deba@326: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@326:  *
deba@326:  * This file is a part of LEMON, a generic C++ optimization library.
deba@326:  *
deba@326:  * Copyright (C) 2003-2008
deba@326:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@326:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@326:  *
deba@326:  * Permission to use, modify and distribute this software is granted
deba@326:  * provided that this copyright notice appears in all copies. For
deba@326:  * precise terms see the accompanying LICENSE file.
deba@326:  *
deba@326:  * This software is provided "AS IS" with no warranty of any kind,
deba@326:  * express or implied, and with no claim as to its suitability for any
deba@326:  * purpose.
deba@326:  *
deba@326:  */
deba@326: 
deba@326: #ifndef LEMON_MAX_MATCHING_H
deba@326: #define LEMON_MAX_MATCHING_H
deba@326: 
deba@326: #include <vector>
deba@326: #include <queue>
deba@326: #include <set>
deba@326: #include <limits>
deba@326: 
deba@326: #include <lemon/core.h>
deba@326: #include <lemon/unionfind.h>
deba@326: #include <lemon/bin_heap.h>
deba@326: #include <lemon/maps.h>
deba@326: 
deba@326: ///\ingroup matching
deba@326: ///\file
deba@326: ///\brief Maximum matching algorithms in graph.
deba@326: 
deba@326: namespace lemon {
deba@326: 
deba@326:   ///\ingroup matching
deba@326:   ///
deba@326:   ///\brief Edmonds' alternating forest maximum matching algorithm.
deba@326:   ///
deba@326:   ///This class provides Edmonds' alternating forest matching
deba@326:   ///algorithm. The starting matching (if any) can be passed to the
deba@326:   ///algorithm using some of init functions.
deba@326:   ///
deba@326:   ///The dual side of a matching is a map of the nodes to
deba@326:   ///MaxMatching::DecompType, having values \c D, \c A and \c C
deba@326:   ///showing the Gallai-Edmonds decomposition of the digraph. The nodes
deba@326:   ///in \c D induce a digraph with factor-critical components, the nodes
deba@326:   ///in \c A form the barrier, and the nodes in \c C induce a digraph
deba@326:   ///having a perfect matching. This decomposition can be attained by
deba@326:   ///calling \c decomposition() after running the algorithm.
deba@326:   ///
deba@326:   ///\param Digraph The graph type the algorithm runs on.
deba@326:   template <typename Graph>
deba@326:   class MaxMatching {
deba@326: 
deba@326:   protected:
deba@326: 
deba@326:     TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<int> UFECrossRef;
deba@326:     typedef UnionFindEnum<UFECrossRef> UFE;
deba@326:     typedef std::vector<Node> NV;
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<int> EFECrossRef;
deba@326:     typedef ExtendFindEnum<EFECrossRef> EFE;
deba@326: 
deba@326:   public:
deba@326: 
deba@326:     ///\brief Indicates the Gallai-Edmonds decomposition of the digraph.
deba@326:     ///
deba@326:     ///Indicates the Gallai-Edmonds decomposition of the digraph, which
deba@326:     ///shows an upper bound on the size of a maximum matching. The
deba@326:     ///nodes with DecompType \c D induce a digraph with factor-critical
deba@326:     ///components, the nodes in \c A form the canonical barrier, and the
deba@326:     ///nodes in \c C induce a digraph having a perfect matching.
deba@326:     enum DecompType {
deba@326:       D=0,
deba@326:       A=1,
deba@326:       C=2
deba@326:     };
deba@326: 
deba@326:   protected:
deba@326: 
deba@326:     static const int HEUR_density=2;
deba@326:     const Graph& g;
deba@326:     typename Graph::template NodeMap<Node> _mate;
deba@326:     typename Graph::template NodeMap<DecompType> position;
deba@326: 
deba@326:   public:
deba@326: 
deba@326:     MaxMatching(const Graph& _g)
deba@326:       : g(_g), _mate(_g), position(_g) {}
deba@326: 
deba@326:     ///\brief Sets the actual matching to the empty matching.
deba@326:     ///
deba@326:     ///Sets the actual matching to the empty matching.
deba@326:     ///
deba@326:     void init() {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         _mate.set(v,INVALID);
deba@326:         position.set(v,C);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     ///\brief Finds a greedy matching for initial matching.
deba@326:     ///
deba@326:     ///For initial matchig it finds a maximal greedy matching.
deba@326:     void greedyInit() {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         _mate.set(v,INVALID);
deba@326:         position.set(v,C);
deba@326:       }
deba@326:       for(NodeIt v(g); v!=INVALID; ++v)
deba@326:         if ( _mate[v]==INVALID ) {
deba@326:           for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
deba@326:             Node y=g.runningNode(e);
deba@326:             if ( _mate[y]==INVALID && y!=v ) {
deba@326:               _mate.set(v,y);
deba@326:               _mate.set(y,v);
deba@326:               break;
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:     }
deba@326: 
deba@326:     ///\brief Initialize the matching from each nodes' mate.
deba@326:     ///
deba@326:     ///Initialize the matching from a \c Node valued \c Node map. This
deba@326:     ///map must be \e symmetric, i.e. if \c map[u]==v then \c
deba@326:     ///map[v]==u must hold, and \c uv will be an arc of the initial
deba@326:     ///matching.
deba@326:     template <typename MateMap>
deba@326:     void mateMapInit(MateMap& map) {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         _mate.set(v,map[v]);
deba@326:         position.set(v,C);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     ///\brief Initialize the matching from a node map with the
deba@326:     ///incident matching arcs.
deba@326:     ///
deba@326:     ///Initialize the matching from an \c Edge valued \c Node map. \c
deba@326:     ///map[v] must be an \c Edge incident to \c v. This map must have
deba@326:     ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c
deba@326:     ///g.oppositeNode(v,map[v])==u holds, and now some arc joining \c
deba@326:     ///u to \c v will be an arc of the matching.
deba@326:     template<typename MatchingMap>
deba@326:     void matchingMapInit(MatchingMap& map) {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         position.set(v,C);
deba@326:         Edge e=map[v];
deba@326:         if ( e!=INVALID )
deba@326:           _mate.set(v,g.oppositeNode(v,e));
deba@326:         else
deba@326:           _mate.set(v,INVALID);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     ///\brief Initialize the matching from the map containing the
deba@326:     ///undirected matching arcs.
deba@326:     ///
deba@326:     ///Initialize the matching from a \c bool valued \c Edge map. This
deba@326:     ///map must have the property that there are no two incident arcs
deba@326:     ///\c e, \c f with \c map[e]==map[f]==true. The arcs \c e with \c
deba@326:     ///map[e]==true form the matching.
deba@326:     template <typename MatchingMap>
deba@326:     void matchingInit(MatchingMap& map) {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         _mate.set(v,INVALID);
deba@326:         position.set(v,C);
deba@326:       }
deba@326:       for(EdgeIt e(g); e!=INVALID; ++e) {
deba@326:         if ( map[e] ) {
deba@326:           Node u=g.u(e);
deba@326:           Node v=g.v(e);
deba@326:           _mate.set(u,v);
deba@326:           _mate.set(v,u);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326: 
deba@326:     ///\brief Runs Edmonds' algorithm.
deba@326:     ///
deba@326:     ///Runs Edmonds' algorithm for sparse digraphs (number of arcs <
deba@326:     ///2*number of nodes), and a heuristical Edmonds' algorithm with a
deba@326:     ///heuristic of postponing shrinks for dense digraphs.
deba@326:     void run() {
deba@326:       if (countEdges(g) < HEUR_density * countNodes(g)) {
deba@326:         greedyInit();
deba@326:         startSparse();
deba@326:       } else {
deba@326:         init();
deba@326:         startDense();
deba@326:       }
deba@326:     }
deba@326: 
deba@326: 
deba@326:     ///\brief Starts Edmonds' algorithm.
deba@326:     ///
deba@326:     ///If runs the original Edmonds' algorithm.
deba@326:     void startSparse() {
deba@326: 
deba@326:       typename Graph::template NodeMap<Node> ear(g,INVALID);
deba@326:       //undefined for the base nodes of the blossoms (i.e. for the
deba@326:       //representative elements of UFE blossom) and for the nodes in C
deba@326: 
deba@326:       UFECrossRef blossom_base(g);
deba@326:       UFE blossom(blossom_base);
deba@326:       NV rep(countNodes(g));
deba@326: 
deba@326:       EFECrossRef tree_base(g);
deba@326:       EFE tree(tree_base);
deba@326: 
deba@326:       //If these UFE's would be members of the class then also
deba@326:       //blossom_base and tree_base should be a member.
deba@326: 
deba@326:       //We build only one tree and the other vertices uncovered by the
deba@326:       //matching belong to C. (They can be considered as singleton
deba@326:       //trees.) If this tree can be augmented or no more
deba@326:       //grow/augmentation/shrink is possible then we return to this
deba@326:       //"for" cycle.
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         if (position[v]==C && _mate[v]==INVALID) {
deba@326:           rep[blossom.insert(v)] = v;
deba@326:           tree.insert(v);
deba@326:           position.set(v,D);
deba@326:           normShrink(v, ear, blossom, rep, tree);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     ///\brief Starts Edmonds' algorithm.
deba@326:     ///
deba@326:     ///It runs Edmonds' algorithm with a heuristic of postponing
deba@326:     ///shrinks, giving a faster algorithm for dense digraphs.
deba@326:     void startDense() {
deba@326: 
deba@326:       typename Graph::template NodeMap<Node> ear(g,INVALID);
deba@326:       //undefined for the base nodes of the blossoms (i.e. for the
deba@326:       //representative elements of UFE blossom) and for the nodes in C
deba@326: 
deba@326:       UFECrossRef blossom_base(g);
deba@326:       UFE blossom(blossom_base);
deba@326:       NV rep(countNodes(g));
deba@326: 
deba@326:       EFECrossRef tree_base(g);
deba@326:       EFE tree(tree_base);
deba@326: 
deba@326:       //If these UFE's would be members of the class then also
deba@326:       //blossom_base and tree_base should be a member.
deba@326: 
deba@326:       //We build only one tree and the other vertices uncovered by the
deba@326:       //matching belong to C. (They can be considered as singleton
deba@326:       //trees.) If this tree can be augmented or no more
deba@326:       //grow/augmentation/shrink is possible then we return to this
deba@326:       //"for" cycle.
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         if ( position[v]==C && _mate[v]==INVALID ) {
deba@326:           rep[blossom.insert(v)] = v;
deba@326:           tree.insert(v);
deba@326:           position.set(v,D);
deba@326:           lateShrink(v, ear, blossom, rep, tree);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326: 
deba@326: 
deba@326:     ///\brief Returns the size of the actual matching stored.
deba@326:     ///
deba@326:     ///Returns the size of the actual matching stored. After \ref
deba@326:     ///run() it returns the size of a maximum matching in the digraph.
deba@326:     int size() const {
deba@326:       int s=0;
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         if ( _mate[v]!=INVALID ) {
deba@326:           ++s;
deba@326:         }
deba@326:       }
deba@326:       return s/2;
deba@326:     }
deba@326: 
deba@326: 
deba@326:     ///\brief Returns the mate of a node in the actual matching.
deba@326:     ///
deba@326:     ///Returns the mate of a \c node in the actual matching.
deba@326:     ///Returns INVALID if the \c node is not covered by the actual matching.
deba@326:     Node mate(const Node& node) const {
deba@326:       return _mate[node];
deba@326:     }
deba@326: 
deba@326:     ///\brief Returns the matching arc incident to the given node.
deba@326:     ///
deba@326:     ///Returns the matching arc of a \c node in the actual matching.
deba@326:     ///Returns INVALID if the \c node is not covered by the actual matching.
deba@326:     Edge matchingArc(const Node& node) const {
deba@326:       if (_mate[node] == INVALID) return INVALID;
deba@326:       Node n = node < _mate[node] ? node : _mate[node];
deba@326:       for (IncEdgeIt e(g, n); e != INVALID; ++e) {
deba@326:         if (g.oppositeNode(n, e) == _mate[n]) {
deba@326:           return e;
deba@326:         }
deba@326:       }
deba@326:       return INVALID;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the class of the node in the Edmonds-Gallai
deba@326:     /// decomposition.
deba@326:     ///
deba@326:     /// Returns the class of the node in the Edmonds-Gallai
deba@326:     /// decomposition.
deba@326:     DecompType decomposition(const Node& n) {
deba@326:       return position[n] == A;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns true when the node is in the barrier.
deba@326:     ///
deba@326:     /// Returns true when the node is in the barrier.
deba@326:     bool barrier(const Node& n) {
deba@326:       return position[n] == A;
deba@326:     }
deba@326: 
deba@326:     ///\brief Gives back the matching in a \c Node of mates.
deba@326:     ///
deba@326:     ///Writes the stored matching to a \c Node valued \c Node map. The
deba@326:     ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
deba@326:     ///map[v]==u will hold, and now \c uv is an arc of the matching.
deba@326:     template <typename MateMap>
deba@326:     void mateMap(MateMap& map) const {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         map.set(v,_mate[v]);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     ///\brief Gives back the matching in an \c Edge valued \c Node
deba@326:     ///map.
deba@326:     ///
deba@326:     ///Writes the stored matching to an \c Edge valued \c Node
deba@326:     ///map. \c map[v] will be an \c Edge incident to \c v. This
deba@326:     ///map will have the property that if \c g.oppositeNode(u,map[u])
deba@326:     ///== v then \c map[u]==map[v] holds, and now this arc is an arc
deba@326:     ///of the matching.
deba@326:     template <typename MatchingMap>
deba@326:     void matchingMap(MatchingMap& map)  const {
deba@326:       typename Graph::template NodeMap<bool> todo(g,true);
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         if (_mate[v]!=INVALID && v < _mate[v]) {
deba@326:           Node u=_mate[v];
deba@326:           for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
deba@326:             if ( g.runningNode(e) == u ) {
deba@326:               map.set(u,e);
deba@326:               map.set(v,e);
deba@326:               todo.set(u,false);
deba@326:               todo.set(v,false);
deba@326:               break;
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326: 
deba@326:     ///\brief Gives back the matching in a \c bool valued \c Edge
deba@326:     ///map.
deba@326:     ///
deba@326:     ///Writes the matching stored to a \c bool valued \c Arc
deba@326:     ///map. This map will have the property that there are no two
deba@326:     ///incident arcs \c e, \c f with \c map[e]==map[f]==true. The
deba@326:     ///arcs \c e with \c map[e]==true form the matching.
deba@326:     template<typename MatchingMap>
deba@326:     void matching(MatchingMap& map) const {
deba@326:       for(EdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
deba@326: 
deba@326:       typename Graph::template NodeMap<bool> todo(g,true);
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@326:         if ( todo[v] && _mate[v]!=INVALID ) {
deba@326:           Node u=_mate[v];
deba@326:           for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
deba@326:             if ( g.runningNode(e) == u ) {
deba@326:               map.set(e,true);
deba@326:               todo.set(u,false);
deba@326:               todo.set(v,false);
deba@326:               break;
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326: 
deba@326:     ///\brief Returns the canonical decomposition of the digraph after running
deba@326:     ///the algorithm.
deba@326:     ///
deba@326:     ///After calling any run methods of the class, it writes the
deba@326:     ///Gallai-Edmonds canonical decomposition of the digraph. \c map
deba@326:     ///must be a node map of \ref DecompType 's.
deba@326:     template <typename DecompositionMap>
deba@326:     void decomposition(DecompositionMap& map) const {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
deba@326:     }
deba@326: 
deba@326:     ///\brief Returns a barrier on the nodes.
deba@326:     ///
deba@326:     ///After calling any run methods of the class, it writes a
deba@326:     ///canonical barrier on the nodes. The odd component number of the
deba@326:     ///remaining digraph minus the barrier size is a lower bound for the
deba@326:     ///uncovered nodes in the digraph. The \c map must be a node map of
deba@326:     ///bools.
deba@326:     template <typename BarrierMap>
deba@326:     void barrier(BarrierMap& barrier) {
deba@326:       for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A);
deba@326:     }
deba@326: 
deba@326:   private:
deba@326: 
deba@326: 
deba@326:     void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
deba@326:                     UFE& blossom, NV& rep, EFE& tree) {
deba@326:       //We have one tree which we grow, and also shrink but only if it
deba@326:       //cannot be postponed. If we augment then we return to the "for"
deba@326:       //cycle of runEdmonds().
deba@326: 
deba@326:       std::queue<Node> Q;   //queue of the totally unscanned nodes
deba@326:       Q.push(v);
deba@326:       std::queue<Node> R;
deba@326:       //queue of the nodes which must be scanned for a possible shrink
deba@326: 
deba@326:       while ( !Q.empty() ) {
deba@326:         Node x=Q.front();
deba@326:         Q.pop();
deba@326:         for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
deba@326:           Node y=g.runningNode(e);
deba@326:           //growOrAugment grows if y is covered by the matching and
deba@326:           //augments if not. In this latter case it returns 1.
deba@326:           if (position[y]==C &&
deba@326:               growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
deba@326:         }
deba@326:         R.push(x);
deba@326:       }
deba@326: 
deba@326:       while ( !R.empty() ) {
deba@326:         Node x=R.front();
deba@326:         R.pop();
deba@326: 
deba@326:         for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
deba@326:           Node y=g.runningNode(e);
deba@326: 
deba@326:           if ( position[y] == D && blossom.find(x) != blossom.find(y) )
deba@326:             //Recall that we have only one tree.
deba@326:             shrink( x, y, ear, blossom, rep, tree, Q);
deba@326: 
deba@326:           while ( !Q.empty() ) {
deba@326:             Node z=Q.front();
deba@326:             Q.pop();
deba@326:             for( IncEdgeIt f(g,z); f!= INVALID; ++f ) {
deba@326:               Node w=g.runningNode(f);
deba@326:               //growOrAugment grows if y is covered by the matching and
deba@326:               //augments if not. In this latter case it returns 1.
deba@326:               if (position[w]==C &&
deba@326:                   growOrAugment(w, z, ear, blossom, rep, tree, Q)) return;
deba@326:             }
deba@326:             R.push(z);
deba@326:           }
deba@326:         } //for e
deba@326:       } // while ( !R.empty() )
deba@326:     }
deba@326: 
deba@326:     void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
deba@326:                     UFE& blossom, NV& rep, EFE& tree) {
deba@326:       //We have one tree, which we grow and shrink. If we augment then we
deba@326:       //return to the "for" cycle of runEdmonds().
deba@326: 
deba@326:       std::queue<Node> Q;   //queue of the unscanned nodes
deba@326:       Q.push(v);
deba@326:       while ( !Q.empty() ) {
deba@326: 
deba@326:         Node x=Q.front();
deba@326:         Q.pop();
deba@326: 
deba@326:         for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
deba@326:           Node y=g.runningNode(e);
deba@326: 
deba@326:           switch ( position[y] ) {
deba@326:           case D:          //x and y must be in the same tree
deba@326:             if ( blossom.find(x) != blossom.find(y))
deba@326:               //x and y are in the same tree
deba@326:               shrink(x, y, ear, blossom, rep, tree, Q);
deba@326:             break;
deba@326:           case C:
deba@326:             //growOrAugment grows if y is covered by the matching and
deba@326:             //augments if not. In this latter case it returns 1.
deba@326:             if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
deba@326:             break;
deba@326:           default: break;
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,
deba@326:                 UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) {
deba@326:       //x and y are the two adjacent vertices in two blossoms.
deba@326: 
deba@326:       typename Graph::template NodeMap<bool> path(g,false);
deba@326: 
deba@326:       Node b=rep[blossom.find(x)];
deba@326:       path.set(b,true);
deba@326:       b=_mate[b];
deba@326:       while ( b!=INVALID ) {
deba@326:         b=rep[blossom.find(ear[b])];
deba@326:         path.set(b,true);
deba@326:         b=_mate[b];
deba@326:       } //we go until the root through bases of blossoms and odd vertices
deba@326: 
deba@326:       Node top=y;
deba@326:       Node middle=rep[blossom.find(top)];
deba@326:       Node bottom=x;
deba@326:       while ( !path[middle] )
deba@326:         shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
deba@326:       //Until we arrive to a node on the path, we update blossom, tree
deba@326:       //and the positions of the odd nodes.
deba@326: 
deba@326:       Node base=middle;
deba@326:       top=x;
deba@326:       middle=rep[blossom.find(top)];
deba@326:       bottom=y;
deba@326:       Node blossom_base=rep[blossom.find(base)];
deba@326:       while ( middle!=blossom_base )
deba@326:         shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
deba@326:       //Until we arrive to a node on the path, we update blossom, tree
deba@326:       //and the positions of the odd nodes.
deba@326: 
deba@326:       rep[blossom.find(base)] = base;
deba@326:     }
deba@326: 
deba@326:     void shrinkStep(Node& top, Node& middle, Node& bottom,
deba@326:                     typename Graph::template NodeMap<Node>& ear,
deba@326:                     UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) {
deba@326:       //We traverse a blossom and update everything.
deba@326: 
deba@326:       ear.set(top,bottom);
deba@326:       Node t=top;
deba@326:       while ( t!=middle ) {
deba@326:         Node u=_mate[t];
deba@326:         t=ear[u];
deba@326:         ear.set(t,u);
deba@326:       }
deba@326:       bottom=_mate[middle];
deba@326:       position.set(bottom,D);
deba@326:       Q.push(bottom);
deba@326:       top=ear[bottom];
deba@326:       Node oldmiddle=middle;
deba@326:       middle=rep[blossom.find(top)];
deba@326:       tree.erase(bottom);
deba@326:       tree.erase(oldmiddle);
deba@326:       blossom.insert(bottom);
deba@326:       blossom.join(bottom, oldmiddle);
deba@326:       blossom.join(top, oldmiddle);
deba@326:     }
deba@326: 
deba@326: 
deba@326: 
deba@326:     bool growOrAugment(Node& y, Node& x, typename Graph::template
deba@326:                        NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree,
deba@326:                        std::queue<Node>& Q) {
deba@326:       //x is in a blossom in the tree, y is outside. If y is covered by
deba@326:       //the matching we grow, otherwise we augment. In this case we
deba@326:       //return 1.
deba@326: 
deba@326:       if ( _mate[y]!=INVALID ) {       //grow
deba@326:         ear.set(y,x);
deba@326:         Node w=_mate[y];
deba@326:         rep[blossom.insert(w)] = w;
deba@326:         position.set(y,A);
deba@326:         position.set(w,D);
deba@326:         int t = tree.find(rep[blossom.find(x)]);
deba@326:         tree.insert(y,t);
deba@326:         tree.insert(w,t);
deba@326:         Q.push(w);
deba@326:       } else {                      //augment
deba@326:         augment(x, ear, blossom, rep, tree);
deba@326:         _mate.set(x,y);
deba@326:         _mate.set(y,x);
deba@326:         return true;
deba@326:       }
deba@326:       return false;
deba@326:     }
deba@326: 
deba@326:     void augment(Node x, typename Graph::template NodeMap<Node>& ear,
deba@326:                  UFE& blossom, NV& rep, EFE& tree) {
deba@326:       Node v=_mate[x];
deba@326:       while ( v!=INVALID ) {
deba@326: 
deba@326:         Node u=ear[v];
deba@326:         _mate.set(v,u);
deba@326:         Node tmp=v;
deba@326:         v=_mate[u];
deba@326:         _mate.set(u,tmp);
deba@326:       }
deba@326:       int y = tree.find(rep[blossom.find(x)]);
deba@326:       for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) {
deba@326:         if ( position[tit] == D ) {
deba@326:           int b = blossom.find(tit);
deba@326:           for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) {
deba@326:             position.set(bit, C);
deba@326:           }
deba@326:           blossom.eraseClass(b);
deba@326:         } else position.set(tit, C);
deba@326:       }
deba@326:       tree.eraseClass(y);
deba@326: 
deba@326:     }
deba@326: 
deba@326:   };
deba@326: 
deba@326:   /// \ingroup matching
deba@326:   ///
deba@326:   /// \brief Weighted matching in general graphs
deba@326:   ///
deba@326:   /// This class provides an efficient implementation of Edmond's
deba@326:   /// maximum weighted matching algorithm. The implementation is based
deba@326:   /// on extensive use of priority queues and provides
deba@326:   /// \f$O(nm\log(n))\f$ time complexity.
deba@326:   ///
deba@326:   /// The maximum weighted matching problem is to find undirected
deba@326:   /// arcs in the digraph with maximum overall weight and no two of
deba@326:   /// them shares their endpoints. The problem can be formulated with
deba@326:   /// the next linear program:
deba@326:   /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
deba@326:   ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f]
deba@326:   /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326:   /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@326:   /// where \f$\delta(X)\f$ is the set of arcs incident to a node in
deba@326:   /// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints in
deba@326:   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
deba@326:   /// the nodes.
deba@326:   ///
deba@326:   /// The algorithm calculates an optimal matching and a proof of the
deba@326:   /// optimality. The solution of the dual problem can be used to check
deba@326:   /// the result of the algorithm. The dual linear problem is the next:
deba@326:   /// \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]
deba@326:   /// \f[y_u \ge 0 \quad \forall u \in V\f]
deba@326:   /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@326:   /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
deba@326:   ///
deba@326:   /// The algorithm can be executed with \c run() or the \c init() and
deba@326:   /// then the \c start() member functions. After it the matching can
deba@326:   /// be asked with \c matching() or mate() functions. The dual
deba@326:   /// solution can be get with \c nodeValue(), \c blossomNum() and \c
deba@326:   /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
deba@326:   /// "BlossomIt" nested class which is able to iterate on the nodes
deba@326:   /// of a blossom. If the value type is integral then the dual
deba@326:   /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
deba@326:   template <typename _Graph,
deba@326:             typename _WeightMap = typename _Graph::template EdgeMap<int> >
deba@326:   class MaxWeightedMatching {
deba@326:   public:
deba@326: 
deba@326:     typedef _Graph Graph;
deba@326:     typedef _WeightMap WeightMap;
deba@326:     typedef typename WeightMap::Value Value;
deba@326: 
deba@326:     /// \brief Scaling factor for dual solution
deba@326:     ///
deba@326:     /// Scaling factor for dual solution, it is equal to 4 or 1
deba@326:     /// according to the value type.
deba@326:     static const int dualScale =
deba@326:       std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@326:     MatchingMap;
deba@326: 
deba@326:   private:
deba@326: 
deba@326:     TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326:     typedef std::vector<Node> BlossomNodeList;
deba@326: 
deba@326:     struct BlossomVariable {
deba@326:       int begin, end;
deba@326:       Value value;
deba@326: 
deba@326:       BlossomVariable(int _begin, int _end, Value _value)
deba@326:         : begin(_begin), end(_end), value(_value) {}
deba@326: 
deba@326:     };
deba@326: 
deba@326:     typedef std::vector<BlossomVariable> BlossomPotential;
deba@326: 
deba@326:     const Graph& _graph;
deba@326:     const WeightMap& _weight;
deba@326: 
deba@326:     MatchingMap* _matching;
deba@326: 
deba@326:     NodePotential* _node_potential;
deba@326: 
deba@326:     BlossomPotential _blossom_potential;
deba@326:     BlossomNodeList _blossom_node_list;
deba@326: 
deba@326:     int _node_num;
deba@326:     int _blossom_num;
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<int> NodeIntMap;
deba@326:     typedef typename Graph::template ArcMap<int> ArcIntMap;
deba@326:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
deba@326:     typedef RangeMap<int> IntIntMap;
deba@326: 
deba@326:     enum Status {
deba@326:       EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
deba@326:     };
deba@326: 
deba@326:     typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
deba@326:     struct BlossomData {
deba@326:       int tree;
deba@326:       Status status;
deba@326:       Arc pred, next;
deba@326:       Value pot, offset;
deba@326:       Node base;
deba@326:     };
deba@326: 
deba@326:     NodeIntMap *_blossom_index;
deba@326:     BlossomSet *_blossom_set;
deba@326:     RangeMap<BlossomData>* _blossom_data;
deba@326: 
deba@326:     NodeIntMap *_node_index;
deba@326:     ArcIntMap *_node_heap_index;
deba@326: 
deba@326:     struct NodeData {
deba@326: 
deba@326:       NodeData(ArcIntMap& node_heap_index)
deba@326:         : heap(node_heap_index) {}
deba@326: 
deba@326:       int blossom;
deba@326:       Value pot;
deba@326:       BinHeap<Value, ArcIntMap> heap;
deba@326:       std::map<int, Arc> heap_index;
deba@326: 
deba@326:       int tree;
deba@326:     };
deba@326: 
deba@326:     RangeMap<NodeData>* _node_data;
deba@326: 
deba@326:     typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326: 
deba@326:     IntIntMap *_tree_set_index;
deba@326:     TreeSet *_tree_set;
deba@326: 
deba@326:     NodeIntMap *_delta1_index;
deba@326:     BinHeap<Value, NodeIntMap> *_delta1;
deba@326: 
deba@326:     IntIntMap *_delta2_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta2;
deba@326: 
deba@326:     EdgeIntMap *_delta3_index;
deba@326:     BinHeap<Value, EdgeIntMap> *_delta3;
deba@326: 
deba@326:     IntIntMap *_delta4_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta4;
deba@326: 
deba@326:     Value _delta_sum;
deba@326: 
deba@326:     void createStructures() {
deba@326:       _node_num = countNodes(_graph);
deba@326:       _blossom_num = _node_num * 3 / 2;
deba@326: 
deba@326:       if (!_matching) {
deba@326:         _matching = new MatchingMap(_graph);
deba@326:       }
deba@326:       if (!_node_potential) {
deba@326:         _node_potential = new NodePotential(_graph);
deba@326:       }
deba@326:       if (!_blossom_set) {
deba@326:         _blossom_index = new NodeIntMap(_graph);
deba@326:         _blossom_set = new BlossomSet(*_blossom_index);
deba@326:         _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326:       }
deba@326: 
deba@326:       if (!_node_index) {
deba@326:         _node_index = new NodeIntMap(_graph);
deba@326:         _node_heap_index = new ArcIntMap(_graph);
deba@326:         _node_data = new RangeMap<NodeData>(_node_num,
deba@326:                                               NodeData(*_node_heap_index));
deba@326:       }
deba@326: 
deba@326:       if (!_tree_set) {
deba@326:         _tree_set_index = new IntIntMap(_blossom_num);
deba@326:         _tree_set = new TreeSet(*_tree_set_index);
deba@326:       }
deba@326:       if (!_delta1) {
deba@326:         _delta1_index = new NodeIntMap(_graph);
deba@326:         _delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index);
deba@326:       }
deba@326:       if (!_delta2) {
deba@326:         _delta2_index = new IntIntMap(_blossom_num);
deba@326:         _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@326:       }
deba@326:       if (!_delta3) {
deba@326:         _delta3_index = new EdgeIntMap(_graph);
deba@326:         _delta3 = new BinHeap<Value, EdgeIntMap>(*_delta3_index);
deba@326:       }
deba@326:       if (!_delta4) {
deba@326:         _delta4_index = new IntIntMap(_blossom_num);
deba@326:         _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void destroyStructures() {
deba@326:       _node_num = countNodes(_graph);
deba@326:       _blossom_num = _node_num * 3 / 2;
deba@326: 
deba@326:       if (_matching) {
deba@326:         delete _matching;
deba@326:       }
deba@326:       if (_node_potential) {
deba@326:         delete _node_potential;
deba@326:       }
deba@326:       if (_blossom_set) {
deba@326:         delete _blossom_index;
deba@326:         delete _blossom_set;
deba@326:         delete _blossom_data;
deba@326:       }
deba@326: 
deba@326:       if (_node_index) {
deba@326:         delete _node_index;
deba@326:         delete _node_heap_index;
deba@326:         delete _node_data;
deba@326:       }
deba@326: 
deba@326:       if (_tree_set) {
deba@326:         delete _tree_set_index;
deba@326:         delete _tree_set;
deba@326:       }
deba@326:       if (_delta1) {
deba@326:         delete _delta1_index;
deba@326:         delete _delta1;
deba@326:       }
deba@326:       if (_delta2) {
deba@326:         delete _delta2_index;
deba@326:         delete _delta2;
deba@326:       }
deba@326:       if (_delta3) {
deba@326:         delete _delta3_index;
deba@326:         delete _delta3;
deba@326:       }
deba@326:       if (_delta4) {
deba@326:         delete _delta4_index;
deba@326:         delete _delta4;
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void matchedToEven(int blossom, int tree) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326: 
deba@326:         (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         _delta1->push(n, (*_node_data)[ni].pot);
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326:               _delta3->push(e, rw);
deba@326:             }
deba@326:           } else {
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset){
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326:     void matchedToOdd(int blossom) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset += _delta_sum;
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326:                      (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void evenToMatched(int blossom, int tree) {
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326:         (*_node_data)[ni].pot -= _delta_sum;
deba@326: 
deba@326:         _delta1->erase(n);
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if (vb == blossom) {
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326:           } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326: 
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326: 
deba@326:             int vt = _tree_set->find(vb);
deba@326: 
deba@326:             if (vt != tree) {
deba@326: 
deba@326:               Arc r = _graph.oppositeArc(e);
deba@326: 
deba@326:               typename std::map<int, Arc>::iterator it =
deba@326:                 (*_node_data)[ni].heap_index.find(vt);
deba@326: 
deba@326:               if (it != (*_node_data)[ni].heap_index.end()) {
deba@326:                 if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326:                   (*_node_data)[ni].heap.replace(it->second, r);
deba@326:                   (*_node_data)[ni].heap.decrease(r, rw);
deba@326:                   it->second = r;
deba@326:                 }
deba@326:               } else {
deba@326:                 (*_node_data)[ni].heap.push(r, rw);
deba@326:                 (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326:               }
deba@326: 
deba@326:               if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326:                 _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326: 
deba@326:                 if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                (*_blossom_data)[blossom].offset);
deba@326:                 } else if ((*_delta2)[blossom] >
deba@326:                            _blossom_set->classPrio(blossom) -
deba@326:                            (*_blossom_data)[blossom].offset){
deba@326:                   _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                    (*_blossom_data)[blossom].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326: 
deba@326:           } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               (*_node_data)[vi].heap.erase(it->second);
deba@326:               (*_node_data)[vi].heap_index.erase(it);
deba@326:               if ((*_node_data)[vi].heap.empty()) {
deba@326:                 _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326:               } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326:                 _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326:               }
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_blossom_set->classPrio(vb) ==
deba@326:                     std::numeric_limits<Value>::max()) {
deba@326:                   _delta2->erase(vb);
deba@326:                 } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void oddToMatched(int blossom) {
deba@326:       (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326: 
deba@326:       if (_blossom_set->classPrio(blossom) !=
deba@326:           std::numeric_limits<Value>::max()) {
deba@326:         _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                        (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->erase(blossom);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void oddToEven(int blossom, int tree) {
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->erase(blossom);
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326:         (*_node_data)[ni].pot +=
deba@326:           2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         _delta1->push(n, (*_node_data)[ni].pot);
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326:               _delta3->push(e, rw);
deba@326:             }
deba@326:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326: 
deba@326:     void matchedToUnmatched(int blossom) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326: 
deba@326:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.target(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326:               _delta3->push(e, rw);
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void unmatchedToMatched(int blossom) {
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if (vb == blossom) {
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326:           } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326: 
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326: 
deba@326:             int vt = _tree_set->find(vb);
deba@326: 
deba@326:             Arc r = _graph.oppositeArc(e);
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[ni].heap_index.find(vt);
deba@326: 
deba@326:             if (it != (*_node_data)[ni].heap_index.end()) {
deba@326:               if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326:                 (*_node_data)[ni].heap.replace(it->second, r);
deba@326:                 (*_node_data)[ni].heap.decrease(r, rw);
deba@326:                 it->second = r;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[ni].heap.push(r, rw);
deba@326:               (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326:               _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326: 
deba@326:               if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326:                 _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                              (*_blossom_data)[blossom].offset);
deba@326:               } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
deba@326:                          (*_blossom_data)[blossom].offset){
deba@326:                 _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                  (*_blossom_data)[blossom].offset);
deba@326:               }
deba@326:             }
deba@326: 
deba@326:           } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void alternatePath(int even, int tree) {
deba@326:       int odd;
deba@326: 
deba@326:       evenToMatched(even, tree);
deba@326:       (*_blossom_data)[even].status = MATCHED;
deba@326: 
deba@326:       while ((*_blossom_data)[even].pred != INVALID) {
deba@326:         odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326:         (*_blossom_data)[odd].status = MATCHED;
deba@326:         oddToMatched(odd);
deba@326:         (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326: 
deba@326:         even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326:         (*_blossom_data)[even].status = MATCHED;
deba@326:         evenToMatched(even, tree);
deba@326:         (*_blossom_data)[even].next =
deba@326:           _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326:       }
deba@326: 
deba@326:     }
deba@326: 
deba@326:     void destroyTree(int tree) {
deba@326:       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326:         if ((*_blossom_data)[b].status == EVEN) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           evenToMatched(b, tree);
deba@326:         } else if ((*_blossom_data)[b].status == ODD) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           oddToMatched(b);
deba@326:         }
deba@326:       }
deba@326:       _tree_set->eraseClass(tree);
deba@326:     }
deba@326: 
deba@326: 
deba@326:     void unmatchNode(const Node& node) {
deba@326:       int blossom = _blossom_set->find(node);
deba@326:       int tree = _tree_set->find(blossom);
deba@326: 
deba@326:       alternatePath(blossom, tree);
deba@326:       destroyTree(tree);
deba@326: 
deba@326:       (*_blossom_data)[blossom].status = UNMATCHED;
deba@326:       (*_blossom_data)[blossom].base = node;
deba@326:       matchedToUnmatched(blossom);
deba@326:     }
deba@326: 
deba@326: 
deba@326:     void augmentOnArc(const Edge& arc) {
deba@326: 
deba@326:       int left = _blossom_set->find(_graph.u(arc));
deba@326:       int right = _blossom_set->find(_graph.v(arc));
deba@326: 
deba@326:       if ((*_blossom_data)[left].status == EVEN) {
deba@326:         int left_tree = _tree_set->find(left);
deba@326:         alternatePath(left, left_tree);
deba@326:         destroyTree(left_tree);
deba@326:       } else {
deba@326:         (*_blossom_data)[left].status = MATCHED;
deba@326:         unmatchedToMatched(left);
deba@326:       }
deba@326: 
deba@326:       if ((*_blossom_data)[right].status == EVEN) {
deba@326:         int right_tree = _tree_set->find(right);
deba@326:         alternatePath(right, right_tree);
deba@326:         destroyTree(right_tree);
deba@326:       } else {
deba@326:         (*_blossom_data)[right].status = MATCHED;
deba@326:         unmatchedToMatched(right);
deba@326:       }
deba@326: 
deba@326:       (*_blossom_data)[left].next = _graph.direct(arc, true);
deba@326:       (*_blossom_data)[right].next = _graph.direct(arc, false);
deba@326:     }
deba@326: 
deba@326:     void extendOnArc(const Arc& arc) {
deba@326:       int base = _blossom_set->find(_graph.target(arc));
deba@326:       int tree = _tree_set->find(base);
deba@326: 
deba@326:       int odd = _blossom_set->find(_graph.source(arc));
deba@326:       _tree_set->insert(odd, tree);
deba@326:       (*_blossom_data)[odd].status = ODD;
deba@326:       matchedToOdd(odd);
deba@326:       (*_blossom_data)[odd].pred = arc;
deba@326: 
deba@326:       int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326:       (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326:       _tree_set->insert(even, tree);
deba@326:       (*_blossom_data)[even].status = EVEN;
deba@326:       matchedToEven(even, tree);
deba@326:     }
deba@326: 
deba@326:     void shrinkOnArc(const Edge& edge, int tree) {
deba@326:       int nca = -1;
deba@326:       std::vector<int> left_path, right_path;
deba@326: 
deba@326:       {
deba@326:         std::set<int> left_set, right_set;
deba@326:         int left = _blossom_set->find(_graph.u(edge));
deba@326:         left_path.push_back(left);
deba@326:         left_set.insert(left);
deba@326: 
deba@326:         int right = _blossom_set->find(_graph.v(edge));
deba@326:         right_path.push_back(right);
deba@326:         right_set.insert(right);
deba@326: 
deba@326:         while (true) {
deba@326: 
deba@326:           if ((*_blossom_data)[left].pred == INVALID) break;
deba@326: 
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326: 
deba@326:           left_set.insert(left);
deba@326: 
deba@326:           if (right_set.find(left) != right_set.end()) {
deba@326:             nca = left;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:           if ((*_blossom_data)[right].pred == INVALID) break;
deba@326: 
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326: 
deba@326:           right_set.insert(right);
deba@326: 
deba@326:           if (left_set.find(right) != left_set.end()) {
deba@326:             nca = right;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:         }
deba@326: 
deba@326:         if (nca == -1) {
deba@326:           if ((*_blossom_data)[left].pred == INVALID) {
deba@326:             nca = right;
deba@326:             while (left_set.find(nca) == left_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:             }
deba@326:           } else {
deba@326:             nca = left;
deba@326:             while (right_set.find(nca) == right_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       Arc prev;
deba@326: 
deba@326:       prev = _graph.direct(edge, true);
deba@326:       for (int i = 0; left_path[i] != nca; i += 2) {
deba@326:         subblossoms.push_back(left_path[i]);
deba@326:         (*_blossom_data)[left_path[i]].next = prev;
deba@326:         _tree_set->erase(left_path[i]);
deba@326: 
deba@326:         subblossoms.push_back(left_path[i + 1]);
deba@326:         (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326:         oddToEven(left_path[i + 1], tree);
deba@326:         _tree_set->erase(left_path[i + 1]);
deba@326:         prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326:       }
deba@326: 
deba@326:       int k = 0;
deba@326:       while (right_path[k] != nca) ++k;
deba@326: 
deba@326:       subblossoms.push_back(nca);
deba@326:       (*_blossom_data)[nca].next = prev;
deba@326: 
deba@326:       for (int i = k - 2; i >= 0; i -= 2) {
deba@326:         subblossoms.push_back(right_path[i + 1]);
deba@326:         (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326:         oddToEven(right_path[i + 1], tree);
deba@326:         _tree_set->erase(right_path[i + 1]);
deba@326: 
deba@326:         (*_blossom_data)[right_path[i + 1]].next =
deba@326:           (*_blossom_data)[right_path[i + 1]].pred;
deba@326: 
deba@326:         subblossoms.push_back(right_path[i]);
deba@326:         _tree_set->erase(right_path[i]);
deba@326:       }
deba@326: 
deba@326:       int surface =
deba@326:         _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326: 
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326:         }
deba@326:         (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326:       }
deba@326: 
deba@326:       (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326:       (*_blossom_data)[surface].offset = 0;
deba@326:       (*_blossom_data)[surface].status = EVEN;
deba@326:       (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326:       (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326: 
deba@326:       _tree_set->insert(surface, tree);
deba@326:       _tree_set->erase(nca);
deba@326:     }
deba@326: 
deba@326:     void splitBlossom(int blossom) {
deba@326:       Arc next = (*_blossom_data)[blossom].next;
deba@326:       Arc pred = (*_blossom_data)[blossom].pred;
deba@326: 
deba@326:       int tree = _tree_set->find(blossom);
deba@326: 
deba@326:       (*_blossom_data)[blossom].status = MATCHED;
deba@326:       oddToMatched(blossom);
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326: 
deba@326:       Value offset = (*_blossom_data)[blossom].offset;
deba@326:       int b = _blossom_set->find(_graph.source(pred));
deba@326:       int d = _blossom_set->find(_graph.source(next));
deba@326: 
deba@326:       int ib = -1, id = -1;
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (subblossoms[i] == b) ib = i;
deba@326:         if (subblossoms[i] == d) id = i;
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326:         }
deba@326:         if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326:             std::numeric_limits<Value>::max()) {
deba@326:           _delta2->push(subblossoms[i],
deba@326:                         _blossom_set->classPrio(subblossoms[i]) -
deba@326:                         (*_blossom_data)[subblossoms[i]].offset);
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326:         for (int i = (id + 1) % subblossoms.size();
deba@326:              i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].pred = pred;
deba@326:           (*_blossom_data)[sb].next =
deba@326:                            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           pred = (*_blossom_data)[ub].next;
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326:         matchedToOdd(subblossoms[id]);
deba@326:         _tree_set->insert(subblossoms[id], tree);
deba@326:         (*_blossom_data)[subblossoms[id]].next = next;
deba@326:         (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326: 
deba@326:       } else {
deba@326: 
deba@326:         for (int i = (ib + 1) % subblossoms.size();
deba@326:              i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].next = next;
deba@326:           (*_blossom_data)[sb].pred =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred =
deba@326:             (*_blossom_data)[tb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326:           next = (*_blossom_data)[ub].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326:         matchedToOdd(subblossoms[ib]);
deba@326:         _tree_set->insert(subblossoms[ib], tree);
deba@326:         (*_blossom_data)[subblossoms[ib]].next = next;
deba@326:         (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326:       }
deba@326:       _tree_set->erase(blossom);
deba@326:     }
deba@326: 
deba@326:     void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326:       if (_blossom_set->trivial(blossom)) {
deba@326:         int bi = (*_node_index)[base];
deba@326:         Value pot = (*_node_data)[bi].pot;
deba@326: 
deba@326:         _matching->set(base, matching);
deba@326:         _blossom_node_list.push_back(base);
deba@326:         _node_potential->set(base, pot);
deba@326:       } else {
deba@326: 
deba@326:         Value pot = (*_blossom_data)[blossom].pot;
deba@326:         int bn = _blossom_node_list.size();
deba@326: 
deba@326:         std::vector<int> subblossoms;
deba@326:         _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326:         int b = _blossom_set->find(base);
deba@326:         int ib = -1;
deba@326:         for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:           if (subblossoms[i] == b) { ib = i; break; }
deba@326:         }
deba@326: 
deba@326:         for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326:           int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326:           int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326: 
deba@326:           Arc m = (*_blossom_data)[tb].next;
deba@326:           extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326:           extractBlossom(tb, _graph.source(m), m);
deba@326:         }
deba@326:         extractBlossom(subblossoms[ib], base, matching);
deba@326: 
deba@326:         int en = _blossom_node_list.size();
deba@326: 
deba@326:         _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void extractMatching() {
deba@326:       std::vector<int> blossoms;
deba@326:       for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326:         blossoms.push_back(c);
deba@326:       }
deba@326: 
deba@326:       for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326:         if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
deba@326: 
deba@326:           Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326:           (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326:           for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326:                n != INVALID; ++n) {
deba@326:             (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326:           }
deba@326: 
deba@326:           Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326:           Node base = _graph.source(matching);
deba@326:           extractBlossom(blossoms[i], base, matching);
deba@326:         } else {
deba@326:           Node base = (*_blossom_data)[blossoms[i]].base;
deba@326:           extractBlossom(blossoms[i], base, INVALID);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:   public:
deba@326: 
deba@326:     /// \brief Constructor
deba@326:     ///
deba@326:     /// Constructor.
deba@326:     MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
deba@326:       : _graph(graph), _weight(weight), _matching(0),
deba@326:         _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326:         _node_num(0), _blossom_num(0),
deba@326: 
deba@326:         _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326:         _node_index(0), _node_heap_index(0), _node_data(0),
deba@326:         _tree_set_index(0), _tree_set(0),
deba@326: 
deba@326:         _delta1_index(0), _delta1(0),
deba@326:         _delta2_index(0), _delta2(0),
deba@326:         _delta3_index(0), _delta3(0),
deba@326:         _delta4_index(0), _delta4(0),
deba@326: 
deba@326:         _delta_sum() {}
deba@326: 
deba@326:     ~MaxWeightedMatching() {
deba@326:       destroyStructures();
deba@326:     }
deba@326: 
deba@326:     /// \name Execution control
deba@326:     /// The simplest way to execute the algorithm is to use the member
deba@326:     /// \c run() member function.
deba@326: 
deba@326:     ///@{
deba@326: 
deba@326:     /// \brief Initialize the algorithm
deba@326:     ///
deba@326:     /// Initialize the algorithm
deba@326:     void init() {
deba@326:       createStructures();
deba@326: 
deba@326:       for (ArcIt e(_graph); e != INVALID; ++e) {
deba@326:         _node_heap_index->set(e, BinHeap<Value, ArcIntMap>::PRE_HEAP);
deba@326:       }
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         _delta1_index->set(n, _delta1->PRE_HEAP);
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326:         _delta3_index->set(e, _delta3->PRE_HEAP);
deba@326:       }
deba@326:       for (int i = 0; i < _blossom_num; ++i) {
deba@326:         _delta2_index->set(i, _delta2->PRE_HEAP);
deba@326:         _delta4_index->set(i, _delta4->PRE_HEAP);
deba@326:       }
deba@326: 
deba@326:       int index = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         Value max = 0;
deba@326:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           if (_graph.target(e) == n) continue;
deba@326:           if ((dualScale * _weight[e]) / 2 > max) {
deba@326:             max = (dualScale * _weight[e]) / 2;
deba@326:           }
deba@326:         }
deba@326:         _node_index->set(n, index);
deba@326:         (*_node_data)[index].pot = max;
deba@326:         _delta1->push(n, max);
deba@326:         int blossom =
deba@326:           _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         _tree_set->insert(blossom);
deba@326: 
deba@326:         (*_blossom_data)[blossom].status = EVEN;
deba@326:         (*_blossom_data)[blossom].pred = INVALID;
deba@326:         (*_blossom_data)[blossom].next = INVALID;
deba@326:         (*_blossom_data)[blossom].pot = 0;
deba@326:         (*_blossom_data)[blossom].offset = 0;
deba@326:         ++index;
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326:         int si = (*_node_index)[_graph.u(e)];
deba@326:         int ti = (*_node_index)[_graph.v(e)];
deba@326:         if (_graph.u(e) != _graph.v(e)) {
deba@326:           _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326:                             dualScale * _weight[e]) / 2);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     /// \brief Starts the algorithm
deba@326:     ///
deba@326:     /// Starts the algorithm
deba@326:     void start() {
deba@326:       enum OpType {
deba@326:         D1, D2, D3, D4
deba@326:       };
deba@326: 
deba@326:       int unmatched = _node_num;
deba@326:       while (unmatched > 0) {
deba@326:         Value d1 = !_delta1->empty() ?
deba@326:           _delta1->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d2 = !_delta2->empty() ?
deba@326:           _delta2->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d3 = !_delta3->empty() ?
deba@326:           _delta3->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d4 = !_delta4->empty() ?
deba@326:           _delta4->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         _delta_sum = d1; OpType ot = D1;
deba@326:         if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
deba@326:         if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@326:         if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326: 
deba@326: 
deba@326:         switch (ot) {
deba@326:         case D1:
deba@326:           {
deba@326:             Node n = _delta1->top();
deba@326:             unmatchNode(n);
deba@326:             --unmatched;
deba@326:           }
deba@326:           break;
deba@326:         case D2:
deba@326:           {
deba@326:             int blossom = _delta2->top();
deba@326:             Node n = _blossom_set->classTop(blossom);
deba@326:             Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326:             extendOnArc(e);
deba@326:           }
deba@326:           break;
deba@326:         case D3:
deba@326:           {
deba@326:             Edge e = _delta3->top();
deba@326: 
deba@326:             int left_blossom = _blossom_set->find(_graph.u(e));
deba@326:             int right_blossom = _blossom_set->find(_graph.v(e));
deba@326: 
deba@326:             if (left_blossom == right_blossom) {
deba@326:               _delta3->pop();
deba@326:             } else {
deba@326:               int left_tree;
deba@326:               if ((*_blossom_data)[left_blossom].status == EVEN) {
deba@326:                 left_tree = _tree_set->find(left_blossom);
deba@326:               } else {
deba@326:                 left_tree = -1;
deba@326:                 ++unmatched;
deba@326:               }
deba@326:               int right_tree;
deba@326:               if ((*_blossom_data)[right_blossom].status == EVEN) {
deba@326:                 right_tree = _tree_set->find(right_blossom);
deba@326:               } else {
deba@326:                 right_tree = -1;
deba@326:                 ++unmatched;
deba@326:               }
deba@326: 
deba@326:               if (left_tree == right_tree) {
deba@326:                 shrinkOnArc(e, left_tree);
deba@326:               } else {
deba@326:                 augmentOnArc(e);
deba@326:                 unmatched -= 2;
deba@326:               }
deba@326:             }
deba@326:           } break;
deba@326:         case D4:
deba@326:           splitBlossom(_delta4->top());
deba@326:           break;
deba@326:         }
deba@326:       }
deba@326:       extractMatching();
deba@326:     }
deba@326: 
deba@326:     /// \brief Runs %MaxWeightedMatching algorithm.
deba@326:     ///
deba@326:     /// This method runs the %MaxWeightedMatching algorithm.
deba@326:     ///
deba@326:     /// \note mwm.run() is just a shortcut of the following code.
deba@326:     /// \code
deba@326:     ///   mwm.init();
deba@326:     ///   mwm.start();
deba@326:     /// \endcode
deba@326:     void run() {
deba@326:       init();
deba@326:       start();
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:     /// \name Primal solution
deba@326:     /// Functions for get the primal solution, ie. the matching.
deba@326: 
deba@326:     /// @{
deba@326: 
deba@326:     /// \brief Returns the matching value.
deba@326:     ///
deba@326:     /// Returns the matching value.
deba@326:     Value matchingValue() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         if ((*_matching)[n] != INVALID) {
deba@326:           sum += _weight[(*_matching)[n]];
deba@326:         }
deba@326:       }
deba@326:       return sum /= 2;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns true when the arc is in the matching.
deba@326:     ///
deba@326:     /// Returns true when the arc is in the matching.
deba@326:     bool matching(const Edge& arc) const {
deba@326:       return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the incident matching arc.
deba@326:     ///
deba@326:     /// Returns the incident matching arc from given node. If the
deba@326:     /// node is not matched then it gives back \c INVALID.
deba@326:     Arc matching(const Node& node) const {
deba@326:       return (*_matching)[node];
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the mate of the node.
deba@326:     ///
deba@326:     /// Returns the adjancent node in a mathcing arc. If the node is
deba@326:     /// not matched then it gives back \c INVALID.
deba@326:     Node mate(const Node& node) const {
deba@326:       return (*_matching)[node] != INVALID ?
deba@326:         _graph.target((*_matching)[node]) : INVALID;
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:     /// \name Dual solution
deba@326:     /// Functions for get the dual solution.
deba@326: 
deba@326:     /// @{
deba@326: 
deba@326:     /// \brief Returns the value of the dual solution.
deba@326:     ///
deba@326:     /// Returns the value of the dual solution. It should be equal to
deba@326:     /// the primal value scaled by \ref dualScale "dual scale".
deba@326:     Value dualValue() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         sum += nodeValue(n);
deba@326:       }
deba@326:       for (int i = 0; i < blossomNum(); ++i) {
deba@326:         sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326:       }
deba@326:       return sum;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the value of the node.
deba@326:     ///
deba@326:     /// Returns the the value of the node.
deba@326:     Value nodeValue(const Node& n) const {
deba@326:       return (*_node_potential)[n];
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the number of the blossoms in the basis.
deba@326:     ///
deba@326:     /// Returns the number of the blossoms in the basis.
deba@326:     /// \see BlossomIt
deba@326:     int blossomNum() const {
deba@326:       return _blossom_potential.size();
deba@326:     }
deba@326: 
deba@326: 
deba@326:     /// \brief Returns the number of the nodes in the blossom.
deba@326:     ///
deba@326:     /// Returns the number of the nodes in the blossom.
deba@326:     int blossomSize(int k) const {
deba@326:       return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the value of the blossom.
deba@326:     ///
deba@326:     /// Returns the the value of the blossom.
deba@326:     /// \see BlossomIt
deba@326:     Value blossomValue(int k) const {
deba@326:       return _blossom_potential[k].value;
deba@326:     }
deba@326: 
deba@326:     /// \brief Lemon iterator for get the items of the blossom.
deba@326:     ///
deba@326:     /// Lemon iterator for get the nodes of the blossom. This class
deba@326:     /// provides a common style lemon iterator which gives back a
deba@326:     /// subset of the nodes.
deba@326:     class BlossomIt {
deba@326:     public:
deba@326: 
deba@326:       /// \brief Constructor.
deba@326:       ///
deba@326:       /// Constructor for get the nodes of the variable.
deba@326:       BlossomIt(const MaxWeightedMatching& algorithm, int variable)
deba@326:         : _algorithm(&algorithm)
deba@326:       {
deba@326:         _index = _algorithm->_blossom_potential[variable].begin;
deba@326:         _last = _algorithm->_blossom_potential[variable].end;
deba@326:       }
deba@326: 
deba@326:       /// \brief Invalid constructor.
deba@326:       ///
deba@326:       /// Invalid constructor.
deba@326:       BlossomIt(Invalid) : _index(-1) {}
deba@326: 
deba@326:       /// \brief Conversion to node.
deba@326:       ///
deba@326:       /// Conversion to node.
deba@326:       operator Node() const {
deba@326:         return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
deba@326:       }
deba@326: 
deba@326:       /// \brief Increment operator.
deba@326:       ///
deba@326:       /// Increment operator.
deba@326:       BlossomIt& operator++() {
deba@326:         ++_index;
deba@326:         if (_index == _last) {
deba@326:           _index = -1;
deba@326:         }
deba@326:         return *this;
deba@326:       }
deba@326: 
deba@326:       bool operator==(const BlossomIt& it) const {
deba@326:         return _index == it._index;
deba@326:       }
deba@326:       bool operator!=(const BlossomIt& it) const {
deba@326:         return _index != it._index;
deba@326:       }
deba@326: 
deba@326:     private:
deba@326:       const MaxWeightedMatching* _algorithm;
deba@326:       int _last;
deba@326:       int _index;
deba@326:     };
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:   };
deba@326: 
deba@326:   /// \ingroup matching
deba@326:   ///
deba@326:   /// \brief Weighted perfect matching in general graphs
deba@326:   ///
deba@326:   /// This class provides an efficient implementation of Edmond's
deba@326:   /// maximum weighted perfecr matching algorithm. The implementation
deba@326:   /// is based on extensive use of priority queues and provides
deba@326:   /// \f$O(nm\log(n))\f$ time complexity.
deba@326:   ///
deba@326:   /// The maximum weighted matching problem is to find undirected
deba@326:   /// arcs in the digraph with maximum overall weight and no two of
deba@326:   /// them shares their endpoints and covers all nodes. The problem
deba@326:   /// can be formulated with the next linear program:
deba@326:   /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
deba@326:   ///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f]
deba@326:   /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326:   /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@326:   /// where \f$\delta(X)\f$ is the set of arcs incident to a node in
deba@326:   /// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints in
deba@326:   /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
deba@326:   /// the nodes.
deba@326:   ///
deba@326:   /// The algorithm calculates an optimal matching and a proof of the
deba@326:   /// optimality. The solution of the dual problem can be used to check
deba@326:   /// the result of the algorithm. The dual linear problem is the next:
deba@326:   /// \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]
deba@326:   /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@326:   /// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
deba@326:   ///
deba@326:   /// The algorithm can be executed with \c run() or the \c init() and
deba@326:   /// then the \c start() member functions. After it the matching can
deba@326:   /// be asked with \c matching() or mate() functions. The dual
deba@326:   /// solution can be get with \c nodeValue(), \c blossomNum() and \c
deba@326:   /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
deba@326:   /// "BlossomIt" nested class which is able to iterate on the nodes
deba@326:   /// of a blossom. If the value type is integral then the dual
deba@326:   /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
deba@326:   template <typename _Graph,
deba@326:             typename _WeightMap = typename _Graph::template EdgeMap<int> >
deba@326:   class MaxWeightedPerfectMatching {
deba@326:   public:
deba@326: 
deba@326:     typedef _Graph Graph;
deba@326:     typedef _WeightMap WeightMap;
deba@326:     typedef typename WeightMap::Value Value;
deba@326: 
deba@326:     /// \brief Scaling factor for dual solution
deba@326:     ///
deba@326:     /// Scaling factor for dual solution, it is equal to 4 or 1
deba@326:     /// according to the value type.
deba@326:     static const int dualScale =
deba@326:       std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@326:     MatchingMap;
deba@326: 
deba@326:   private:
deba@326: 
deba@326:     TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326:     typedef std::vector<Node> BlossomNodeList;
deba@326: 
deba@326:     struct BlossomVariable {
deba@326:       int begin, end;
deba@326:       Value value;
deba@326: 
deba@326:       BlossomVariable(int _begin, int _end, Value _value)
deba@326:         : begin(_begin), end(_end), value(_value) {}
deba@326: 
deba@326:     };
deba@326: 
deba@326:     typedef std::vector<BlossomVariable> BlossomPotential;
deba@326: 
deba@326:     const Graph& _graph;
deba@326:     const WeightMap& _weight;
deba@326: 
deba@326:     MatchingMap* _matching;
deba@326: 
deba@326:     NodePotential* _node_potential;
deba@326: 
deba@326:     BlossomPotential _blossom_potential;
deba@326:     BlossomNodeList _blossom_node_list;
deba@326: 
deba@326:     int _node_num;
deba@326:     int _blossom_num;
deba@326: 
deba@326:     typedef typename Graph::template NodeMap<int> NodeIntMap;
deba@326:     typedef typename Graph::template ArcMap<int> ArcIntMap;
deba@326:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
deba@326:     typedef RangeMap<int> IntIntMap;
deba@326: 
deba@326:     enum Status {
deba@326:       EVEN = -1, MATCHED = 0, ODD = 1
deba@326:     };
deba@326: 
deba@326:     typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
deba@326:     struct BlossomData {
deba@326:       int tree;
deba@326:       Status status;
deba@326:       Arc pred, next;
deba@326:       Value pot, offset;
deba@326:     };
deba@326: 
deba@326:     NodeIntMap *_blossom_index;
deba@326:     BlossomSet *_blossom_set;
deba@326:     RangeMap<BlossomData>* _blossom_data;
deba@326: 
deba@326:     NodeIntMap *_node_index;
deba@326:     ArcIntMap *_node_heap_index;
deba@326: 
deba@326:     struct NodeData {
deba@326: 
deba@326:       NodeData(ArcIntMap& node_heap_index)
deba@326:         : heap(node_heap_index) {}
deba@326: 
deba@326:       int blossom;
deba@326:       Value pot;
deba@326:       BinHeap<Value, ArcIntMap> heap;
deba@326:       std::map<int, Arc> heap_index;
deba@326: 
deba@326:       int tree;
deba@326:     };
deba@326: 
deba@326:     RangeMap<NodeData>* _node_data;
deba@326: 
deba@326:     typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326: 
deba@326:     IntIntMap *_tree_set_index;
deba@326:     TreeSet *_tree_set;
deba@326: 
deba@326:     IntIntMap *_delta2_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta2;
deba@326: 
deba@326:     EdgeIntMap *_delta3_index;
deba@326:     BinHeap<Value, EdgeIntMap> *_delta3;
deba@326: 
deba@326:     IntIntMap *_delta4_index;
deba@326:     BinHeap<Value, IntIntMap> *_delta4;
deba@326: 
deba@326:     Value _delta_sum;
deba@326: 
deba@326:     void createStructures() {
deba@326:       _node_num = countNodes(_graph);
deba@326:       _blossom_num = _node_num * 3 / 2;
deba@326: 
deba@326:       if (!_matching) {
deba@326:         _matching = new MatchingMap(_graph);
deba@326:       }
deba@326:       if (!_node_potential) {
deba@326:         _node_potential = new NodePotential(_graph);
deba@326:       }
deba@326:       if (!_blossom_set) {
deba@326:         _blossom_index = new NodeIntMap(_graph);
deba@326:         _blossom_set = new BlossomSet(*_blossom_index);
deba@326:         _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326:       }
deba@326: 
deba@326:       if (!_node_index) {
deba@326:         _node_index = new NodeIntMap(_graph);
deba@326:         _node_heap_index = new ArcIntMap(_graph);
deba@326:         _node_data = new RangeMap<NodeData>(_node_num,
deba@326:                                               NodeData(*_node_heap_index));
deba@326:       }
deba@326: 
deba@326:       if (!_tree_set) {
deba@326:         _tree_set_index = new IntIntMap(_blossom_num);
deba@326:         _tree_set = new TreeSet(*_tree_set_index);
deba@326:       }
deba@326:       if (!_delta2) {
deba@326:         _delta2_index = new IntIntMap(_blossom_num);
deba@326:         _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@326:       }
deba@326:       if (!_delta3) {
deba@326:         _delta3_index = new EdgeIntMap(_graph);
deba@326:         _delta3 = new BinHeap<Value, EdgeIntMap>(*_delta3_index);
deba@326:       }
deba@326:       if (!_delta4) {
deba@326:         _delta4_index = new IntIntMap(_blossom_num);
deba@326:         _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void destroyStructures() {
deba@326:       _node_num = countNodes(_graph);
deba@326:       _blossom_num = _node_num * 3 / 2;
deba@326: 
deba@326:       if (_matching) {
deba@326:         delete _matching;
deba@326:       }
deba@326:       if (_node_potential) {
deba@326:         delete _node_potential;
deba@326:       }
deba@326:       if (_blossom_set) {
deba@326:         delete _blossom_index;
deba@326:         delete _blossom_set;
deba@326:         delete _blossom_data;
deba@326:       }
deba@326: 
deba@326:       if (_node_index) {
deba@326:         delete _node_index;
deba@326:         delete _node_heap_index;
deba@326:         delete _node_data;
deba@326:       }
deba@326: 
deba@326:       if (_tree_set) {
deba@326:         delete _tree_set_index;
deba@326:         delete _tree_set;
deba@326:       }
deba@326:       if (_delta2) {
deba@326:         delete _delta2_index;
deba@326:         delete _delta2;
deba@326:       }
deba@326:       if (_delta3) {
deba@326:         delete _delta3_index;
deba@326:         delete _delta3;
deba@326:       }
deba@326:       if (_delta4) {
deba@326:         delete _delta4_index;
deba@326:         delete _delta4;
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void matchedToEven(int blossom, int tree) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326: 
deba@326:         (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else {
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset){
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326:     void matchedToOdd(int blossom) {
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset += _delta_sum;
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326:                      (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void evenToMatched(int blossom, int tree) {
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326:         (*_node_data)[ni].pot -= _delta_sum;
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if (vb == blossom) {
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326:           } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326: 
deba@326:             if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326:               _delta3->erase(e);
deba@326:             }
deba@326: 
deba@326:             int vt = _tree_set->find(vb);
deba@326: 
deba@326:             if (vt != tree) {
deba@326: 
deba@326:               Arc r = _graph.oppositeArc(e);
deba@326: 
deba@326:               typename std::map<int, Arc>::iterator it =
deba@326:                 (*_node_data)[ni].heap_index.find(vt);
deba@326: 
deba@326:               if (it != (*_node_data)[ni].heap_index.end()) {
deba@326:                 if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326:                   (*_node_data)[ni].heap.replace(it->second, r);
deba@326:                   (*_node_data)[ni].heap.decrease(r, rw);
deba@326:                   it->second = r;
deba@326:                 }
deba@326:               } else {
deba@326:                 (*_node_data)[ni].heap.push(r, rw);
deba@326:                 (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326:               }
deba@326: 
deba@326:               if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326:                 _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326: 
deba@326:                 if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                (*_blossom_data)[blossom].offset);
deba@326:                 } else if ((*_delta2)[blossom] >
deba@326:                            _blossom_set->classPrio(blossom) -
deba@326:                            (*_blossom_data)[blossom].offset){
deba@326:                   _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326:                                    (*_blossom_data)[blossom].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               (*_node_data)[vi].heap.erase(it->second);
deba@326:               (*_node_data)[vi].heap_index.erase(it);
deba@326:               if ((*_node_data)[vi].heap.empty()) {
deba@326:                 _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326:               } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326:                 _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326:               }
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_blossom_set->classPrio(vb) ==
deba@326:                     std::numeric_limits<Value>::max()) {
deba@326:                   _delta2->erase(vb);
deba@326:                 } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void oddToMatched(int blossom) {
deba@326:       (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326: 
deba@326:       if (_blossom_set->classPrio(blossom) !=
deba@326:           std::numeric_limits<Value>::max()) {
deba@326:         _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326:                        (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->erase(blossom);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void oddToEven(int blossom, int tree) {
deba@326:       if (!_blossom_set->trivial(blossom)) {
deba@326:         _delta4->erase(blossom);
deba@326:         (*_blossom_data)[blossom].pot -=
deba@326:           2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326:       }
deba@326: 
deba@326:       for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326:            n != INVALID; ++n) {
deba@326:         int ni = (*_node_index)[n];
deba@326: 
deba@326:         _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         (*_node_data)[ni].heap.clear();
deba@326:         (*_node_data)[ni].heap_index.clear();
deba@326:         (*_node_data)[ni].pot +=
deba@326:           2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326: 
deba@326:         for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           Node v = _graph.source(e);
deba@326:           int vb = _blossom_set->find(v);
deba@326:           int vi = (*_node_index)[v];
deba@326: 
deba@326:           Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326:             dualScale * _weight[e];
deba@326: 
deba@326:           if ((*_blossom_data)[vb].status == EVEN) {
deba@326:             if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326:               _delta3->push(e, rw / 2);
deba@326:             }
deba@326:           } else {
deba@326: 
deba@326:             typename std::map<int, Arc>::iterator it =
deba@326:               (*_node_data)[vi].heap_index.find(tree);
deba@326: 
deba@326:             if (it != (*_node_data)[vi].heap_index.end()) {
deba@326:               if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326:                 (*_node_data)[vi].heap.replace(it->second, e);
deba@326:                 (*_node_data)[vi].heap.decrease(e, rw);
deba@326:                 it->second = e;
deba@326:               }
deba@326:             } else {
deba@326:               (*_node_data)[vi].heap.push(e, rw);
deba@326:               (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326:             }
deba@326: 
deba@326:             if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326:               _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326: 
deba@326:               if ((*_blossom_data)[vb].status == MATCHED) {
deba@326:                 if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326:                   _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326:                                (*_blossom_data)[vb].offset);
deba@326:                 } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326:                            (*_blossom_data)[vb].offset) {
deba@326:                   _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326:                                    (*_blossom_data)[vb].offset);
deba@326:                 }
deba@326:               }
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326:       (*_blossom_data)[blossom].offset = 0;
deba@326:     }
deba@326: 
deba@326:     void alternatePath(int even, int tree) {
deba@326:       int odd;
deba@326: 
deba@326:       evenToMatched(even, tree);
deba@326:       (*_blossom_data)[even].status = MATCHED;
deba@326: 
deba@326:       while ((*_blossom_data)[even].pred != INVALID) {
deba@326:         odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326:         (*_blossom_data)[odd].status = MATCHED;
deba@326:         oddToMatched(odd);
deba@326:         (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326: 
deba@326:         even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326:         (*_blossom_data)[even].status = MATCHED;
deba@326:         evenToMatched(even, tree);
deba@326:         (*_blossom_data)[even].next =
deba@326:           _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326:       }
deba@326: 
deba@326:     }
deba@326: 
deba@326:     void destroyTree(int tree) {
deba@326:       for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326:         if ((*_blossom_data)[b].status == EVEN) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           evenToMatched(b, tree);
deba@326:         } else if ((*_blossom_data)[b].status == ODD) {
deba@326:           (*_blossom_data)[b].status = MATCHED;
deba@326:           oddToMatched(b);
deba@326:         }
deba@326:       }
deba@326:       _tree_set->eraseClass(tree);
deba@326:     }
deba@326: 
deba@326:     void augmentOnArc(const Edge& arc) {
deba@326: 
deba@326:       int left = _blossom_set->find(_graph.u(arc));
deba@326:       int right = _blossom_set->find(_graph.v(arc));
deba@326: 
deba@326:       int left_tree = _tree_set->find(left);
deba@326:       alternatePath(left, left_tree);
deba@326:       destroyTree(left_tree);
deba@326: 
deba@326:       int right_tree = _tree_set->find(right);
deba@326:       alternatePath(right, right_tree);
deba@326:       destroyTree(right_tree);
deba@326: 
deba@326:       (*_blossom_data)[left].next = _graph.direct(arc, true);
deba@326:       (*_blossom_data)[right].next = _graph.direct(arc, false);
deba@326:     }
deba@326: 
deba@326:     void extendOnArc(const Arc& arc) {
deba@326:       int base = _blossom_set->find(_graph.target(arc));
deba@326:       int tree = _tree_set->find(base);
deba@326: 
deba@326:       int odd = _blossom_set->find(_graph.source(arc));
deba@326:       _tree_set->insert(odd, tree);
deba@326:       (*_blossom_data)[odd].status = ODD;
deba@326:       matchedToOdd(odd);
deba@326:       (*_blossom_data)[odd].pred = arc;
deba@326: 
deba@326:       int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326:       (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326:       _tree_set->insert(even, tree);
deba@326:       (*_blossom_data)[even].status = EVEN;
deba@326:       matchedToEven(even, tree);
deba@326:     }
deba@326: 
deba@326:     void shrinkOnArc(const Edge& edge, int tree) {
deba@326:       int nca = -1;
deba@326:       std::vector<int> left_path, right_path;
deba@326: 
deba@326:       {
deba@326:         std::set<int> left_set, right_set;
deba@326:         int left = _blossom_set->find(_graph.u(edge));
deba@326:         left_path.push_back(left);
deba@326:         left_set.insert(left);
deba@326: 
deba@326:         int right = _blossom_set->find(_graph.v(edge));
deba@326:         right_path.push_back(right);
deba@326:         right_set.insert(right);
deba@326: 
deba@326:         while (true) {
deba@326: 
deba@326:           if ((*_blossom_data)[left].pred == INVALID) break;
deba@326: 
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326:           left =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326:           left_path.push_back(left);
deba@326: 
deba@326:           left_set.insert(left);
deba@326: 
deba@326:           if (right_set.find(left) != right_set.end()) {
deba@326:             nca = left;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:           if ((*_blossom_data)[right].pred == INVALID) break;
deba@326: 
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326:           right =
deba@326:             _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326:           right_path.push_back(right);
deba@326: 
deba@326:           right_set.insert(right);
deba@326: 
deba@326:           if (left_set.find(right) != left_set.end()) {
deba@326:             nca = right;
deba@326:             break;
deba@326:           }
deba@326: 
deba@326:         }
deba@326: 
deba@326:         if (nca == -1) {
deba@326:           if ((*_blossom_data)[left].pred == INVALID) {
deba@326:             nca = right;
deba@326:             while (left_set.find(nca) == left_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               right_path.push_back(nca);
deba@326:             }
deba@326:           } else {
deba@326:             nca = left;
deba@326:             while (right_set.find(nca) == right_set.end()) {
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:               nca =
deba@326:                 _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326:               left_path.push_back(nca);
deba@326:             }
deba@326:           }
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       Arc prev;
deba@326: 
deba@326:       prev = _graph.direct(edge, true);
deba@326:       for (int i = 0; left_path[i] != nca; i += 2) {
deba@326:         subblossoms.push_back(left_path[i]);
deba@326:         (*_blossom_data)[left_path[i]].next = prev;
deba@326:         _tree_set->erase(left_path[i]);
deba@326: 
deba@326:         subblossoms.push_back(left_path[i + 1]);
deba@326:         (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326:         oddToEven(left_path[i + 1], tree);
deba@326:         _tree_set->erase(left_path[i + 1]);
deba@326:         prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326:       }
deba@326: 
deba@326:       int k = 0;
deba@326:       while (right_path[k] != nca) ++k;
deba@326: 
deba@326:       subblossoms.push_back(nca);
deba@326:       (*_blossom_data)[nca].next = prev;
deba@326: 
deba@326:       for (int i = k - 2; i >= 0; i -= 2) {
deba@326:         subblossoms.push_back(right_path[i + 1]);
deba@326:         (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326:         oddToEven(right_path[i + 1], tree);
deba@326:         _tree_set->erase(right_path[i + 1]);
deba@326: 
deba@326:         (*_blossom_data)[right_path[i + 1]].next =
deba@326:           (*_blossom_data)[right_path[i + 1]].pred;
deba@326: 
deba@326:         subblossoms.push_back(right_path[i]);
deba@326:         _tree_set->erase(right_path[i]);
deba@326:       }
deba@326: 
deba@326:       int surface =
deba@326:         _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326: 
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326:         }
deba@326:         (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326:       }
deba@326: 
deba@326:       (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326:       (*_blossom_data)[surface].offset = 0;
deba@326:       (*_blossom_data)[surface].status = EVEN;
deba@326:       (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326:       (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326: 
deba@326:       _tree_set->insert(surface, tree);
deba@326:       _tree_set->erase(nca);
deba@326:     }
deba@326: 
deba@326:     void splitBlossom(int blossom) {
deba@326:       Arc next = (*_blossom_data)[blossom].next;
deba@326:       Arc pred = (*_blossom_data)[blossom].pred;
deba@326: 
deba@326:       int tree = _tree_set->find(blossom);
deba@326: 
deba@326:       (*_blossom_data)[blossom].status = MATCHED;
deba@326:       oddToMatched(blossom);
deba@326:       if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326:         _delta2->erase(blossom);
deba@326:       }
deba@326: 
deba@326:       std::vector<int> subblossoms;
deba@326:       _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326: 
deba@326:       Value offset = (*_blossom_data)[blossom].offset;
deba@326:       int b = _blossom_set->find(_graph.source(pred));
deba@326:       int d = _blossom_set->find(_graph.source(next));
deba@326: 
deba@326:       int ib = -1, id = -1;
deba@326:       for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:         if (subblossoms[i] == b) ib = i;
deba@326:         if (subblossoms[i] == d) id = i;
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326:         if (!_blossom_set->trivial(subblossoms[i])) {
deba@326:           (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326:         }
deba@326:         if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326:             std::numeric_limits<Value>::max()) {
deba@326:           _delta2->push(subblossoms[i],
deba@326:                         _blossom_set->classPrio(subblossoms[i]) -
deba@326:                         (*_blossom_data)[subblossoms[i]].offset);
deba@326:         }
deba@326:       }
deba@326: 
deba@326:       if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326:         for (int i = (id + 1) % subblossoms.size();
deba@326:              i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].pred = pred;
deba@326:           (*_blossom_data)[sb].next =
deba@326:                            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           pred = (*_blossom_data)[ub].next;
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326:         matchedToOdd(subblossoms[id]);
deba@326:         _tree_set->insert(subblossoms[id], tree);
deba@326:         (*_blossom_data)[subblossoms[id]].next = next;
deba@326:         (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326: 
deba@326:       } else {
deba@326: 
deba@326:         for (int i = (ib + 1) % subblossoms.size();
deba@326:              i != id; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           (*_blossom_data)[sb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326:         }
deba@326: 
deba@326:         for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326:           int sb = subblossoms[i];
deba@326:           int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326:           int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326: 
deba@326:           (*_blossom_data)[sb].status = ODD;
deba@326:           matchedToOdd(sb);
deba@326:           _tree_set->insert(sb, tree);
deba@326:           (*_blossom_data)[sb].next = next;
deba@326:           (*_blossom_data)[sb].pred =
deba@326:             _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326: 
deba@326:           (*_blossom_data)[tb].status = EVEN;
deba@326:           matchedToEven(tb, tree);
deba@326:           _tree_set->insert(tb, tree);
deba@326:           (*_blossom_data)[tb].pred =
deba@326:             (*_blossom_data)[tb].next =
deba@326:             _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326:           next = (*_blossom_data)[ub].next;
deba@326:         }
deba@326: 
deba@326:         (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326:         matchedToOdd(subblossoms[ib]);
deba@326:         _tree_set->insert(subblossoms[ib], tree);
deba@326:         (*_blossom_data)[subblossoms[ib]].next = next;
deba@326:         (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326:       }
deba@326:       _tree_set->erase(blossom);
deba@326:     }
deba@326: 
deba@326:     void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326:       if (_blossom_set->trivial(blossom)) {
deba@326:         int bi = (*_node_index)[base];
deba@326:         Value pot = (*_node_data)[bi].pot;
deba@326: 
deba@326:         _matching->set(base, matching);
deba@326:         _blossom_node_list.push_back(base);
deba@326:         _node_potential->set(base, pot);
deba@326:       } else {
deba@326: 
deba@326:         Value pot = (*_blossom_data)[blossom].pot;
deba@326:         int bn = _blossom_node_list.size();
deba@326: 
deba@326:         std::vector<int> subblossoms;
deba@326:         _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326:         int b = _blossom_set->find(base);
deba@326:         int ib = -1;
deba@326:         for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326:           if (subblossoms[i] == b) { ib = i; break; }
deba@326:         }
deba@326: 
deba@326:         for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326:           int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326:           int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326: 
deba@326:           Arc m = (*_blossom_data)[tb].next;
deba@326:           extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326:           extractBlossom(tb, _graph.source(m), m);
deba@326:         }
deba@326:         extractBlossom(subblossoms[ib], base, matching);
deba@326: 
deba@326:         int en = _blossom_node_list.size();
deba@326: 
deba@326:         _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     void extractMatching() {
deba@326:       std::vector<int> blossoms;
deba@326:       for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326:         blossoms.push_back(c);
deba@326:       }
deba@326: 
deba@326:       for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326: 
deba@326:         Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326:         (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326:         for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326:              n != INVALID; ++n) {
deba@326:           (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326:         }
deba@326: 
deba@326:         Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326:         Node base = _graph.source(matching);
deba@326:         extractBlossom(blossoms[i], base, matching);
deba@326:       }
deba@326:     }
deba@326: 
deba@326:   public:
deba@326: 
deba@326:     /// \brief Constructor
deba@326:     ///
deba@326:     /// Constructor.
deba@326:     MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
deba@326:       : _graph(graph), _weight(weight), _matching(0),
deba@326:         _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326:         _node_num(0), _blossom_num(0),
deba@326: 
deba@326:         _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326:         _node_index(0), _node_heap_index(0), _node_data(0),
deba@326:         _tree_set_index(0), _tree_set(0),
deba@326: 
deba@326:         _delta2_index(0), _delta2(0),
deba@326:         _delta3_index(0), _delta3(0),
deba@326:         _delta4_index(0), _delta4(0),
deba@326: 
deba@326:         _delta_sum() {}
deba@326: 
deba@326:     ~MaxWeightedPerfectMatching() {
deba@326:       destroyStructures();
deba@326:     }
deba@326: 
deba@326:     /// \name Execution control
deba@326:     /// The simplest way to execute the algorithm is to use the member
deba@326:     /// \c run() member function.
deba@326: 
deba@326:     ///@{
deba@326: 
deba@326:     /// \brief Initialize the algorithm
deba@326:     ///
deba@326:     /// Initialize the algorithm
deba@326:     void init() {
deba@326:       createStructures();
deba@326: 
deba@326:       for (ArcIt e(_graph); e != INVALID; ++e) {
deba@326:         _node_heap_index->set(e, BinHeap<Value, ArcIntMap>::PRE_HEAP);
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326:         _delta3_index->set(e, _delta3->PRE_HEAP);
deba@326:       }
deba@326:       for (int i = 0; i < _blossom_num; ++i) {
deba@326:         _delta2_index->set(i, _delta2->PRE_HEAP);
deba@326:         _delta4_index->set(i, _delta4->PRE_HEAP);
deba@326:       }
deba@326: 
deba@326:       int index = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         Value max = - std::numeric_limits<Value>::max();
deba@326:         for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326:           if (_graph.target(e) == n) continue;
deba@326:           if ((dualScale * _weight[e]) / 2 > max) {
deba@326:             max = (dualScale * _weight[e]) / 2;
deba@326:           }
deba@326:         }
deba@326:         _node_index->set(n, index);
deba@326:         (*_node_data)[index].pot = max;
deba@326:         int blossom =
deba@326:           _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326: 
deba@326:         _tree_set->insert(blossom);
deba@326: 
deba@326:         (*_blossom_data)[blossom].status = EVEN;
deba@326:         (*_blossom_data)[blossom].pred = INVALID;
deba@326:         (*_blossom_data)[blossom].next = INVALID;
deba@326:         (*_blossom_data)[blossom].pot = 0;
deba@326:         (*_blossom_data)[blossom].offset = 0;
deba@326:         ++index;
deba@326:       }
deba@326:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326:         int si = (*_node_index)[_graph.u(e)];
deba@326:         int ti = (*_node_index)[_graph.v(e)];
deba@326:         if (_graph.u(e) != _graph.v(e)) {
deba@326:           _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326:                             dualScale * _weight[e]) / 2);
deba@326:         }
deba@326:       }
deba@326:     }
deba@326: 
deba@326:     /// \brief Starts the algorithm
deba@326:     ///
deba@326:     /// Starts the algorithm
deba@326:     bool start() {
deba@326:       enum OpType {
deba@326:         D2, D3, D4
deba@326:       };
deba@326: 
deba@326:       int unmatched = _node_num;
deba@326:       while (unmatched > 0) {
deba@326:         Value d2 = !_delta2->empty() ?
deba@326:           _delta2->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d3 = !_delta3->empty() ?
deba@326:           _delta3->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         Value d4 = !_delta4->empty() ?
deba@326:           _delta4->prio() : std::numeric_limits<Value>::max();
deba@326: 
deba@326:         _delta_sum = d2; OpType ot = D2;
deba@326:         if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@326:         if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326: 
deba@326:         if (_delta_sum == std::numeric_limits<Value>::max()) {
deba@326:           return false;
deba@326:         }
deba@326: 
deba@326:         switch (ot) {
deba@326:         case D2:
deba@326:           {
deba@326:             int blossom = _delta2->top();
deba@326:             Node n = _blossom_set->classTop(blossom);
deba@326:             Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326:             extendOnArc(e);
deba@326:           }
deba@326:           break;
deba@326:         case D3:
deba@326:           {
deba@326:             Edge e = _delta3->top();
deba@326: 
deba@326:             int left_blossom = _blossom_set->find(_graph.u(e));
deba@326:             int right_blossom = _blossom_set->find(_graph.v(e));
deba@326: 
deba@326:             if (left_blossom == right_blossom) {
deba@326:               _delta3->pop();
deba@326:             } else {
deba@326:               int left_tree = _tree_set->find(left_blossom);
deba@326:               int right_tree = _tree_set->find(right_blossom);
deba@326: 
deba@326:               if (left_tree == right_tree) {
deba@326:                 shrinkOnArc(e, left_tree);
deba@326:               } else {
deba@326:                 augmentOnArc(e);
deba@326:                 unmatched -= 2;
deba@326:               }
deba@326:             }
deba@326:           } break;
deba@326:         case D4:
deba@326:           splitBlossom(_delta4->top());
deba@326:           break;
deba@326:         }
deba@326:       }
deba@326:       extractMatching();
deba@326:       return true;
deba@326:     }
deba@326: 
deba@326:     /// \brief Runs %MaxWeightedPerfectMatching algorithm.
deba@326:     ///
deba@326:     /// This method runs the %MaxWeightedPerfectMatching algorithm.
deba@326:     ///
deba@326:     /// \note mwm.run() is just a shortcut of the following code.
deba@326:     /// \code
deba@326:     ///   mwm.init();
deba@326:     ///   mwm.start();
deba@326:     /// \endcode
deba@326:     bool run() {
deba@326:       init();
deba@326:       return start();
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:     /// \name Primal solution
deba@326:     /// Functions for get the primal solution, ie. the matching.
deba@326: 
deba@326:     /// @{
deba@326: 
deba@326:     /// \brief Returns the matching value.
deba@326:     ///
deba@326:     /// Returns the matching value.
deba@326:     Value matchingValue() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         if ((*_matching)[n] != INVALID) {
deba@326:           sum += _weight[(*_matching)[n]];
deba@326:         }
deba@326:       }
deba@326:       return sum /= 2;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns true when the arc is in the matching.
deba@326:     ///
deba@326:     /// Returns true when the arc is in the matching.
deba@326:     bool matching(const Edge& arc) const {
deba@326:       return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the incident matching arc.
deba@326:     ///
deba@326:     /// Returns the incident matching arc from given node.
deba@326:     Arc matching(const Node& node) const {
deba@326:       return (*_matching)[node];
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the mate of the node.
deba@326:     ///
deba@326:     /// Returns the adjancent node in a mathcing arc.
deba@326:     Node mate(const Node& node) const {
deba@326:       return _graph.target((*_matching)[node]);
deba@326:     }
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:     /// \name Dual solution
deba@326:     /// Functions for get the dual solution.
deba@326: 
deba@326:     /// @{
deba@326: 
deba@326:     /// \brief Returns the value of the dual solution.
deba@326:     ///
deba@326:     /// Returns the value of the dual solution. It should be equal to
deba@326:     /// the primal value scaled by \ref dualScale "dual scale".
deba@326:     Value dualValue() const {
deba@326:       Value sum = 0;
deba@326:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326:         sum += nodeValue(n);
deba@326:       }
deba@326:       for (int i = 0; i < blossomNum(); ++i) {
deba@326:         sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326:       }
deba@326:       return sum;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the value of the node.
deba@326:     ///
deba@326:     /// Returns the the value of the node.
deba@326:     Value nodeValue(const Node& n) const {
deba@326:       return (*_node_potential)[n];
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the number of the blossoms in the basis.
deba@326:     ///
deba@326:     /// Returns the number of the blossoms in the basis.
deba@326:     /// \see BlossomIt
deba@326:     int blossomNum() const {
deba@326:       return _blossom_potential.size();
deba@326:     }
deba@326: 
deba@326: 
deba@326:     /// \brief Returns the number of the nodes in the blossom.
deba@326:     ///
deba@326:     /// Returns the number of the nodes in the blossom.
deba@326:     int blossomSize(int k) const {
deba@326:       return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326:     }
deba@326: 
deba@326:     /// \brief Returns the value of the blossom.
deba@326:     ///
deba@326:     /// Returns the the value of the blossom.
deba@326:     /// \see BlossomIt
deba@326:     Value blossomValue(int k) const {
deba@326:       return _blossom_potential[k].value;
deba@326:     }
deba@326: 
deba@326:     /// \brief Lemon iterator for get the items of the blossom.
deba@326:     ///
deba@326:     /// Lemon iterator for get the nodes of the blossom. This class
deba@326:     /// provides a common style lemon iterator which gives back a
deba@326:     /// subset of the nodes.
deba@326:     class BlossomIt {
deba@326:     public:
deba@326: 
deba@326:       /// \brief Constructor.
deba@326:       ///
deba@326:       /// Constructor for get the nodes of the variable.
deba@326:       BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
deba@326:         : _algorithm(&algorithm)
deba@326:       {
deba@326:         _index = _algorithm->_blossom_potential[variable].begin;
deba@326:         _last = _algorithm->_blossom_potential[variable].end;
deba@326:       }
deba@326: 
deba@326:       /// \brief Invalid constructor.
deba@326:       ///
deba@326:       /// Invalid constructor.
deba@326:       BlossomIt(Invalid) : _index(-1) {}
deba@326: 
deba@326:       /// \brief Conversion to node.
deba@326:       ///
deba@326:       /// Conversion to node.
deba@326:       operator Node() const {
deba@326:         return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
deba@326:       }
deba@326: 
deba@326:       /// \brief Increment operator.
deba@326:       ///
deba@326:       /// Increment operator.
deba@326:       BlossomIt& operator++() {
deba@326:         ++_index;
deba@326:         if (_index == _last) {
deba@326:           _index = -1;
deba@326:         }
deba@326:         return *this;
deba@326:       }
deba@326: 
deba@326:       bool operator==(const BlossomIt& it) const {
deba@326:         return _index == it._index;
deba@326:       }
deba@326:       bool operator!=(const BlossomIt& it) const {
deba@326:         return _index != it._index;
deba@326:       }
deba@326: 
deba@326:     private:
deba@326:       const MaxWeightedPerfectMatching* _algorithm;
deba@326:       int _last;
deba@326:       int _index;
deba@326:     };
deba@326: 
deba@326:     /// @}
deba@326: 
deba@326:   };
deba@326: 
deba@326: 
deba@326: } //END OF NAMESPACE LEMON
deba@326: 
deba@326: #endif //LEMON_MAX_MATCHING_H