/* -*- 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;