LEMON/LEMON-main Changeset - r326:64ad48007fb2

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Changeset - r326:64ad48007fb2

« 322:6dbd51

327:91d63b »

r326:64ad48007fb2

Mon, 13 Oct 2008 13:56:00

[Not Reviewed]

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deba@inf.elte.hu
deba@inf.elte.hu

Port maximum matching algorithms from svn 3498 (ticket #48)

0 3 3

default

6 files changed with 3550 insertions and 0 deletions:

lemon/max_matching.h

3112

test/max_matching_test.cc

181

test/max_weighted_matching_test.cc

250

lemon/Makefile.am

test/CMakeLists.txt

test/Makefile.am

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lemon/max_matching.h

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 		/* -*- 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 -=
 * (_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 * _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 +=
 * _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 -=
 * (_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 * _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 +=
 * _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

test/max_matching_test.cc

Show inline comments

 		/* -*- 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.
+		 *
 		 */
 		#include <iostream>
 		#include <vector>
 		#include <queue>
 		#include <lemon/math.h>
 		#include <cstdlib>
 		#include "test_tools.h"
 		#include <lemon/list_graph.h>
 		#include <lemon/max_matching.h>
 		using namespace std;
 		using namespace lemon;
 		int main() {
 		  typedef ListGraph Graph;
 		  GRAPH_TYPEDEFS(Graph);
 		  Graph g;
 		  g.clear();
 		  std::vector<Graph::Node> nodes;
 		  for (int i=0; i<13; ++i)
 		      nodes.push_back(g.addNode());
 		  g.addEdge(nodes[0], nodes[0]);
 		  g.addEdge(nodes[6], nodes[10]);
 		  g.addEdge(nodes[5], nodes[10]);
 		  g.addEdge(nodes[4], nodes[10]);
 		  g.addEdge(nodes[3], nodes[11]);
 		  g.addEdge(nodes[1], nodes[6]);
 		  g.addEdge(nodes[4], nodes[7]);
 		  g.addEdge(nodes[1], nodes[8]);
 		  g.addEdge(nodes[0], nodes[8]);
 		  g.addEdge(nodes[3], nodes[12]);
 		  g.addEdge(nodes[6], nodes[9]);
 		  g.addEdge(nodes[9], nodes[11]);
 		  g.addEdge(nodes[2], nodes[10]);
 		  g.addEdge(nodes[10], nodes[8]);
 		  g.addEdge(nodes[5], nodes[8]);
 		  g.addEdge(nodes[6], nodes[3]);
 		  g.addEdge(nodes[0], nodes[5]);
 		  g.addEdge(nodes[6], nodes[12]);
 		  MaxMatching<Graph> max_matching(g);
 		  max_matching.init();
 		  max_matching.startDense();
 		  int s=0;
 		  Graph::NodeMap<Node> mate(g,INVALID);
 		  max_matching.mateMap(mate);
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    if ( mate[v]!=INVALID ) ++s;
+		  }
 		  int size=int(s/2);  //size will be used as the size of a maxmatching
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    max_matching.mate(v);
+		  }
 		  check ( size == max_matching.size(), "mate() returns a different size matching than max_matching.size()" );
 		  Graph::NodeMap<MaxMatching<Graph>::DecompType> pos0(g);
 		  max_matching.decomposition(pos0);
 		  max_matching.init();
 		  max_matching.startSparse();
 		  s=0;
 		  max_matching.mateMap(mate);
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    if ( mate[v]!=INVALID ) ++s;
+		  }
 		  check ( int(s/2) == size, "The size does not equal!" );
 		  Graph::NodeMap<MaxMatching<Graph>::DecompType> pos1(g);
 		  max_matching.decomposition(pos1);
 		  max_matching.run();
 		  s=0;
 		  max_matching.mateMap(mate);
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    if ( mate[v]!=INVALID ) ++s;
+		  }
 		  check ( int(s/2) == size, "The size does not equal!" );
 		  Graph::NodeMap<MaxMatching<Graph>::DecompType> pos2(g);
 		  max_matching.decomposition(pos2);
 		  max_matching.run();
 		  s=0;
 		  max_matching.mateMap(mate);
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    if ( mate[v]!=INVALID ) ++s;
+		  }
 		  check ( int(s/2) == size, "The size does not equal!" );
 		  Graph::NodeMap<MaxMatching<Graph>::DecompType> pos(g);
 		  max_matching.decomposition(pos);
 		  bool ismatching=true;
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    if ( mate[v]!=INVALID ) {
 		      Node u=mate[v];
 		      if (mate[u]!=v) ismatching=false;
+		    }
+		  }
 		  check ( ismatching, "It is not a matching!" );
 		  bool coincide=true;
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		   if ( pos0[v] != pos1[v] || pos1[v]!=pos2[v] || pos2[v]!=pos[v] ) {
 		     coincide=false;
+		    }
+		  }
 		  check ( coincide, "The decompositions do not coincide! " );
 		  bool noarc=true;
 		  for(EdgeIt e(g); e!=INVALID; ++e) {
 		   if ( (pos[g.v(e)]==max_matching.C &&
 		         pos[g.u(e)]==max_matching.D) ||
 		         (pos[g.v(e)]==max_matching.D &&
 		          pos[g.u(e)]==max_matching.C) )
 		      noarc=false;
+		  }
 		  check ( noarc, "There are arcs between D and C!" );
 		  bool oddcomp=true;
 		  Graph::NodeMap<bool> todo(g,true);
 		  int num_comp=0;
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		   if ( pos[v]==max_matching.D && todo[v] ) {
 		      int comp_size=1;
 		      ++num_comp;
 		      std::queue<Node> Q;
 		      Q.push(v);
 		      todo.set(v,false);
 		      while (!Q.empty()) {
 		        Node w=Q.front();
 		        Q.pop();
 		        for(IncEdgeIt e(g,w); e!=INVALID; ++e) {
 		          Node u=g.runningNode(e);
 		          if ( pos[u]==max_matching.D && todo[u] ) {
 		            ++comp_size;
 		            Q.push(u);
 		            todo.set(u,false);
+		          }
+		        }
+		      }
 		      if ( !(comp_size % 2) ) oddcomp=false;
+		    }
+		  }
 		  check ( oddcomp, "A component of g[D] is not odd." );
 		  int barrier=0;
 		  for(NodeIt v(g); v!=INVALID; ++v) {
 		    if ( pos[v]==max_matching.A ) ++barrier;
+		  }
 		  int expected_size=int( countNodes(g)-num_comp+barrier)/2;
 		  check ( size==expected_size, "The size of the matching is wrong." );
 		  return 0;
+		}

test/max_weighted_matching_test.cc

Show inline comments

 		/* -*- 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.
+		 *
 		 */
 		#include <iostream>
 		#include <sstream>
 		#include <vector>
 		#include <queue>
 		#include <lemon/math.h>
 		#include <cstdlib>
 		#include "test_tools.h"
 		#include <lemon/smart_graph.h>
 		#include <lemon/max_matching.h>
 		#include <lemon/lgf_reader.h>
 		using namespace std;
 		using namespace lemon;
 		GRAPH_TYPEDEFS(SmartGraph);
 		const int lgfn = 3;
 		const std::string lgf[lgfn] = {
 		  "@nodes\n"
 		  "label\n"
 		  "0\n"
 		  "1\n"
 		  "2\n"
 		  "3\n"
 		  "4\n"
 		  "5\n"
 		  "6\n"
 		  "7\n"
 		  "@edges\n"
 		  "label        weight\n"
 		  "7    4       0       984\n"
 		  "0    7       1       73\n"
 		  "7    1       2       204\n"
 		  "2    3       3       583\n"
 		  "2    7       4       565\n"
 		  "2    1       5       582\n"
 		  "0    4       6       551\n"
 		  "2    5       7       385\n"
 		  "1    5       8       561\n"
 		  "5    3       9       484\n"
 		  "7    5       10      904\n"
 		  "3    6       11      47\n"
 		  "7    6       12      888\n"
 		  "3    0       13      747\n"
 		  "6    1       14      310\n",
 		  "@nodes\n"
 		  "label\n"
 		  "0\n"
 		  "1\n"
 		  "2\n"
 		  "3\n"
 		  "4\n"
 		  "5\n"
 		  "6\n"
 		  "7\n"
 		  "@edges\n"
 		  "label        weight\n"
 		  "2    5       0       710\n"
 		  "0    5       1       241\n"
 		  "2    4       2       856\n"
 		  "2    6       3       762\n"
 		  "4    1       4       747\n"
 		  "6    1       5       962\n"
 		  "4    7       6       723\n"
 		  "1    7       7       661\n"
 		  "2    3       8       376\n"
 		  "1    0       9       416\n"
 		  "6    7       10      391\n",
 		  "@nodes\n"
 		  "label\n"
 		  "0\n"
 		  "1\n"
 		  "2\n"
 		  "3\n"
 		  "4\n"
 		  "5\n"
 		  "6\n"
 		  "7\n"
 		  "@edges\n"
 		  "label        weight\n"
 		  "6    2       0       553\n"
 		  "0    7       1       653\n"
 		  "6    3       2       22\n"
 		  "4    7       3       846\n"
 		  "7    2       4       981\n"
 		  "7    6       5       250\n"
 		  "5    2       6       539\n"
 		};
 		void checkMatching(const SmartGraph& graph,
 		                   const SmartGraph::EdgeMap<int>& weight,
 		                   const MaxWeightedMatching<SmartGraph>& mwm) {
 		  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
 		    if (graph.u(e) == graph.v(e)) continue;
 		    int rw =
 		      mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
 		    for (int i = 0; i < mwm.blossomNum(); ++i) {
 		      bool s = false, t = false;
 		      for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
 		           n != INVALID; ++n) {
 		        if (graph.u(e) == n) s = true;
 		        if (graph.v(e) == n) t = true;
+		      }
 		      if (s == true && t == true) {
 		        rw += mwm.blossomValue(i);
+		      }
+		    }
 		    rw -= weight[e] * mwm.dualScale;
 		    check(rw >= 0, "Negative reduced weight");
 		    check(rw == 0 || !mwm.matching(e),
 		          "Non-zero reduced weight on matching arc");
+		  }
 		  int pv = 0;
 		  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
 		    if (mwm.matching(n) != INVALID) {
 		      check(mwm.nodeValue(n) >= 0, "Invalid node value");
 		      pv += weight[mwm.matching(n)];
 		      SmartGraph::Node o = graph.target(mwm.matching(n));
 		      check(mwm.mate(n) == o, "Invalid matching");
 		      check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
 		            "Invalid matching");
 		    } else {
 		      check(mwm.mate(n) == INVALID, "Invalid matching");
 		      check(mwm.nodeValue(n) == 0, "Invalid matching");
+		    }
+		  }
 		  int dv = 0;
 		  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
 		    dv += mwm.nodeValue(n);
+		  }
 		  for (int i = 0; i < mwm.blossomNum(); ++i) {
 		    check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
 		    check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
 		    dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
+		  }
 		  check(pv * mwm.dualScale == dv * 2, "Wrong duality");
 		  return;
+		}
 		void checkPerfectMatching(const SmartGraph& graph,
 		                          const SmartGraph::EdgeMap<int>& weight,
 		                          const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
 		  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
 		    if (graph.u(e) == graph.v(e)) continue;
 		    int rw =
 		      mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
 		    for (int i = 0; i < mwpm.blossomNum(); ++i) {
 		      bool s = false, t = false;
 		      for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
 		           n != INVALID; ++n) {
 		        if (graph.u(e) == n) s = true;
 		        if (graph.v(e) == n) t = true;
+		      }
 		      if (s == true && t == true) {
 		        rw += mwpm.blossomValue(i);
+		      }
+		    }
 		    rw -= weight[e] * mwpm.dualScale;
 		    check(rw >= 0, "Negative reduced weight");
 		    check(rw == 0 || !mwpm.matching(e),
 		          "Non-zero reduced weight on matching arc");
+		  }
 		  int pv = 0;
 		  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
 		    check(mwpm.matching(n) != INVALID, "Non perfect");
 		    pv += weight[mwpm.matching(n)];
 		    SmartGraph::Node o = graph.target(mwpm.matching(n));
 		    check(mwpm.mate(n) == o, "Invalid matching");
 		    check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
 		          "Invalid matching");
+		  }
 		  int dv = 0;
 		  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
 		    dv += mwpm.nodeValue(n);
+		  }
 		  for (int i = 0; i < mwpm.blossomNum(); ++i) {
 		    check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
 		    check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
 		    dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
+		  }
 		  check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
 		  return;
+		}
 		int main() {
 		  for (int i = 0; i < lgfn; ++i) {
 		    SmartGraph graph;
 		    SmartGraph::EdgeMap<int> weight(graph);
 		    istringstream lgfs(lgf[i]);
 		    graphReader(graph, lgfs).
 		      edgeMap("weight", weight).run();
 		    MaxWeightedMatching<SmartGraph> mwm(graph, weight);
 		    mwm.run();
 		    checkMatching(graph, weight, mwm);
 		    MaxMatching<SmartGraph> mm(graph);
 		    mm.run();
 		    MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
 		    bool perfect = mwpm.run();
 		    check(perfect == (mm.size() * 2 == countNodes(graph)),
 		          "Perfect matching found");
 		    if (perfect) {
 		      checkPerfectMatching(graph, weight, mwpm);
+		    }
+		  }
 		  return 0;
+		}

lemon/Makefile.am

Show inline comments

@@ -35,6 +35,7 @@
 			lemon/list_graph.h \
 			lemon/maps.h \
 			lemon/math.h \
 			lemon/max_matching.h \
 			lemon/path.h \
 		        lemon/random.h \
 			lemon/smart_graph.h \

test/CMakeLists.txt

Show inline comments

@@ -16,6 +16,8 @@
 		  heap_test
 		  kruskal_test
 		  maps_test
 		  max_matching_test
 		  max_weighted_matching_test
 		  random_test
 		  path_test
 		  time_measure_test

test/Makefile.am

Show inline comments

@@ -19,6 +19,8 @@
 			test/heap_test \
 			test/kruskal_test \
 		        test/maps_test \
 			test/max_matching_test \
 			test/max_weighted_matching_test \
 		        test/random_test \
 		        test/path_test \
 		        test/test_tools_fail \
@@ -42,6 +44,8 @@
 		test_heap_test_SOURCES = test/heap_test.cc
 		test_kruskal_test_SOURCES = test/kruskal_test.cc
 		test_maps_test_SOURCES = test/maps_test.cc
 		test_max_matching_test_SOURCES = test/max_matching_test.cc
 		test_max_weighted_matching_test_SOURCES = test/max_weighted_matching_test.cc
 		test_path_test_SOURCES = test/path_test.cc
 		test_random_test_SOURCES = test/random_test.cc
 		test_test_tools_fail_SOURCES = test/test_tools_fail.cc

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