// -*- C++ -*-

#ifndef LEMON_MAX_MATCHING_H

#define LEMON_MAX_MATCHING_H

///\ingroup galgs

///\file

///\brief Maximum matching algorithm.

#include <queue>

#include <invalid.h>

#include <unionfind.h>

namespace lemon {

  /// \addtogroup galgs

  /// @{

  ///Maximum matching algorithms class.

  ///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 mathcing 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::EdgeIt EdgeIt;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    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:

    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 (edgeNum >=

    ///2*nodeNum), 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

    ///now \c uv is an edge of the matching.

    template<typename NMapN>

    void readNMapNode(NMapN& map) {

      NodeIt v;

      for( G.first(v); G.valid(v); G.next(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 {

      NodeIt v;

      for( G.first(v); G.valid(v); G.next(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.bNode(map[u])=v then \c

    ///G.bNode(map[v])=u must hold, and now this edge is an edge of

    ///the matching.

    template<typename NMapE>

    void readNMapEdge(NMapE& map) {

      NodeIt v;

      for( G.first(v); G.valid(v); G.next(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.bNode(map[u])=v then \c G.bNode(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,false); 

      NodeIt v;

      for( G.first(v); G.valid(v); G.next(v)) {

	if ( mate[v]!=INVALID ) todo.set(v,true); 

      }

      NodeIt e;

      for( G.first(e); G.valid(e); G.next(e)) {

	if ( todo[G.target(e)] && todo[G.source(e)] ) {

	  Node u=G.source(e);

	  Node v=G.target(e); 

	  if ( mate[u]=v && mate[v]=u ) {

	    map.set(u,e);

	    map.set(v,e);

	    todo.set(u,false);

	    todo.set(v,false);

	  }

	}

      }

    } 

    ///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) {

      EdgeIt e;

      for( G.first(e); G.valid(e); G.next(e)) {

	if ( G.valid(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 {

      typename Graph::template NodeMap<bool> todo(G,false); 

      NodeIt v;

      for( G.first(v); G.valid(v); G.next(v)) {

	if ( mate[v]!=INVALID ) todo.set(v,true); 

      }

      NodeIt e;

      for( G.first(e); G.valid(e); G.next(e)) {

	map.set(e,false);

	if ( todo[G.target(e)] && todo[G.source(e)] ) {

	  Node u=G.source(e);

	  Node v=G.target(e); 

	  if ( mate[u]=v && mate[v]=u ) {

	    map.set(e,true);

	    todo.set(u,false);

	    todo.set(v,false);

	  }

	}

      }

    }

    ///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 {

      NodeIt v;

      for( G.first(v); G.valid(v); G.next(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 ( G.edgeNum() > 2*G.nodeNum() ) {

      greedyMatching();

      runEdmonds(1);

    } else runEdmonds(0);

  }

  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);

    NodeIt v;

    for( G.first(v); G.valid(v); G.next(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();

      OutEdgeIt e;

      for( G.first(e,x); G.valid(e); G.next(e) ) {

	Node y=G.bNode(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();

      OutEdgeIt e;

      for( G.first(e,x); G.valid(e); G.next(e) ) {

	Node y=G.bNode(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() {

    NodeIt v;

    for( G.first(v); G.valid(v); G.next(v) )

      if ( mate[v]==INVALID ) {

	OutEdgeIt e;

	for( G.first(e,v); G.valid(e); G.next(e) ) {

	  Node y=G.bNode(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;

    NodeIt v;

    for(G.first(v); G.valid(v); G.next(v) ) {

      if ( G.valid(mate[v]) ) {

	++s;

      }

    }

    return (int)s/2;

  }

  template <typename Graph>

  void MaxMatching<Graph>::resetPos() {

    NodeIt v;

    for( G.first(v); G.valid(v); G.next(v))

      position.set(v,C);      

  }

  template <typename Graph>

  void MaxMatching<Graph>::resetMatching() {

    NodeIt v;

    for( G.first(v); G.valid(v); G.next(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) {

    OutEdgeIt e;

    for( G.first(e,x); G.valid(e); G.next(e) ) {

      Node y=G.bNode(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 ( G.valid(v) ) {

      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