lemon-main: comparison lemon/max

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+:376252efbe62
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+*
+* This file is a part of LEMON, a generic C++ optimization library.
+*
+* Copyright (C) 2003-2008
+* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+* (Egervary Research Group on Combinatorial Optimization, EGRES).
+*
+* Permission to use, modify and distribute this software is granted
+* provided that this copyright notice appears in all copies. For
+* precise terms see the accompanying LICENSE file.
+*
+* This software is provided "AS IS" with no warranty of any kind,
+* express or implied, and with no claim as to its suitability for any
+* purpose.
+*
+*/
+#ifndef LEMON_MAX_MATCHING_H
+#define LEMON_MAX_MATCHING_H
+#include <vector>
+#include <queue>
+#include <set>
+#include <limits>
+#include <lemon/core.h>
+#include <lemon/unionfind.h>
+#include <lemon/bin_heap.h>
+#include <lemon/maps.h>
+///\ingroup matching
+///\file
+///\brief Maximum matching algorithms in graph.
+namespace lemon {
+///\ingroup matching
+///
+///\brief Edmonds' alternating forest maximum matching algorithm.
+///
+///This class provides Edmonds' alternating forest matching
+///algorithm. The starting matching (if any) can be passed to the
+///algorithm using some of init functions.
+///
+///The dual side of a matching is a map of the nodes to
+///MaxMatching::DecompType, having values \c D, \c A and \c C
+///showing the Gallai-Edmonds decomposition of the digraph. The nodes
+///in \c D induce a digraph with factor-critical components, the nodes
+///in \c A form the barrier, and the nodes in \c C induce a digraph
+///having a perfect matching. This decomposition can be attained by
+///calling \c decomposition() after running the algorithm.
+///
+///\param Digraph The graph type the algorithm runs on.
+template <typename Graph>
+class MaxMatching {
+protected:
+TEMPLATE_GRAPH_TYPEDEFS(Graph);
+typedef typename Graph::template NodeMap<int> UFECrossRef;
+typedef UnionFindEnum<UFECrossRef> UFE;
+typedef std::vector<Node> NV;
+typedef typename Graph::template NodeMap<int> EFECrossRef;
+typedef ExtendFindEnum<EFECrossRef> EFE;
+public:
+///\brief Indicates the Gallai-Edmonds decomposition of the digraph.
+///
+///Indicates the Gallai-Edmonds decomposition of the digraph, which
+///shows an upper bound on the size of a maximum matching. The
+///nodes with DecompType \c D induce a digraph with factor-critical
+///components, the nodes in \c A form the canonical barrier, and the
+///nodes in \c C induce a digraph having a perfect matching.
+enum DecompType {
+D=0,
+A=1,
+C=2
+};
+protected:
+static const int HEUR_density=2;
+const Graph& g;
+typename Graph::template NodeMap<Node> _mate;
+typename Graph::template NodeMap<DecompType> position;
+public:
+MaxMatching(const Graph& _g)
+: g(_g), _mate(_g), position(_g) {}
+///\brief Sets the actual matching to the empty matching.
+///
+///Sets the actual matching to the empty matching.
+///
+void init() {
+for(NodeIt v(g); v!=INVALID; ++v) {
+_mate.set(v,INVALID);
+position.set(v,C);
+}
+}
+///\brief Finds a greedy matching for initial matching.
+///
+///For initial matchig it finds a maximal greedy matching.
+void greedyInit() {
+for(NodeIt v(g); v!=INVALID; ++v) {
+_mate.set(v,INVALID);
+position.set(v,C);
+}
+for(NodeIt v(g); v!=INVALID; ++v)
+if ( _mate[v]==INVALID ) {
+for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
+Node y=g.runningNode(e);
+if ( _mate[y]==INVALID && y!=v ) {
+_mate.set(v,y);
+_mate.set(y,v);
+break;
+}
+}
+}
+}
+///\brief Initialize the matching from each nodes' mate.
+///
+///Initialize the matching from a \c Node valued \c Node map. This
+///map must be \e symmetric, i.e. if \c map[u]==v then \c
+///map[v]==u must hold, and \c uv will be an arc of the initial
+///matching.
+template <typename MateMap>
+void mateMapInit(MateMap& map) {
+for(NodeIt v(g); v!=INVALID; ++v) {
+_mate.set(v,map[v]);
+position.set(v,C);
+}
+}
+///\brief Initialize the matching from a node map with the
+///incident matching arcs.
+///
+///Initialize the matching from an \c Edge valued \c Node map. \c
+///map[v] must be an \c Edge incident to \c v. This map must have
+///the property that if \c g.oppositeNode(u,map[u])==v then \c \c
+///g.oppositeNode(v,map[v])==u holds, and now some arc joining \c
+///u to \c v will be an arc of the matching.
+template<typename MatchingMap>
+void matchingMapInit(MatchingMap& map) {
+for(NodeIt v(g); v!=INVALID; ++v) {
+position.set(v,C);
+Edge e=map[v];
+if ( e!=INVALID )
+_mate.set(v,g.oppositeNode(v,e));
+else
+_mate.set(v,INVALID);
+}
+}
+///\brief Initialize the matching from the map containing the
+///undirected matching arcs.
+///
+///Initialize the matching from a \c bool valued \c Edge map. This
+///map must have the property that there are no two incident arcs
+///\c e, \c f with \c map[e]==map[f]==true. The arcs \c e with \c
+///map[e]==true form the matching.
+template <typename MatchingMap>
+void matchingInit(MatchingMap& map) {
+for(NodeIt v(g); v!=INVALID; ++v) {
+_mate.set(v,INVALID);
+position.set(v,C);
+}
+for(EdgeIt e(g); e!=INVALID; ++e) {
+if ( map[e] ) {
+Node u=g.u(e);
+Node v=g.v(e);
+_mate.set(u,v);
+_mate.set(v,u);
+}
+}
+}
+///\brief Runs Edmonds' algorithm.
+///
+///Runs Edmonds' algorithm for sparse digraphs (number of arcs <
+///2*number of nodes), and a heuristical Edmonds' algorithm with a
+///heuristic of postponing shrinks for dense digraphs.
+void run() {
+if (countEdges(g) < HEUR_density * countNodes(g)) {
+greedyInit();
+startSparse();
+} else {
+init();
+startDense();
+}
+}
+///\brief Starts Edmonds' algorithm.
+///
+///If runs the original Edmonds' algorithm.
+void startSparse() {
+typename Graph::template NodeMap<Node> ear(g,INVALID);
+//undefined for the base nodes of the blossoms (i.e. for the
+//representative elements of UFE blossom) and for the nodes in C
+UFECrossRef blossom_base(g);
+UFE blossom(blossom_base);
+NV rep(countNodes(g));
+EFECrossRef tree_base(g);
+EFE tree(tree_base);
+//If these UFE's would be members of the class then also
+//blossom_base and tree_base should be a member.
+//We build only one tree and the other vertices uncovered by the
+//matching belong to C. (They can be considered as singleton
+//trees.) If this tree can be augmented or no more
+//grow/augmentation/shrink is possible then we return to this
+//"for" cycle.
+for(NodeIt v(g); v!=INVALID; ++v) {
+if (position[v]==C && _mate[v]==INVALID) {
+rep[blossom.insert(v)] = v;
+tree.insert(v);
+position.set(v,D);
+normShrink(v, ear, blossom, rep, tree);
+}
+}
+}
+///\brief Starts Edmonds' algorithm.
+///
+///It runs Edmonds' algorithm with a heuristic of postponing
+///shrinks, giving a faster algorithm for dense digraphs.
+void startDense() {
+typename Graph::template NodeMap<Node> ear(g,INVALID);
+//undefined for the base nodes of the blossoms (i.e. for the
+//representative elements of UFE blossom) and for the nodes in C
+UFECrossRef blossom_base(g);
+UFE blossom(blossom_base);
+NV rep(countNodes(g));
+EFECrossRef tree_base(g);
+EFE tree(tree_base);
+//If these UFE's would be members of the class then also
+//blossom_base and tree_base should be a member.
+//We build only one tree and the other vertices uncovered by the
+//matching belong to C. (They can be considered as singleton
+//trees.) If this tree can be augmented or no more
+//grow/augmentation/shrink is possible then we return to this
+//"for" cycle.
+for(NodeIt v(g); v!=INVALID; ++v) {
+if ( position[v]==C && _mate[v]==INVALID ) {
+rep[blossom.insert(v)] = v;
+tree.insert(v);
+position.set(v,D);
+lateShrink(v, ear, blossom, rep, tree);
+}
+}
+}
+///\brief Returns the size of the actual matching stored.
+///
+///Returns the size of the actual matching stored. After \ref
+///run() it returns the size of a maximum matching in the digraph.
+int size() const {
+int s=0;
+for(NodeIt v(g); v!=INVALID; ++v) {
+if ( _mate[v]!=INVALID ) {
+++s;
+}
+}
+return s/2;
+}
+///\brief Returns the mate of a node in the actual matching.
+///
+///Returns the mate of a \c node in the actual matching.
+///Returns INVALID if the \c node is not covered by the actual matching.
+Node mate(const Node& node) const {
+return _mate[node];
+}
+///\brief Returns the matching arc incident to the given node.
+///
+///Returns the matching arc of a \c node in the actual matching.
+///Returns INVALID if the \c node is not covered by the actual matching.
+Edge matchingArc(const Node& node) const {
+if (_mate[node] == INVALID) return INVALID;
+Node n = node < _mate[node] ? node : _mate[node];
+for (IncEdgeIt e(g, n); e != INVALID; ++e) {
+if (g.oppositeNode(n, e) == _mate[n]) {
+return e;
+}
+}
+return INVALID;
+}
+/// \brief Returns the class of the node in the Edmonds-Gallai
+/// decomposition.
+///
+/// Returns the class of the node in the Edmonds-Gallai
+/// decomposition.
+DecompType decomposition(const Node& n) {
+return position[n] == A;
+}
+/// \brief Returns true when the node is in the barrier.
+///
+/// Returns true when the node is in the barrier.
+bool barrier(const Node& n) {
+return position[n] == A;
+}
+///\brief Gives back the matching in a \c Node of mates.
+///
+///Writes the stored matching to a \c Node valued \c Node map. The
+///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
+///map[v]==u will hold, and now \c uv is an arc of the matching.
+template <typename MateMap>
+void mateMap(MateMap& map) const {
+for(NodeIt v(g); v!=INVALID; ++v) {
+map.set(v,_mate[v]);
+}
+}
+///\brief Gives back the matching in an \c Edge valued \c Node
+///map.
+///
+///Writes the stored matching to an \c Edge valued \c Node
+///map. \c map[v] will be an \c Edge incident to \c v. This
+///map will have the property that if \c g.oppositeNode(u,map[u])
+///== v then \c map[u]==map[v] holds, and now this arc is an arc
+///of the matching.
+template <typename MatchingMap>
+void matchingMap(MatchingMap& map)  const {
+typename Graph::template NodeMap<bool> todo(g,true);
+for(NodeIt v(g); v!=INVALID; ++v) {
+if (_mate[v]!=INVALID && v < _mate[v]) {
+Node u=_mate[v];
+for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
+if ( g.runningNode(e) == u ) {
+map.set(u,e);
+map.set(v,e);
+todo.set(u,false);
+todo.set(v,false);
+break;
+}
+}
+}
+}
+}
+///\brief Gives back the matching in a \c bool valued \c Edge
+///map.
+///
+///Writes the matching stored to a \c bool valued \c Arc
+///map. This map will have the property that there are no two
+///incident arcs \c e, \c f with \c map[e]==map[f]==true. The
+///arcs \c e with \c map[e]==true form the matching.
+template<typename MatchingMap>
+void matching(MatchingMap& map) const {
+for(EdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
+typename Graph::template NodeMap<bool> todo(g,true);
+for(NodeIt v(g); v!=INVALID; ++v) {
+if ( todo[v] && _mate[v]!=INVALID ) {
+Node u=_mate[v];
+for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
+if ( g.runningNode(e) == u ) {
+map.set(e,true);
+todo.set(u,false);
+todo.set(v,false);
+break;
+}
+}
+}
+}
+}
+///\brief Returns the canonical decomposition of the digraph after running
+///the algorithm.
+///
+///After calling any run methods of the class, it writes the
+///Gallai-Edmonds canonical decomposition of the digraph. \c map
+///must be a node map of \ref DecompType 's.
+template <typename DecompositionMap>
+void decomposition(DecompositionMap& map) const {
+for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
+}
+///\brief Returns a barrier on the nodes.
+///
+///After calling any run methods of the class, it writes a
+///canonical barrier on the nodes. The odd component number of the
+///remaining digraph minus the barrier size is a lower bound for the
+///uncovered nodes in the digraph. The \c map must be a node map of
+///bools.
+template <typename BarrierMap>
+void barrier(BarrierMap& barrier) {
+for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A);
+}
+private:
+void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
+UFE& blossom, NV& rep, EFE& tree) {
+//We have one tree which we grow, and also shrink but only if it
+//cannot be postponed. If we augment then we return to the "for"
+//cycle of runEdmonds().
+std::queue<Node> Q;   //queue of the totally unscanned nodes
+Q.push(v);
+std::queue<Node> R;
+//queue of the nodes which must be scanned for a possible shrink
+while ( !Q.empty() ) {
+Node x=Q.front();
+Q.pop();
+for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
+Node y=g.runningNode(e);
+//growOrAugment grows if y is covered by the matching and
+//augments if not. In this latter case it returns 1.
+if (position[y]==C &&
+growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
+}
+R.push(x);
+}
+while ( !R.empty() ) {
+Node x=R.front();
+R.pop();
+for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
+Node y=g.runningNode(e);
+if ( position[y] == D && blossom.find(x) != blossom.find(y) )
+//Recall that we have only one tree.
+shrink( x, y, ear, blossom, rep, tree, Q);
+while ( !Q.empty() ) {
+Node z=Q.front();
+Q.pop();
+for( IncEdgeIt f(g,z); f!= INVALID; ++f ) {
+Node w=g.runningNode(f);
+//growOrAugment grows if y is covered by the matching and
+//augments if not. In this latter case it returns 1.
+if (position[w]==C &&
+growOrAugment(w, z, ear, blossom, rep, tree, Q)) return;
+}
+R.push(z);
+}
+} //for e
+} // while ( !R.empty() )
+}
+void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
+UFE& blossom, NV& rep, EFE& tree) {
+//We have one tree, which we grow and shrink. If we augment then we
+//return to the "for" cycle of runEdmonds().
+std::queue<Node> Q;   //queue of the unscanned nodes
+Q.push(v);
+while ( !Q.empty() ) {
+Node x=Q.front();
+Q.pop();
+for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
+Node y=g.runningNode(e);
+switch ( position[y] ) {
+case D:          //x and y must be in the same tree
+if ( blossom.find(x) != blossom.find(y))
+//x and y are in the same tree
+shrink(x, y, ear, blossom, rep, tree, Q);
+break;
+case C:
+//growOrAugment grows if y is covered by the matching and
+//augments if not. In this latter case it returns 1.
+if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
+break;
+default: break;
+}
+}
+}
+}
+void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,
+UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) {
+//x and y are the two adjacent vertices in two blossoms.
+typename Graph::template NodeMap<bool> path(g,false);
+Node b=rep[blossom.find(x)];
+path.set(b,true);
+b=_mate[b];
+while ( b!=INVALID ) {
+b=rep[blossom.find(ear[b])];
+path.set(b,true);
+b=_mate[b];
+} //we go until the root through bases of blossoms and odd vertices
+Node top=y;
+Node middle=rep[blossom.find(top)];
+Node bottom=x;
+while ( !path[middle] )
+shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
+//Until we arrive to a node on the path, we update blossom, tree
+//and the positions of the odd nodes.
+Node base=middle;
+top=x;
+middle=rep[blossom.find(top)];
+bottom=y;
+Node blossom_base=rep[blossom.find(base)];
+while ( middle!=blossom_base )
+shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
+//Until we arrive to a node on the path, we update blossom, tree
+//and the positions of the odd nodes.
+rep[blossom.find(base)] = base;
+}
+void shrinkStep(Node& top, Node& middle, Node& bottom,
+typename Graph::template NodeMap<Node>& ear,
+UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) {
+//We traverse a blossom and update everything.
+ear.set(top,bottom);
+Node t=top;
+while ( t!=middle ) {
+Node u=_mate[t];
+t=ear[u];
+ear.set(t,u);
+}
+bottom=_mate[middle];
+position.set(bottom,D);
+Q.push(bottom);
+top=ear[bottom];
+Node oldmiddle=middle;
+middle=rep[blossom.find(top)];
+tree.erase(bottom);
+tree.erase(oldmiddle);
+blossom.insert(bottom);
+blossom.join(bottom, oldmiddle);
+blossom.join(top, oldmiddle);
+}
+bool growOrAugment(Node& y, Node& x, typename Graph::template
+NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree,
+std::queue<Node>& Q) {
+//x is in a blossom in the tree, y is outside. If y is covered by
+//the matching we grow, otherwise we augment. In this case we
+//return 1.
+if ( _mate[y]!=INVALID ) {       //grow
+ear.set(y,x);
+Node w=_mate[y];
+rep[blossom.insert(w)] = w;
+position.set(y,A);
+position.set(w,D);
+int t = tree.find(rep[blossom.find(x)]);
+tree.insert(y,t);
+tree.insert(w,t);
+Q.push(w);
+} else {                      //augment
+augment(x, ear, blossom, rep, tree);
+_mate.set(x,y);
+_mate.set(y,x);
+return true;
+}
+return false;
+}
+void augment(Node x, typename Graph::template NodeMap<Node>& ear,
+UFE& blossom, NV& rep, EFE& tree) {
+Node v=_mate[x];
+while ( v!=INVALID ) {
+Node u=ear[v];
+_mate.set(v,u);
+Node tmp=v;
+v=_mate[u];
+_mate.set(u,tmp);
+}
+int y = tree.find(rep[blossom.find(x)]);
+for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) {
+if ( position[tit] == D ) {
+int b = blossom.find(tit);
+for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) {
+position.set(bit, C);
+}
+blossom.eraseClass(b);
+} else position.set(tit, C);
+}
+tree.eraseClass(y);
+}
+};
+/// \ingroup matching
+///
+/// \brief Weighted matching in general graphs
+///
+/// This class provides an efficient implementation of Edmond's
+/// maximum weighted matching algorithm. The implementation is based
+/// on extensive use of priority queues and provides
+/// \f$O(nm\log(n))\f$ time complexity.
+///
+/// The maximum weighted matching problem is to find undirected
+/// arcs in the digraph with maximum overall weight and no two of
+/// them shares their endpoints. The problem can be formulated with
+/// the next linear program:
+/// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
+///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f]
+/// \f[x_e \ge 0\quad \forall e\in E\f]
+/// \f[\max \sum_{e\in E}x_ew_e\f]
+/// where \f$\delta(X)\f$ is the set of arcs incident to a node in
+/// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints in
+/// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
+/// the nodes.
+///
+/// The algorithm calculates an optimal matching and a proof of the
+/// optimality. The solution of the dual problem can be used to check
+/// the result of the algorithm. The dual linear problem is the next:
+/// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f]
+/// \f[y_u \ge 0 \quad \forall u \in V\f]
+/// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
+/// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
+///
+/// The algorithm can be executed with \c run() or the \c init() and
+/// then the \c start() member functions. After it the matching can
+/// be asked with \c matching() or mate() functions. The dual
+/// solution can be get with \c nodeValue(), \c blossomNum() and \c
+/// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
+/// "BlossomIt" nested class which is able to iterate on the nodes
+/// of a blossom. If the value type is integral then the dual
+/// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
+template <typename _Graph,
+typename _WeightMap = typename _Graph::template EdgeMap<int> >
+class MaxWeightedMatching {
+public:
+typedef _Graph Graph;
+typedef _WeightMap WeightMap;
+typedef typename WeightMap::Value Value;
+/// \brief Scaling factor for dual solution
+///
+/// Scaling factor for dual solution, it is equal to 4 or 1
+/// according to the value type.
+static const int dualScale =
+std::numeric_limits<Value>::is_integer ? 4 : 1;
+typedef typename Graph::template NodeMap<typename Graph::Arc>
+MatchingMap;
+private:
+TEMPLATE_GRAPH_TYPEDEFS(Graph);
+typedef typename Graph::template NodeMap<Value> NodePotential;
+typedef std::vector<Node> BlossomNodeList;
+struct BlossomVariable {
+int begin, end;
+Value value;
+BlossomVariable(int _begin, int _end, Value _value)
+: begin(_begin), end(_end), value(_value) {}
+};
+typedef std::vector<BlossomVariable> BlossomPotential;
+const Graph& _graph;
+const WeightMap& _weight;
+MatchingMap* _matching;
+NodePotential* _node_potential;
+BlossomPotential _blossom_potential;
+BlossomNodeList _blossom_node_list;
+int _node_num;
+int _blossom_num;
+typedef typename Graph::template NodeMap<int> NodeIntMap;
+typedef typename Graph::template ArcMap<int> ArcIntMap;
+typedef typename Graph::template EdgeMap<int> EdgeIntMap;
+typedef RangeMap<int> IntIntMap;
+enum Status {
+EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
+};
+typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
+struct BlossomData {
+int tree;
+Status status;
+Arc pred, next;
+Value pot, offset;
+Node base;
+};
+NodeIntMap *_blossom_index;
+BlossomSet *_blossom_set;
+RangeMap<BlossomData>* _blossom_data;
+NodeIntMap *_node_index;
+ArcIntMap *_node_heap_index;
+struct NodeData {
+NodeData(ArcIntMap& node_heap_index)
+: heap(node_heap_index) {}
+int blossom;
+Value pot;
+BinHeap<Value, ArcIntMap> heap;
+std::map<int, Arc> heap_index;
+int tree;
+};
+RangeMap<NodeData>* _node_data;
+typedef ExtendFindEnum<IntIntMap> TreeSet;
+IntIntMap *_tree_set_index;
+TreeSet *_tree_set;
+NodeIntMap *_delta1_index;
+BinHeap<Value, NodeIntMap> *_delta1;
+IntIntMap *_delta2_index;
+BinHeap<Value, IntIntMap> *_delta2;
+EdgeIntMap *_delta3_index;
+BinHeap<Value, EdgeIntMap> *_delta3;
+IntIntMap *_delta4_index;
+BinHeap<Value, IntIntMap> *_delta4;
+Value _delta_sum;
+void createStructures() {
+_node_num = countNodes(_graph);
+_blossom_num = _node_num * 3 / 2;
+if (!_matching) {
+_matching = new MatchingMap(_graph);
+}
+if (!_node_potential) {
+_node_potential = new NodePotential(_graph);
+}
+if (!_blossom_set) {
+_blossom_index = new NodeIntMap(_graph);
+_blossom_set = new BlossomSet(*_blossom_index);
+_blossom_data = new RangeMap<BlossomData>(_blossom_num);
+}
+if (!_node_index) {
+_node_index = new NodeIntMap(_graph);
+_node_heap_index = new ArcIntMap(_graph);
+_node_data = new RangeMap<NodeData>(_node_num,
+NodeData(*_node_heap_index));
+}
+if (!_tree_set) {
+_tree_set_index = new IntIntMap(_blossom_num);
+_tree_set = new TreeSet(*_tree_set_index);
+}
+if (!_delta1) {
+_delta1_index = new NodeIntMap(_graph);
+_delta1 = new BinHeap<Value, NodeIntMap>(*_delta1_index);
+}
+if (!_delta2) {
+_delta2_index = new IntIntMap(_blossom_num);
+_delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
+}
+if (!_delta3) {
+_delta3_index = new EdgeIntMap(_graph);
+_delta3 = new BinHeap<Value, EdgeIntMap>(*_delta3_index);
+}
+if (!_delta4) {
+_delta4_index = new IntIntMap(_blossom_num);
+_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
+}
+}
+void destroyStructures() {
+_node_num = countNodes(_graph);
+_blossom_num = _node_num * 3 / 2;
+if (_matching) {
+delete _matching;
+}
+if (_node_potential) {
+delete _node_potential;
+}
+if (_blossom_set) {
+delete _blossom_index;
+delete _blossom_set;
+delete _blossom_data;
+}
+if (_node_index) {
+delete _node_index;
+delete _node_heap_index;
+delete _node_data;
+}
+if (_tree_set) {
+delete _tree_set_index;
+delete _tree_set;
+}
+if (_delta1) {
+delete _delta1_index;
+delete _delta1;
+}
+if (_delta2) {
+delete _delta2_index;
+delete _delta2;
+}
+if (_delta3) {
+delete _delta3_index;
+delete _delta3;
+}
+if (_delta4) {
+delete _delta4_index;
+delete _delta4;
+}
+}
+void matchedToEven(int blossom, int tree) {
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+if (!_blossom_set->trivial(blossom)) {
+(*_blossom_data)[blossom].pot -=
+2 * (_delta_sum - (*_blossom_data)[blossom].offset);
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+_blossom_set->increase(n, std::numeric_limits<Value>::max());
+int ni = (*_node_index)[n];
+(*_node_data)[ni].heap.clear();
+(*_node_data)[ni].heap_index.clear();
+(*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
+_delta1->push(n, (*_node_data)[ni].pot);
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+_delta3->push(e, rw / 2);
+}
+} else if ((*_blossom_data)[vb].status == UNMATCHED) {
+if (_delta3->state(e) != _delta3->IN_HEAP) {
+_delta3->push(e, rw);
+}
+} else {
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[vi].heap_index.find(tree);
+if (it != (*_node_data)[vi].heap_index.end()) {
+if ((*_node_data)[vi].heap[it->second] > rw) {
+(*_node_data)[vi].heap.replace(it->second, e);
+(*_node_data)[vi].heap.decrease(e, rw);
+it->second = e;
+}
+} else {
+(*_node_data)[vi].heap.push(e, rw);
+(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+}
+if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+if ((*_blossom_data)[vb].status == MATCHED) {
+if (_delta2->state(vb) != _delta2->IN_HEAP) {
+_delta2->push(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset){
+_delta2->decrease(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+}
+}
+}
+}
+}
+}
+(*_blossom_data)[blossom].offset = 0;
+}
+void matchedToOdd(int blossom) {
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+(*_blossom_data)[blossom].offset += _delta_sum;
+if (!_blossom_set->trivial(blossom)) {
+_delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
+(*_blossom_data)[blossom].offset);
+}
+}
+void evenToMatched(int blossom, int tree) {
+if (!_blossom_set->trivial(blossom)) {
+(*_blossom_data)[blossom].pot += 2 * _delta_sum;
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+int ni = (*_node_index)[n];
+(*_node_data)[ni].pot -= _delta_sum;
+_delta1->erase(n);
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if (vb == blossom) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+} else if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+int vt = _tree_set->find(vb);
+if (vt != tree) {
+Arc r = _graph.oppositeArc(e);
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[ni].heap_index.find(vt);
+if (it != (*_node_data)[ni].heap_index.end()) {
+if ((*_node_data)[ni].heap[it->second] > rw) {
+(*_node_data)[ni].heap.replace(it->second, r);
+(*_node_data)[ni].heap.decrease(r, rw);
+it->second = r;
+}
+} else {
+(*_node_data)[ni].heap.push(r, rw);
+(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+}
+if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+_delta2->push(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+} else if ((*_delta2)[blossom] >
+_blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset){
+_delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+}
+}
+}
+} else if ((*_blossom_data)[vb].status == UNMATCHED) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+} else {
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[vi].heap_index.find(tree);
+if (it != (*_node_data)[vi].heap_index.end()) {
+(*_node_data)[vi].heap.erase(it->second);
+(*_node_data)[vi].heap_index.erase(it);
+if ((*_node_data)[vi].heap.empty()) {
+_blossom_set->increase(v, std::numeric_limits<Value>::max());
+} else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
+_blossom_set->increase(v, (*_node_data)[vi].heap.prio());
+}
+if ((*_blossom_data)[vb].status == MATCHED) {
+if (_blossom_set->classPrio(vb) ==
+std::numeric_limits<Value>::max()) {
+_delta2->erase(vb);
+} else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset) {
+_delta2->increase(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+}
+}
+}
+}
+}
+}
+}
+void oddToMatched(int blossom) {
+(*_blossom_data)[blossom].offset -= _delta_sum;
+if (_blossom_set->classPrio(blossom) !=
+std::numeric_limits<Value>::max()) {
+_delta2->push(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+}
+if (!_blossom_set->trivial(blossom)) {
+_delta4->erase(blossom);
+}
+}
+void oddToEven(int blossom, int tree) {
+if (!_blossom_set->trivial(blossom)) {
+_delta4->erase(blossom);
+(*_blossom_data)[blossom].pot -=
+2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+int ni = (*_node_index)[n];
+_blossom_set->increase(n, std::numeric_limits<Value>::max());
+(*_node_data)[ni].heap.clear();
+(*_node_data)[ni].heap_index.clear();
+(*_node_data)[ni].pot +=
+2 * _delta_sum - (*_blossom_data)[blossom].offset;
+_delta1->push(n, (*_node_data)[ni].pot);
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+_delta3->push(e, rw / 2);
+}
+} else if ((*_blossom_data)[vb].status == UNMATCHED) {
+if (_delta3->state(e) != _delta3->IN_HEAP) {
+_delta3->push(e, rw);
+}
+} else {
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[vi].heap_index.find(tree);
+if (it != (*_node_data)[vi].heap_index.end()) {
+if ((*_node_data)[vi].heap[it->second] > rw) {
+(*_node_data)[vi].heap.replace(it->second, e);
+(*_node_data)[vi].heap.decrease(e, rw);
+it->second = e;
+}
+} else {
+(*_node_data)[vi].heap.push(e, rw);
+(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+}
+if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+if ((*_blossom_data)[vb].status == MATCHED) {
+if (_delta2->state(vb) != _delta2->IN_HEAP) {
+_delta2->push(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset) {
+_delta2->decrease(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+}
+}
+}
+}
+}
+}
+(*_blossom_data)[blossom].offset = 0;
+}
+void matchedToUnmatched(int blossom) {
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+int ni = (*_node_index)[n];
+_blossom_set->increase(n, std::numeric_limits<Value>::max());
+(*_node_data)[ni].heap.clear();
+(*_node_data)[ni].heap_index.clear();
+for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.target(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) != _delta3->IN_HEAP) {
+_delta3->push(e, rw);
+}
+}
+}
+}
+}
+void unmatchedToMatched(int blossom) {
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+int ni = (*_node_index)[n];
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if (vb == blossom) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+} else if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+int vt = _tree_set->find(vb);
+Arc r = _graph.oppositeArc(e);
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[ni].heap_index.find(vt);
+if (it != (*_node_data)[ni].heap_index.end()) {
+if ((*_node_data)[ni].heap[it->second] > rw) {
+(*_node_data)[ni].heap.replace(it->second, r);
+(*_node_data)[ni].heap.decrease(r, rw);
+it->second = r;
+}
+} else {
+(*_node_data)[ni].heap.push(r, rw);
+(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+}
+if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+_delta2->push(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+} else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
+(*_blossom_data)[blossom].offset){
+_delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+}
+}
+} else if ((*_blossom_data)[vb].status == UNMATCHED) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+}
+}
+}
+}
+void alternatePath(int even, int tree) {
+int odd;
+evenToMatched(even, tree);
+(*_blossom_data)[even].status = MATCHED;
+while ((*_blossom_data)[even].pred != INVALID) {
+odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
+(*_blossom_data)[odd].status = MATCHED;
+oddToMatched(odd);
+(*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
+even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
+(*_blossom_data)[even].status = MATCHED;
+evenToMatched(even, tree);
+(*_blossom_data)[even].next =
+_graph.oppositeArc((*_blossom_data)[odd].pred);
+}
+}
+void destroyTree(int tree) {
+for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
+if ((*_blossom_data)[b].status == EVEN) {
+(*_blossom_data)[b].status = MATCHED;
+evenToMatched(b, tree);
+} else if ((*_blossom_data)[b].status == ODD) {
+(*_blossom_data)[b].status = MATCHED;
+oddToMatched(b);
+}
+}
+_tree_set->eraseClass(tree);
+}
+void unmatchNode(const Node& node) {
+int blossom = _blossom_set->find(node);
+int tree = _tree_set->find(blossom);
+alternatePath(blossom, tree);
+destroyTree(tree);
+(*_blossom_data)[blossom].status = UNMATCHED;
+(*_blossom_data)[blossom].base = node;
+matchedToUnmatched(blossom);
+}
+void augmentOnArc(const Edge& arc) {
+int left = _blossom_set->find(_graph.u(arc));
+int right = _blossom_set->find(_graph.v(arc));
+if ((*_blossom_data)[left].status == EVEN) {
+int left_tree = _tree_set->find(left);
+alternatePath(left, left_tree);
+destroyTree(left_tree);
+} else {
+(*_blossom_data)[left].status = MATCHED;
+unmatchedToMatched(left);
+}
+if ((*_blossom_data)[right].status == EVEN) {
+int right_tree = _tree_set->find(right);
+alternatePath(right, right_tree);
+destroyTree(right_tree);
+} else {
+(*_blossom_data)[right].status = MATCHED;
+unmatchedToMatched(right);
+}
+(*_blossom_data)[left].next = _graph.direct(arc, true);
+(*_blossom_data)[right].next = _graph.direct(arc, false);
+}
+void extendOnArc(const Arc& arc) {
+int base = _blossom_set->find(_graph.target(arc));
+int tree = _tree_set->find(base);
+int odd = _blossom_set->find(_graph.source(arc));
+_tree_set->insert(odd, tree);
+(*_blossom_data)[odd].status = ODD;
+matchedToOdd(odd);
+(*_blossom_data)[odd].pred = arc;
+int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
+(*_blossom_data)[even].pred = (*_blossom_data)[even].next;
+_tree_set->insert(even, tree);
+(*_blossom_data)[even].status = EVEN;
+matchedToEven(even, tree);
+}
+void shrinkOnArc(const Edge& edge, int tree) {
+int nca = -1;
+std::vector<int> left_path, right_path;
+{
+std::set<int> left_set, right_set;
+int left = _blossom_set->find(_graph.u(edge));
+left_path.push_back(left);
+left_set.insert(left);
+int right = _blossom_set->find(_graph.v(edge));
+right_path.push_back(right);
+right_set.insert(right);
+while (true) {
+if ((*_blossom_data)[left].pred == INVALID) break;
+left =
+_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+left_path.push_back(left);
+left =
+_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+left_path.push_back(left);
+left_set.insert(left);
+if (right_set.find(left) != right_set.end()) {
+nca = left;
+break;
+}
+if ((*_blossom_data)[right].pred == INVALID) break;
+right =
+_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+right_path.push_back(right);
+right =
+_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+right_path.push_back(right);
+right_set.insert(right);
+if (left_set.find(right) != left_set.end()) {
+nca = right;
+break;
+}
+}
+if (nca == -1) {
+if ((*_blossom_data)[left].pred == INVALID) {
+nca = right;
+while (left_set.find(nca) == left_set.end()) {
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+right_path.push_back(nca);
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+right_path.push_back(nca);
+}
+} else {
+nca = left;
+while (right_set.find(nca) == right_set.end()) {
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+left_path.push_back(nca);
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+left_path.push_back(nca);
+}
+}
+}
+}
+std::vector<int> subblossoms;
+Arc prev;
+prev = _graph.direct(edge, true);
+for (int i = 0; left_path[i] != nca; i += 2) {
+subblossoms.push_back(left_path[i]);
+(*_blossom_data)[left_path[i]].next = prev;
+_tree_set->erase(left_path[i]);
+subblossoms.push_back(left_path[i + 1]);
+(*_blossom_data)[left_path[i + 1]].status = EVEN;
+oddToEven(left_path[i + 1], tree);
+_tree_set->erase(left_path[i + 1]);
+prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
+}
+int k = 0;
+while (right_path[k] != nca) ++k;
+subblossoms.push_back(nca);
+(*_blossom_data)[nca].next = prev;
+for (int i = k - 2; i >= 0; i -= 2) {
+subblossoms.push_back(right_path[i + 1]);
+(*_blossom_data)[right_path[i + 1]].status = EVEN;
+oddToEven(right_path[i + 1], tree);
+_tree_set->erase(right_path[i + 1]);
+(*_blossom_data)[right_path[i + 1]].next =
+(*_blossom_data)[right_path[i + 1]].pred;
+subblossoms.push_back(right_path[i]);
+_tree_set->erase(right_path[i]);
+}
+int surface =
+_blossom_set->join(subblossoms.begin(), subblossoms.end());
+for (int i = 0; i < int(subblossoms.size()); ++i) {
+if (!_blossom_set->trivial(subblossoms[i])) {
+(*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
+}
+(*_blossom_data)[subblossoms[i]].status = MATCHED;
+}
+(*_blossom_data)[surface].pot = -2 * _delta_sum;
+(*_blossom_data)[surface].offset = 0;
+(*_blossom_data)[surface].status = EVEN;
+(*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
+(*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
+_tree_set->insert(surface, tree);
+_tree_set->erase(nca);
+}
+void splitBlossom(int blossom) {
+Arc next = (*_blossom_data)[blossom].next;
+Arc pred = (*_blossom_data)[blossom].pred;
+int tree = _tree_set->find(blossom);
+(*_blossom_data)[blossom].status = MATCHED;
+oddToMatched(blossom);
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+std::vector<int> subblossoms;
+_blossom_set->split(blossom, std::back_inserter(subblossoms));
+Value offset = (*_blossom_data)[blossom].offset;
+int b = _blossom_set->find(_graph.source(pred));
+int d = _blossom_set->find(_graph.source(next));
+int ib = -1, id = -1;
+for (int i = 0; i < int(subblossoms.size()); ++i) {
+if (subblossoms[i] == b) ib = i;
+if (subblossoms[i] == d) id = i;
+(*_blossom_data)[subblossoms[i]].offset = offset;
+if (!_blossom_set->trivial(subblossoms[i])) {
+(*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
+}
+if (_blossom_set->classPrio(subblossoms[i]) !=
+std::numeric_limits<Value>::max()) {
+_delta2->push(subblossoms[i],
+_blossom_set->classPrio(subblossoms[i]) -
+(*_blossom_data)[subblossoms[i]].offset);
+}
+}
+if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
+for (int i = (id + 1) % subblossoms.size();
+i != ib; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+(*_blossom_data)[sb].next =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+}
+for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+int ub = subblossoms[(i + 2) % subblossoms.size()];
+(*_blossom_data)[sb].status = ODD;
+matchedToOdd(sb);
+_tree_set->insert(sb, tree);
+(*_blossom_data)[sb].pred = pred;
+(*_blossom_data)[sb].next =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+pred = (*_blossom_data)[ub].next;
+(*_blossom_data)[tb].status = EVEN;
+matchedToEven(tb, tree);
+_tree_set->insert(tb, tree);
+(*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
+}
+(*_blossom_data)[subblossoms[id]].status = ODD;
+matchedToOdd(subblossoms[id]);
+_tree_set->insert(subblossoms[id], tree);
+(*_blossom_data)[subblossoms[id]].next = next;
+(*_blossom_data)[subblossoms[id]].pred = pred;
+} else {
+for (int i = (ib + 1) % subblossoms.size();
+i != id; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+(*_blossom_data)[sb].next =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+}
+for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+int ub = subblossoms[(i + 2) % subblossoms.size()];
+(*_blossom_data)[sb].status = ODD;
+matchedToOdd(sb);
+_tree_set->insert(sb, tree);
+(*_blossom_data)[sb].next = next;
+(*_blossom_data)[sb].pred =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+(*_blossom_data)[tb].status = EVEN;
+matchedToEven(tb, tree);
+_tree_set->insert(tb, tree);
+(*_blossom_data)[tb].pred =
+(*_blossom_data)[tb].next =
+_graph.oppositeArc((*_blossom_data)[ub].next);
+next = (*_blossom_data)[ub].next;
+}
+(*_blossom_data)[subblossoms[ib]].status = ODD;
+matchedToOdd(subblossoms[ib]);
+_tree_set->insert(subblossoms[ib], tree);
+(*_blossom_data)[subblossoms[ib]].next = next;
+(*_blossom_data)[subblossoms[ib]].pred = pred;
+}
+_tree_set->erase(blossom);
+}
+void extractBlossom(int blossom, const Node& base, const Arc& matching) {
+if (_blossom_set->trivial(blossom)) {
+int bi = (*_node_index)[base];
+Value pot = (*_node_data)[bi].pot;
+_matching->set(base, matching);
+_blossom_node_list.push_back(base);
+_node_potential->set(base, pot);
+} else {
+Value pot = (*_blossom_data)[blossom].pot;
+int bn = _blossom_node_list.size();
+std::vector<int> subblossoms;
+_blossom_set->split(blossom, std::back_inserter(subblossoms));
+int b = _blossom_set->find(base);
+int ib = -1;
+for (int i = 0; i < int(subblossoms.size()); ++i) {
+if (subblossoms[i] == b) { ib = i; break; }
+}
+for (int i = 1; i < int(subblossoms.size()); i += 2) {
+int sb = subblossoms[(ib + i) % subblossoms.size()];
+int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
+Arc m = (*_blossom_data)[tb].next;
+extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
+extractBlossom(tb, _graph.source(m), m);
+}
+extractBlossom(subblossoms[ib], base, matching);
+int en = _blossom_node_list.size();
+_blossom_potential.push_back(BlossomVariable(bn, en, pot));
+}
+}
+void extractMatching() {
+std::vector<int> blossoms;
+for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
+blossoms.push_back(c);
+}
+for (int i = 0; i < int(blossoms.size()); ++i) {
+if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
+Value offset = (*_blossom_data)[blossoms[i]].offset;
+(*_blossom_data)[blossoms[i]].pot += 2 * offset;
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
+n != INVALID; ++n) {
+(*_node_data)[(*_node_index)[n]].pot -= offset;
+}
+Arc matching = (*_blossom_data)[blossoms[i]].next;
+Node base = _graph.source(matching);
+extractBlossom(blossoms[i], base, matching);
+} else {
+Node base = (*_blossom_data)[blossoms[i]].base;
+extractBlossom(blossoms[i], base, INVALID);
+}
+}
+}
+public:
+/// \brief Constructor
+///
+/// Constructor.
+MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
+: _graph(graph), _weight(weight), _matching(0),
+_node_potential(0), _blossom_potential(), _blossom_node_list(),
+_node_num(0), _blossom_num(0),
+_blossom_index(0), _blossom_set(0), _blossom_data(0),
+_node_index(0), _node_heap_index(0), _node_data(0),
+_tree_set_index(0), _tree_set(0),
+_delta1_index(0), _delta1(0),
+_delta2_index(0), _delta2(0),
+_delta3_index(0), _delta3(0),
+_delta4_index(0), _delta4(0),
+_delta_sum() {}
+~MaxWeightedMatching() {
+destroyStructures();
+}
+/// \name Execution control
+/// The simplest way to execute the algorithm is to use the member
+/// \c run() member function.
+///@{
+/// \brief Initialize the algorithm
+///
+/// Initialize the algorithm
+void init() {
+createStructures();
+for (ArcIt e(_graph); e != INVALID; ++e) {
+_node_heap_index->set(e, BinHeap<Value, ArcIntMap>::PRE_HEAP);
+}
+for (NodeIt n(_graph); n != INVALID; ++n) {
+_delta1_index->set(n, _delta1->PRE_HEAP);
+}
+for (EdgeIt e(_graph); e != INVALID; ++e) {
+_delta3_index->set(e, _delta3->PRE_HEAP);
+}
+for (int i = 0; i < _blossom_num; ++i) {
+_delta2_index->set(i, _delta2->PRE_HEAP);
+_delta4_index->set(i, _delta4->PRE_HEAP);
+}
+int index = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+Value max = 0;
+for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+if (_graph.target(e) == n) continue;
+if ((dualScale * _weight[e]) / 2 > max) {
+max = (dualScale * _weight[e]) / 2;
+}
+}
+_node_index->set(n, index);
+(*_node_data)[index].pot = max;
+_delta1->push(n, max);
+int blossom =
+_blossom_set->insert(n, std::numeric_limits<Value>::max());
+_tree_set->insert(blossom);
+(*_blossom_data)[blossom].status = EVEN;
+(*_blossom_data)[blossom].pred = INVALID;
+(*_blossom_data)[blossom].next = INVALID;
+(*_blossom_data)[blossom].pot = 0;
+(*_blossom_data)[blossom].offset = 0;
+++index;
+}
+for (EdgeIt e(_graph); e != INVALID; ++e) {
+int si = (*_node_index)[_graph.u(e)];
+int ti = (*_node_index)[_graph.v(e)];
+if (_graph.u(e) != _graph.v(e)) {
+_delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
+dualScale * _weight[e]) / 2);
+}
+}
+}
+/// \brief Starts the algorithm
+///
+/// Starts the algorithm
+void start() {
+enum OpType {
+D1, D2, D3, D4
+};
+int unmatched = _node_num;
+while (unmatched > 0) {
+Value d1 = !_delta1->empty() ?
+_delta1->prio() : std::numeric_limits<Value>::max();
+Value d2 = !_delta2->empty() ?
+_delta2->prio() : std::numeric_limits<Value>::max();
+Value d3 = !_delta3->empty() ?
+_delta3->prio() : std::numeric_limits<Value>::max();
+Value d4 = !_delta4->empty() ?
+_delta4->prio() : std::numeric_limits<Value>::max();
+_delta_sum = d1; OpType ot = D1;
+if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
+if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
+if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
+switch (ot) {
+case D1:
+{
+Node n = _delta1->top();
+unmatchNode(n);
+--unmatched;
+}
+break;
+case D2:
+{
+int blossom = _delta2->top();
+Node n = _blossom_set->classTop(blossom);
+Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
+extendOnArc(e);
+}
+break;
+case D3:
+{
+Edge e = _delta3->top();
+int left_blossom = _blossom_set->find(_graph.u(e));
+int right_blossom = _blossom_set->find(_graph.v(e));
+if (left_blossom == right_blossom) {
+_delta3->pop();
+} else {
+int left_tree;
+if ((*_blossom_data)[left_blossom].status == EVEN) {
+left_tree = _tree_set->find(left_blossom);
+} else {
+left_tree = -1;
+++unmatched;
+}
+int right_tree;
+if ((*_blossom_data)[right_blossom].status == EVEN) {
+right_tree = _tree_set->find(right_blossom);
+} else {
+right_tree = -1;
+++unmatched;
+}
+if (left_tree == right_tree) {
+shrinkOnArc(e, left_tree);
+} else {
+augmentOnArc(e);
+unmatched -= 2;
+}
+}
+} break;
+case D4:
+splitBlossom(_delta4->top());
+break;
+}
+}
+extractMatching();
+}
+/// \brief Runs %MaxWeightedMatching algorithm.
+///
+/// This method runs the %MaxWeightedMatching algorithm.
+///
+/// \note mwm.run() is just a shortcut of the following code.
+/// \code
+///   mwm.init();
+///   mwm.start();
+/// \endcode
+void run() {
+init();
+start();
+}
+/// @}
+/// \name Primal solution
+/// Functions for get the primal solution, ie. the matching.
+/// @{
+/// \brief Returns the matching value.
+///
+/// Returns the matching value.
+Value matchingValue() const {
+Value sum = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+if ((*_matching)[n] != INVALID) {
+sum += _weight[(*_matching)[n]];
+}
+}
+return sum /= 2;
+}
+/// \brief Returns true when the arc is in the matching.
+///
+/// Returns true when the arc is in the matching.
+bool matching(const Edge& arc) const {
+return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
+}
+/// \brief Returns the incident matching arc.
+///
+/// Returns the incident matching arc from given node. If the
+/// node is not matched then it gives back \c INVALID.
+Arc matching(const Node& node) const {
+return (*_matching)[node];
+}
+/// \brief Returns the mate of the node.
+///
+/// Returns the adjancent node in a mathcing arc. If the node is
+/// not matched then it gives back \c INVALID.
+Node mate(const Node& node) const {
+return (*_matching)[node] != INVALID ?
+_graph.target((*_matching)[node]) : INVALID;
+}
+/// @}
+/// \name Dual solution
+/// Functions for get the dual solution.
+/// @{
+/// \brief Returns the value of the dual solution.
+///
+/// Returns the value of the dual solution. It should be equal to
+/// the primal value scaled by \ref dualScale "dual scale".
+Value dualValue() const {
+Value sum = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+sum += nodeValue(n);
+}
+for (int i = 0; i < blossomNum(); ++i) {
+sum += blossomValue(i) * (blossomSize(i) / 2);
+}
+return sum;
+}
+/// \brief Returns the value of the node.
+///
+/// Returns the the value of the node.
+Value nodeValue(const Node& n) const {
+return (*_node_potential)[n];
+}
+/// \brief Returns the number of the blossoms in the basis.
+///
+/// Returns the number of the blossoms in the basis.
+/// \see BlossomIt
+int blossomNum() const {
+return _blossom_potential.size();
+}
+/// \brief Returns the number of the nodes in the blossom.
+///
+/// Returns the number of the nodes in the blossom.
+int blossomSize(int k) const {
+return _blossom_potential[k].end - _blossom_potential[k].begin;
+}
+/// \brief Returns the value of the blossom.
+///
+/// Returns the the value of the blossom.
+/// \see BlossomIt
+Value blossomValue(int k) const {
+return _blossom_potential[k].value;
+}
+/// \brief Lemon iterator for get the items of the blossom.
+///
+/// Lemon iterator for get the nodes of the blossom. This class
+/// provides a common style lemon iterator which gives back a
+/// subset of the nodes.
+class BlossomIt {
+public:
+/// \brief Constructor.
+///
+/// Constructor for get the nodes of the variable.
+BlossomIt(const MaxWeightedMatching& algorithm, int variable)
+: _algorithm(&algorithm)
+{
+_index = _algorithm->_blossom_potential[variable].begin;
+_last = _algorithm->_blossom_potential[variable].end;
+}
+/// \brief Invalid constructor.
+///
+/// Invalid constructor.
+BlossomIt(Invalid) : _index(-1) {}
+/// \brief Conversion to node.
+///
+/// Conversion to node.
+operator Node() const {
+return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
+}
+/// \brief Increment operator.
+///
+/// Increment operator.
+BlossomIt& operator++() {
+++_index;
+if (_index == _last) {
+_index = -1;
+}
+return *this;
+}
+bool operator==(const BlossomIt& it) const {
+return _index == it._index;
+}
+bool operator!=(const BlossomIt& it) const {
+return _index != it._index;
+}
+private:
+const MaxWeightedMatching* _algorithm;
+int _last;
+int _index;
+};
+/// @}
+};
+/// \ingroup matching
+///
+/// \brief Weighted perfect matching in general graphs
+///
+/// This class provides an efficient implementation of Edmond's
+/// maximum weighted perfecr matching algorithm. The implementation
+/// is based on extensive use of priority queues and provides
+/// \f$O(nm\log(n))\f$ time complexity.
+///
+/// The maximum weighted matching problem is to find undirected
+/// arcs in the digraph with maximum overall weight and no two of
+/// them shares their endpoints and covers all nodes. The problem
+/// can be formulated with the next linear program:
+/// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
+///\f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} \quad \forall B\in\mathcal{O}\f]
+/// \f[x_e \ge 0\quad \forall e\in E\f]
+/// \f[\max \sum_{e\in E}x_ew_e\f]
+/// where \f$\delta(X)\f$ is the set of arcs incident to a node in
+/// \f$X\f$, \f$\gamma(X)\f$ is the set of arcs with both endpoints in
+/// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality subsets of
+/// the nodes.
+///
+/// The algorithm calculates an optimal matching and a proof of the
+/// optimality. The solution of the dual problem can be used to check
+/// the result of the algorithm. The dual linear problem is the next:
+/// \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge w_{uv} \quad \forall uv\in E\f]
+/// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
+/// \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}\frac{\vert B \vert - 1}{2}z_B\f]
+///
+/// The algorithm can be executed with \c run() or the \c init() and
+/// then the \c start() member functions. After it the matching can
+/// be asked with \c matching() or mate() functions. The dual
+/// solution can be get with \c nodeValue(), \c blossomNum() and \c
+/// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
+/// "BlossomIt" nested class which is able to iterate on the nodes
+/// of a blossom. If the value type is integral then the dual
+/// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
+template <typename _Graph,
+typename _WeightMap = typename _Graph::template EdgeMap<int> >
+class MaxWeightedPerfectMatching {
+public:
+typedef _Graph Graph;
+typedef _WeightMap WeightMap;
+typedef typename WeightMap::Value Value;
+/// \brief Scaling factor for dual solution
+///
+/// Scaling factor for dual solution, it is equal to 4 or 1
+/// according to the value type.
+static const int dualScale =
+std::numeric_limits<Value>::is_integer ? 4 : 1;
+typedef typename Graph::template NodeMap<typename Graph::Arc>
+MatchingMap;
+private:
+TEMPLATE_GRAPH_TYPEDEFS(Graph);
+typedef typename Graph::template NodeMap<Value> NodePotential;
+typedef std::vector<Node> BlossomNodeList;
+struct BlossomVariable {
+int begin, end;
+Value value;
+BlossomVariable(int _begin, int _end, Value _value)
+: begin(_begin), end(_end), value(_value) {}
+};
+typedef std::vector<BlossomVariable> BlossomPotential;
+const Graph& _graph;
+const WeightMap& _weight;
+MatchingMap* _matching;
+NodePotential* _node_potential;
+BlossomPotential _blossom_potential;
+BlossomNodeList _blossom_node_list;
+int _node_num;
+int _blossom_num;
+typedef typename Graph::template NodeMap<int> NodeIntMap;
+typedef typename Graph::template ArcMap<int> ArcIntMap;
+typedef typename Graph::template EdgeMap<int> EdgeIntMap;
+typedef RangeMap<int> IntIntMap;
+enum Status {
+EVEN = -1, MATCHED = 0, ODD = 1
+};
+typedef HeapUnionFind<Value, NodeIntMap> BlossomSet;
+struct BlossomData {
+int tree;
+Status status;
+Arc pred, next;
+Value pot, offset;
+};
+NodeIntMap *_blossom_index;
+BlossomSet *_blossom_set;
+RangeMap<BlossomData>* _blossom_data;
+NodeIntMap *_node_index;
+ArcIntMap *_node_heap_index;
+struct NodeData {
+NodeData(ArcIntMap& node_heap_index)
+: heap(node_heap_index) {}
+int blossom;
+Value pot;
+BinHeap<Value, ArcIntMap> heap;
+std::map<int, Arc> heap_index;
+int tree;
+};
+RangeMap<NodeData>* _node_data;
+typedef ExtendFindEnum<IntIntMap> TreeSet;
+IntIntMap *_tree_set_index;
+TreeSet *_tree_set;
+IntIntMap *_delta2_index;
+BinHeap<Value, IntIntMap> *_delta2;
+EdgeIntMap *_delta3_index;
+BinHeap<Value, EdgeIntMap> *_delta3;
+IntIntMap *_delta4_index;
+BinHeap<Value, IntIntMap> *_delta4;
+Value _delta_sum;
+void createStructures() {
+_node_num = countNodes(_graph);
+_blossom_num = _node_num * 3 / 2;
+if (!_matching) {
+_matching = new MatchingMap(_graph);
+}
+if (!_node_potential) {
+_node_potential = new NodePotential(_graph);
+}
+if (!_blossom_set) {
+_blossom_index = new NodeIntMap(_graph);
+_blossom_set = new BlossomSet(*_blossom_index);
+_blossom_data = new RangeMap<BlossomData>(_blossom_num);
+}
+if (!_node_index) {
+_node_index = new NodeIntMap(_graph);
+_node_heap_index = new ArcIntMap(_graph);
+_node_data = new RangeMap<NodeData>(_node_num,
+NodeData(*_node_heap_index));
+}
+if (!_tree_set) {
+_tree_set_index = new IntIntMap(_blossom_num);
+_tree_set = new TreeSet(*_tree_set_index);
+}
+if (!_delta2) {
+_delta2_index = new IntIntMap(_blossom_num);
+_delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
+}
+if (!_delta3) {
+_delta3_index = new EdgeIntMap(_graph);
+_delta3 = new BinHeap<Value, EdgeIntMap>(*_delta3_index);
+}
+if (!_delta4) {
+_delta4_index = new IntIntMap(_blossom_num);
+_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
+}
+}
+void destroyStructures() {
+_node_num = countNodes(_graph);
+_blossom_num = _node_num * 3 / 2;
+if (_matching) {
+delete _matching;
+}
+if (_node_potential) {
+delete _node_potential;
+}
+if (_blossom_set) {
+delete _blossom_index;
+delete _blossom_set;
+delete _blossom_data;
+}
+if (_node_index) {
+delete _node_index;
+delete _node_heap_index;
+delete _node_data;
+}
+if (_tree_set) {
+delete _tree_set_index;
+delete _tree_set;
+}
+if (_delta2) {
+delete _delta2_index;
+delete _delta2;
+}
+if (_delta3) {
+delete _delta3_index;
+delete _delta3;
+}
+if (_delta4) {
+delete _delta4_index;
+delete _delta4;
+}
+}
+void matchedToEven(int blossom, int tree) {
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+if (!_blossom_set->trivial(blossom)) {
+(*_blossom_data)[blossom].pot -=
+2 * (_delta_sum - (*_blossom_data)[blossom].offset);
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+_blossom_set->increase(n, std::numeric_limits<Value>::max());
+int ni = (*_node_index)[n];
+(*_node_data)[ni].heap.clear();
+(*_node_data)[ni].heap_index.clear();
+(*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+_delta3->push(e, rw / 2);
+}
+} else {
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[vi].heap_index.find(tree);
+if (it != (*_node_data)[vi].heap_index.end()) {
+if ((*_node_data)[vi].heap[it->second] > rw) {
+(*_node_data)[vi].heap.replace(it->second, e);
+(*_node_data)[vi].heap.decrease(e, rw);
+it->second = e;
+}
+} else {
+(*_node_data)[vi].heap.push(e, rw);
+(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+}
+if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+if ((*_blossom_data)[vb].status == MATCHED) {
+if (_delta2->state(vb) != _delta2->IN_HEAP) {
+_delta2->push(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset){
+_delta2->decrease(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+}
+}
+}
+}
+}
+}
+(*_blossom_data)[blossom].offset = 0;
+}
+void matchedToOdd(int blossom) {
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+(*_blossom_data)[blossom].offset += _delta_sum;
+if (!_blossom_set->trivial(blossom)) {
+_delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
+(*_blossom_data)[blossom].offset);
+}
+}
+void evenToMatched(int blossom, int tree) {
+if (!_blossom_set->trivial(blossom)) {
+(*_blossom_data)[blossom].pot += 2 * _delta_sum;
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+int ni = (*_node_index)[n];
+(*_node_data)[ni].pot -= _delta_sum;
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if (vb == blossom) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+} else if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) == _delta3->IN_HEAP) {
+_delta3->erase(e);
+}
+int vt = _tree_set->find(vb);
+if (vt != tree) {
+Arc r = _graph.oppositeArc(e);
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[ni].heap_index.find(vt);
+if (it != (*_node_data)[ni].heap_index.end()) {
+if ((*_node_data)[ni].heap[it->second] > rw) {
+(*_node_data)[ni].heap.replace(it->second, r);
+(*_node_data)[ni].heap.decrease(r, rw);
+it->second = r;
+}
+} else {
+(*_node_data)[ni].heap.push(r, rw);
+(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
+}
+if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
+_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
+if (_delta2->state(blossom) != _delta2->IN_HEAP) {
+_delta2->push(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+} else if ((*_delta2)[blossom] >
+_blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset){
+_delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+}
+}
+}
+} else {
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[vi].heap_index.find(tree);
+if (it != (*_node_data)[vi].heap_index.end()) {
+(*_node_data)[vi].heap.erase(it->second);
+(*_node_data)[vi].heap_index.erase(it);
+if ((*_node_data)[vi].heap.empty()) {
+_blossom_set->increase(v, std::numeric_limits<Value>::max());
+} else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
+_blossom_set->increase(v, (*_node_data)[vi].heap.prio());
+}
+if ((*_blossom_data)[vb].status == MATCHED) {
+if (_blossom_set->classPrio(vb) ==
+std::numeric_limits<Value>::max()) {
+_delta2->erase(vb);
+} else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset) {
+_delta2->increase(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+}
+}
+}
+}
+}
+}
+}
+void oddToMatched(int blossom) {
+(*_blossom_data)[blossom].offset -= _delta_sum;
+if (_blossom_set->classPrio(blossom) !=
+std::numeric_limits<Value>::max()) {
+_delta2->push(blossom, _blossom_set->classPrio(blossom) -
+(*_blossom_data)[blossom].offset);
+}
+if (!_blossom_set->trivial(blossom)) {
+_delta4->erase(blossom);
+}
+}
+void oddToEven(int blossom, int tree) {
+if (!_blossom_set->trivial(blossom)) {
+_delta4->erase(blossom);
+(*_blossom_data)[blossom].pot -=
+2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
+}
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
+n != INVALID; ++n) {
+int ni = (*_node_index)[n];
+_blossom_set->increase(n, std::numeric_limits<Value>::max());
+(*_node_data)[ni].heap.clear();
+(*_node_data)[ni].heap_index.clear();
+(*_node_data)[ni].pot +=
+2 * _delta_sum - (*_blossom_data)[blossom].offset;
+for (InArcIt e(_graph, n); e != INVALID; ++e) {
+Node v = _graph.source(e);
+int vb = _blossom_set->find(v);
+int vi = (*_node_index)[v];
+Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
+dualScale * _weight[e];
+if ((*_blossom_data)[vb].status == EVEN) {
+if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
+_delta3->push(e, rw / 2);
+}
+} else {
+typename std::map<int, Arc>::iterator it =
+(*_node_data)[vi].heap_index.find(tree);
+if (it != (*_node_data)[vi].heap_index.end()) {
+if ((*_node_data)[vi].heap[it->second] > rw) {
+(*_node_data)[vi].heap.replace(it->second, e);
+(*_node_data)[vi].heap.decrease(e, rw);
+it->second = e;
+}
+} else {
+(*_node_data)[vi].heap.push(e, rw);
+(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
+}
+if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
+_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
+if ((*_blossom_data)[vb].status == MATCHED) {
+if (_delta2->state(vb) != _delta2->IN_HEAP) {
+_delta2->push(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset) {
+_delta2->decrease(vb, _blossom_set->classPrio(vb) -
+(*_blossom_data)[vb].offset);
+}
+}
+}
+}
+}
+}
+(*_blossom_data)[blossom].offset = 0;
+}
+void alternatePath(int even, int tree) {
+int odd;
+evenToMatched(even, tree);
+(*_blossom_data)[even].status = MATCHED;
+while ((*_blossom_data)[even].pred != INVALID) {
+odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
+(*_blossom_data)[odd].status = MATCHED;
+oddToMatched(odd);
+(*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
+even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
+(*_blossom_data)[even].status = MATCHED;
+evenToMatched(even, tree);
+(*_blossom_data)[even].next =
+_graph.oppositeArc((*_blossom_data)[odd].pred);
+}
+}
+void destroyTree(int tree) {
+for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
+if ((*_blossom_data)[b].status == EVEN) {
+(*_blossom_data)[b].status = MATCHED;
+evenToMatched(b, tree);
+} else if ((*_blossom_data)[b].status == ODD) {
+(*_blossom_data)[b].status = MATCHED;
+oddToMatched(b);
+}
+}
+_tree_set->eraseClass(tree);
+}
+void augmentOnArc(const Edge& arc) {
+int left = _blossom_set->find(_graph.u(arc));
+int right = _blossom_set->find(_graph.v(arc));
+int left_tree = _tree_set->find(left);
+alternatePath(left, left_tree);
+destroyTree(left_tree);
+int right_tree = _tree_set->find(right);
+alternatePath(right, right_tree);
+destroyTree(right_tree);
+(*_blossom_data)[left].next = _graph.direct(arc, true);
+(*_blossom_data)[right].next = _graph.direct(arc, false);
+}
+void extendOnArc(const Arc& arc) {
+int base = _blossom_set->find(_graph.target(arc));
+int tree = _tree_set->find(base);
+int odd = _blossom_set->find(_graph.source(arc));
+_tree_set->insert(odd, tree);
+(*_blossom_data)[odd].status = ODD;
+matchedToOdd(odd);
+(*_blossom_data)[odd].pred = arc;
+int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
+(*_blossom_data)[even].pred = (*_blossom_data)[even].next;
+_tree_set->insert(even, tree);
+(*_blossom_data)[even].status = EVEN;
+matchedToEven(even, tree);
+}
+void shrinkOnArc(const Edge& edge, int tree) {
+int nca = -1;
+std::vector<int> left_path, right_path;
+{
+std::set<int> left_set, right_set;
+int left = _blossom_set->find(_graph.u(edge));
+left_path.push_back(left);
+left_set.insert(left);
+int right = _blossom_set->find(_graph.v(edge));
+right_path.push_back(right);
+right_set.insert(right);
+while (true) {
+if ((*_blossom_data)[left].pred == INVALID) break;
+left =
+_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+left_path.push_back(left);
+left =
+_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
+left_path.push_back(left);
+left_set.insert(left);
+if (right_set.find(left) != right_set.end()) {
+nca = left;
+break;
+}
+if ((*_blossom_data)[right].pred == INVALID) break;
+right =
+_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+right_path.push_back(right);
+right =
+_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
+right_path.push_back(right);
+right_set.insert(right);
+if (left_set.find(right) != left_set.end()) {
+nca = right;
+break;
+}
+}
+if (nca == -1) {
+if ((*_blossom_data)[left].pred == INVALID) {
+nca = right;
+while (left_set.find(nca) == left_set.end()) {
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+right_path.push_back(nca);
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+right_path.push_back(nca);
+}
+} else {
+nca = left;
+while (right_set.find(nca) == right_set.end()) {
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+left_path.push_back(nca);
+nca =
+_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
+left_path.push_back(nca);
+}
+}
+}
+}
+std::vector<int> subblossoms;
+Arc prev;
+prev = _graph.direct(edge, true);
+for (int i = 0; left_path[i] != nca; i += 2) {
+subblossoms.push_back(left_path[i]);
+(*_blossom_data)[left_path[i]].next = prev;
+_tree_set->erase(left_path[i]);
+subblossoms.push_back(left_path[i + 1]);
+(*_blossom_data)[left_path[i + 1]].status = EVEN;
+oddToEven(left_path[i + 1], tree);
+_tree_set->erase(left_path[i + 1]);
+prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
+}
+int k = 0;
+while (right_path[k] != nca) ++k;
+subblossoms.push_back(nca);
+(*_blossom_data)[nca].next = prev;
+for (int i = k - 2; i >= 0; i -= 2) {
+subblossoms.push_back(right_path[i + 1]);
+(*_blossom_data)[right_path[i + 1]].status = EVEN;
+oddToEven(right_path[i + 1], tree);
+_tree_set->erase(right_path[i + 1]);
+(*_blossom_data)[right_path[i + 1]].next =
+(*_blossom_data)[right_path[i + 1]].pred;
+subblossoms.push_back(right_path[i]);
+_tree_set->erase(right_path[i]);
+}
+int surface =
+_blossom_set->join(subblossoms.begin(), subblossoms.end());
+for (int i = 0; i < int(subblossoms.size()); ++i) {
+if (!_blossom_set->trivial(subblossoms[i])) {
+(*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
+}
+(*_blossom_data)[subblossoms[i]].status = MATCHED;
+}
+(*_blossom_data)[surface].pot = -2 * _delta_sum;
+(*_blossom_data)[surface].offset = 0;
+(*_blossom_data)[surface].status = EVEN;
+(*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
+(*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
+_tree_set->insert(surface, tree);
+_tree_set->erase(nca);
+}
+void splitBlossom(int blossom) {
+Arc next = (*_blossom_data)[blossom].next;
+Arc pred = (*_blossom_data)[blossom].pred;
+int tree = _tree_set->find(blossom);
+(*_blossom_data)[blossom].status = MATCHED;
+oddToMatched(blossom);
+if (_delta2->state(blossom) == _delta2->IN_HEAP) {
+_delta2->erase(blossom);
+}
+std::vector<int> subblossoms;
+_blossom_set->split(blossom, std::back_inserter(subblossoms));
+Value offset = (*_blossom_data)[blossom].offset;
+int b = _blossom_set->find(_graph.source(pred));
+int d = _blossom_set->find(_graph.source(next));
+int ib = -1, id = -1;
+for (int i = 0; i < int(subblossoms.size()); ++i) {
+if (subblossoms[i] == b) ib = i;
+if (subblossoms[i] == d) id = i;
+(*_blossom_data)[subblossoms[i]].offset = offset;
+if (!_blossom_set->trivial(subblossoms[i])) {
+(*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
+}
+if (_blossom_set->classPrio(subblossoms[i]) !=
+std::numeric_limits<Value>::max()) {
+_delta2->push(subblossoms[i],
+_blossom_set->classPrio(subblossoms[i]) -
+(*_blossom_data)[subblossoms[i]].offset);
+}
+}
+if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
+for (int i = (id + 1) % subblossoms.size();
+i != ib; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+(*_blossom_data)[sb].next =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+}
+for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+int ub = subblossoms[(i + 2) % subblossoms.size()];
+(*_blossom_data)[sb].status = ODD;
+matchedToOdd(sb);
+_tree_set->insert(sb, tree);
+(*_blossom_data)[sb].pred = pred;
+(*_blossom_data)[sb].next =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+pred = (*_blossom_data)[ub].next;
+(*_blossom_data)[tb].status = EVEN;
+matchedToEven(tb, tree);
+_tree_set->insert(tb, tree);
+(*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
+}
+(*_blossom_data)[subblossoms[id]].status = ODD;
+matchedToOdd(subblossoms[id]);
+_tree_set->insert(subblossoms[id], tree);
+(*_blossom_data)[subblossoms[id]].next = next;
+(*_blossom_data)[subblossoms[id]].pred = pred;
+} else {
+for (int i = (ib + 1) % subblossoms.size();
+i != id; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+(*_blossom_data)[sb].next =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+}
+for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
+int sb = subblossoms[i];
+int tb = subblossoms[(i + 1) % subblossoms.size()];
+int ub = subblossoms[(i + 2) % subblossoms.size()];
+(*_blossom_data)[sb].status = ODD;
+matchedToOdd(sb);
+_tree_set->insert(sb, tree);
+(*_blossom_data)[sb].next = next;
+(*_blossom_data)[sb].pred =
+_graph.oppositeArc((*_blossom_data)[tb].next);
+(*_blossom_data)[tb].status = EVEN;
+matchedToEven(tb, tree);
+_tree_set->insert(tb, tree);
+(*_blossom_data)[tb].pred =
+(*_blossom_data)[tb].next =
+_graph.oppositeArc((*_blossom_data)[ub].next);
+next = (*_blossom_data)[ub].next;
+}
+(*_blossom_data)[subblossoms[ib]].status = ODD;
+matchedToOdd(subblossoms[ib]);
+_tree_set->insert(subblossoms[ib], tree);
+(*_blossom_data)[subblossoms[ib]].next = next;
+(*_blossom_data)[subblossoms[ib]].pred = pred;
+}
+_tree_set->erase(blossom);
+}
+void extractBlossom(int blossom, const Node& base, const Arc& matching) {
+if (_blossom_set->trivial(blossom)) {
+int bi = (*_node_index)[base];
+Value pot = (*_node_data)[bi].pot;
+_matching->set(base, matching);
+_blossom_node_list.push_back(base);
+_node_potential->set(base, pot);
+} else {
+Value pot = (*_blossom_data)[blossom].pot;
+int bn = _blossom_node_list.size();
+std::vector<int> subblossoms;
+_blossom_set->split(blossom, std::back_inserter(subblossoms));
+int b = _blossom_set->find(base);
+int ib = -1;
+for (int i = 0; i < int(subblossoms.size()); ++i) {
+if (subblossoms[i] == b) { ib = i; break; }
+}
+for (int i = 1; i < int(subblossoms.size()); i += 2) {
+int sb = subblossoms[(ib + i) % subblossoms.size()];
+int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
+Arc m = (*_blossom_data)[tb].next;
+extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
+extractBlossom(tb, _graph.source(m), m);
+}
+extractBlossom(subblossoms[ib], base, matching);
+int en = _blossom_node_list.size();
+_blossom_potential.push_back(BlossomVariable(bn, en, pot));
+}
+}
+void extractMatching() {
+std::vector<int> blossoms;
+for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
+blossoms.push_back(c);
+}
+for (int i = 0; i < int(blossoms.size()); ++i) {
+Value offset = (*_blossom_data)[blossoms[i]].offset;
+(*_blossom_data)[blossoms[i]].pot += 2 * offset;
+for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
+n != INVALID; ++n) {
+(*_node_data)[(*_node_index)[n]].pot -= offset;
+}
+Arc matching = (*_blossom_data)[blossoms[i]].next;
+Node base = _graph.source(matching);
+extractBlossom(blossoms[i], base, matching);
+}
+}
+public:
+/// \brief Constructor
+///
+/// Constructor.
+MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
+: _graph(graph), _weight(weight), _matching(0),
+_node_potential(0), _blossom_potential(), _blossom_node_list(),
+_node_num(0), _blossom_num(0),
+_blossom_index(0), _blossom_set(0), _blossom_data(0),
+_node_index(0), _node_heap_index(0), _node_data(0),
+_tree_set_index(0), _tree_set(0),
+_delta2_index(0), _delta2(0),
+_delta3_index(0), _delta3(0),
+_delta4_index(0), _delta4(0),
+_delta_sum() {}
+~MaxWeightedPerfectMatching() {
+destroyStructures();
+}
+/// \name Execution control
+/// The simplest way to execute the algorithm is to use the member
+/// \c run() member function.
+///@{
+/// \brief Initialize the algorithm
+///
+/// Initialize the algorithm
+void init() {
+createStructures();
+for (ArcIt e(_graph); e != INVALID; ++e) {
+_node_heap_index->set(e, BinHeap<Value, ArcIntMap>::PRE_HEAP);
+}
+for (EdgeIt e(_graph); e != INVALID; ++e) {
+_delta3_index->set(e, _delta3->PRE_HEAP);
+}
+for (int i = 0; i < _blossom_num; ++i) {
+_delta2_index->set(i, _delta2->PRE_HEAP);
+_delta4_index->set(i, _delta4->PRE_HEAP);
+}
+int index = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+Value max = - std::numeric_limits<Value>::max();
+for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+if (_graph.target(e) == n) continue;
+if ((dualScale * _weight[e]) / 2 > max) {
+max = (dualScale * _weight[e]) / 2;
+}
+}
+_node_index->set(n, index);
+(*_node_data)[index].pot = max;
+int blossom =
+_blossom_set->insert(n, std::numeric_limits<Value>::max());
+_tree_set->insert(blossom);
+(*_blossom_data)[blossom].status = EVEN;
+(*_blossom_data)[blossom].pred = INVALID;
+(*_blossom_data)[blossom].next = INVALID;
+(*_blossom_data)[blossom].pot = 0;
+(*_blossom_data)[blossom].offset = 0;
+++index;
+}
+for (EdgeIt e(_graph); e != INVALID; ++e) {
+int si = (*_node_index)[_graph.u(e)];
+int ti = (*_node_index)[_graph.v(e)];
+if (_graph.u(e) != _graph.v(e)) {
+_delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
+dualScale * _weight[e]) / 2);
+}
+}
+}
+/// \brief Starts the algorithm
+///
+/// Starts the algorithm
+bool start() {
+enum OpType {
+D2, D3, D4
+};
+int unmatched = _node_num;
+while (unmatched > 0) {
+Value d2 = !_delta2->empty() ?
+_delta2->prio() : std::numeric_limits<Value>::max();
+Value d3 = !_delta3->empty() ?
+_delta3->prio() : std::numeric_limits<Value>::max();
+Value d4 = !_delta4->empty() ?
+_delta4->prio() : std::numeric_limits<Value>::max();
+_delta_sum = d2; OpType ot = D2;
+if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
+if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
+if (_delta_sum == std::numeric_limits<Value>::max()) {
+return false;
+}
+switch (ot) {
+case D2:
+{
+int blossom = _delta2->top();
+Node n = _blossom_set->classTop(blossom);
+Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
+extendOnArc(e);
+}
+break;
+case D3:
+{
+Edge e = _delta3->top();
+int left_blossom = _blossom_set->find(_graph.u(e));
+int right_blossom = _blossom_set->find(_graph.v(e));
+if (left_blossom == right_blossom) {
+_delta3->pop();
+} else {
+int left_tree = _tree_set->find(left_blossom);
+int right_tree = _tree_set->find(right_blossom);
+if (left_tree == right_tree) {
+shrinkOnArc(e, left_tree);
+} else {
+augmentOnArc(e);
+unmatched -= 2;
+}
+}
+} break;
+case D4:
+splitBlossom(_delta4->top());
+break;
+}
+}
+extractMatching();
+return true;
+}
+/// \brief Runs %MaxWeightedPerfectMatching algorithm.
+///
+/// This method runs the %MaxWeightedPerfectMatching algorithm.
+///
+/// \note mwm.run() is just a shortcut of the following code.
+/// \code
+///   mwm.init();
+///   mwm.start();
+/// \endcode
+bool run() {
+init();
+return start();
+}
+/// @}
+/// \name Primal solution
+/// Functions for get the primal solution, ie. the matching.
+/// @{
+/// \brief Returns the matching value.
+///
+/// Returns the matching value.
+Value matchingValue() const {
+Value sum = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+if ((*_matching)[n] != INVALID) {
+sum += _weight[(*_matching)[n]];
+}
+}
+return sum /= 2;
+}
+/// \brief Returns true when the arc is in the matching.
+///
+/// Returns true when the arc is in the matching.
+bool matching(const Edge& arc) const {
+return (*_matching)[_graph.u(arc)] == _graph.direct(arc, true);
+}
+/// \brief Returns the incident matching arc.
+///
+/// Returns the incident matching arc from given node.
+Arc matching(const Node& node) const {
+return (*_matching)[node];
+}
+/// \brief Returns the mate of the node.
+///
+/// Returns the adjancent node in a mathcing arc.
+Node mate(const Node& node) const {
+return _graph.target((*_matching)[node]);
+}
+/// @}
+/// \name Dual solution
+/// Functions for get the dual solution.
+/// @{
+/// \brief Returns the value of the dual solution.
+///
+/// Returns the value of the dual solution. It should be equal to
+/// the primal value scaled by \ref dualScale "dual scale".
+Value dualValue() const {
+Value sum = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+sum += nodeValue(n);
+}
+for (int i = 0; i < blossomNum(); ++i) {
+sum += blossomValue(i) * (blossomSize(i) / 2);
+}
+return sum;
+}
+/// \brief Returns the value of the node.
+///
+/// Returns the the value of the node.
+Value nodeValue(const Node& n) const {
+return (*_node_potential)[n];
+}
+/// \brief Returns the number of the blossoms in the basis.
+///
+/// Returns the number of the blossoms in the basis.
+/// \see BlossomIt
+int blossomNum() const {
+return _blossom_potential.size();
+}
+/// \brief Returns the number of the nodes in the blossom.
+///
+/// Returns the number of the nodes in the blossom.
+int blossomSize(int k) const {
+return _blossom_potential[k].end - _blossom_potential[k].begin;
+}
+/// \brief Returns the value of the blossom.
+///
+/// Returns the the value of the blossom.
+/// \see BlossomIt
+Value blossomValue(int k) const {
+return _blossom_potential[k].value;
+}
+/// \brief Lemon iterator for get the items of the blossom.
+///
+/// Lemon iterator for get the nodes of the blossom. This class
+/// provides a common style lemon iterator which gives back a
+/// subset of the nodes.
+class BlossomIt {
+public:
+/// \brief Constructor.
+///
+/// Constructor for get the nodes of the variable.
+BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
+: _algorithm(&algorithm)
+{
+_index = _algorithm->_blossom_potential[variable].begin;
+_last = _algorithm->_blossom_potential[variable].end;
+}
+/// \brief Invalid constructor.
+///
+/// Invalid constructor.
+BlossomIt(Invalid) : _index(-1) {}
+/// \brief Conversion to node.
+///
+/// Conversion to node.
+operator Node() const {
+return _algorithm ? _algorithm->_blossom_node_list[_index] : INVALID;
+}
+/// \brief Increment operator.
+///
+/// Increment operator.
+BlossomIt& operator++() {
+++_index;
+if (_index == _last) {
+_index = -1;
+}
+return *this;
+}
+bool operator==(const BlossomIt& it) const {
+return _index == it._index;
+}
+bool operator!=(const BlossomIt& it) const {
+return _index != it._index;
+}
+private:
+const MaxWeightedPerfectMatching* _algorithm;
+int _last;
+int _index;
+};
+/// @}
+};
+} //END OF NAMESPACE LEMON
+#endif //LEMON_MAX_MATCHING_H

changeset 326	64ad48007fb2
child 327	91d63b8b1a4c