodes of the blossom. This class
    /// provides a common lemon style iterator for listing a
    /// subset of the nodes.
    class BlossomIt {
    public:

      /// \brief Constructor.
      ///
      /// Constructor to get the nodes of the variable.
      BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
        : _algorithm(&algorithm)
      {
        _index = _algorithm->_blossom_potential[variable].begin;
        _last = _algorithm->_blossom_potential[variable].end;
      }

      /// \brief Conversion to node.
      ///
      /// Conversion to node.
      operator Node() const {
        return _algorithm->_blossom_node_list[_index];
      }

      /// \brief Increment operator.
      ///
      /// Increment operator.
      BlossomIt& operator++() {
        ++_index;
        return *this;
      }

      /// \brief Validity checking
      ///
      /// Checks whether the iterator is invalid.
      bool operator==(Invalid) const { return _index == _last; }

      /// \brief Validity checking
      ///
      /// Checks whether the iterator is valid.
      bool operator!=(Invalid) const { return _index != _last; }

    private:
      const MaxWeightedPerfectMatching* _algorithm;
      int _last;
      int _index;
    };

    /// @}

  };


} //END OF NAMESPACE LEMON

#endif //LEMON_MAX_MATCHING_H