jacint@1077: /* -*- C++ -*-
jacint@1077:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@1956:  * Copyright (C) 2003-2006
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
jacint@1077:  *
jacint@1077:  * Permission to use, modify and distribute this software is granted
jacint@1077:  * provided that this copyright notice appears in all copies. For
jacint@1077:  * precise terms see the accompanying LICENSE file.
jacint@1077:  *
jacint@1077:  * This software is provided "AS IS" with no warranty of any kind,
jacint@1077:  * express or implied, and with no claim as to its suitability for any
jacint@1077:  * purpose.
jacint@1077:  *
jacint@1077:  */
jacint@1077: 
jacint@1077: #ifndef LEMON_MAX_MATCHING_H
jacint@1077: #define LEMON_MAX_MATCHING_H
jacint@1077: 
jacint@1077: #include <queue>
jacint@1093: #include <lemon/invalid.h>
jacint@1093: #include <lemon/unionfind.h>
jacint@1077: #include <lemon/graph_utils.h>
jacint@1077: 
jacint@1077: ///\ingroup galgs
jacint@1077: ///\file
jacint@1077: ///\brief Maximum matching algorithm.
jacint@1077: 
jacint@1077: namespace lemon {
jacint@1077: 
jacint@1077:   /// \addtogroup galgs
jacint@1077:   /// @{
jacint@1077: 
jacint@1077:   ///Edmonds' alternating forest maximum matching algorithm.
jacint@1077: 
jacint@1077:   ///This class provides Edmonds' alternating forest matching
jacint@1077:   ///algorithm. The starting matching (if any) can be passed to the
jacint@1077:   ///algorithm using read-in functions \ref readNMapNode, \ref
jacint@1077:   ///readNMapEdge or \ref readEMapBool depending on the container. The
jacint@1077:   ///resulting maximum matching can be attained by write-out functions
jacint@1077:   ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
jacint@1077:   ///depending on the preferred container. 
jacint@1077:   ///
jacint@1077:   ///The dual side of a matching is a map of the nodes to
jacint@1077:   ///MaxMatching::pos_enum, having values D, A and C showing the
jacint@1077:   ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
jacint@1077:   ///a graph with factor-critical components, the nodes in A form the
jacint@1077:   ///barrier, and the nodes in C induce a graph having a perfect
jacint@1077:   ///matching. This decomposition can be attained by calling \ref
jacint@1090:   ///writePos after running the algorithm. 
jacint@1077:   ///
jacint@1077:   ///\param Graph The undirected graph type the algorithm runs on.
jacint@1077:   ///
jacint@1077:   ///\author Jacint Szabo  
jacint@1077:   template <typename Graph>
jacint@1077:   class MaxMatching {
jacint@1165: 
jacint@1165:   protected:
jacint@1165: 
jacint@1077:     typedef typename Graph::Node Node;
jacint@1077:     typedef typename Graph::Edge Edge;
klao@1909:     typedef typename Graph::UEdge UEdge;
klao@1909:     typedef typename Graph::UEdgeIt UEdgeIt;
jacint@1077:     typedef typename Graph::NodeIt NodeIt;
jacint@1077:     typedef typename Graph::IncEdgeIt IncEdgeIt;
jacint@1077: 
jacint@1077:     typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;
jacint@1077: 
jacint@1077:   public:
jacint@1077:     
jacint@1077:     ///Indicates the Gallai-Edmonds decomposition of the graph.
jacint@1077: 
jacint@1077:     ///Indicates the Gallai-Edmonds decomposition of the graph, which
jacint@1077:     ///shows an upper bound on the size of a maximum matching. The
jacint@1077:     ///nodes with pos_enum \c D induce a graph with factor-critical
jacint@1077:     ///components, the nodes in \c A form the canonical barrier, and the
jacint@1077:     ///nodes in \c C induce a graph having a perfect matching. 
jacint@1077:     enum pos_enum {
jacint@1077:       D=0,
jacint@1077:       A=1,
jacint@1077:       C=2
jacint@1077:     }; 
jacint@1077: 
jacint@1165:   protected:
jacint@1077: 
jacint@1077:     static const int HEUR_density=2;
jacint@1077:     const Graph& g;
jacint@1093:     typename Graph::template NodeMap<Node> _mate;
jacint@1077:     typename Graph::template NodeMap<pos_enum> position;
jacint@1077:      
jacint@1077:   public:
jacint@1077:     
jacint@1093:     MaxMatching(const Graph& _g) : g(_g), _mate(_g,INVALID), position(_g) {}
jacint@1077: 
jacint@1077:     ///Runs Edmonds' algorithm.
jacint@1077: 
jacint@1077:     ///Runs Edmonds' algorithm for sparse graphs (number of edges <
jacint@1077:     ///2*number of nodes), and a heuristical Edmonds' algorithm with a
jacint@1090:     ///heuristic of postponing shrinks for dense graphs. 
alpar@1587:     void run() {
klao@1909:       if ( countUEdges(g) < HEUR_density*countNodes(g) ) {
alpar@1587: 	greedyMatching();
alpar@1587: 	runEdmonds(0);
alpar@1587:       } else runEdmonds(1);
alpar@1587:     }
alpar@1587: 
jacint@1077: 
jacint@1077:     ///Runs Edmonds' algorithm.
jacint@1077:     
jacint@1077:     ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
jacint@1077:     ///Edmonds' algorithm with a heuristic of postponing shrinks,
jacint@1090:     ///giving a faster algorithm for dense graphs.  
alpar@1587:     void runEdmonds( int heur = 1 ) {
alpar@1587:       
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v)
alpar@1587: 	position.set(v,C);      
alpar@1587:       
alpar@1587:       typename Graph::template NodeMap<Node> ear(g,INVALID); 
alpar@1587:       //undefined for the base nodes of the blossoms (i.e. for the
alpar@1587:       //representative elements of UFE blossom) and for the nodes in C 
alpar@1587:       
alpar@1587:       typename UFE::MapType blossom_base(g);
alpar@1587:       UFE blossom(blossom_base);
alpar@1587:       typename UFE::MapType tree_base(g);
alpar@1587:       UFE tree(tree_base);
alpar@1587:       //If these UFE's would be members of the class then also
alpar@1587:       //blossom_base and tree_base should be a member.
alpar@1587:       
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v) {
alpar@1587: 	if ( position[v]==C && _mate[v]==INVALID ) {
alpar@1587: 	  blossom.insert(v);
alpar@1587: 	  tree.insert(v); 
alpar@1587: 	  position.set(v,D);
alpar@1587: 	  if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
alpar@1587: 	  else normShrink( v, ear, blossom, tree );
alpar@1587: 	}
alpar@1587:       }
alpar@1587:     }
alpar@1587: 
jacint@1077: 
jacint@1077:     ///Finds a greedy matching starting from the actual matching.
jacint@1077:     
jacint@1077:     ///Starting form the actual matching stored, it finds a maximal
jacint@1077:     ///greedy matching.
alpar@1587:     void greedyMatching() {
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v)
alpar@1587: 	if ( _mate[v]==INVALID ) {
alpar@1587: 	  for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
alpar@1587: 	    Node y=g.runningNode(e);
alpar@1587: 	    if ( _mate[y]==INVALID && y!=v ) {
alpar@1587: 	      _mate.set(v,y);
alpar@1587: 	      _mate.set(y,v);
alpar@1587: 	      break;
alpar@1587: 	    }
alpar@1587: 	  }
alpar@1587: 	} 
alpar@1587:     }
jacint@1077: 
jacint@1077:     ///Returns the size of the actual matching stored.
jacint@1077: 
jacint@1077:     ///Returns the size of the actual matching stored. After \ref
jacint@1077:     ///run() it returns the size of a maximum matching in the graph.
alpar@1587:     int size() const {
alpar@1587:       int s=0;
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v) {
alpar@1587: 	if ( _mate[v]!=INVALID ) {
alpar@1587: 	  ++s;
alpar@1587: 	}
alpar@1587:       }
alpar@1587:       return s/2;
alpar@1587:     }
alpar@1587: 
jacint@1077: 
jacint@1077:     ///Resets the actual matching to the empty matching.
jacint@1077: 
jacint@1077:     ///Resets the actual matching to the empty matching.  
jacint@1077:     ///
alpar@1587:     void resetMatching() {
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v)
alpar@1587: 	_mate.set(v,INVALID);      
alpar@1587:     }
jacint@1077: 
jacint@1093:     ///Returns the mate of a node in the actual matching.
jacint@1093: 
jacint@1093:     ///Returns the mate of a \c node in the actual matching. 
jacint@1093:     ///Returns INVALID if the \c node is not covered by the actual matching. 
jacint@1093:     Node mate(Node& node) const {
jacint@1093:       return _mate[node];
jacint@1093:     } 
jacint@1093: 
jacint@1165:     ///Reads a matching from a \c Node valued \c Node map.
jacint@1077: 
jacint@1165:     ///Reads a matching from a \c Node valued \c Node map. This map
jacint@1165:     ///must be \e symmetric, i.e. if \c map[u]==v then \c map[v]==u
jacint@1165:     ///must hold, and \c uv will be an edge of the matching.
jacint@1077:     template<typename NMapN>
jacint@1077:     void readNMapNode(NMapN& map) {
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	_mate.set(v,map[v]);   
jacint@1077:       } 
jacint@1077:     } 
jacint@1077:     
jacint@1165:     ///Writes the stored matching to a \c Node valued \c Node map.
jacint@1077: 
jacint@1165:     ///Writes the stored matching to a \c Node valued \c Node map. The
jacint@1077:     ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
jacint@1077:     ///map[v]==u will hold, and now \c uv is an edge of the matching.
jacint@1077:     template<typename NMapN>
jacint@1077:     void writeNMapNode (NMapN& map) const {
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	map.set(v,_mate[v]);   
jacint@1077:       } 
jacint@1077:     } 
jacint@1077: 
klao@1909:     ///Reads a matching from an \c UEdge valued \c Node map.
jacint@1077: 
klao@1909:     ///Reads a matching from an \c UEdge valued \c Node map. \c
klao@1909:     ///map[v] must be an \c UEdge incident to \c v. This map must
jacint@1165:     ///have the property that if \c g.oppositeNode(u,map[u])==v then
jacint@1165:     ///\c \c g.oppositeNode(v,map[v])==u holds, and now some edge
marci@1172:     ///joining \c u to \c v will be an edge of the matching.
jacint@1077:     template<typename NMapE>
jacint@1077:     void readNMapEdge(NMapE& map) {
jacint@1077:      for(NodeIt v(g); v!=INVALID; ++v) {
klao@1909:        UEdge e=map[v];
jacint@1165: 	if ( e!=INVALID )
jacint@1166: 	  _mate.set(v,g.oppositeNode(v,e));
jacint@1077:       } 
jacint@1077:     } 
jacint@1077:     
klao@1909:     ///Writes the matching stored to an \c UEdge valued \c Node map.
jacint@1077: 
klao@1909:     ///Writes the stored matching to an \c UEdge valued \c Node
klao@1909:     ///map. \c map[v] will be an \c UEdge incident to \c v. This
jacint@1165:     ///map will have the property that if \c g.oppositeNode(u,map[u])
jacint@1165:     ///== v then \c map[u]==map[v] holds, and now this edge is an edge
jacint@1165:     ///of the matching.
jacint@1077:     template<typename NMapE>
jacint@1077:     void writeNMapEdge (NMapE& map)  const {
jacint@1077:       typename Graph::template NodeMap<bool> todo(g,true); 
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	if ( todo[v] && _mate[v]!=INVALID ) {
jacint@1093: 	  Node u=_mate[v];
jacint@1077: 	  for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
klao@1158: 	    if ( g.runningNode(e) == u ) {
jacint@1077: 	      map.set(u,e);
jacint@1077: 	      map.set(v,e);
jacint@1077: 	      todo.set(u,false);
jacint@1077: 	      todo.set(v,false);
jacint@1077: 	      break;
jacint@1077: 	    }
jacint@1077: 	  }
jacint@1077: 	}
jacint@1077:       } 
jacint@1077:     }
jacint@1077: 
jacint@1077: 
jacint@1165:     ///Reads a matching from a \c bool valued \c Edge map.
jacint@1077:     
jacint@1165:     ///Reads a matching from a \c bool valued \c Edge map. This map
jacint@1165:     ///must have the property that there are no two incident edges \c
jacint@1165:     ///e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
jacint@1077:     ///map[e]==true form the matching.
jacint@1077:     template<typename EMapB>
jacint@1077:     void readEMapBool(EMapB& map) {
klao@1909:       for(UEdgeIt e(g); e!=INVALID; ++e) {
jacint@1077: 	if ( map[e] ) {
jacint@1077: 	  Node u=g.source(e);	  
jacint@1077: 	  Node v=g.target(e);
jacint@1093: 	  _mate.set(u,v);
jacint@1093: 	  _mate.set(v,u);
jacint@1077: 	} 
jacint@1077:       } 
jacint@1077:     }
jacint@1077: 
jacint@1077: 
jacint@1165:     ///Writes the matching stored to a \c bool valued \c Edge map.
jacint@1077: 
jacint@1165:     ///Writes the matching stored to a \c bool valued \c Edge
jacint@1165:     ///map. This map will have the property that there are no two
jacint@1165:     ///incident edges \c e, \c f with \c map[e]==map[f]==true. The
jacint@1165:     ///edges \c e with \c map[e]==true form the matching.
jacint@1077:     template<typename EMapB>
jacint@1077:     void writeEMapBool (EMapB& map) const {
klao@1909:       for(UEdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
jacint@1077: 
jacint@1077:       typename Graph::template NodeMap<bool> todo(g,true); 
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	if ( todo[v] && _mate[v]!=INVALID ) {
jacint@1093: 	  Node u=_mate[v];
jacint@1077: 	  for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
klao@1158: 	    if ( g.runningNode(e) == u ) {
jacint@1077: 	      map.set(e,true);
jacint@1077: 	      todo.set(u,false);
jacint@1077: 	      todo.set(v,false);
jacint@1077: 	      break;
jacint@1077: 	    }
jacint@1077: 	  }
jacint@1077: 	}
jacint@1077:       } 
jacint@1077:     }
jacint@1077: 
jacint@1077: 
jacint@1077:     ///Writes the canonical decomposition of the graph after running
jacint@1077:     ///the algorithm.
jacint@1077: 
jacint@1090:     ///After calling any run methods of the class, it writes the
jacint@1090:     ///Gallai-Edmonds canonical decomposition of the graph. \c map
jacint@1090:     ///must be a node map of \ref pos_enum 's.
jacint@1077:     template<typename NMapEnum>
jacint@1077:     void writePos (NMapEnum& map) const {
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v)  map.set(v,position[v]);
jacint@1077:     }
jacint@1077: 
jacint@1077:   private: 
jacint@1077: 
jacint@1165:  
jacint@1077:     void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 		    UFE& blossom, UFE& tree);
jacint@1077: 
alpar@1234:     void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 		    UFE& blossom, UFE& tree);
jacint@1077: 
alpar@1234:     bool noShrinkStep(Node x, typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 		      UFE& blossom, UFE& tree, std::queue<Node>& Q);
jacint@1077: 
alpar@1234:     void shrinkStep(Node& top, Node& middle, Node& bottom,
alpar@1234: 		    typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 		    UFE& blossom, UFE& tree, std::queue<Node>& Q);
jacint@1077: 
alpar@1234:     void augment(Node x, typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 		 UFE& blossom, UFE& tree);
jacint@1077: 
jacint@1077:   };
jacint@1077: 
jacint@1077: 
jacint@1077:   // **********************************************************************
jacint@1077:   //  IMPLEMENTATIONS
jacint@1077:   // **********************************************************************
jacint@1077: 
jacint@1077: 
jacint@1077:   template <typename Graph>
jacint@1077:   void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 				      UFE& blossom, UFE& tree) {
jacint@1077: 
jacint@1077:     std::queue<Node> Q;   //queue of the totally unscanned nodes
jacint@1077:     Q.push(v);  
jacint@1077:     std::queue<Node> R;   
jacint@1077:     //queue of the nodes which must be scanned for a possible shrink
jacint@1077:       
jacint@1077:     while ( !Q.empty() ) {
jacint@1077:       Node x=Q.front();
jacint@1077:       Q.pop();
jacint@1077:       if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
jacint@1077:       else R.push(x);
jacint@1077:     }
jacint@1077:       
jacint@1077:     while ( !R.empty() ) {
jacint@1077:       Node x=R.front();
jacint@1077:       R.pop();
jacint@1077: 	
jacint@1077:       for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
klao@1158: 	Node y=g.runningNode(e);
jacint@1077: 
jacint@1077: 	if ( position[y] == D && blossom.find(x) != blossom.find(y) ) { 
jacint@1077: 	  //x and y must be in the same tree
jacint@1077: 	
jacint@1077: 	  typename Graph::template NodeMap<bool> path(g,false);
jacint@1077: 
jacint@1077: 	  Node b=blossom.find(x);
jacint@1077: 	  path.set(b,true);
jacint@1093: 	  b=_mate[b];
jacint@1077: 	  while ( b!=INVALID ) { 
jacint@1077: 	    b=blossom.find(ear[b]);
jacint@1077: 	    path.set(b,true);
jacint@1093: 	    b=_mate[b];
jacint@1077: 	  } //going till the root
jacint@1077: 	
jacint@1077: 	  Node top=y;
jacint@1077: 	  Node middle=blossom.find(top);
jacint@1077: 	  Node bottom=x;
jacint@1077: 	  while ( !path[middle] )
jacint@1077: 	    shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077: 		  
jacint@1077: 	  Node base=middle;
jacint@1077: 	  top=x;
jacint@1077: 	  middle=blossom.find(top);
jacint@1077: 	  bottom=y;
jacint@1077: 	  Node blossom_base=blossom.find(base);
jacint@1077: 	  while ( middle!=blossom_base )
jacint@1077: 	    shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077: 		  
jacint@1077: 	  blossom.makeRep(base);
jacint@1077: 	} // if shrink is needed
jacint@1077: 
jacint@1077: 	while ( !Q.empty() ) {
jacint@1077: 	  Node x=Q.front();
jacint@1077: 	  Q.pop();
jacint@1077: 	  if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
jacint@1077: 	  else R.push(x);
jacint@1077: 	}
jacint@1077:       } //for e
jacint@1077:     } // while ( !R.empty() )
jacint@1077:   }
jacint@1077: 
jacint@1077: 
jacint@1077:   template <typename Graph>
alpar@1234:   void MaxMatching<Graph>::normShrink(Node v,
alpar@1234: 				      typename Graph::template
alpar@1234: 				      NodeMap<Node>& ear,  
jacint@1077: 				      UFE& blossom, UFE& tree) {
jacint@1077:     std::queue<Node> Q;   //queue of the unscanned nodes
jacint@1077:     Q.push(v);  
jacint@1077:     while ( !Q.empty() ) {
jacint@1077: 
jacint@1077:       Node x=Q.front();
jacint@1077:       Q.pop();
jacint@1077: 	
jacint@1077:       for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
klao@1158: 	Node y=g.runningNode(e);
jacint@1077: 	      
jacint@1077: 	switch ( position[y] ) {
jacint@1077: 	case D:          //x and y must be in the same tree
jacint@1077: 
jacint@1077: 	  if ( blossom.find(x) != blossom.find(y) ) { //shrink
jacint@1077: 	    typename Graph::template NodeMap<bool> path(g,false);
jacint@1077: 	      
jacint@1077: 	    Node b=blossom.find(x);
jacint@1077: 	    path.set(b,true);
jacint@1093: 	    b=_mate[b];
jacint@1077: 	    while ( b!=INVALID ) { 
jacint@1077: 	      b=blossom.find(ear[b]);
jacint@1077: 	      path.set(b,true);
jacint@1093: 	      b=_mate[b];
jacint@1077: 	    } //going till the root
jacint@1077: 	
jacint@1077: 	    Node top=y;
jacint@1077: 	    Node middle=blossom.find(top);
jacint@1077: 	    Node bottom=x;
jacint@1077: 	    while ( !path[middle] )
jacint@1077: 	      shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077: 		
jacint@1077: 	    Node base=middle;
jacint@1077: 	    top=x;
jacint@1077: 	    middle=blossom.find(top);
jacint@1077: 	    bottom=y;
jacint@1077: 	    Node blossom_base=blossom.find(base);
jacint@1077: 	    while ( middle!=blossom_base )
jacint@1077: 	      shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
jacint@1077: 		
jacint@1077: 	    blossom.makeRep(base);
jacint@1077: 	  }
jacint@1077: 	  break;
jacint@1077: 	case C:
jacint@1093: 	  if ( _mate[y]!=INVALID ) {   //grow
jacint@1077: 
jacint@1077: 	    ear.set(y,x);
jacint@1093: 	    Node w=_mate[y];
jacint@1077: 	    blossom.insert(w);
jacint@1077: 	    position.set(y,A); 
jacint@1077: 	    position.set(w,D); 
jacint@1077: 	    tree.insert(y);
jacint@1077: 	    tree.insert(w);
jacint@1077: 	    tree.join(y,blossom.find(x));  
jacint@1077: 	    tree.join(w,y);  
jacint@1077: 	    Q.push(w);
jacint@1077: 	  } else {                 //augment  
jacint@1077: 	    augment(x, ear, blossom, tree);
jacint@1093: 	    _mate.set(x,y);
jacint@1093: 	    _mate.set(y,x);
jacint@1077: 	    return;
jacint@1077: 	  } //if 
jacint@1077: 	  break;
jacint@1077: 	default: break;
jacint@1077: 	}
jacint@1077:       }
jacint@1077:     }
jacint@1077:   }
jacint@1077: 
jacint@1077:   template <typename Graph>
alpar@1234:   bool MaxMatching<Graph>::noShrinkStep(Node x,
alpar@1234: 					typename Graph::template 
alpar@1234: 					NodeMap<Node>& ear,  
alpar@1234: 					UFE& blossom, UFE& tree,
alpar@1234: 					std::queue<Node>& Q) {
jacint@1077:     for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
klao@1158:       Node y=g.runningNode(e);
jacint@1077: 	
jacint@1077:       if ( position[y]==C ) {
jacint@1093: 	if ( _mate[y]!=INVALID ) {       //grow
jacint@1077: 	  ear.set(y,x);
jacint@1093: 	  Node w=_mate[y];
jacint@1077: 	  blossom.insert(w);
jacint@1077: 	  position.set(y,A);
jacint@1077: 	  position.set(w,D);
jacint@1077: 	  tree.insert(y);
jacint@1077: 	  tree.insert(w);
jacint@1077: 	  tree.join(y,blossom.find(x));  
jacint@1077: 	  tree.join(w,y);  
jacint@1077: 	  Q.push(w);
jacint@1077: 	} else {                      //augment 
jacint@1077: 	  augment(x, ear, blossom, tree);
jacint@1093: 	  _mate.set(x,y);
jacint@1093: 	  _mate.set(y,x);
jacint@1077: 	  return true;
jacint@1077: 	}
jacint@1077:       }
jacint@1077:     }
jacint@1077:     return false;
jacint@1077:   }
jacint@1077: 
jacint@1077:   template <typename Graph>
alpar@1234:   void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom,
alpar@1234: 				      typename Graph::template
alpar@1234: 				      NodeMap<Node>& ear,  
alpar@1234: 				      UFE& blossom, UFE& tree,
alpar@1234: 				      std::queue<Node>& Q) {
jacint@1077:     ear.set(top,bottom);
jacint@1077:     Node t=top;
jacint@1077:     while ( t!=middle ) {
jacint@1093:       Node u=_mate[t];
jacint@1077:       t=ear[u];
jacint@1077:       ear.set(t,u);
jacint@1077:     } 
jacint@1093:     bottom=_mate[middle];
jacint@1077:     position.set(bottom,D);
jacint@1077:     Q.push(bottom);
jacint@1077:     top=ear[bottom];		
jacint@1077:     Node oldmiddle=middle;
jacint@1077:     middle=blossom.find(top);
jacint@1077:     tree.erase(bottom);
jacint@1077:     tree.erase(oldmiddle);
jacint@1077:     blossom.insert(bottom);
jacint@1077:     blossom.join(bottom, oldmiddle);
jacint@1077:     blossom.join(top, oldmiddle);
jacint@1077:   }
jacint@1077: 
jacint@1077:   template <typename Graph>
alpar@1234:   void MaxMatching<Graph>::augment(Node x,
alpar@1234: 				   typename Graph::template NodeMap<Node>& ear,  
jacint@1077: 				   UFE& blossom, UFE& tree) { 
jacint@1093:     Node v=_mate[x];
jacint@1077:     while ( v!=INVALID ) {
jacint@1077: 	
jacint@1077:       Node u=ear[v];
jacint@1093:       _mate.set(v,u);
jacint@1077:       Node tmp=v;
jacint@1093:       v=_mate[u];
jacint@1093:       _mate.set(u,tmp);
jacint@1077:     }
jacint@1077:     typename UFE::ItemIt it;
jacint@1077:     for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {   
jacint@1077:       if ( position[it] == D ) {
jacint@1077: 	typename UFE::ItemIt b_it;
jacint@1077: 	for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {  
jacint@1077: 	  position.set( b_it ,C);
jacint@1077: 	}
jacint@1077: 	blossom.eraseClass(it);
jacint@1077:       } else position.set( it ,C);
jacint@1077:     }
jacint@1077:     tree.eraseClass(x);
jacint@1077: 
jacint@1077:   }
jacint@1077: 
jacint@1077:   /// @}
jacint@1077:   
jacint@1077: } //END OF NAMESPACE LEMON
jacint@1077: 
jacint@1165: #endif //LEMON_MAX_MATCHING_H