/* -*- C++ -*-
 * src/lemon/max_matching.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, 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 <queue>
#include <invalid.h>
#include <unionfind.h>
#include <lemon/graph_utils.h>

///\ingroup galgs
///\file
///\brief Maximum matching algorithm.

namespace lemon {

  /// \addtogroup galgs
  /// @{

  ///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 read-in functions \ref readNMapNode, \ref
  ///readNMapEdge or \ref readEMapBool depending on the container. The
  ///resulting maximum matching can be attained by write-out functions
  ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
  ///depending on the preferred container. 
  ///
  ///The dual side of a matching is a map of the nodes to
  ///MaxMatching::pos_enum, having values D, A and C showing the
  ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
  ///a graph with factor-critical components, the nodes in A form the
  ///barrier, and the nodes in C induce a graph having a perfect
  ///matching. This decomposition can be attained by calling \ref
  ///writePos after running the algorithm. Before subsequent runs,
  ///the function \ref resetPos() must be called.
  ///
  ///\param Graph The undirected graph type the algorithm runs on.
  ///
  ///\author Jacint Szabo  
  template <typename Graph>
  class MaxMatching {
    typedef typename Graph::Node Node;
    typedef typename Graph::Edge Edge;
    typedef typename Graph::UndirEdgeIt UndirEdgeIt;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::IncEdgeIt IncEdgeIt;

    typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;

  public:
    
    ///Indicates the Gallai-Edmonds decomposition of the graph.

    ///Indicates the Gallai-Edmonds decomposition of the graph, which
    ///shows an upper bound on the size of a maximum matching. The
    ///nodes with pos_enum \c D induce a graph with factor-critical
    ///components, the nodes in \c A form the canonical barrier, and the
    ///nodes in \c C induce a graph having a perfect matching. 
    enum pos_enum {
      D=0,
      A=1,
      C=2
    }; 

  private:

    static const int HEUR_density=2;
    const Graph& g;
    typename Graph::template NodeMap<Node> mate;
    typename Graph::template NodeMap<pos_enum> position;
     
  public:
    
    MaxMatching(const Graph& _g) : g(_g), mate(_g,INVALID), position(_g,C) {}

    ///Runs Edmonds' algorithm.

    ///Runs Edmonds' algorithm for sparse graphs (number of edges <
    ///2*number of nodes), and a heuristical Edmonds' algorithm with a
    ///heuristic of postponing shrinks for dense graphs. \pre Before
    ///the subsequent calls \ref resetPos must be called.
    inline void run();

    ///Runs Edmonds' algorithm.
    
    ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
    ///Edmonds' algorithm with a heuristic of postponing shrinks,
    ///giving a faster algorithm for dense graphs.  \pre Before the
    ///subsequent calls \ref resetPos must be called.
    void runEdmonds( int heur );

    ///Finds a greedy matching starting from the actual matching.
    
    ///Starting form the actual matching stored, it finds a maximal
    ///greedy matching.
    void greedyMatching();

    ///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 graph.
    int size() const;

    ///Resets the map storing the Gallai-Edmonds decomposition.
    
    ///Resets the map storing the Gallai-Edmonds decomposition of the
    ///graph, making it possible to run the algorithm. Must be called
    ///before all runs of the Edmonds algorithm, except for the first
    ///run.
    void resetPos();

    ///Resets the actual matching to the empty matching.

    ///Resets the actual matching to the empty matching.  
    ///
    void resetMatching();

    ///Reads a matching from a \c Node map of \c Nodes.

    ///Reads a matching from a \c Node map of \c Nodes. 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 edge of the matching.
    template<typename NMapN>
    void readNMapNode(NMapN& map) {
      for(NodeIt v(g); v!=INVALID; ++v) {
	mate.set(v,map[v]);   
      } 
    } 
    
    ///Writes the stored matching to a \c Node map of \c Nodes.

    ///Writes the stored matching to a \c Node map of \c Nodes. 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 edge of the matching.
    template<typename NMapN>
    void writeNMapNode (NMapN& map) const {
      for(NodeIt v(g); v!=INVALID; ++v) {
	map.set(v,mate[v]);   
      } 
    } 

    ///Reads a matching from a \c Node map of \c Edges.

    ///Reads a matching from a \c Node map of incident \c Edges. This
    ///map must have the property that if \c G.target(map[u])==v then \c
    ///G.target(map[v])==u must hold, and now this edge is an edge of
    ///the matching.
    template<typename NMapE>
    void readNMapEdge(NMapE& map) {
     for(NodeIt v(g); v!=INVALID; ++v) {
	Edge e=map[v];
	if ( g.valid(e) )
	  g.source(e) == v ? mate.set(v,g.target(e)) : mate.set(v,g.source(e)); 
      } 
    } 
    
    ///Writes the matching stored to a \c Node map of \c Edges.

    ///Writes the stored matching to a \c Node map of incident \c
    ///Edges. This map will have the property that if \c
    ///g.target(map[u])==v then \c g.target(map[v])==u holds, and now this
    ///edge is an edge of the matching.
    template<typename NMapE>
    void writeNMapEdge (NMapE& map)  const {
      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.target(e) == u ) {
	      map.set(u,e);
	      map.set(v,e);
	      todo.set(u,false);
	      todo.set(v,false);
	      break;
	    }
	  }
	}
      } 
    }


    ///Reads a matching from an \c Edge map of \c bools.
    
    ///Reads a matching from an \c Edge map of \c bools. This map must
    ///have the property that there are no two adjacent edges \c e, \c
    ///f with \c map[e]==map[f]==true. The edges \c e with \c
    ///map[e]==true form the matching.
    template<typename EMapB>
    void readEMapBool(EMapB& map) {
      for(UndirEdgeIt e(g); e!=INVALID; ++e) {
	if ( map[e] ) {
	  Node u=g.source(e);	  
	  Node v=g.target(e);
	  mate.set(u,v);
	  mate.set(v,u);
	} 
      } 
    }


    ///Writes the matching stored to an \c Edge map of \c bools.

    ///Writes the matching stored to an \c Edge map of \c bools. This
    ///map will have the property that there are no two adjacent edges
    ///\c e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
    ///map[e]==true form the matching.
    template<typename EMapB>
    void writeEMapBool (EMapB& map) const {
      for(UndirEdgeIt 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.target(e) == u ) {
	      map.set(e,true);
	      todo.set(u,false);
	      todo.set(v,false);
	      break;
	    }
	  }
	}
      } 
    }


    ///Writes the canonical decomposition of the graph after running
    ///the algorithm.

    ///After calling any run methods of the class, and before calling
    ///\ref resetPos(), it writes the Gallai-Edmonds canonical
    ///decomposition of the graph. \c map must be a node map
    ///of \ref pos_enum 's.
    template<typename NMapEnum>
    void writePos (NMapEnum& map) const {
      for(NodeIt v(g); v!=INVALID; ++v)  map.set(v,position[v]);
    }

  private: 

    void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
		    UFE& blossom, UFE& tree);

    void normShrink(Node v, typename Graph::NodeMap<Node>& ear,  
		    UFE& blossom, UFE& tree);

    bool noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,  
		      UFE& blossom, UFE& tree, std::queue<Node>& Q);

    void shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,  
		    UFE& blossom, UFE& tree, std::queue<Node>& Q);

    void augment(Node x, typename Graph::NodeMap<Node>& ear,  
		 UFE& blossom, UFE& tree);

  };


  // **********************************************************************
  //  IMPLEMENTATIONS
  // **********************************************************************


  template <typename Graph>
  void MaxMatching<Graph>::run() {
    if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) {
      greedyMatching();
      runEdmonds(0);
    } else runEdmonds(1);
  }


  template <typename Graph>
  void MaxMatching<Graph>::runEdmonds( int heur=1 ) {
      
    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
 
    typename UFE::MapType blossom_base(g);
    UFE blossom(blossom_base);
    typename UFE::MapType tree_base(g);
    UFE tree(tree_base);

    for(NodeIt v(g); v!=INVALID; ++v) {
      if ( position[v]==C && mate[v]==INVALID ) {
	blossom.insert(v);
	tree.insert(v); 
	position.set(v,D);
	if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
	else normShrink( v, ear, blossom, tree );
      }
    }
  }

    
  template <typename Graph>
  void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,  
				      UFE& blossom, UFE& tree) {

    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();
      if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
      else R.push(x);
    }
      
    while ( !R.empty() ) {
      Node x=R.front();
      R.pop();
	
      for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
	Node y=g.target(e);

	if ( position[y] == D && blossom.find(x) != blossom.find(y) ) { 
	  //x and y must be in the same tree
	
	  typename Graph::template NodeMap<bool> path(g,false);

	  Node b=blossom.find(x);
	  path.set(b,true);
	  b=mate[b];
	  while ( b!=INVALID ) { 
	    b=blossom.find(ear[b]);
	    path.set(b,true);
	    b=mate[b];
	  } //going till the root
	
	  Node top=y;
	  Node middle=blossom.find(top);
	  Node bottom=x;
	  while ( !path[middle] )
	    shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
		  
	  Node base=middle;
	  top=x;
	  middle=blossom.find(top);
	  bottom=y;
	  Node blossom_base=blossom.find(base);
	  while ( middle!=blossom_base )
	    shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
		  
	  blossom.makeRep(base);
	} // if shrink is needed

	while ( !Q.empty() ) {
	  Node x=Q.front();
	  Q.pop();
	  if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
	  else R.push(x);
	}
      } //for e
    } // while ( !R.empty() )
  }


  template <typename Graph>
  void MaxMatching<Graph>::normShrink(Node v, typename Graph::NodeMap<Node>& ear,  
				      UFE& blossom, UFE& tree) {

    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.target(e);
	      
	switch ( position[y] ) {
	case D:          //x and y must be in the same tree

	  if ( blossom.find(x) != blossom.find(y) ) { //shrink
	    typename Graph::template NodeMap<bool> path(g,false);
	      
	    Node b=blossom.find(x);
	    path.set(b,true);
	    b=mate[b];
	    while ( b!=INVALID ) { 
	      b=blossom.find(ear[b]);
	      path.set(b,true);
	      b=mate[b];
	    } //going till the root
	
	    Node top=y;
	    Node middle=blossom.find(top);
	    Node bottom=x;
	    while ( !path[middle] )
	      shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
		
	    Node base=middle;
	    top=x;
	    middle=blossom.find(top);
	    bottom=y;
	    Node blossom_base=blossom.find(base);
	    while ( middle!=blossom_base )
	      shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
		
	    blossom.makeRep(base);
	  }
	  break;
	case C:
	  if ( mate[y]!=INVALID ) {   //grow

	    ear.set(y,x);
	    Node w=mate[y];
	    blossom.insert(w);
	    position.set(y,A); 
	    position.set(w,D); 
	    tree.insert(y);
	    tree.insert(w);
	    tree.join(y,blossom.find(x));  
	    tree.join(w,y);  
	    Q.push(w);
	  } else {                 //augment  
	    augment(x, ear, blossom, tree);
	    mate.set(x,y);
	    mate.set(y,x);
	    return;
	  } //if 
	  break;
	default: break;
	}
      }
    }
  }

  template <typename Graph>
  void MaxMatching<Graph>::greedyMatching() {
    for(NodeIt v(g); v!=INVALID; ++v)
      if ( mate[v]==INVALID ) {
	for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
	  Node y=g.target(e);
	  if ( mate[y]==INVALID && y!=v ) {
	    mate.set(v,y);
	    mate.set(y,v);
	    break;
	  }
	}
      } 
  }
   
  template <typename Graph>
  int MaxMatching<Graph>::size() const {
    int s=0;
    for(NodeIt v(g); v!=INVALID; ++v) {
      if ( mate[v]!=INVALID ) {
	++s;
      }
    }
    return (int)s/2;
  }

  template <typename Graph>
  void MaxMatching<Graph>::resetPos() {
    for(NodeIt v(g); v!=INVALID; ++v)
      position.set(v,C);      
  }

  template <typename Graph>
  void MaxMatching<Graph>::resetMatching() {
    for(NodeIt v(g); v!=INVALID; ++v)
      mate.set(v,INVALID);      
  }

  template <typename Graph>
  bool MaxMatching<Graph>::noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,  
					UFE& blossom, UFE& tree, std::queue<Node>& Q) {
    for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
      Node y=g.target(e);
	
      if ( position[y]==C ) {
	if ( mate[y]!=INVALID ) {       //grow
	  ear.set(y,x);
	  Node w=mate[y];
	  blossom.insert(w);
	  position.set(y,A);
	  position.set(w,D);
	  tree.insert(y);
	  tree.insert(w);
	  tree.join(y,blossom.find(x));  
	  tree.join(w,y);  
	  Q.push(w);
	} else {                      //augment 
	  augment(x, ear, blossom, tree);
	  mate.set(x,y);
	  mate.set(y,x);
	  return true;
	}
      }
    }
    return false;
  }

  template <typename Graph>
  void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,  
				      UFE& blossom, UFE& tree, std::queue<Node>& Q) {
    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=blossom.find(top);
    tree.erase(bottom);
    tree.erase(oldmiddle);
    blossom.insert(bottom);
    blossom.join(bottom, oldmiddle);
    blossom.join(top, oldmiddle);
  }

  template <typename Graph>
  void MaxMatching<Graph>::augment(Node x, typename Graph::NodeMap<Node>& ear,  
				   UFE& blossom, UFE& 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);
    }
    typename UFE::ItemIt it;
    for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {   
      if ( position[it] == D ) {
	typename UFE::ItemIt b_it;
	for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {  
	  position.set( b_it ,C);
	}
	blossom.eraseClass(it);
      } else position.set( it ,C);
    }
    tree.eraseClass(x);

  }

  /// @}
  
} //END OF NAMESPACE LEMON

#endif //EDMONDS_H