/* -*- C++ -*-

  *

  * 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 <lemon/bits/invalid.h>

 #include <lemon/unionfind.h>

 #include <lemon/graph_utils.h>

 #include <lemon/bin_heap.h>

 ///\ingroup matching

 ///\file

 ///\brief Maximum matching algorithms in undirected 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 graph. The nodes

   ///in \c D induce a graph with factor-critical components, the nodes

   ///in \c A form the barrier, and the nodes in \c C induce a graph

   ///having a perfect matching. This decomposition can be attained by

   ///calling \c decomposition() after running the algorithm.

   ///

   ///\param Graph The undirected graph type the algorithm runs on.

   ///

   ///\author Jacint Szabo  

   template <typename Graph>

   class MaxMatching {

   protected:

     typedef typename Graph::Node Node;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::UEdge UEdge;

     typedef typename Graph::UEdgeIt UEdgeIt;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::IncEdgeIt IncEdgeIt;

     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 graph.

     ///

     ///Indicates the Gallai-Edmonds decomposition of the graph, which

     ///shows an upper bound on the size of a maximum matching. The

     ///nodes with DecompType \c D induce a graph with factor-critical

     ///components, the nodes in \c A form the canonical barrier, and the

     ///nodes in \c C induce a graph 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 edge 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 edges.

     ///

     ///Initialize the matching from an \c UEdge valued \c Node map. \c

     ///map[v] must be an \c UEdge 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 edge joining \c

     ///u to \c v will be an edge of the matching.

     template<typename MatchingMap>

     void matchingMapInit(MatchingMap& map) {

       for(NodeIt v(g); v!=INVALID; ++v) {

 	position.set(v,C);

 	UEdge 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 edges.

     ///

     ///Initialize the matching from a \c bool valued \c UEdge map. This

     ///map must have the property that there are no two incident edges

     ///\c e, \c f with \c map[e]==map[f]==true. The edges \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(UEdgeIt e(g); e!=INVALID; ++e) {

 	if ( map[e] ) {

 	  Node u=g.source(e);	  

 	  Node v=g.target(e);

 	  _mate.set(u,v);

 	  _mate.set(v,u);

 	} 

       } 

     }

     ///\brief Runs Edmonds' algorithm.

     ///

     ///Runs Edmonds' algorithm for sparse graphs (number of edges <

     ///2*number of nodes), and a heuristical Edmonds' algorithm with a

     ///heuristic of postponing shrinks for dense graphs. 

     void run() {

       if (countUEdges(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 graphs.

     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 graph.

     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 edge incident to the given node.

     ///

     ///Returns the matching edge of a \c node in the actual matching. 

     ///Returns INVALID if the \c node is not covered by the actual matching. 

     UEdge matchingEdge(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 edge 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 UEdge valued \c Node

     ///map.

     ///

     ///Writes the stored matching to an \c UEdge valued \c Node

     ///map. \c map[v] will be an \c UEdge 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 edge is an edge

     ///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 UEdge

     ///map.

     ///

     ///Writes the matching stored to a \c bool valued \c Edge

     ///map. This map will have the property that there are no two

     ///incident edges \c e, \c f with \c map[e]==map[f]==true. The

     ///edges \c e with \c map[e]==true form the matching.

     template<typename MatchingMap>

     void matching(MatchingMap& map) const {

       for(UEdgeIt 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 graph after running

     ///the algorithm.

     ///

     ///After calling any run methods of the class, it writes the

     ///Gallai-Edmonds canonical decomposition of the graph. \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 graph minus the barrier size is a lower bound for the

     ///uncovered nodes in the graph. 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 undirected graphs

   ///

   /// This class provides an efficient implementation of Edmond's

   /// maximum weighted matching algorithm. The implementation is based

   /// on extensive use of priority queues and provides

   /// \f$O(nm\log(n))\f$ time complexity.

   ///

   /// The maximum weighted matching problem is to find undirected

   /// edges in the graph with maximum overall weight and no two of

   /// them shares their 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 edges incident to a node in

   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges 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".

   ///

   /// \author Balazs Dezso

   template <typename _UGraph, 

 	    typename _WeightMap = typename _UGraph::template UEdgeMap<int> >

   class MaxWeightedMatching {

   public:

     typedef _UGraph UGraph;

     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 UGraph::template NodeMap<typename UGraph::Edge> 

     MatchingMap;

   private:

     UGRAPH_TYPEDEFS(typename UGraph);

     typedef typename UGraph::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 UGraph& _ugraph;

     const WeightMap& _weight;

     MatchingMap* _matching;

     NodePotential* _node_potential;

     BlossomPotential _blossom_potential;

     BlossomNodeList _blossom_node_list;

     int _node_num;

     int _blossom_num;

     typedef typename UGraph::template NodeMap<int> NodeIntMap;

     typedef typename UGraph::template EdgeMap<int> EdgeIntMap;

     typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap;

     typedef IntegerMap<int> IntIntMap;

     enum Status {

       EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2

     };

     typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;

     struct BlossomData {

       int tree;

       Status status;

       Edge pred, next;

       Value pot, offset;

       Node base;

     };

     NodeIntMap *_blossom_index;

     BlossomSet *_blossom_set;

     IntegerMap<BlossomData>* _blossom_data;

     NodeIntMap *_node_index;

     EdgeIntMap *_node_heap_index;

     struct NodeData {

       NodeData(EdgeIntMap& node_heap_index) 

 	: heap(node_heap_index) {}

       int blossom;

       Value pot;

       BinHeap<Value, EdgeIntMap> heap;

       std::map<int, Edge> heap_index;

       int tree;

     };

     IntegerMap<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;

     UEdgeIntMap *_delta3_index;

     BinHeap<Value, UEdgeIntMap> *_delta3;

     IntIntMap *_delta4_index;

     BinHeap<Value, IntIntMap> *_delta4;

     Value _delta_sum;

     void createStructures() {

       _node_num = countNodes(_ugraph); 

       _blossom_num = _node_num * 3 / 2;

       if (!_matching) {

 	_matching = new MatchingMap(_ugraph);

       }

       if (!_node_potential) {

 	_node_potential = new NodePotential(_ugraph);

       }

       if (!_blossom_set) {

 	_blossom_index = new NodeIntMap(_ugraph);

 	_blossom_set = new BlossomSet(*_blossom_index);

 	_blossom_data = new IntegerMap<BlossomData>(_blossom_num);

       }

       if (!_node_index) {

 	_node_index = new NodeIntMap(_ugraph);

 	_node_heap_index = new EdgeIntMap(_ugraph);

 	_node_data = new IntegerMap<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(_ugraph);

 	_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 UEdgeIntMap(_ugraph);

 	_delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index);

       }

       if (!_delta4) {

 	_delta4_index = new IntIntMap(_blossom_num);

 	_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);

       }

     }

     void destroyStructures() {

       _node_num = countNodes(_ugraph); 

       _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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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, Edge>::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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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) {

 	      Edge r = _ugraph.oppositeEdge(e);

 	      typename std::map<int, Edge>::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, Edge>::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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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, Edge>::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 (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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);

 	    Edge r = _ugraph.oppositeEdge(e);

 	    typename std::map<int, Edge>::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(_ugraph.target((*_blossom_data)[even].pred));

 	(*_blossom_data)[odd].status = MATCHED;

 	oddToMatched(odd);

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

 	even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred));

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

 	evenToMatched(even, tree);

 	(*_blossom_data)[even].next = 

 	  _ugraph.oppositeEdge((*_blossom_data)[odd].pred);

       }

     }

     void destroyTree(int tree) {

       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {

 	if ((*_blossom_data)[b].status == EVEN) {

 	  (*_blossom_data)[b].status = MATCHED;

 	  evenToMatched(b, tree);

 	} else if ((*_blossom_data)[b].status == ODD) {

 	  (*_blossom_data)[b].status = MATCHED;

 	  oddToMatched(b);

 	}

       }

       _tree_set->eraseClass(tree);

     }

     void unmatchNode(const Node& node) {

       int blossom = _blossom_set->find(node);

       int tree = _tree_set->find(blossom);

       alternatePath(blossom, tree);

       destroyTree(tree);

       (*_blossom_data)[blossom].status = UNMATCHED;

       (*_blossom_data)[blossom].base = node;

       matchedToUnmatched(blossom);

     }

     void augmentOnEdge(const UEdge& edge) {

       int left = _blossom_set->find(_ugraph.source(edge));

       int right = _blossom_set->find(_ugraph.target(edge));

       if ((*_blossom_data)[left].status == EVEN) {

 	int left_tree = _tree_set->find(left);

 	alternatePath(left, left_tree);

 	destroyTree(left_tree);

       } else {

 	(*_blossom_data)[left].status = MATCHED;

 	unmatchedToMatched(left);

       }

       if ((*_blossom_data)[right].status == EVEN) {

 	int right_tree = _tree_set->find(right);

 	alternatePath(right, right_tree);

 	destroyTree(right_tree);

       } else {

 	(*_blossom_data)[right].status = MATCHED;

 	unmatchedToMatched(right);

       }

       (*_blossom_data)[left].next = _ugraph.direct(edge, true);

       (*_blossom_data)[right].next = _ugraph.direct(edge, false);

     }

     void extendOnEdge(const Edge& edge) {

       int base = _blossom_set->find(_ugraph.target(edge));

       int tree = _tree_set->find(base);

       int odd = _blossom_set->find(_ugraph.source(edge));

       _tree_set->insert(odd, tree);

       (*_blossom_data)[odd].status = ODD;

       matchedToOdd(odd);

       (*_blossom_data)[odd].pred = edge;

       int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next));

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

       _tree_set->insert(even, tree);

       (*_blossom_data)[even].status = EVEN;

       matchedToEven(even, tree);

     }

     void shrinkOnEdge(const UEdge& uedge, int tree) {

       int nca = -1;

       std::vector<int> left_path, right_path;

       {

 	std::set<int> left_set, right_set;

 	int left = _blossom_set->find(_ugraph.source(uedge));

 	left_path.push_back(left);

 	left_set.insert(left);

 	int right = _blossom_set->find(_ugraph.target(uedge));

 	right_path.push_back(right);

 	right_set.insert(right);

 	while (true) {

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

 	  left = 

 	    _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred));

 	  left_path.push_back(left);

 	  left = 

 	    _blossom_set->find(_ugraph.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(_ugraph.target((*_blossom_data)[right].pred));

 	  right_path.push_back(right);

 	  right = 

 	    _blossom_set->find(_ugraph.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(_ugraph.target((*_blossom_data)[nca].pred));

 	      right_path.push_back(nca);

 	      nca = 

 		_blossom_set->find(_ugraph.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(_ugraph.target((*_blossom_data)[nca].pred));

 	      left_path.push_back(nca);

 	      nca = 

 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));

 	      left_path.push_back(nca);

 	    }

 	  }

 	}

       }

       std::vector<int> subblossoms;

       Edge prev;

       prev = _ugraph.direct(uedge, 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 = _ugraph.oppositeEdge((*_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) {

       Edge next = (*_blossom_data)[blossom].next; 

       Edge 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(_ugraph.source(pred));

       int d = _blossom_set->find(_ugraph.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 = 

 	    _ugraph.oppositeEdge((*_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 = 

 			   _ugraph.oppositeEdge((*_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 = 

 	    _ugraph.oppositeEdge((*_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 =

 	    _ugraph.oppositeEdge((*_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 = 

 	    _ugraph.oppositeEdge((*_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 Edge& 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()];

 	  Edge m = (*_blossom_data)[tb].next;

 	  extractBlossom(sb, _ugraph.target(m), _ugraph.oppositeEdge(m));

 	  extractBlossom(tb, _ugraph.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;

 	  }

 	  Edge matching = (*_blossom_data)[blossoms[i]].next;

 	  Node base = _ugraph.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 UGraph& ugraph, const WeightMap& weight)

       : _ugraph(ugraph), _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 (EdgeIt e(_ugraph); e != INVALID; ++e) {

 	_node_heap_index->set(e, BinHeap<Value, EdgeIntMap>::PRE_HEAP);

       }

       for (NodeIt n(_ugraph); n != INVALID; ++n) {

 	_delta1_index->set(n, _delta1->PRE_HEAP);

       }

       for (UEdgeIt e(_ugraph); 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(_ugraph); n != INVALID; ++n) {

 	Value max = 0;

 	for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  if (_ugraph.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 (UEdgeIt e(_ugraph); e != INVALID; ++e) {

 	int si = (*_node_index)[_ugraph.source(e)];

 	int ti = (*_node_index)[_ugraph.target(e)];

 	if (_ugraph.source(e) != _ugraph.target(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);

 	    Edge e = (*_node_data)[(*_node_index)[n]].heap.top();

 	    extendOnEdge(e);

 	  }

 	  break;

 	case D3:

 	  {

 	    UEdge e = _delta3->top();

 	    int left_blossom = _blossom_set->find(_ugraph.source(e));

 	    int right_blossom = _blossom_set->find(_ugraph.target(e));

 	    if (left_blossom == right_blossom) {

 	      _delta3->pop();

 	    } else {

 	      int left_tree;

 	      if ((*_blossom_data)[left_blossom].status == EVEN) {

 		left_tree = _tree_set->find(left_blossom);

 	      } else {

 		left_tree = -1;

 		++unmatched;

 	      }

 	      int right_tree;

 	      if ((*_blossom_data)[right_blossom].status == EVEN) {

 		right_tree = _tree_set->find(right_blossom);

 	      } else {

 		right_tree = -1;

 		++unmatched;

 	      }

 	      if (left_tree == right_tree) {

 		shrinkOnEdge(e, left_tree);

 	      } else {

 		augmentOnEdge(e);

 		unmatched -= 2;

 	      }

 	    }

 	  } break;

 	case D4:

 	  splitBlossom(_delta4->top());

 	  break;

 	}

       }

       extractMatching();

     }

     /// \brief Runs %MaxWeightedMatching algorithm.

     ///

     /// This method runs the %MaxWeightedMatching algorithm.

     ///

     /// \note mwm.run() is just a shortcut of the following code.

     /// \code

     ///   mwm.init();

     ///   mwm.start();

     /// \endcode

     void run() {

       init();

       start();

     }

     /// @}

     /// \name Primal solution

     /// Functions 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(_ugraph); n != INVALID; ++n) {

 	if ((*_matching)[n] != INVALID) {

 	  sum += _weight[(*_matching)[n]];

 	}

       }

       return sum /= 2;

     }

     /// \brief Returns true when the edge is in the matching.

     ///

     /// Returns true when the edge is in the matching.

     bool matching(const UEdge& edge) const {

       return (*_matching)[_ugraph.source(edge)] == _ugraph.direct(edge, true);

     }

     /// \brief Returns the incident matching edge.

     ///

     /// Returns the incident matching edge from given node. If the

     /// node is not matched then it gives back \c INVALID.

     Edge matching(const Node& node) const {

       return (*_matching)[node];

     }

     /// \brief Returns the mate of the node.

     ///

     /// Returns the adjancent node in a mathcing edge. If the node is

     /// not matched then it gives back \c INVALID.

     Node mate(const Node& node) const {

       return (*_matching)[node] != INVALID ?

 	_ugraph.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(_ugraph); 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 undirected 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

   /// edges in the graph 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 edges incident to a node in

   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges 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".

   ///

   /// \author Balazs Dezso

   template <typename _UGraph, 

 	    typename _WeightMap = typename _UGraph::template UEdgeMap<int> >

   class MaxWeightedPerfectMatching {

   public:

     typedef _UGraph UGraph;

     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 UGraph::template NodeMap<typename UGraph::Edge> 

     MatchingMap;

   private:

     UGRAPH_TYPEDEFS(typename UGraph);

     typedef typename UGraph::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 UGraph& _ugraph;

     const WeightMap& _weight;

     MatchingMap* _matching;

     NodePotential* _node_potential;

     BlossomPotential _blossom_potential;

     BlossomNodeList _blossom_node_list;

     int _node_num;

     int _blossom_num;

     typedef typename UGraph::template NodeMap<int> NodeIntMap;

     typedef typename UGraph::template EdgeMap<int> EdgeIntMap;

     typedef typename UGraph::template UEdgeMap<int> UEdgeIntMap;

     typedef IntegerMap<int> IntIntMap;

     enum Status {

       EVEN = -1, MATCHED = 0, ODD = 1

     };

     typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;

     struct BlossomData {

       int tree;

       Status status;

       Edge pred, next;

       Value pot, offset;

     };

     NodeIntMap *_blossom_index;

     BlossomSet *_blossom_set;

     IntegerMap<BlossomData>* _blossom_data;

     NodeIntMap *_node_index;

     EdgeIntMap *_node_heap_index;

     struct NodeData {

       NodeData(EdgeIntMap& node_heap_index) 

 	: heap(node_heap_index) {}

       int blossom;

       Value pot;

       BinHeap<Value, EdgeIntMap> heap;

       std::map<int, Edge> heap_index;

       int tree;

     };

     IntegerMap<NodeData>* _node_data;

     typedef ExtendFindEnum<IntIntMap> TreeSet;

     IntIntMap *_tree_set_index;

     TreeSet *_tree_set;

     IntIntMap *_delta2_index;

     BinHeap<Value, IntIntMap> *_delta2;

     UEdgeIntMap *_delta3_index;

     BinHeap<Value, UEdgeIntMap> *_delta3;

     IntIntMap *_delta4_index;

     BinHeap<Value, IntIntMap> *_delta4;

     Value _delta_sum;

     void createStructures() {

       _node_num = countNodes(_ugraph); 

       _blossom_num = _node_num * 3 / 2;

       if (!_matching) {

 	_matching = new MatchingMap(_ugraph);

       }

       if (!_node_potential) {

 	_node_potential = new NodePotential(_ugraph);

       }

       if (!_blossom_set) {

 	_blossom_index = new NodeIntMap(_ugraph);

 	_blossom_set = new BlossomSet(*_blossom_index);

 	_blossom_data = new IntegerMap<BlossomData>(_blossom_num);

       }

       if (!_node_index) {

 	_node_index = new NodeIntMap(_ugraph);

 	_node_heap_index = new EdgeIntMap(_ugraph);

 	_node_data = new IntegerMap<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 UEdgeIntMap(_ugraph);

 	_delta3 = new BinHeap<Value, UEdgeIntMap>(*_delta3_index);

       }

       if (!_delta4) {

 	_delta4_index = new IntIntMap(_blossom_num);

 	_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);

       }

     }

     void destroyStructures() {

       _node_num = countNodes(_ugraph); 

       _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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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, Edge>::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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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) {

 	      Edge r = _ugraph.oppositeEdge(e);

 	      typename std::map<int, Edge>::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, Edge>::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 (InEdgeIt e(_ugraph, n); e != INVALID; ++e) {

 	  Node v = _ugraph.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, Edge>::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(_ugraph.target((*_blossom_data)[even].pred));

 	(*_blossom_data)[odd].status = MATCHED;

 	oddToMatched(odd);

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

 	even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].pred));

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

 	evenToMatched(even, tree);

 	(*_blossom_data)[even].next = 

 	  _ugraph.oppositeEdge((*_blossom_data)[odd].pred);

       }

     }

     void destroyTree(int tree) {

       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {

 	if ((*_blossom_data)[b].status == EVEN) {

 	  (*_blossom_data)[b].status = MATCHED;

 	  evenToMatched(b, tree);

 	} else if ((*_blossom_data)[b].status == ODD) {

 	  (*_blossom_data)[b].status = MATCHED;

 	  oddToMatched(b);

 	}

       }

       _tree_set->eraseClass(tree);

     }

     void augmentOnEdge(const UEdge& edge) {

       int left = _blossom_set->find(_ugraph.source(edge));

       int right = _blossom_set->find(_ugraph.target(edge));

       int left_tree = _tree_set->find(left);

       alternatePath(left, left_tree);

       destroyTree(left_tree);

       int right_tree = _tree_set->find(right);

       alternatePath(right, right_tree);

       destroyTree(right_tree);

       (*_blossom_data)[left].next = _ugraph.direct(edge, true);

       (*_blossom_data)[right].next = _ugraph.direct(edge, false);

     }

     void extendOnEdge(const Edge& edge) {

       int base = _blossom_set->find(_ugraph.target(edge));

       int tree = _tree_set->find(base);

       int odd = _blossom_set->find(_ugraph.source(edge));

       _tree_set->insert(odd, tree);

       (*_blossom_data)[odd].status = ODD;

       matchedToOdd(odd);

       (*_blossom_data)[odd].pred = edge;

       int even = _blossom_set->find(_ugraph.target((*_blossom_data)[odd].next));

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

       _tree_set->insert(even, tree);

       (*_blossom_data)[even].status = EVEN;

       matchedToEven(even, tree);

     }

     void shrinkOnEdge(const UEdge& uedge, int tree) {

       int nca = -1;

       std::vector<int> left_path, right_path;

       {

 	std::set<int> left_set, right_set;

 	int left = _blossom_set->find(_ugraph.source(uedge));

 	left_path.push_back(left);

 	left_set.insert(left);

 	int right = _blossom_set->find(_ugraph.target(uedge));

 	right_path.push_back(right);

 	right_set.insert(right);

 	while (true) {

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

 	  left = 

 	    _blossom_set->find(_ugraph.target((*_blossom_data)[left].pred));

 	  left_path.push_back(left);

 	  left = 

 	    _blossom_set->find(_ugraph.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(_ugraph.target((*_blossom_data)[right].pred));

 	  right_path.push_back(right);

 	  right = 

 	    _blossom_set->find(_ugraph.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(_ugraph.target((*_blossom_data)[nca].pred));

 	      right_path.push_back(nca);

 	      nca = 

 		_blossom_set->find(_ugraph.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(_ugraph.target((*_blossom_data)[nca].pred));

 	      left_path.push_back(nca);

 	      nca = 

 		_blossom_set->find(_ugraph.target((*_blossom_data)[nca].pred));

 	      left_path.push_back(nca);

 	    }

 	  }

 	}

       }

       std::vector<int> subblossoms;

       Edge prev;

       prev = _ugraph.direct(uedge, 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 = _ugraph.oppositeEdge((*_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) {

       Edge next = (*_blossom_data)[blossom].next; 

       Edge 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;