jacint@1077: /* -*- C++ -*-
jacint@1077:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@2391:  * Copyright (C) 2003-2007
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>
deba@1993: #include <lemon/bits/invalid.h>
jacint@1093: #include <lemon/unionfind.h>
jacint@1077: #include <lemon/graph_utils.h>
jacint@1077: 
deba@2042: ///\ingroup matching
jacint@1077: ///\file
deba@2042: ///\brief Maximum matching algorithm in undirected graph.
jacint@1077: 
jacint@1077: namespace lemon {
jacint@1077: 
deba@2505:   ///\ingroup matching
jacint@1077: 
deba@2505:   ///\brief Edmonds' alternating forest maximum matching algorithm.
deba@2505:   ///
jacint@1077:   ///This class provides Edmonds' alternating forest matching
jacint@1077:   ///algorithm. The starting matching (if any) can be passed to the
deba@2505:   ///algorithm using some of init functions.
jacint@1077:   ///
jacint@1077:   ///The dual side of a matching is a map of the nodes to
deba@2505:   ///MaxMatching::DecompType, having values \c D, \c A and \c C
deba@2505:   ///showing the Gallai-Edmonds decomposition of the graph. The nodes
deba@2505:   ///in \c D induce a graph with factor-critical components, the nodes
deba@2505:   ///in \c A form the barrier, and the nodes in \c C induce a graph
deba@2505:   ///having a perfect matching. This decomposition can be attained by
deba@2505:   ///calling \c decomposition() 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: 
deba@2205:     typedef typename Graph::template NodeMap<int> UFECrossRef;
deba@2308:     typedef UnionFindEnum<UFECrossRef> UFE;
deba@2505:     typedef std::vector<Node> NV;
deba@2505: 
deba@2505:     typedef typename Graph::template NodeMap<int> EFECrossRef;
deba@2505:     typedef ExtendFindEnum<EFECrossRef> EFE;
jacint@1077: 
jacint@1077:   public:
jacint@1077:     
deba@2505:     ///\brief Indicates the Gallai-Edmonds decomposition of the graph.
deba@2505:     ///
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
deba@2505:     ///nodes with DecompType \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. 
deba@2505:     enum DecompType {
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;
deba@2505:     typename Graph::template NodeMap<DecompType> position;
jacint@1077:      
jacint@1077:   public:
jacint@1077:     
deba@2505:     MaxMatching(const Graph& _g) 
deba@2505:       : g(_g), _mate(_g), position(_g) {}
jacint@1077: 
deba@2505:     ///\brief Sets the actual matching to the empty matching.
deba@2505:     ///
deba@2505:     ///Sets the actual matching to the empty matching.  
deba@2505:     ///
deba@2505:     void init() {
alpar@1587:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,INVALID);      
deba@2505: 	position.set(v,C);
alpar@1587:       }
alpar@1587:     }
alpar@1587: 
deba@2505:     ///\brief Finds a greedy matching for initial matching.
deba@2505:     ///
deba@2505:     ///For initial matchig it finds a maximal greedy matching.
deba@2505:     void greedyInit() {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,INVALID);      
deba@2505: 	position.set(v,C);
deba@2505:       }
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: 
deba@2505:     ///\brief Initialize the matching from each nodes' mate.
deba@2505:     ///
deba@2505:     ///Initialize the matching from a \c Node valued \c Node map. This
deba@2505:     ///map must be \e symmetric, i.e. if \c map[u]==v then \c
deba@2505:     ///map[v]==u must hold, and \c uv will be an edge of the initial
deba@2505:     ///matching.
deba@2505:     template <typename MateMap>
deba@2505:     void mateMapInit(MateMap& map) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,map[v]);
deba@2505: 	position.set(v,C);
deba@2505:       } 
deba@2505:     }
jacint@1077: 
deba@2505:     ///\brief Initialize the matching from a node map with the
deba@2505:     ///incident matching edges.
deba@2505:     ///
deba@2505:     ///Initialize the matching from an \c UEdge valued \c Node map. \c
deba@2505:     ///map[v] must be an \c UEdge incident to \c v. This map must have
deba@2505:     ///the property that if \c g.oppositeNode(u,map[u])==v then \c \c
deba@2505:     ///g.oppositeNode(v,map[v])==u holds, and now some edge joining \c
deba@2505:     ///u to \c v will be an edge of the matching.
deba@2505:     template<typename MatchingMap>
deba@2505:     void matchingMapInit(MatchingMap& map) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	position.set(v,C);
deba@2505: 	UEdge e=map[v];
deba@2505: 	if ( e!=INVALID )
deba@2505: 	  _mate.set(v,g.oppositeNode(v,e));
deba@2505: 	else 
deba@2505: 	  _mate.set(v,INVALID);
deba@2505:       } 
deba@2505:     } 
deba@2505: 
deba@2505:     ///\brief Initialize the matching from the map containing the
deba@2505:     ///undirected matching edges.
deba@2505:     ///
deba@2505:     ///Initialize the matching from a \c bool valued \c UEdge map. This
deba@2505:     ///map must have the property that there are no two incident edges
deba@2505:     ///\c e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
deba@2505:     ///map[e]==true form the matching.
deba@2505:     template <typename MatchingMap>
deba@2505:     void matchingInit(MatchingMap& map) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	_mate.set(v,INVALID);      
deba@2505: 	position.set(v,C);
deba@2505:       }
deba@2505:       for(UEdgeIt e(g); e!=INVALID; ++e) {
deba@2505: 	if ( map[e] ) {
deba@2505: 	  Node u=g.source(e);	  
deba@2505: 	  Node v=g.target(e);
deba@2505: 	  _mate.set(u,v);
deba@2505: 	  _mate.set(v,u);
deba@2505: 	} 
deba@2505:       } 
deba@2505:     }
deba@2505: 
deba@2505: 
deba@2505:     ///\brief Runs Edmonds' algorithm.
deba@2505:     ///
deba@2505:     ///Runs Edmonds' algorithm for sparse graphs (number of edges <
deba@2505:     ///2*number of nodes), and a heuristical Edmonds' algorithm with a
deba@2505:     ///heuristic of postponing shrinks for dense graphs. 
deba@2505:     void run() {
deba@2505:       if (countUEdges(g) < HEUR_density * countNodes(g)) {
deba@2505: 	greedyInit();
deba@2505: 	startSparse();
deba@2505:       } else {
deba@2505: 	init();
deba@2505: 	startDense();
deba@2505:       }
deba@2505:     }
deba@2505: 
deba@2505: 
deba@2505:     ///\brief Starts Edmonds' algorithm.
deba@2505:     /// 
deba@2505:     ///If runs the original Edmonds' algorithm.  
deba@2505:     void startSparse() {
deba@2505:             
deba@2505:       typename Graph::template NodeMap<Node> ear(g,INVALID); 
deba@2505:       //undefined for the base nodes of the blossoms (i.e. for the
deba@2505:       //representative elements of UFE blossom) and for the nodes in C 
deba@2505:       
deba@2505:       UFECrossRef blossom_base(g);
deba@2505:       UFE blossom(blossom_base);
deba@2505:       NV rep(countNodes(g));
deba@2505: 
deba@2505:       EFECrossRef tree_base(g);
deba@2505:       EFE tree(tree_base);
deba@2505: 
deba@2505:       //If these UFE's would be members of the class then also
deba@2505:       //blossom_base and tree_base should be a member.
deba@2505:       
deba@2505:       //We build only one tree and the other vertices uncovered by the
deba@2505:       //matching belong to C. (They can be considered as singleton
deba@2505:       //trees.) If this tree can be augmented or no more
deba@2505:       //grow/augmentation/shrink is possible then we return to this
deba@2505:       //"for" cycle.
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	if (position[v]==C && _mate[v]==INVALID) {
deba@2505: 	  rep[blossom.insert(v)] = v;
deba@2505: 	  tree.insert(v); 
deba@2505: 	  position.set(v,D);
deba@2505: 	  normShrink(v, ear, blossom, rep, tree);
deba@2505: 	}
deba@2505:       }
deba@2505:     }
deba@2505: 
deba@2505:     ///\brief Starts Edmonds' algorithm.
deba@2505:     /// 
deba@2505:     ///It runs Edmonds' algorithm with a heuristic of postponing
deba@2505:     ///shrinks, giving a faster algorithm for dense graphs.
deba@2505:     void startDense() {
deba@2505:             
deba@2505:       typename Graph::template NodeMap<Node> ear(g,INVALID); 
deba@2505:       //undefined for the base nodes of the blossoms (i.e. for the
deba@2505:       //representative elements of UFE blossom) and for the nodes in C 
deba@2505:       
deba@2505:       UFECrossRef blossom_base(g);
deba@2505:       UFE blossom(blossom_base);
deba@2505:       NV rep(countNodes(g));
deba@2505: 
deba@2505:       EFECrossRef tree_base(g);
deba@2505:       EFE tree(tree_base);
deba@2505: 
deba@2505:       //If these UFE's would be members of the class then also
deba@2505:       //blossom_base and tree_base should be a member.
deba@2505:       
deba@2505:       //We build only one tree and the other vertices uncovered by the
deba@2505:       //matching belong to C. (They can be considered as singleton
deba@2505:       //trees.) If this tree can be augmented or no more
deba@2505:       //grow/augmentation/shrink is possible then we return to this
deba@2505:       //"for" cycle.
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	if ( position[v]==C && _mate[v]==INVALID ) {
deba@2505: 	  rep[blossom.insert(v)] = v;
deba@2505: 	  tree.insert(v); 
deba@2505: 	  position.set(v,D);
deba@2505: 	  lateShrink(v, ear, blossom, rep, tree);
deba@2505: 	}
deba@2505:       }
deba@2505:     }
deba@2505: 
deba@2505: 
deba@2505: 
deba@2505:     ///\brief Returns the size of the actual matching stored.
deba@2505:     ///
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: 
deba@2505:     ///\brief Returns the mate of a node in the actual matching.
jacint@1077:     ///
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. 
deba@2505:     Node mate(const Node& node) const {
jacint@1093:       return _mate[node];
jacint@1093:     } 
jacint@1093: 
deba@2505:     ///\brief Returns the matching edge incident to the given node.
deba@2505:     ///
deba@2505:     ///Returns the matching edge of a \c node in the actual matching. 
deba@2505:     ///Returns INVALID if the \c node is not covered by the actual matching. 
deba@2505:     UEdge matchingEdge(const Node& node) const {
deba@2505:       if (_mate[node] == INVALID) return INVALID;
deba@2505:       Node n = node < _mate[node] ? node : _mate[node];
deba@2505:       for (IncEdgeIt e(g, n); e != INVALID; ++e) {
deba@2505: 	if (g.oppositeNode(n, e) == _mate[n]) {
deba@2505: 	  return e;
deba@2505: 	}
deba@2505:       }
deba@2505:       return INVALID;
deba@2505:     } 
jacint@1077: 
deba@2505:     /// \brief Returns the class of the node in the Edmonds-Gallai
deba@2505:     /// decomposition.
deba@2505:     ///
deba@2505:     /// Returns the class of the node in the Edmonds-Gallai
deba@2505:     /// decomposition.
deba@2505:     DecompType decomposition(const Node& n) {
deba@2505:       return position[n] == A;
deba@2505:     }
deba@2505: 
deba@2505:     /// \brief Returns true when the node is in the barrier.
deba@2505:     ///
deba@2505:     /// Returns true when the node is in the barrier.
deba@2505:     bool barrier(const Node& n) {
deba@2505:       return position[n] == A;
deba@2505:     }
jacint@1077:     
deba@2505:     ///\brief Gives back the matching in a \c Node of mates.
deba@2505:     ///
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.
deba@2505:     template <typename MateMap>
deba@2505:     void mateMap(MateMap& map) const {
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
jacint@1093: 	map.set(v,_mate[v]);   
jacint@1077:       } 
jacint@1077:     } 
jacint@1077:     
deba@2505:     ///\brief Gives back the matching in an \c UEdge valued \c Node
deba@2505:     ///map.
deba@2505:     ///
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.
deba@2505:     template <typename MatchingMap>
deba@2505:     void matchingMap(MatchingMap& map)  const {
jacint@1077:       typename Graph::template NodeMap<bool> todo(g,true); 
jacint@1077:       for(NodeIt v(g); v!=INVALID; ++v) {
deba@2505: 	if (_mate[v]!=INVALID && v < _mate[v]) {
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: 
deba@2505:     ///\brief Gives back the matching in a \c bool valued \c UEdge
deba@2505:     ///map.
deba@2505:     ///
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.
deba@2505:     template<typename MatchingMap>
deba@2505:     void matching(MatchingMap& 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: 
deba@2505:     ///\brief Returns the canonical decomposition of the graph after running
jacint@1077:     ///the algorithm.
deba@2505:     ///
jacint@1090:     ///After calling any run methods of the class, it writes the
jacint@1090:     ///Gallai-Edmonds canonical decomposition of the graph. \c map
deba@2505:     ///must be a node map of \ref DecompType 's.
deba@2505:     template <typename DecompositionMap>
deba@2505:     void decomposition(DecompositionMap& map) const {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
deba@2505:     }
deba@2505: 
deba@2505:     ///\brief Returns a barrier on the nodes.
deba@2505:     ///
deba@2505:     ///After calling any run methods of the class, it writes a
deba@2505:     ///canonical barrier on the nodes. The odd component number of the
deba@2505:     ///remaining graph minus the barrier size is a lower bound for the
deba@2505:     ///uncovered nodes in the graph. The \c map must be a node map of
deba@2505:     ///bools.
deba@2505:     template <typename BarrierMap>
deba@2505:     void barrier(BarrierMap& barrier) {
deba@2505:       for(NodeIt v(g); v!=INVALID; ++v) barrier.set(v,position[v] == A);    
jacint@1077:     }
jacint@1077: 
jacint@1077:   private: 
jacint@1077: 
jacint@1165:  
jacint@1077:     void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		    UFE& blossom, NV& rep, EFE& tree) {
deba@2505:       //We have one tree which we grow, and also shrink but only if it
deba@2505:       //cannot be postponed. If we augment then we return to the "for"
deba@2505:       //cycle of runEdmonds().
deba@2505: 
deba@2505:       std::queue<Node> Q;   //queue of the totally unscanned nodes
deba@2505:       Q.push(v);  
deba@2505:       std::queue<Node> R;   
deba@2505:       //queue of the nodes which must be scanned for a possible shrink
deba@2505:       
deba@2505:       while ( !Q.empty() ) {
deba@2505: 	Node x=Q.front();
deba@2505: 	Q.pop();
deba@2505: 	for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
deba@2505: 	  Node y=g.runningNode(e);
deba@2505: 	  //growOrAugment grows if y is covered by the matching and
deba@2505: 	  //augments if not. In this latter case it returns 1.
deba@2505: 	  if (position[y]==C && 
deba@2505: 	      growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
deba@2505: 	}
deba@2505: 	R.push(x);
deba@2505:       }
deba@2505:       
deba@2505:       while ( !R.empty() ) {
deba@2505: 	Node x=R.front();
deba@2505: 	R.pop();
deba@2505: 	
deba@2505: 	for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
deba@2505: 	  Node y=g.runningNode(e);
deba@2505: 
deba@2505: 	  if ( position[y] == D && blossom.find(x) != blossom.find(y) )  
deba@2505: 	    //Recall that we have only one tree.
deba@2505: 	    shrink( x, y, ear, blossom, rep, tree, Q);	
deba@2505: 	
deba@2505: 	  while ( !Q.empty() ) {
deba@2505: 	    Node z=Q.front();
deba@2505: 	    Q.pop();
deba@2505: 	    for( IncEdgeIt f(g,z); f!= INVALID; ++f ) {
deba@2505: 	      Node w=g.runningNode(f);
deba@2505: 	      //growOrAugment grows if y is covered by the matching and
deba@2505: 	      //augments if not. In this latter case it returns 1.
deba@2505: 	      if (position[w]==C && 
deba@2505: 		  growOrAugment(w, z, ear, blossom, rep, tree, Q)) return;
deba@2505: 	    }
deba@2505: 	    R.push(z);
deba@2505: 	  }
deba@2505: 	} //for e
deba@2505:       } // while ( !R.empty() )
deba@2505:     }
jacint@1077: 
alpar@1234:     void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		    UFE& blossom, NV& rep, EFE& tree) {
deba@2505:       //We have one tree, which we grow and shrink. If we augment then we
deba@2505:       //return to the "for" cycle of runEdmonds().
deba@2505:     
deba@2505:       std::queue<Node> Q;   //queue of the unscanned nodes
deba@2505:       Q.push(v);  
deba@2505:       while ( !Q.empty() ) {
deba@2505: 
deba@2505: 	Node x=Q.front();
deba@2505: 	Q.pop();
deba@2505: 	
deba@2505: 	for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
deba@2505: 	  Node y=g.runningNode(e);
deba@2505: 	      
deba@2505: 	  switch ( position[y] ) {
deba@2505: 	  case D:          //x and y must be in the same tree
deba@2505: 	    if ( blossom.find(x) != blossom.find(y))
deba@2505: 	      //x and y are in the same tree
deba@2505: 	      shrink(x, y, ear, blossom, rep, tree, Q);
deba@2505: 	    break;
deba@2505: 	  case C:
deba@2505: 	    //growOrAugment grows if y is covered by the matching and
deba@2505: 	    //augments if not. In this latter case it returns 1.
deba@2505: 	    if (growOrAugment(y, x, ear, blossom, rep, tree, Q)) return;
deba@2505: 	    break;
deba@2505: 	  default: break;
deba@2505: 	  }
deba@2505: 	}
deba@2505:       }
deba@2505:     }
jacint@1077: 
jacint@2023:     void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		UFE& blossom, NV& rep, EFE& tree,std::queue<Node>& Q) {
deba@2505:       //x and y are the two adjacent vertices in two blossoms.
deba@2505:    
deba@2505:       typename Graph::template NodeMap<bool> path(g,false);
deba@2505:     
deba@2505:       Node b=rep[blossom.find(x)];
deba@2505:       path.set(b,true);
deba@2505:       b=_mate[b];
deba@2505:       while ( b!=INVALID ) { 
deba@2505: 	b=rep[blossom.find(ear[b])];
deba@2505: 	path.set(b,true);
deba@2505: 	b=_mate[b];
deba@2505:       } //we go until the root through bases of blossoms and odd vertices
deba@2505:     
deba@2505:       Node top=y;
deba@2505:       Node middle=rep[blossom.find(top)];
deba@2505:       Node bottom=x;
deba@2505:       while ( !path[middle] )
deba@2505: 	shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
deba@2505:       //Until we arrive to a node on the path, we update blossom, tree
deba@2505:       //and the positions of the odd nodes.
deba@2505:     
deba@2505:       Node base=middle;
deba@2505:       top=x;
deba@2505:       middle=rep[blossom.find(top)];
deba@2505:       bottom=y;
deba@2505:       Node blossom_base=rep[blossom.find(base)];
deba@2505:       while ( middle!=blossom_base )
deba@2505: 	shrinkStep(top, middle, bottom, ear, blossom, rep, tree, Q);
deba@2505:       //Until we arrive to a node on the path, we update blossom, tree
deba@2505:       //and the positions of the odd nodes.
deba@2505:     
deba@2505:       rep[blossom.find(base)] = base;
deba@2505:     }
jacint@1077: 
alpar@1234:     void shrinkStep(Node& top, Node& middle, Node& bottom,
alpar@1234: 		    typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		    UFE& blossom, NV& rep, EFE& tree, std::queue<Node>& Q) {
deba@2505:       //We traverse a blossom and update everything.
deba@2505:     
deba@2505:       ear.set(top,bottom);
deba@2505:       Node t=top;
deba@2505:       while ( t!=middle ) {
deba@2505: 	Node u=_mate[t];
deba@2505: 	t=ear[u];
deba@2505: 	ear.set(t,u);
deba@2505:       } 
deba@2505:       bottom=_mate[middle];
deba@2505:       position.set(bottom,D);
deba@2505:       Q.push(bottom);
deba@2505:       top=ear[bottom];		
deba@2505:       Node oldmiddle=middle;
deba@2505:       middle=rep[blossom.find(top)];
deba@2505:       tree.erase(bottom);
deba@2505:       tree.erase(oldmiddle);
deba@2505:       blossom.insert(bottom);
deba@2505:       blossom.join(bottom, oldmiddle);
deba@2505:       blossom.join(top, oldmiddle);
deba@2505:     }
deba@2505: 
deba@2505: 
jacint@1077: 
jacint@2023:     bool growOrAugment(Node& y, Node& x, typename Graph::template 
deba@2505: 		       NodeMap<Node>& ear, UFE& blossom, NV& rep, EFE& tree, 
deba@2505: 		       std::queue<Node>& Q) {
deba@2505:       //x is in a blossom in the tree, y is outside. If y is covered by
deba@2505:       //the matching we grow, otherwise we augment. In this case we
deba@2505:       //return 1.
deba@2505:     
deba@2505:       if ( _mate[y]!=INVALID ) {       //grow
deba@2505: 	ear.set(y,x);
deba@2505: 	Node w=_mate[y];
deba@2505: 	rep[blossom.insert(w)] = w;
deba@2505: 	position.set(y,A);
deba@2505: 	position.set(w,D);
deba@2505: 	int t = tree.find(rep[blossom.find(x)]);
deba@2505: 	tree.insert(y,t);  
deba@2505: 	tree.insert(w,t);  
deba@2505: 	Q.push(w);
deba@2505:       } else {                      //augment 
deba@2505: 	augment(x, ear, blossom, rep, tree);
deba@2505: 	_mate.set(x,y);
deba@2505: 	_mate.set(y,x);
deba@2505: 	return true;
deba@2505:       }
deba@2505:       return false;
deba@2505:     }
jacint@2023: 
alpar@1234:     void augment(Node x, typename Graph::template NodeMap<Node>& ear,  
deba@2505: 		 UFE& blossom, NV& rep, EFE& tree) {
deba@2505:       Node v=_mate[x];
deba@2505:       while ( v!=INVALID ) {
deba@2505: 	
deba@2505: 	Node u=ear[v];
deba@2505: 	_mate.set(v,u);
deba@2505: 	Node tmp=v;
deba@2505: 	v=_mate[u];
deba@2505: 	_mate.set(u,tmp);
deba@2505:       }
deba@2505:       int y = tree.find(rep[blossom.find(x)]);
deba@2505:       for (typename EFE::ItemIt tit(tree, y); tit != INVALID; ++tit) {   
deba@2505: 	if ( position[tit] == D ) {
deba@2505: 	  int b = blossom.find(tit);
deba@2505: 	  for (typename UFE::ItemIt bit(blossom, b); bit != INVALID; ++bit) { 
deba@2505: 	    position.set(bit, C);
deba@2505: 	  }
deba@2505: 	  blossom.eraseClass(b);
deba@2505: 	} else position.set(tit, C);
deba@2505:       }
deba@2505:       tree.eraseClass(y);
deba@2505: 
deba@2505:     }
jacint@1077: 
jacint@1077:   };
jacint@1077:   
jacint@1077: } //END OF NAMESPACE LEMON
jacint@1077: 
jacint@1165: #endif //LEMON_MAX_MATCHING_H