/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_MAX_MATCHING_H

 #define LEMON_MAX_MATCHING_H

 #include <vector>

 #include <queue>

 #include <set>

 #include <limits>

 #include <lemon/core.h>

 #include <lemon/unionfind.h>

 #include <lemon/bin_heap.h>

 #include <lemon/maps.h>

 ///\ingroup matching

 ///\file

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

 namespace lemon {

   /// \ingroup matching

   ///

   /// \brief Maximum cardinality matching in general graphs

   ///

   /// This class implements Edmonds' alternating forest matching algorithm

   /// for finding a maximum cardinality matching in a general undirected graph.

   /// It can be started from an arbitrary initial matching 

   /// (the default is the empty one).

   ///

   /// The dual solution of the problem is a map of the nodes to

   /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D),

   /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds

   /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph

   /// with factor-critical components, the nodes in \c ODD/A form the

   /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having

   /// a perfect matching. The number of the factor-critical components

   /// minus the number of barrier nodes is a lower bound on the

   /// unmatched nodes, and the matching is optimal if and only if this bound is

   /// tight. This decomposition can be obtained using \ref status() or

   /// \ref statusMap() after running the algorithm.

   ///

   /// \tparam GR The undirected graph type the algorithm runs on.

   template <typename GR>

   class MaxMatching {

   public:

     /// The graph type of the algorithm

     typedef GR Graph;

     /// The type of the matching map

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

     MatchingMap;

     ///\brief Status constants for Gallai-Edmonds decomposition.

     ///

     ///These constants are used for indicating the Gallai-Edmonds 

     ///decomposition of a graph. The nodes with status \c EVEN (or \c D)

     ///induce a subgraph with factor-critical components, the nodes with

     ///status \c ODD (or \c A) form the canonical barrier, and the nodes

     ///with status \c MATCHED (or \c C) induce a subgraph having a 

     ///perfect matching.

     enum Status {

       EVEN = 1,       ///< = 1. (\c D is an alias for \c EVEN.)

       D = 1,

       MATCHED = 0,    ///< = 0. (\c C is an alias for \c MATCHED.)

       C = 0,

       ODD = -1,       ///< = -1. (\c A is an alias for \c ODD.)

       A = -1,

       UNMATCHED = -2  ///< = -2.

     };

     /// The type of the status map

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

   private:

     TEMPLATE_GRAPH_TYPEDEFS(Graph);

     typedef UnionFindEnum<IntNodeMap> BlossomSet;

     typedef ExtendFindEnum<IntNodeMap> TreeSet;

     typedef RangeMap<Node> NodeIntMap;

     typedef MatchingMap EarMap;

     typedef std::vector<Node> NodeQueue;

     const Graph& _graph;

     MatchingMap* _matching;

     StatusMap* _status;

     EarMap* _ear;

     IntNodeMap* _blossom_set_index;

     BlossomSet* _blossom_set;

     NodeIntMap* _blossom_rep;

     IntNodeMap* _tree_set_index;

     TreeSet* _tree_set;

     NodeQueue _node_queue;

     int _process, _postpone, _last;

     int _node_num;

   private:

     void createStructures() {

       _node_num = countNodes(_graph);

       if (!_matching) {

         _matching = new MatchingMap(_graph);

       }

       if (!_status) {

         _status = new StatusMap(_graph);

       }

       if (!_ear) {

         _ear = new EarMap(_graph);

       }

       if (!_blossom_set) {

         _blossom_set_index = new IntNodeMap(_graph);

         _blossom_set = new BlossomSet(*_blossom_set_index);

       }

       if (!_blossom_rep) {

         _blossom_rep = new NodeIntMap(_node_num);

       }

       if (!_tree_set) {

         _tree_set_index = new IntNodeMap(_graph);

         _tree_set = new TreeSet(*_tree_set_index);

       }

       _node_queue.resize(_node_num);

     }

     void destroyStructures() {

       if (_matching) {

         delete _matching;

       }

       if (_status) {

         delete _status;

       }

       if (_ear) {

         delete _ear;

       }

       if (_blossom_set) {

         delete _blossom_set;

         delete _blossom_set_index;

       }

       if (_blossom_rep) {

         delete _blossom_rep;

       }

       if (_tree_set) {

         delete _tree_set_index;

         delete _tree_set;

       }

     }

     void processDense(const Node& n) {

       _process = _postpone = _last = 0;

       _node_queue[_last++] = n;

       while (_process != _last) {

         Node u = _node_queue[_process++];

         for (OutArcIt a(_graph, u); a != INVALID; ++a) {

           Node v = _graph.target(a);

           if ((*_status)[v] == MATCHED) {

             extendOnArc(a);

           } else if ((*_status)[v] == UNMATCHED) {

             augmentOnArc(a);

             return;

           }

         }

       }

       while (_postpone != _last) {

         Node u = _node_queue[_postpone++];

         for (OutArcIt a(_graph, u); a != INVALID ; ++a) {

           Node v = _graph.target(a);

           if ((*_status)[v] == EVEN) {

             if (_blossom_set->find(u) != _blossom_set->find(v)) {

               shrinkOnEdge(a);

             }

           }

           while (_process != _last) {

             Node w = _node_queue[_process++];

             for (OutArcIt b(_graph, w); b != INVALID; ++b) {

               Node x = _graph.target(b);

               if ((*_status)[x] == MATCHED) {

                 extendOnArc(b);

               } else if ((*_status)[x] == UNMATCHED) {

                 augmentOnArc(b);

                 return;

               }

             }

           }

         }

       }

     }

     void processSparse(const Node& n) {

       _process = _last = 0;

       _node_queue[_last++] = n;

       while (_process != _last) {

         Node u = _node_queue[_process++];

         for (OutArcIt a(_graph, u); a != INVALID; ++a) {

           Node v = _graph.target(a);

           if ((*_status)[v] == EVEN) {

             if (_blossom_set->find(u) != _blossom_set->find(v)) {

               shrinkOnEdge(a);

             }

           } else if ((*_status)[v] == MATCHED) {

             extendOnArc(a);

           } else if ((*_status)[v] == UNMATCHED) {

             augmentOnArc(a);

             return;

           }

         }

       }

     }

     void shrinkOnEdge(const Edge& e) {

       Node nca = INVALID;

       {

         std::set<Node> left_set, right_set;

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

         left_set.insert(left);

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

         right_set.insert(right);

         while (true) {

           if ((*_matching)[left] == INVALID) break;

           left = _graph.target((*_matching)[left]);

           left = (*_blossom_rep)[_blossom_set->

                                  find(_graph.target((*_ear)[left]))];

           if (right_set.find(left) != right_set.end()) {

             nca = left;

             break;

           }

           left_set.insert(left);

           if ((*_matching)[right] == INVALID) break;

           right = _graph.target((*_matching)[right]);

           right = (*_blossom_rep)[_blossom_set->

                                   find(_graph.target((*_ear)[right]))];

           if (left_set.find(right) != left_set.end()) {

             nca = right;

             break;

           }

           right_set.insert(right);

         }

         if (nca == INVALID) {

           if ((*_matching)[left] == INVALID) {

             nca = right;

             while (left_set.find(nca) == left_set.end()) {

               nca = _graph.target((*_matching)[nca]);

               nca =(*_blossom_rep)[_blossom_set->

                                    find(_graph.target((*_ear)[nca]))];

             }

           } else {

             nca = left;

             while (right_set.find(nca) == right_set.end()) {

               nca = _graph.target((*_matching)[nca]);

               nca = (*_blossom_rep)[_blossom_set->

                                    find(_graph.target((*_ear)[nca]))];

             }

           }

         }

       }

       {

         Node node = _graph.u(e);

         Arc arc = _graph.direct(e, true);

         Node base = (*_blossom_rep)[_blossom_set->find(node)];

         while (base != nca) {

           (*_ear)[node] = arc;

           Node n = node;

           while (n != base) {

             n = _graph.target((*_matching)[n]);

             Arc a = (*_ear)[n];

             n = _graph.target(a);

             (*_ear)[n] = _graph.oppositeArc(a);

           }

           node = _graph.target((*_matching)[base]);

           _tree_set->erase(base);

           _tree_set->erase(node);

           _blossom_set->insert(node, _blossom_set->find(base));

           (*_status)[node] = EVEN;

           _node_queue[_last++] = node;

           arc = _graph.oppositeArc((*_ear)[node]);

           node = _graph.target((*_ear)[node]);

           base = (*_blossom_rep)[_blossom_set->find(node)];

           _blossom_set->join(_graph.target(arc), base);

         }

       }

       (*_blossom_rep)[_blossom_set->find(nca)] = nca;

       {

         Node node = _graph.v(e);

         Arc arc = _graph.direct(e, false);

         Node base = (*_blossom_rep)[_blossom_set->find(node)];

         while (base != nca) {

           (*_ear)[node] = arc;

           Node n = node;

           while (n != base) {

             n = _graph.target((*_matching)[n]);

             Arc a = (*_ear)[n];

             n = _graph.target(a);

             (*_ear)[n] = _graph.oppositeArc(a);

           }

           node = _graph.target((*_matching)[base]);

           _tree_set->erase(base);

           _tree_set->erase(node);

           _blossom_set->insert(node, _blossom_set->find(base));

           (*_status)[node] = EVEN;

           _node_queue[_last++] = node;

           arc = _graph.oppositeArc((*_ear)[node]);

           node = _graph.target((*_ear)[node]);

           base = (*_blossom_rep)[_blossom_set->find(node)];

           _blossom_set->join(_graph.target(arc), base);

         }

       }

       (*_blossom_rep)[_blossom_set->find(nca)] = nca;

     }

     void extendOnArc(const Arc& a) {

       Node base = _graph.source(a);

       Node odd = _graph.target(a);

       (*_ear)[odd] = _graph.oppositeArc(a);

       Node even = _graph.target((*_matching)[odd]);

       (*_blossom_rep)[_blossom_set->insert(even)] = even;

       (*_status)[odd] = ODD;

       (*_status)[even] = EVEN;

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

       _tree_set->insert(odd, tree);

       _tree_set->insert(even, tree);

       _node_queue[_last++] = even;

     }

     void augmentOnArc(const Arc& a) {

       Node even = _graph.source(a);

       Node odd = _graph.target(a);

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

       (*_matching)[odd] = _graph.oppositeArc(a);

       (*_status)[odd] = MATCHED;

       Arc arc = (*_matching)[even];

       (*_matching)[even] = a;

       while (arc != INVALID) {

         odd = _graph.target(arc);

         arc = (*_ear)[odd];

         even = _graph.target(arc);

         (*_matching)[odd] = arc;

         arc = (*_matching)[even];

         (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]);

       }

       for (typename TreeSet::ItemIt it(*_tree_set, tree);

            it != INVALID; ++it) {

         if ((*_status)[it] == ODD) {

           (*_status)[it] = MATCHED;

         } else {

           int blossom = _blossom_set->find(it);

           for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);

                jt != INVALID; ++jt) {

             (*_status)[jt] = MATCHED;

           }

           _blossom_set->eraseClass(blossom);

         }

       }

       _tree_set->eraseClass(tree);

     }

   public:

     /// \brief Constructor

     ///

     /// Constructor.

     MaxMatching(const Graph& graph)

       : _graph(graph), _matching(0), _status(0), _ear(0),

         _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),

         _tree_set_index(0), _tree_set(0) {}

     ~MaxMatching() {

       destroyStructures();

     }

     /// \name Execution Control

     /// The simplest way to execute the algorithm is to use the

     /// \c run() member function.\n

     /// If you need better control on the execution, you have to call

     /// one of the functions \ref init(), \ref greedyInit() or

     /// \ref matchingInit() first, then you can start the algorithm with

     /// \ref startSparse() or \ref startDense().

     ///@{

     /// \brief Set the initial matching to the empty matching.

     ///

     /// This function sets the initial matching to the empty matching.

     void init() {

       createStructures();

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

         (*_matching)[n] = INVALID;

         (*_status)[n] = UNMATCHED;

       }

     }

     /// \brief Find an initial matching in a greedy way.

     ///

     /// This function finds an initial matching in a greedy way.

     void greedyInit() {

       createStructures();

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

         (*_matching)[n] = INVALID;

         (*_status)[n] = UNMATCHED;

       }

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

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

           for (OutArcIt a(_graph, n); a != INVALID ; ++a) {

             Node v = _graph.target(a);

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

               (*_matching)[n] = a;

               (*_status)[n] = MATCHED;

               (*_matching)[v] = _graph.oppositeArc(a);

               (*_status)[v] = MATCHED;

               break;

             }

           }

         }

       }

     }

     /// \brief Initialize the matching from a map.

     ///

     /// This function initializes the matching from a \c bool valued edge

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

     /// edges with \c true value, i.e. it really contains a matching.

     /// \return \c true if the map contains a matching.

     template <typename MatchingMap>

     bool matchingInit(const MatchingMap& matching) {

       createStructures();

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

         (*_matching)[n] = INVALID;

         (*_status)[n] = UNMATCHED;

       }

       for(EdgeIt e(_graph); e!=INVALID; ++e) {

         if (matching[e]) {

           Node u = _graph.u(e);

           if ((*_matching)[u] != INVALID) return false;

           (*_matching)[u] = _graph.direct(e, true);

           (*_status)[u] = MATCHED;

           Node v = _graph.v(e);

           if ((*_matching)[v] != INVALID) return false;

           (*_matching)[v] = _graph.direct(e, false);

           (*_status)[v] = MATCHED;

         }

       }

       return true;

     }

     /// \brief Start Edmonds' algorithm

     ///

     /// This function runs the original Edmonds' algorithm.

     ///

     /// \pre \ref Init(), \ref greedyInit() or \ref matchingInit() must be

     /// called before using this function.

     void startSparse() {

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

         if ((*_status)[n] == UNMATCHED) {

           (*_blossom_rep)[_blossom_set->insert(n)] = n;

           _tree_set->insert(n);

           (*_status)[n] = EVEN;

           processSparse(n);

         }

       }

     }

     /// \brief Start Edmonds' algorithm with a heuristic improvement 

     /// for dense graphs

     ///

     /// This function runs Edmonds' algorithm with a heuristic of postponing

     /// shrinks, therefore resulting in a faster algorithm for dense graphs.

     ///

     /// \pre \ref Init(), \ref greedyInit() or \ref matchingInit() must be

     /// called before using this function.

     void startDense() {

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

         if ((*_status)[n] == UNMATCHED) {

           (*_blossom_rep)[_blossom_set->insert(n)] = n;

           _tree_set->insert(n);

           (*_status)[n] = EVEN;

           processDense(n);

         }

       }

     }

     /// \brief Run Edmonds' algorithm

     ///

     /// This function runs Edmonds' algorithm. An additional heuristic of 

     /// postponing shrinks is used for relatively dense graphs 

     /// (for which <tt>m>=2*n</tt> holds).

     void run() {

       if (countEdges(_graph) < 2 * countNodes(_graph)) {

         greedyInit();

         startSparse();

       } else {

         init();

         startDense();

       }

     }

     /// @}

     /// \name Primal Solution

     /// Functions to get the primal solution, i.e. the maximum matching.

     /// @{

     /// \brief Return the size (cardinality) of the matching.

     ///

     /// This function returns the size (cardinality) of the current matching. 

     /// After run() it returns the size of the maximum matching in the graph.

     int matchingSize() const {

       int size = 0;

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

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

           ++size;

         }

       }

       return size / 2;

     }

     /// \brief Return \c true if the given edge is in the matching.

     ///

     /// This function returns \c true if the given edge is in the current 

     /// matching.

     bool matching(const Edge& edge) const {

       return edge == (*_matching)[_graph.u(edge)];

     }

     /// \brief Return the matching arc (or edge) incident to the given node.

     ///

     /// This function returns the matching arc (or edge) incident to the

     /// given node in the current matching or \c INVALID if the node is 

     /// not covered by the matching.

     Arc matching(const Node& n) const {

       return (*_matching)[n];

     }

     /// \brief Return a const reference to the matching map.

     ///

     /// This function returns a const reference to a node map that stores

     /// the matching arc (or edge) incident to each node.

     const MatchingMap& matchingMap() const {

       return *_matching;

     }

     /// \brief Return the mate of the given node.

     ///

     /// This function returns the mate of the given node in the current 

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

     Node mate(const Node& n) const {

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

         _graph.target((*_matching)[n]) : INVALID;

     }

     /// @}

     /// \name Dual Solution

     /// Functions to get the dual solution, i.e. the Gallai-Edmonds 

     /// decomposition.

     /// @{

     /// \brief Return the status of the given node in the Edmonds-Gallai

     /// decomposition.

     ///

     /// This function returns the \ref Status "status" of the given node

     /// in the Edmonds-Gallai decomposition.

     Status status(const Node& n) const {

       return (*_status)[n];

     }

     /// \brief Return a const reference to the status map, which stores

     /// the Edmonds-Gallai decomposition.

     ///

     /// This function returns a const reference to a node map that stores the

     /// \ref Status "status" of each node in the Edmonds-Gallai decomposition.

     const StatusMap& statusMap() const {

       return *_status;

     }

     /// \brief Return \c true if the given node is in the barrier.

     ///

     /// This function returns \c true if the given node is in the barrier.

     bool barrier(const Node& n) const {

       return (*_status)[n] == ODD;

     }

     /// @}

   };

   /// \ingroup matching

   ///

   /// \brief Weighted matching in general graphs

   ///

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

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

   /// on extensive use of priority queues and provides

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

   ///

   /// The maximum weighted matching problem is to find a subset of the 

   /// edges in an undirected graph with maximum overall weight for which 

   /// each node has at most one incident edge.

   /// It can be formulated with the following linear program.

   /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]

   /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}

       \quad \forall B\in\mathcal{O}\f] */

   /// \f[x_e \ge 0\quad \forall e\in E\f]

   /// \f[\max \sum_{e\in E}x_ew_e\f]

   /// where \f$\delta(X)\f$ is the set of edges incident to a node in

   /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in

   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality

   /// subsets of the nodes.

   ///

   /// The algorithm calculates an optimal matching and a proof of the

   /// optimality. The solution of the dual problem can be used to check

   /// the result of the algorithm. The dual linear problem is the

   /// following.

   /** \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 the run() function. 

   /// After it the matching (the primal solution) and the dual solution

   /// can be obtained using the query functions and the 

   /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class, 

   /// which is able to iterate on the nodes of a blossom. 

   /// If the value type is integer, then the dual solution is multiplied

   /// by \ref MaxWeightedMatching::dualScale "4".

   ///

   /// \tparam GR The undirected graph type the algorithm runs on.

   /// \tparam WM The type edge weight map. The default type is 

   /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".

 #ifdef DOXYGEN

   template <typename GR, typename WM>

 #else

   template <typename GR,

             typename WM = typename GR::template EdgeMap<int> >

 #endif

   class MaxWeightedMatching {

   public:

     /// The graph type of the algorithm

     typedef GR Graph;

     /// The type of the edge weight map

     typedef WM WeightMap;

     /// The value type of the edge weights

     typedef typename WeightMap::Value Value;

     /// The type of the matching map

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

     MatchingMap;

     /// \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;

   private:

     TEMPLATE_GRAPH_TYPEDEFS(Graph);

     typedef typename Graph::template NodeMap<Value> NodePotential;

     typedef std::vector<Node> BlossomNodeList;

     struct BlossomVariable {

       int begin, end;

       Value value;

       BlossomVariable(int _begin, int _end, Value _value)

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

     };

     typedef std::vector<BlossomVariable> BlossomPotential;

     const Graph& _graph;

     const WeightMap& _weight;

     MatchingMap* _matching;

     NodePotential* _node_potential;

     BlossomPotential _blossom_potential;

     BlossomNodeList _blossom_node_list;

     int _node_num;

     int _blossom_num;

     typedef RangeMap<int> IntIntMap;

     enum Status {

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

     };

     typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;

     struct BlossomData {

       int tree;

       Status status;

       Arc pred, next;

       Value pot, offset;

       Node base;

     };

     IntNodeMap *_blossom_index;

     BlossomSet *_blossom_set;

     RangeMap<BlossomData>* _blossom_data;

     IntNodeMap *_node_index;

     IntArcMap *_node_heap_index;

     struct NodeData {

       NodeData(IntArcMap& node_heap_index)

         : heap(node_heap_index) {}

       int blossom;

       Value pot;

       BinHeap<Value, IntArcMap> heap;

       std::map<int, Arc> heap_index;

       int tree;

     };

     RangeMap<NodeData>* _node_data;

     typedef ExtendFindEnum<IntIntMap> TreeSet;

     IntIntMap *_tree_set_index;

     TreeSet *_tree_set;

     IntNodeMap *_delta1_index;

     BinHeap<Value, IntNodeMap> *_delta1;

     IntIntMap *_delta2_index;

     BinHeap<Value, IntIntMap> *_delta2;

     IntEdgeMap *_delta3_index;

     BinHeap<Value, IntEdgeMap> *_delta3;

     IntIntMap *_delta4_index;

     BinHeap<Value, IntIntMap> *_delta4;

     Value _delta_sum;

     void createStructures() {

       _node_num = countNodes(_graph);

       _blossom_num = _node_num * 3 / 2;

       if (!_matching) {

         _matching = new MatchingMap(_graph);

       }

       if (!_node_potential) {

         _node_potential = new NodePotential(_graph);

       }

       if (!_blossom_set) {

         _blossom_index = new IntNodeMap(_graph);

         _blossom_set = new BlossomSet(*_blossom_index);

         _blossom_data = new RangeMap<BlossomData>(_blossom_num);

       }

       if (!_node_index) {

         _node_index = new IntNodeMap(_graph);

         _node_heap_index = new IntArcMap(_graph);

         _node_data = new RangeMap<NodeData>(_node_num,

                                               NodeData(*_node_heap_index));

       }

       if (!_tree_set) {

         _tree_set_index = new IntIntMap(_blossom_num);

         _tree_set = new TreeSet(*_tree_set_index);

       }

       if (!_delta1) {

         _delta1_index = new IntNodeMap(_graph);

         _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);

       }

       if (!_delta2) {

         _delta2_index = new IntIntMap(_blossom_num);

         _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);

       }

       if (!_delta3) {

         _delta3_index = new IntEdgeMap(_graph);

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

       }

       if (!_delta4) {

         _delta4_index = new IntIntMap(_blossom_num);

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

       }

     }

     void destroyStructures() {

       _node_num = countNodes(_graph);

       _blossom_num = _node_num * 3 / 2;

       if (_matching) {

         delete _matching;

       }

       if (_node_potential) {

         delete _node_potential;

       }

       if (_blossom_set) {

         delete _blossom_index;

         delete _blossom_set;

         delete _blossom_data;

       }

       if (_node_index) {

         delete _node_index;

         delete _node_heap_index;

         delete _node_data;

       }

       if (_tree_set) {

         delete _tree_set_index;

         delete _tree_set;

       }

       if (_delta1) {

         delete _delta1_index;

         delete _delta1;

       }

       if (_delta2) {

         delete _delta2_index;

         delete _delta2;

       }

       if (_delta3) {

         delete _delta3_index;

         delete _delta3;

       }

       if (_delta4) {

         delete _delta4_index;

         delete _delta4;

       }

     }

     void matchedToEven(int blossom, int tree) {

       if (_delta2->state(blossom) == _delta2->IN_HEAP) {

         _delta2->erase(blossom);

       }

       if (!_blossom_set->trivial(blossom)) {

         (*_blossom_data)[blossom].pot -=

           2 * (_delta_sum - (*_blossom_data)[blossom].offset);

       }

       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);

            n != INVALID; ++n) {

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

         int ni = (*_node_index)[n];

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

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

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

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

         for (InArcIt e(_graph, n); e != INVALID; ++e) {

           Node v = _graph.source(e);

           int vb = _blossom_set->find(v);

           int vi = (*_node_index)[v];

           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -

             dualScale * _weight[e];

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

             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {

               _delta3->push(e, rw / 2);

             }

           } else if ((*_blossom_data)[vb].status == UNMATCHED) {

             if (_delta3->state(e) != _delta3->IN_HEAP) {

               _delta3->push(e, rw);

             }

           } else {

             typename std::map<int, Arc>::iterator it =

               (*_node_data)[vi].heap_index.find(tree);

             if (it != (*_node_data)[vi].heap_index.end()) {

               if ((*_node_data)[vi].heap[it->second] > rw) {

                 (*_node_data)[vi].heap.replace(it->second, e);

                 (*_node_data)[vi].heap.decrease(e, rw);

                 it->second = e;

               }

             } else {

               (*_node_data)[vi].heap.push(e, rw);

               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));

             }

             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {

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

               if ((*_blossom_data)[vb].status == MATCHED) {

                 if (_delta2->state(vb) != _delta2->IN_HEAP) {

                   _delta2->push(vb, _blossom_set->classPrio(vb) -

                                (*_blossom_data)[vb].offset);

                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -

                            (*_blossom_data)[vb].offset){

                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -

                                    (*_blossom_data)[vb].offset);

                 }

               }

             }

           }

         }

       }

       (*_blossom_data)[blossom].offset = 0;

     }

     void matchedToOdd(int blossom) {

       if (_delta2->state(blossom) == _delta2->IN_HEAP) {

         _delta2->erase(blossom);

       }

       (*_blossom_data)[blossom].offset += _delta_sum;

       if (!_blossom_set->trivial(blossom)) {

         _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +

                      (*_blossom_data)[blossom].offset);

       }

     }

     void evenToMatched(int blossom, int tree) {

       if (!_blossom_set->trivial(blossom)) {

         (*_blossom_data)[blossom].pot += 2 * _delta_sum;

       }

       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);

            n != INVALID; ++n) {

         int ni = (*_node_index)[n];

         (*_node_data)[ni].pot -= _delta_sum;

         _delta1->erase(n);

         for (InArcIt e(_graph, n); e != INVALID; ++e) {

           Node v = _graph.source(e);

           int vb = _blossom_set->find(v);

           int vi = (*_node_index)[v];

           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -

             dualScale * _weight[e];

           if (vb == blossom) {

             if (_delta3->state(e) == _delta3->IN_HEAP) {

               _delta3->erase(e);

             }

           } else if ((*_blossom_data)[vb].status == EVEN) {

             if (_delta3->state(e) == _delta3->IN_HEAP) {

               _delta3->erase(e);

             }

             int vt = _tree_set->find(vb);

             if (vt != tree) {

               Arc r = _graph.oppositeArc(e);

               typename std::map<int, Arc>::iterator it =

                 (*_node_data)[ni].heap_index.find(vt);

               if (it != (*_node_data)[ni].heap_index.end()) {

                 if ((*_node_data)[ni].heap[it->second] > rw) {

                   (*_node_data)[ni].heap.replace(it->second, r);

                   (*_node_data)[ni].heap.decrease(r, rw);

                   it->second = r;

                 }

               } else {

                 (*_node_data)[ni].heap.push(r, rw);

                 (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));

               }

               if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {

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

                 if (_delta2->state(blossom) != _delta2->IN_HEAP) {

                   _delta2->push(blossom, _blossom_set->classPrio(blossom) -

                                (*_blossom_data)[blossom].offset);

                 } else if ((*_delta2)[blossom] >

                            _blossom_set->classPrio(blossom) -

                            (*_blossom_data)[blossom].offset){

                   _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -

                                    (*_blossom_data)[blossom].offset);

                 }

               }

             }

           } else if ((*_blossom_data)[vb].status == UNMATCHED) {

             if (_delta3->state(e) == _delta3->IN_HEAP) {

               _delta3->erase(e);

             }

           } else {

             typename std::map<int, Arc>::iterator it =

               (*_node_data)[vi].heap_index.find(tree);

             if (it != (*_node_data)[vi].heap_index.end()) {

               (*_node_data)[vi].heap.erase(it->second);

               (*_node_data)[vi].heap_index.erase(it);

               if ((*_node_data)[vi].heap.empty()) {

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

               } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {

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

               }

               if ((*_blossom_data)[vb].status == MATCHED) {

                 if (_blossom_set->classPrio(vb) ==

                     std::numeric_limits<Value>::max()) {

                   _delta2->erase(vb);

                 } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -

                            (*_blossom_data)[vb].offset) {

                   _delta2->increase(vb, _blossom_set->classPrio(vb) -

                                    (*_blossom_data)[vb].offset);

                 }

               }

             }

           }

         }

       }

     }

     void oddToMatched(int blossom) {

       (*_blossom_data)[blossom].offset -= _delta_sum;

       if (_blossom_set->classPrio(blossom) !=

           std::numeric_limits<Value>::max()) {

         _delta2->push(blossom, _blossom_set->classPrio(blossom) -

                        (*_blossom_data)[blossom].offset);

       }

       if (!_blossom_set->trivial(blossom)) {

         _delta4->erase(blossom);

       }

     }

     void oddToEven(int blossom, int tree) {

       if (!_blossom_set->trivial(blossom)) {

         _delta4->erase(blossom);

         (*_blossom_data)[blossom].pot -=

           2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);

       }

       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);

            n != INVALID; ++n) {

         int ni = (*_node_index)[n];

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

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

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

         (*_node_data)[ni].pot +=

           2 * _delta_sum - (*_blossom_data)[blossom].offset;

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

         for (InArcIt e(_graph, n); e != INVALID; ++e) {

           Node v = _graph.source(e);

           int vb = _blossom_set->find(v);

           int vi = (*_node_index)[v];

           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -

             dualScale * _weight[e];

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

             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {

               _delta3->push(e, rw / 2);

             }

           } else if ((*_blossom_data)[vb].status == UNMATCHED) {

             if (_delta3->state(e) != _delta3->IN_HEAP) {

               _delta3->push(e, rw);

             }

           } else {

             typename std::map<int, Arc>::iterator it =

               (*_node_data)[vi].heap_index.find(tree);

             if (it != (*_node_data)[vi].heap_index.end()) {

               if ((*_node_data)[vi].heap[it->second] > rw) {

                 (*_node_data)[vi].heap.replace(it->second, e);

                 (*_node_data)[vi].heap.decrease(e, rw);

                 it->second = e;

               }

             } else {

               (*_node_data)[vi].heap.push(e, rw);