source: lemon-main/lemon/max_matching.h @ 326:64ad48007fb2

/* -*- 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 graph.

namespace lemon {

  ///\ingroup matching
  ///
  ///\brief Edmonds' alternating forest maximum matching algorithm.
  ///
  ///This class provides Edmonds' alternating forest matching
  ///algorithm. The starting matching (if any) can be passed to the
  ///algorithm using some of init functions.
  ///
  ///The dual side of a matching is a map of the nodes to
  ///MaxMatching::DecompType, having values \c D, \c A and \c C
  ///showing the Gallai-Edmonds decomposition of the digraph. The nodes
  ///in \c D induce a digraph with factor-critical components, the nodes
  ///in \c A form the barrier, and the nodes in \c C induce a digraph
  ///having a perfect matching. This decomposition can be attained by
  ///calling \c decomposition() after running the algorithm.
  ///
  ///\param Digraph The graph type the algorithm runs on.
  template <typename Graph>
  class MaxMatching {

  protected:

    TEMPLATE_GRAPH_TYPEDEFS(Graph);

    typedef typename Graph::template NodeMap<int> UFECrossRef;
    typedef UnionFindEnum<UFECrossRef> UFE;
    typedef std::vector<Node> NV;

    typedef typename Graph::template NodeMap<int> EFECrossRef;
    typedef ExtendFindEnum<EFECrossRef> EFE;

  public:

    ///\brief Indicates the Gallai-Edmonds decomposition of the digraph.
    ///
    ///Indicates the Gallai-Edmonds decomposition of the digraph, which
    ///shows an upper bound on the size of a maximum matching. The
    ///nodes with DecompType \c D induce a digraph with factor-critical
    ///components, the nodes in \c A form the canonical barrier, and the
    ///nodes in \c C induce a digraph having a perfect matching.
    enum DecompType {
      D=0,
      A=1,
      C=2
    };

  protected:

    static const int HEUR_density=2;
    const Graph& g;
    typename Graph::template NodeMap<Node> _mate;
    typename Graph::template NodeMap<DecompType> position;

  public:

    MaxMatching(const Graph& _g)
      : g(_g), _mate(_g), position(_g) {}

    ///\brief Sets the actual matching to the empty matching.
    ///
    ///Sets the actual matching to the empty matching.
    ///
    void init() {
      for(NodeIt v(g); v!=INVALID; ++v) {
        _mate.set(v,INVALID);
        position.set(v,C);
      }
    }

    ///\brief Finds a greedy matching for initial matching.
    ///
    ///For initial matchig it finds a maximal greedy matching.
    void greedyInit() {
      for(NodeIt v(g); v!=INVALID; ++v) {
        _mate.set(v,INVALID);
        position.set(v,C);
      }
      for(NodeIt v(g); v!=INVALID; ++v)
        if ( _mate[v]==INVALID ) {
          for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
            Node y=g.runningNode(e);
            if ( _mate[y]==INVALID && y!=v ) {
              _mate.set(v,y);
              _mate.set(y,v);
              break;
            }
          }
        }
    }

    ///\brief Initialize the matching from each nodes' mate.
    ///
    ///Initialize the matching from a \c Node valued \c Node map. This
    ///map must be \e symmetric, i.e. if \c map[u]==v then \c
    ///map[v]==u must hold, and \c uv will be an arc of the initial
    ///matching.
    template <typename MateMap>
    void mateMapInit(MateMap& map) {
      for(NodeIt v(g); v!=INVALID; ++v) {
        _mate.set(v,map[v]);
        position.set(v,C);
      }
    }

    ///\brief Initialize the matching from a node map with the
    ///incident matching arcs.
    ///
    ///Initialize the matching from an \c Edge valued \c Node map. \c
    ///map[v] must be an \c Edge incident to \c v. This map must have
    ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c
    ///g.oppositeNode(v,map[v])==u holds, and now some arc joining \c
    ///u to \c v will be an arc of the matching.
    template<typename MatchingMap>
    void matchingMapInit(MatchingMap& map) {
      for(NodeIt v(g); v!=INVALID; ++v) {
        position.set(v,C);
        Edge e=map[v];
        if ( e!=INVALID )
          _mate.set(v,g.oppositeNode(v,e));
        else
          _mate.set(v,INVALID);
      }
    }

    ///\brief Initialize the matching from the map containing the
    ///undirected matching arcs.
    ///
    ///Initialize the matching from a \c bool valued \c Edge map. This
    ///map must have the property that there are no two incident arcs
    ///\c e, \c f with \c map[e]==map[f]==true. The arcs \c e with \c
    ///map[e]==true form the matching.
    template <typename MatchingMap>
    void matchingInit(MatchingMap& map) {
      for(NodeIt v(g); v!=INVALID; ++v) {
        _mate.set(v,INVALID);
        position.set(v,C);
      }
      for(EdgeIt e(g); e!=INVALID; ++e) {
        if ( map[e] ) {
          Node u=g.u(e);
          Node v=g.v(e);
          _mate.set(u,v);
          _mate.set(v,u);
        }
      }
    }


    ///\brief Runs Edmonds' algorithm.
    ///
    ///Runs Edmonds' algorithm for sparse digraphs (number of arcs <
    ///2*number of nodes), and a heuristical Edmonds' algorithm with a
    ///heuristic of postponing shrinks for dense digraphs.
    void run() {
      if (countEdges(g) < HEUR_density * countNodes(g)) {
        greedyInit();
        startSparse();
      } else {
        init();
        startDense();
      }
    }


    ///\brief Starts Edmonds' algorithm.
    ///
    ///If runs the original Edmonds' algorithm.
    void startSparse() {

      typename Graph::template NodeMap<Node> ear(g,INVALID);
      //undefined for the base nodes of the blossoms (i.e. for the
      //representative elements of UFE blossom) and for the nodes in C

      UFECrossRef blossom_base(g);
      UFE blossom(blossom_base);
      NV rep(countNodes(g));

      EFECrossRef tree_base(g);
      EFE tree(tree_base);

      //If these UFE's would be members of the class then also
      //blossom_base and tree_base should be a member.

      //We build only one tree and the other vertices uncovered by the
      //matching belong to C. (They can be considered as singleton
      //trees.) If this tree can be augmented or no more
      //grow/augmentation/shrink is possible then we return to this
      //"for" cycle.
      for(NodeIt v(g); v!=INVALID; ++v) {
        if (position[v]==C && _mate[v]==INVALID) {
          rep[blossom.insert(v)] = v;
          tree.insert(v);
          position.set(v,D);
          normShrink(v, ear, blossom, rep, tree);
        }
      }
    }

    ///\brief Starts Edmonds' algorithm.
    ///
    ///It runs Edmonds' algorithm with a heuristic of postponing
    ///shrinks, giving a faster algorithm for dense digraphs.
    void startDense() {

      typename Graph::template NodeMap<Node> ear(g,INVALID);
      //undefined for the base nodes of the blossoms (i.e. for the
      //representative elements of UFE blossom) and for the nodes in C

      UFECrossRef blossom_base(g);
      UFE blossom(blossom_base);
      NV rep(countNodes(g));

      EFECrossRef tree_base(g);
      EFE tree(tree_base);

      //If these UFE's would be members of the class then also
      //blossom_base and tree_base should be a member.

      //We build only one tree and the other vertices uncovered by the
      //matching belong to C. (They can be considered as singleton
      //trees.) If this tree can be augmented or no more
      //grow/augmentation/shrink is possible then we return to this
      //"for" cycle.
      for(NodeIt v(g); v!=INVALID; ++v) {
        if ( position[v]==C && _mate[v]==INVALID ) {
          rep[blossom.insert(v)] = v;
          tree.insert(v);
          position.set(v,D);
          lateShrink(v, ear, blossom, rep, tree);
        }
      }
    }



    ///\brief Returns the size of the actual matching stored.
    ///
    ///Returns the size of the actual matching stored. After \ref
    ///run() it returns the size of a maximum matching in the digraph.
    int size() const {
      int s=0;
      for(NodeIt v(g); v!=INVALID; ++v) {
        if ( _mate[v]!=INVALID ) {
          ++s;
        }
      }
      return s/2;
    }


    ///\brief Returns the mate of a node in the actual matching.
    ///
    ///Returns the mate of a \c node in the actual matching.
    ///Returns INVALID if the \c node is not covered by the actual matching.
    Node mate(const Node& node) const {
      return _mate[node];
    }

    ///\brief Returns the matching arc incident to the given node.
    ///
    ///Returns the matching arc of a \c node in the actual matching.
    ///Returns INVALID if the \c node is not covered by the actual matching.
    Edge matchingArc(const Node& node) const {
      if (_mate[node] == INVALID) return INVALID;
      Node n = node < _mate[node] ? node : _mate[node];
      for (IncEdgeIt e(g, n); e != INVALID; ++e) {
        if (g.oppositeNode(n, e) == _mate[n]) {
          return e;
        }
      }
      return INVALID;
    }

    /// \brief Returns the class of the node in the Edmonds-Gallai
    /// decomposition.
    ///
    /// Returns the class of the node in the Edmonds-Gallai
    /// decomposition.
    DecompType decomposition(const Node& n) {
      return position[n] == A;
    }

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

    ///\brief Gives back the matching in a \c Node of mates.
    ///
    ///Writes the stored matching to a \c Node valued \c Node map. The
    ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
    ///map[v]==u will hold, and now \c uv is an arc of the matching.
    template <typename MateMap>
    void mateMap(MateMap& map) const {
      for(NodeIt v(g); v!=INVALID; ++v) {
        map.set(v,_mate[v]);
      }
    }

    ///\brief Gives back the matching in an \c Edge valued \c Node
    ///map.
    ///
    ///Writes the stored matching to an \c Edge valued \c Node
    ///map. \c map[v] will be an \c Edge incident to \c v. This
    ///map will have the property that if \c g.oppositeNode(u,map[u])
    ///== v then \c map[u]==map[v] holds, and now this arc is an arc
    ///of the matching.
    template <typename MatchingMap>
    void matchingMap(MatchingMap& map)  const {
      typename Graph::template NodeMap<bool> todo(g,true);
      for(NodeIt v(g); v!=INVALID; ++v) {
        if (_mate[v]!=INVALID && v < _mate[v]) {
          Node u=_mate[v];
          for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
            if ( g.runningNode(e) == u ) {
              map.set(u,e);
              map.set(v,e);
              todo.set(u,false);
              todo.set(v,false);
              break;
            }
          }
        }
      }
    }


    ///\brief Gives back the matching in a \c bool valued \c Edge
    ///map.
    ///
    ///Writes the matching stored to a \c bool valued \c Arc
    ///map. This map will have the property that there are no two
    ///incident arcs \c e, \c f with \c map[e]==map[f]==true. The
    ///arcs \c e with \c map[e]==true form the matching.
    template<typename MatchingMap>
    void matching(MatchingMap& map) const {
      for(EdgeIt e(g); e!=INVALID; ++e) map.set(e,false);

      typename Graph::template NodeMap<bool> todo(g,true);
      for(NodeIt v(g); v!=INVALID; ++v) {
        if ( todo[v] && _mate[v]!=INVALID ) {
          Node u=_mate[v];
          for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
            if ( g.runningNode(e) == u ) {
              map.set(e,true);
              todo.set(u,false);
              todo.set(v,false);
              break;
            }
          }
        }
      }
    }


    ///\brief Returns the canonical decomposition of the digraph after running
    ///the algorithm.
    ///
    ///After calling any run methods of the class, it writes the
    ///Gallai-Edmonds canonical decomposition of the digraph. \c map
    ///must be a node map of \ref DecompType 's.
    template <typename DecompositionMap>
    void decomposition(DecompositionMap& map) const {
      for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
    }

    ///\brief Returns a barrier on the nodes.
    ///
    ///After calling any run methods of the class, it writes a
    ///canonical barrier on the nodes. The odd component number of the
    ///remaining digraph minus the barrier size is a lower bound for the
    ///uncovered nodes in the digraph. The \c map must be a node map of
    ///bools.
    template <typename BarrierMap>
    void barrier(BarrierMap& barrier) {
      for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A);
    }

  private:


    void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
                    UFE& blossom, NV& rep, EFE& tree) {
      //We have one tree which we grow, and also shrink but only if it
      //cannot be postponed. If we augment then we return to the "for"
      //cycle of runEdmonds().

      std::queue<Node> Q;   //queue of the totally unscanned nodes
      Q.push(v);
      std::queue<Node> R;
      //queue of the nodes which must be scanned for a possible shrink

      while ( !Q.empty() ) {
        Node x=Q.front();
        Q.pop();
        for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
          Node y=g.runningNode(e);
          //growOrAugment grows if y is covered by the matching and
          //augments if not. In this latter case it returns 1.
          if (position[y]==C &&
              growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
        }
        R.push(x);
      }

      while ( !R.empty() ) {
        Node x=R.front();
        R.pop();

        for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
          Node y=g.runningNode(e);

          if ( position[y] == D && blossom.find(x) != blossom.find(y) )
            //Recall that we have only one tree.
            shrink( x, y, ear, blossom, rep, tree, Q);

          while ( !Q.empty() ) {
            Node z=Q.front();
            Q.pop();
            for( IncEdgeIt f(g,z); f!= INVALID; ++f ) {
              Node w=g.runningNode(f);
              //growOrAugment grows if y is covered by the matching and
              //augments if not. In this latter case it returns 1.
              if (position[w]==C &&
                  growOrAugment(w, z, ear, blossom, rep, tree, Q)) return;
            }
            R.push(z);
          }
        } //for e
      } // while ( !R.empty() )
    }

    void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
                    UFE& blossom, NV& rep, EFE& tree) {
      //We have one tree, which we grow and shrink. If we augment then we
      //return to the "for" cycle of runEdmonds().

      std::queue<Node> Q;   //queue of the unscanned nodes
      Q.push(v);
      while ( !Q.empty() ) {

        Node x=Q.front();
        Q.pop();

        for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
          Node y=g.runningNode(e);

          switch ( position[y] ) {
          case D:          //x and y must be in the same tree
            if ( blossom.find(x) != blossom.find(y))
              //x and y are in the same tree
              shrink(x, y, ear, blossom, rep, tree, Q);
            break;
          case C:
            //growOrAugment grows if y is covered by the matching and
            //augments if not. In this latter case it returns 1.
            if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
            break;
          default: break;
          }
        }
      }
    }

    void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,
                UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) {
      //x and y are the two adjacent vertices in two blossoms.

      typename Graph::template NodeMap<bool> path(g,false);

      Node b=rep[blossom.find(x)];
      path.set(b,true);
      b=_mate[b];
      while ( b!=INVALID ) {
        b=rep[blossom.find(ear[b])];
        path.set(b,true);
        b=_mate[b];
      } //we go until the root through bases of blossoms and odd vertices

      Node top=y;
      Node middle=rep[blossom.find(top)];
      Node bottom=x;
      while ( !path[middle] )
        shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
      //Until we arrive to a node on the path, we update blossom, tree
      //and the positions of the odd nodes.

      Node base=middle;
      top=x;
      middle=rep[blossom.find(top)];
      bottom=y;
      Node blossom_base=rep[blossom.find(base)];
      while ( middle!=blossom_base )
        shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
      //Until we arrive to a node on the path, we update blossom, tree
      //and the positions of the odd nodes.

      rep[blossom.find(base)] = base;
    }

    void shrinkStep(Node& top, Node& middle, Node& bottom,
                    typename Graph::template NodeMap<Node>& ear,
                    UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) {
      //We traverse a blossom and update everything.

      ear.set(top,bottom);
      Node t=top;
      while ( t!=middle ) {
        Node u=_mate[t];
        t=ear[u];
        ear.set(t,u);
      }
      bottom=_mate[middle];
      position.set(bottom,D);
      Q.push(bottom);
      top=ear[bottom];
      Node oldmiddle=middle;
      middle=rep[blossom.find(top)];
      tree.erase(bottom);
      tree.erase(oldmiddle);
      blossom.insert(bottom);
      blossom.join(bottom, oldmiddle);
      blossom.join(top, oldmiddle);
    }



    bool growOrAugment(Node& y, Node& x, typename Graph::template
                       NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree,
                       std::queue<Node>& Q) {
      //x is in a blossom in the tree, y is outside. If y is covered by
      //the matching we grow, otherwise we augment. In this case we
      //return 1.

      if ( _mate[y]!=INVALID ) {       //grow
        ear.set(y,x);
        Node w=_mate[y];
        rep[blossom.insert(w)] = w;
        position.set(y,A);
        position.set(w,D);
        int t = tree.find(rep[blossom.find(x)]);
        tree.insert(y,t);
        tree.insert(w,t);
        Q.push(w);
      } else {                      //augment
        augment(x, ear, blossom, rep, tree);
        _mate.set(x,y);
        _mate.set(y,x);
        return true;
      }
      return false;
    }

    void augment(Node x, typename Graph::template NodeMap<Node>& ear,
                 UFE& blossom, NV& rep, EFE& tree) {
      Node v=_mate[x];
      while ( v!=INVALID ) {

        Node u=ear[v];
        _mate.set(v,u);
        Node tmp=v;
        v=_mate[u];
        _mate.set(u,tmp);
      }
      int y = tree.find(rep[blossom.find(x)]);
      for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) {
        if ( position[tit] == D ) {
          int b = blossom.find(tit);
          for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) {
            position.set(bit, C);
          }
          blossom.eraseClass(b);
        } else position.set(tit, C);
      }
      tree.eraseClass(y);

    }

  };

  /// \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
  /// arcs in the digraph with maximum overall weight and no two of
  /// them shares their endpoints. The problem can be formulated with
  /// the next 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 arcs incident to a node in
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints 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 next:
  /// \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 typename Graph::template NodeMap<int> NodeIntMap;
    typedef typename Graph::template ArcMap<int> ArcIntMap;
    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
    typedef RangeMap<int> IntIntMap;

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

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

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

    NodeIntMap *_node_index;
    ArcIntMap *_node_heap_index;

    struct NodeData {

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

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

      int tree;
    };

    RangeMap<NodeData>* _node_data;

    typedef ExtendFindEnum<IntIntMap> TreeSet;

    IntIntMap *_tree_set_index;
    TreeSet *_tree_set;

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

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

    EdgeIntMap *_delta3_index;
    BinHeap<Value, EdgeIntMap> *_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 NodeIntMap(_graph);
        _blossom_set = new BlossomSet(*_blossom_index);
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
      }

      if (!_node_index) {
        _node_index = new NodeIntMap(_graph);
        _node_heap_index = new ArcIntMap(_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 NodeIntMap(_graph);
        _delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index);
      }
      if (!_delta2) {
        _delta2_index = new IntIntMap(_blossom_num);
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
      }
      if (!_delta3) {
        _delta3_index = new EdgeIntMap(_graph);
        _delta3 = new BinHeap<Value, EdgeIntMap>(*_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 augmentOnArc(const Edge& arc) {

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

      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(arc, true);
      (*_blossom_data)[right].next = _graph.direct(arc, 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 shrinkOnArc(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 member
    /// \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, ArcIntMap>::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) {
                shrinkOnArc(e, left_tree);
              } else {
                augmentOnArc(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 for 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 arc is in the matching.
    ///
    /// Returns true when the arc is in the matching.
    bool matching(const Edge& arc) const {
      return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
    }

    /// \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 for 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 Lemon iterator for get the items of the blossom.
    ///
    /// Lemon iterator for get the nodes of the blossom. This class
    /// provides a common style lemon iterator which gives back a
    /// subset of the nodes.
    class BlossomIt {
    public:

      /// \brief Constructor.
      ///
      /// Constructor for 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 Invalid constructor.
      ///
      /// Invalid constructor.
      BlossomIt(Invalid) : _index(-1) {}

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

      /// \brief Increment operator.
      ///
      /// Increment operator.
      BlossomIt& operator++() {
        ++_index;
        if (_index == _last) {
          _index = -1;
        }
        return *this;
      }

      bool operator==(const BlossomIt& it) const {
        return _index == it._index;
      }
      bool operator!=(const BlossomIt& it) const {
        return _index != it._index;
      }

    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 perfecr 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
  /// arcs in the digraph with maximum overall weight and no two of
  /// them shares their endpoints and covers all nodes. The problem
  /// can be formulated with the next 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 arcs incident to a node in
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints 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 next:
  /// \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 typename Graph::template NodeMap<int> NodeIntMap;
    typedef typename Graph::template ArcMap<int> ArcIntMap;
    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
    typedef RangeMap<int> IntIntMap;

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

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

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

    NodeIntMap *_node_index;
    ArcIntMap *_node_heap_index;

    struct NodeData {

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

      int blossom;
      Value pot;
      BinHeap<Value, ArcIntMap> 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;

    EdgeIntMap *_delta3_index;
    BinHeap<Value, EdgeIntMap> *_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 NodeIntMap(_graph);
        _blossom_set = new BlossomSet(*_blossom_index);
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
      }

      if (!_node_index) {
        _node_index = new NodeIntMap(_graph);
        _node_heap_index = new ArcIntMap(_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 EdgeIntMap(_graph);
        _delta3 = new BinHeap<Value, EdgeIntMap>(*_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 augmentOnArc(const Edge& arc) {

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

      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(arc, true);
      (*_blossom_data)[right].next = _graph.direct(arc, 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 shrinkOnArc(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 member
    /// \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, ArcIntMap>::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) {
                shrinkOnArc(e, left_tree);
              } else {
                augmentOnArc(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 for 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 arc is in the matching.
    ///
    /// Returns true when the arc is in the matching.
    bool matching(const Edge& arc) const {
      return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
    }

    /// \brief Returns the incident matching arc.
    ///
    /// Returns the incident matching arc from given node.
    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 for 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 Lemon iterator for get the items of the blossom.
    ///
    /// Lemon iterator for get the nodes of the blossom. This class
    /// provides a common style lemon iterator which gives back a
    /// subset of the nodes.
    class BlossomIt {
    public:

      /// \brief Constructor.
      ///
      /// Constructor for 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 Invalid constructor.
      ///
      /// Invalid constructor.
      BlossomIt(Invalid) : _index(-1) {}

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

      /// \brief Increment operator.
      ///
      /// Increment operator.
      BlossomIt& operator++() {
        ++_index;
        if (_index == _last) {
          _index = -1;
        }
        return *this;
      }

      bool operator==(const BlossomIt& it) const {
        return _index == it._index;
      }
      bool operator!=(const BlossomIt& it) const {
        return _index != it._index;
      }

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

    /// @}

  };


} //END OF NAMESPACE LEMON

#endif //LEMON_MAX_MATCHING_H