/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2006

  * 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_LIST_GRAPH_H

 #define LEMON_LIST_GRAPH_H

 ///\ingroup graphs

 ///\file

 ///\brief ListGraph, ListUGraph classes.

 #include <lemon/bits/base_extender.h>

 #include <lemon/bits/graph_extender.h>

 #include <lemon/error.h>

 #include <vector>

 #include <list>

 namespace lemon {

   class ListGraphBase {

   protected:

     struct NodeT {

       int first_in, first_out;

       int prev, next;

     };

     struct EdgeT {

       int target, source;

       int prev_in, prev_out;

       int next_in, next_out;

     };

     std::vector<NodeT> nodes;

     int first_node;

     int first_free_node;

     std::vector<EdgeT> edges;

     int first_free_edge;

   public:

     typedef ListGraphBase Graph;

     class Node {

       friend class ListGraphBase;

     protected:

       int id;

       explicit Node(int pid) { id = pid;}

     public:

       Node() {}

       Node (Invalid) { id = -1; }

       bool operator==(const Node& node) const {return id == node.id;}

       bool operator!=(const Node& node) const {return id != node.id;}

       bool operator<(const Node& node) const {return id < node.id;}

     };

     class Edge {

       friend class ListGraphBase;

     protected:

       int id;

       explicit Edge(int pid) { id = pid;}

     public:

       Edge() {}

       Edge (Invalid) { id = -1; }

       bool operator==(const Edge& edge) const {return id == edge.id;}

       bool operator!=(const Edge& edge) const {return id != edge.id;}

       bool operator<(const Edge& edge) const {return id < edge.id;}

     };

     ListGraphBase()

       : nodes(), first_node(-1),

 	first_free_node(-1), edges(), first_free_edge(-1) {}

     /// Maximum node ID.

     /// Maximum node ID.

     ///\sa id(Node)

     int maxNodeId() const { return nodes.size()-1; } 

     /// Maximum edge ID.

     /// Maximum edge ID.

     ///\sa id(Edge)

     int maxEdgeId() const { return edges.size()-1; }

     Node source(Edge e) const { return Node(edges[e.id].source); }

     Node target(Edge e) const { return Node(edges[e.id].target); }

     void first(Node& node) const { 

       node.id = first_node;

     }

     void next(Node& node) const {

       node.id = nodes[node.id].next;

     }

     void first(Edge& e) const { 

       int n;

       for(n = first_node; 

 	  n!=-1 && nodes[n].first_in == -1; 

 	  n = nodes[n].next);

       e.id = (n == -1) ? -1 : nodes[n].first_in;

     }

     void next(Edge& edge) const {

       if (edges[edge.id].next_in != -1) {

 	edge.id = edges[edge.id].next_in;

       } else {

 	int n;

 	for(n = nodes[edges[edge.id].target].next;

 	  n!=-1 && nodes[n].first_in == -1; 

 	  n = nodes[n].next);

 	edge.id = (n == -1) ? -1 : nodes[n].first_in;

       }      

     }

     void firstOut(Edge &e, const Node& v) const {

       e.id = nodes[v.id].first_out;

     }

     void nextOut(Edge &e) const {

       e.id=edges[e.id].next_out;

     }

     void firstIn(Edge &e, const Node& v) const {

       e.id = nodes[v.id].first_in;

     }

     void nextIn(Edge &e) const {

       e.id=edges[e.id].next_in;

     }

     static int id(Node v) { return v.id; }

     static int id(Edge e) { return e.id; }

     static Node nodeFromId(int id) { return Node(id);}

     static Edge edgeFromId(int id) { return Edge(id);}

     /// Adds a new node to the graph.

     /// \warning It adds the new node to the front of the list.

     /// (i.e. the lastly added node becomes the first.)

     Node addNode() {     

       int n;

       if(first_free_node==-1) {

 	n = nodes.size();

 	nodes.push_back(NodeT());

       } else {

 	n = first_free_node;

 	first_free_node = nodes[n].next;

       }

       nodes[n].next = first_node;

       if(first_node != -1) nodes[first_node].prev = n;

       first_node = n;

       nodes[n].prev = -1;

       nodes[n].first_in = nodes[n].first_out = -1;

       return Node(n);

     }

     Edge addEdge(Node u, Node v) {

       int n;      

       if (first_free_edge == -1) {

 	n = edges.size();

 	edges.push_back(EdgeT());

       } else {

 	n = first_free_edge;

 	first_free_edge = edges[n].next_in;

       }

       edges[n].source = u.id; 

       edges[n].target = v.id;

       edges[n].next_out = nodes[u.id].first_out;

       if(nodes[u.id].first_out != -1) {

 	edges[nodes[u.id].first_out].prev_out = n;

       }

       edges[n].next_in = nodes[v.id].first_in;

       if(nodes[v.id].first_in != -1) {

 	edges[nodes[v.id].first_in].prev_in = n;

       }

       edges[n].prev_in = edges[n].prev_out = -1;

       nodes[u.id].first_out = nodes[v.id].first_in = n;

       return Edge(n);

     }

     void erase(const Node& node) {

       int n = node.id;

       if(nodes[n].next != -1) {

 	nodes[nodes[n].next].prev = nodes[n].prev;

       }

       if(nodes[n].prev != -1) {

 	nodes[nodes[n].prev].next = nodes[n].next;

       } else {

 	first_node = nodes[n].next;

       }

       nodes[n].next = first_free_node;

       first_free_node = n;

     }

     void erase(const Edge& edge) {

       int n = edge.id;

       if(edges[n].next_in!=-1) {

 	edges[edges[n].next_in].prev_in = edges[n].prev_in;

       }

       if(edges[n].prev_in!=-1) {

 	edges[edges[n].prev_in].next_in = edges[n].next_in;

       } else {

 	nodes[edges[n].target].first_in = edges[n].next_in;

       }

       if(edges[n].next_out!=-1) {

 	edges[edges[n].next_out].prev_out = edges[n].prev_out;

       } 

       if(edges[n].prev_out!=-1) {

 	edges[edges[n].prev_out].next_out = edges[n].next_out;

       } else {

 	nodes[edges[n].source].first_out = edges[n].next_out;

       }

       edges[n].next_in = first_free_edge;

       first_free_edge = n;      

     }

     void clear() {

       edges.clear();

       nodes.clear();

       first_node = first_free_node = first_free_edge = -1;

     }

   protected:

     void _changeTarget(Edge e, Node n) 

     {

       if(edges[e.id].next_in != -1)

 	edges[edges[e.id].next_in].prev_in = edges[e.id].prev_in;

       if(edges[e.id].prev_in != -1)

 	edges[edges[e.id].prev_in].next_in = edges[e.id].next_in;

       else nodes[edges[e.id].target].first_in = edges[e.id].next_in;

       if (nodes[n.id].first_in != -1) {

 	edges[nodes[n.id].first_in].prev_in = e.id;

       }

       edges[e.id].target = n.id;

       edges[e.id].prev_in = -1;

       edges[e.id].next_in = nodes[n.id].first_in;

       nodes[n.id].first_in = e.id;

     }

     void _changeSource(Edge e, Node n) 

     {

       if(edges[e.id].next_out != -1)

 	edges[edges[e.id].next_out].prev_out = edges[e.id].prev_out;

       if(edges[e.id].prev_out != -1)

 	edges[edges[e.id].prev_out].next_out = edges[e.id].next_out;

       else nodes[edges[e.id].source].first_out = edges[e.id].next_out;

       if (nodes[n.id].first_out != -1) {

 	edges[nodes[n.id].first_out].prev_out = e.id;

       }

       edges[e.id].source = n.id;

       edges[e.id].prev_out = -1;

       edges[e.id].next_out = nodes[n.id].first_out;

       nodes[n.id].first_out = e.id;

     }

   };

   typedef GraphExtender<ListGraphBase> ExtendedListGraphBase;

   /// \addtogroup graphs

   /// @{

   ///A list graph class.

   ///This is a simple and fast erasable graph implementation.

   ///

   ///It conforms to the

   ///\ref concept::ErasableGraph "ErasableGraph" concept and

   ///it also provides several additional useful extra functionalities.

   ///\sa concept::ErasableGraph.

   class ListGraph : public ExtendedListGraphBase {

   public:

     typedef ExtendedListGraphBase Parent;

     /// Changes the target of \c e to \c n

     /// Changes the target of \c e to \c n

     ///

     ///\note The <tt>Edge</tt>s and <tt>OutEdge</tt>s

     ///referencing the changed edge remain

     ///valid. However <tt>InEdge</tt>s are invalidated.

     void changeTarget(Edge e, Node n) { 

       _changeTarget(e,n); 

     }

     /// Changes the source of \c e to \c n

     /// Changes the source of \c e to \c n

     ///

     ///\note The <tt>Edge</tt>s and <tt>InEdge</tt>s

     ///referencing the changed edge remain

     ///valid. However <tt>OutEdge</tt>s are invalidated.

     void changeSource(Edge e, Node n) { 

       _changeSource(e,n);

     }

     /// Invert the direction of an edge.

     ///\note The <tt>Edge</tt>s

     ///referencing the changed edge remain

     ///valid. However <tt>OutEdge</tt>s  and <tt>InEdge</tt>s are invalidated.

     void reverseEdge(Edge e) {

       Node t=target(e);

       _changeTarget(e,source(e));

       _changeSource(e,t);

     }

     ///Using this it is possible to avoid the superfluous memory

     ///allocation.

     ///Using this it is possible to avoid the superfluous memory

     ///allocation: if you know that the graph you want to build will

     ///contain at least 10 million nodes then it is worth to reserve

     ///space for this amount before starting to build the graph.

     void reserveNode(int n) { nodes.reserve(n); };

     ///Using this it is possible to avoid the superfluous memory

     ///allocation.

     ///Using this it is possible to avoid the superfluous memory

     ///allocation: see the \ref reserveNode function.

     void reserveEdge(int n) { edges.reserve(n); };

     ///Contract two nodes.

     ///This function contracts two nodes.

     ///

     ///Node \p b will be removed but instead of deleting

     ///incident edges, they will be joined to \p a.

     ///The last parameter \p r controls whether to remove loops. \c true

     ///means that loops will be removed.

     ///

     ///\note The <tt>Edge</tt>s

     ///referencing a moved edge remain

     ///valid. However <tt>InEdge</tt>s and <tt>OutEdge</tt>s

     ///may be invalidated.

     void contract(Node a, Node b, bool r = true) 

     {

       for(OutEdgeIt e(*this,b);e!=INVALID;) {

 	OutEdgeIt f=e;

 	++f;

 	if(r && target(e)==a) erase(e);

 	else changeSource(e,a);

 	e=f;

       }

       for(InEdgeIt e(*this,b);e!=INVALID;) {

 	InEdgeIt f=e;

 	++f;

 	if(r && source(e)==a) erase(e);

 	else changeTarget(e,a);

 	e=f;

       }

       erase(b);

     }

     ///Split a node.

     ///This function splits a node. First a new node is added to the graph,

     ///then the source of each outgoing edge of \c n is moved to this new node.

     ///If \c connect is \c true (this is the default value), then a new edge

     ///from \c n to the newly created node is also added.

     ///\return The newly created node.

     ///

     ///\note The <tt>Edge</tt>s

     ///referencing a moved edge remain

     ///valid. However <tt>InEdge</tt>s and <tt>OutEdge</tt>s

     ///may be invalidated.

     ///\warning This functionality cannot be used together with the Snapshot

     ///feature.

     ///\todo It could be implemented in a bit faster way.

     Node split(Node n, bool connect = true) 

     {

       Node b = addNode();

       for(OutEdgeIt e(*this,n);e!=INVALID;) {

  	OutEdgeIt f=e;

 	++f;

 	changeSource(e,b);

 	e=f;

       }

       if(connect) addEdge(n,b);

       return b;

     }

     ///Split an edge.

     ///This function splits an edge. First a new node \c b is added to

     ///the graph, then the original edge is re-targeted to \c

     ///b. Finally an edge from \c b to the original target is added.

     ///\return The newly created node.  

     ///\warning This functionality

     ///cannot be used together with the Snapshot feature.

     Node split(Edge e) 

     {

       Node b = addNode();

       addEdge(b,target(e));

       changeTarget(e,b);

       return b;

     }

     ///Class to make a snapshot of the graph and to restore  it later.

     ///Class to make a snapshot of the graph and to restore  it later.

     ///

     ///The newly added nodes and edges can be removed using the

     ///restore() function.

     ///

     ///\warning Edge and node deletions cannot be restored.

     ///\warning Snapshots cannot be nested.

     class Snapshot : protected Parent::NodeNotifier::ObserverBase,

 		     protected Parent::EdgeNotifier::ObserverBase

     {

     public:

       class UnsupportedOperation : public LogicError {

       public:

 	virtual const char* exceptionName() const {

 	  return "lemon::ListGraph::Snapshot::UnsupportedOperation";

 	}

       };

     protected:

       ListGraph *g;

       std::list<Node> added_nodes;

       std::list<Edge> added_edges;

       bool active;

       virtual void add(const Node& n) {

 	added_nodes.push_back(n);

       };

       virtual void erase(const Node&) 

       {

 	throw UnsupportedOperation();

       }

       virtual void add(const Edge& n) {

 	added_edges.push_back(n);

       };

       virtual void erase(const Edge&) 

       {

 	throw UnsupportedOperation();

       }

       ///\bug What is this used for?

       ///

       virtual void build() {}

       ///\bug What is this used for?

       ///

       virtual void clear() {}

       void regist(ListGraph &_g) {

 	g=&_g;

 	Parent::NodeNotifier::ObserverBase::attach(g->getNotifier(Node()));

 	Parent::EdgeNotifier::ObserverBase::attach(g->getNotifier(Edge()));

       }

       void deregist() {

 	Parent::NodeNotifier::ObserverBase::detach();

 	Parent::EdgeNotifier::ObserverBase::detach();

 	g=0;

       }

     public:

       ///Default constructur.

       ///Default constructur.

       ///To actually make a snapshot you must call save().

       ///

       Snapshot() : g(0) {}

       ///Constructor that immediately makes a snapshot.

       ///This constructor immediately makes a snapshot of the graph.

       ///\param _g The graph we make a snapshot of.

       Snapshot(ListGraph &_g) {

 	regist(_g);

       }

       ///\bug Is it necessary?

       ///

       ~Snapshot() 

       {

 	if(g) deregist();

       }

       ///Make a snapshot.

       ///Make a snapshot of the graph.

       ///

       ///This function can be called more than once. In case of a repeated

       ///call, the previous snapshot gets lost.

       ///\param _g The graph we make the snapshot of.

       void save(ListGraph &_g) 

       {

 	if(g!=&_g) {

 	  if(g) deregist();

 	  regist(_g);

 	}

 	added_nodes.clear();

 	added_edges.clear();

       }

     ///Undo the changes until the last snapshot.

     ///Undo the changes until last snapshot created by save().

     ///

     ///\todo This function might be called undo().

       void restore() {

 	ListGraph &old_g=*g;

 	deregist();

 	while(!added_edges.empty()) {

 	  old_g.erase(added_edges.front());

 	  added_edges.pop_front();

 	}

  	while(!added_nodes.empty()) {

 	  old_g.erase(added_nodes.front());

 	  added_nodes.pop_front();

 	}

       }

     };

   };

   ///@}

   /**************** Undirected List Graph ****************/

   typedef UGraphExtender<UndirGraphExtender<ListGraphBase> > 

   ExtendedListUGraphBase;

   /// \addtogroup graphs

   /// @{

   ///An undirected list graph class.

   ///This is a simple and fast erasable undirected graph implementation.

   ///

   ///It conforms to the

   ///\ref concept::UGraph "UGraph" concept.

   ///

   ///\sa concept::UGraph.

   ///

   ///\todo Snapshot, reverseEdge(), changeTarget(), changeSource(), contract()

   ///haven't been implemented yet.

   ///

   class ListUGraph : public ExtendedListUGraphBase {

   public:

     typedef ExtendedListUGraphBase Parent;

     /// \brief Changes the target of \c e to \c n

     ///

     /// Changes the target of \c e to \c n

     ///

     /// \note The <tt>Edge</tt>'s and <tt>OutEdge</tt>'s

     /// referencing the changed edge remain

     /// valid. However <tt>InEdge</tt>'s are invalidated.

     void changeTarget(UEdge e, Node n) { 

       _changeTarget(e,n); 

     }

     /// Changes the source of \c e to \c n

     ///

     /// Changes the source of \c e to \c n

     ///

     ///\note The <tt>Edge</tt>'s and <tt>InEdge</tt>'s

     ///referencing the changed edge remain

     ///valid. However <tt>OutEdge</tt>'s are invalidated.

     void changeSource(UEdge e, Node n) { 

       _changeSource(e,n); 

     }

     /// \brief Contract two nodes.

     ///

     /// This function contracts two nodes.

     ///

     /// Node \p b will be removed but instead of deleting

     /// its neighboring edges, they will be joined to \p a.

     /// The last parameter \p r controls whether to remove loops. \c true

     /// means that loops will be removed.

     ///

     /// \note The <tt>Edge</tt>s

     /// referencing a moved edge remain

     /// valid.

     void contract(Node a, Node b, bool r = true) {

       for(IncEdgeIt e(*this, b); e!=INVALID;) {

 	IncEdgeIt f = e; ++f;

 	if (r && runningNode(e) == a) {

 	  erase(e);

 	} else if (source(e) == b) {

 	  changeSource(e, a);

 	} else {

 	  changeTarget(e, a);

 	}

 	e = f;

       }

       erase(b);

     }

   };

   class ListBpUGraphBase {

   public:

     class NodeSetError : public LogicError {

       virtual const char* exceptionName() const { 

 	return "lemon::ListBpUGraph::NodeSetError";

       }

     };

   protected:

     struct NodeT {

       int first_edge, prev, next;

     };

     struct UEdgeT {

       int aNode, prev_out, next_out;

       int bNode, prev_in, next_in;

     };

     std::vector<NodeT> aNodes;

     std::vector<NodeT> bNodes;

     std::vector<UEdgeT> edges;

     int first_anode;

     int first_free_anode;

     int first_bnode;

     int first_free_bnode;

     int first_free_edge;

   public:

     class Node {

       friend class ListBpUGraphBase;

     protected:

       int id;

       explicit Node(int _id) : id(_id) {}

     public:

       Node() {}

       Node(Invalid) { id = -1; }

       bool operator==(const Node i) const {return id==i.id;}

       bool operator!=(const Node i) const {return id!=i.id;}

       bool operator<(const Node i) const {return id<i.id;}

     };

     class UEdge {

       friend class ListBpUGraphBase;

     protected:

       int id;

       explicit UEdge(int _id) { id = _id;}

     public:

       UEdge() {}

       UEdge (Invalid) { id = -1; }

       bool operator==(const UEdge i) const {return id==i.id;}

       bool operator!=(const UEdge i) const {return id!=i.id;}

       bool operator<(const UEdge i) const {return id<i.id;}

     };

     ListBpUGraphBase()

       : first_anode(-1), first_free_anode(-1),

         first_bnode(-1), first_free_bnode(-1),

         first_free_edge(-1) {}

     void firstANode(Node& node) const {

       node.id = first_anode != -1 ? (first_anode << 1) : -1;

     }

     void nextANode(Node& node) const {

       node.id = aNodes[node.id >> 1].next;

     }

     void firstBNode(Node& node) const {

       node.id = first_bnode != -1 ? (first_bnode << 1) + 1 : -1;

     }

     void nextBNode(Node& node) const {

       node.id = bNodes[node.id >> 1].next;

     }

     void first(Node& node) const {

       if (first_anode != -1) {

         node.id = (first_anode << 1);

       } else if (first_bnode != -1) {

         node.id = (first_bnode << 1) + 1;

       } else {

         node.id = -1;

       }

     }

     void next(Node& node) const {

       if (aNode(node)) {

         node.id = aNodes[node.id >> 1].next;

         if (node.id == -1) {

           if (first_bnode != -1) {

             node.id = (first_bnode << 1) + 1;

           }

         }

       } else {

         node.id = bNodes[node.id >> 1].next;

       }

     }

     void first(UEdge& edge) const {

       int aNodeId = first_anode;

       while (aNodeId != -1 && aNodes[aNodeId].first_edge == -1) {

         aNodeId = aNodes[aNodeId].next != -1 ? 

           aNodes[aNodeId].next >> 1 : -1;

       }

       if (aNodeId != -1) {

         edge.id = aNodes[aNodeId].first_edge;

       } else {

         edge.id = -1;

       }

     }

     void next(UEdge& edge) const {

       int aNodeId = edges[edge.id].aNode >> 1;

       edge.id = edges[edge.id].next_out;

       if (edge.id == -1) {

         aNodeId = aNodes[aNodeId].next != -1 ? 

           aNodes[aNodeId].next >> 1 : -1;

         while (aNodeId != -1 && aNodes[aNodeId].first_edge == -1) {

           aNodeId = aNodes[aNodeId].next != -1 ? 

           aNodes[aNodeId].next >> 1 : -1;

         }

         if (aNodeId != -1) {

           edge.id = aNodes[aNodeId].first_edge;

         } else {

           edge.id = -1;

         }

       }

     }

     void firstFromANode(UEdge& edge, const Node& node) const {

       LEMON_ASSERT((node.id & 1) == 0, NodeSetError());

       edge.id = aNodes[node.id >> 1].first_edge;

     }

     void nextFromANode(UEdge& edge) const {

       edge.id = edges[edge.id].next_out;

     }

     void firstFromBNode(UEdge& edge, const Node& node) const {

       LEMON_ASSERT((node.id & 1) == 1, NodeSetError());

       edge.id = bNodes[node.id >> 1].first_edge;

     }

     void nextFromBNode(UEdge& edge) const {

       edge.id = edges[edge.id].next_in;

     }

     static int id(const Node& node) {

       return node.id;

     }

     static Node nodeFromId(int id) {

       return Node(id);

     }

     int maxNodeId() const {

       return aNodes.size() > bNodes.size() ?

 	aNodes.size() * 2 - 2 : bNodes.size() * 2 - 1;

     }

     static int id(const UEdge& edge) {

       return edge.id;

     }

     static UEdge uEdgeFromId(int id) {

       return UEdge(id);

     }

     int maxUEdgeId() const {

       return edges.size();

     }

     static int aNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node fromANodeId(int id) {

       return Node(id << 1);

     }

     int maxANodeId() const {

       return aNodes.size();

     }

     static int bNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node fromBNodeId(int id) {

       return Node((id << 1) + 1);

     }

     int maxBNodeId() const {

       return bNodes.size();

     }

     Node aNode(const UEdge& edge) const {

       return Node(edges[edge.id].aNode);

     }

     Node bNode(const UEdge& edge) const {

       return Node(edges[edge.id].bNode);

     }

     static bool aNode(const Node& node) {

       return (node.id & 1) == 0;

     }

     static bool bNode(const Node& node) {

       return (node.id & 1) == 1;

     }

     Node addANode() {

       int aNodeId;

       if (first_free_anode == -1) {

         aNodeId = aNodes.size();

         aNodes.push_back(NodeT());

       } else {

         aNodeId = first_free_anode;

         first_free_anode = aNodes[first_free_anode].next;

       }

       if (first_anode != -1) {

         aNodes[aNodeId].next = first_anode << 1;

         aNodes[first_anode].prev = aNodeId << 1;

       } else {

         aNodes[aNodeId].next = -1;

       }

       aNodes[aNodeId].prev = -1;

       first_anode = aNodeId;

       aNodes[aNodeId].first_edge = -1;

       return Node(aNodeId << 1);

     }

     Node addBNode() {

       int bNodeId;

       if (first_free_bnode == -1) {

         bNodeId = bNodes.size();

         bNodes.push_back(NodeT());

       } else {

         bNodeId = first_free_bnode;

         first_free_bnode = bNodes[first_free_bnode].next;

       }

       if (first_bnode != -1) {

         bNodes[bNodeId].next = (first_bnode << 1) + 1;

         bNodes[first_bnode].prev = (bNodeId << 1) + 1;

       } else {

         bNodes[bNodeId].next = -1;

       }

       first_bnode = bNodeId;

       bNodes[bNodeId].first_edge = -1;

       return Node((bNodeId << 1) + 1);

     }

     UEdge addEdge(const Node& source, const Node& target) {

       LEMON_ASSERT(((source.id ^ target.id) & 1) == 1, NodeSetError());

       int edgeId;

       if (first_free_edge != -1) {

         edgeId = first_free_edge;

         first_free_edge = edges[edgeId].next_out;

       } else {

         edgeId = edges.size();

         edges.push_back(UEdgeT());

       }

       if ((source.id & 1) == 0) {

 	edges[edgeId].aNode = source.id;

 	edges[edgeId].bNode = target.id;

       } else {

 	edges[edgeId].aNode = target.id;

 	edges[edgeId].bNode = source.id;

       }

       edges[edgeId].next_out = aNodes[edges[edgeId].aNode >> 1].first_edge;

       edges[edgeId].prev_out = -1;

       if (aNodes[edges[edgeId].aNode >> 1].first_edge != -1) {

         edges[aNodes[edges[edgeId].aNode >> 1].first_edge].prev_out = edgeId;

       }

       aNodes[edges[edgeId].aNode >> 1].first_edge = edgeId;

       edges[edgeId].next_in = bNodes[edges[edgeId].bNode >> 1].first_edge;

       edges[edgeId].prev_in = -1;

       if (bNodes[edges[edgeId].bNode >> 1].first_edge != -1) {

         edges[bNodes[edges[edgeId].bNode >> 1].first_edge].prev_in = edgeId;

       }

       bNodes[edges[edgeId].bNode >> 1].first_edge = edgeId;

       return UEdge(edgeId);

     }

     void erase(const Node& node) {

       if (aNode(node)) {

         int aNodeId = node.id >> 1;

         if (aNodes[aNodeId].prev != -1) {

           aNodes[aNodes[aNodeId].prev >> 1].next = aNodes[aNodeId].next;

         } else {

           first_anode = aNodes[aNodeId].next >> 1;

         }

         if (aNodes[aNodeId].next != -1) {

           aNodes[aNodes[aNodeId].next >> 1].prev = aNodes[aNodeId].prev;

         }

         aNodes[aNodeId].next = first_free_anode;

         first_free_anode = aNodeId;

       } else {

         int bNodeId = node.id >> 1;

         if (bNodes[bNodeId].prev != -1) {

           bNodes[bNodes[bNodeId].prev >> 1].next = bNodes[bNodeId].next;

         } else {

           first_bnode = bNodes[bNodeId].next >> 1;

         }

         if (bNodes[bNodeId].next != -1) {

           bNodes[bNodes[bNodeId].next >> 1].prev = bNodes[bNodeId].prev;

         }

         bNodes[bNodeId].next = first_free_bnode;

         first_free_bnode = bNodeId;

       }

     }

     void erase(const UEdge& edge) {

       if (edges[edge.id].prev_out != -1) {

         edges[edges[edge.id].prev_out].next_out = edges[edge.id].next_out;

       } else {

         aNodes[edges[edge.id].aNode >> 1].first_edge = edges[edge.id].next_out;

       }

       if (edges[edge.id].next_out != -1) {

         edges[edges[edge.id].next_out].prev_out = edges[edge.id].prev_out;

       }

       if (edges[edge.id].prev_in != -1) {

         edges[edges[edge.id].prev_in].next_in = edges[edge.id].next_in;

       } else {

         bNodes[edges[edge.id].bNode >> 1].first_edge = edges[edge.id].next_in;

       }

       if (edges[edge.id].next_in != -1) {

         edges[edges[edge.id].next_in].prev_in = edges[edge.id].prev_in;

       }

       edges[edge.id].next_out = first_free_edge;

       first_free_edge = edge.id;

     }

     void clear() {

       aNodes.clear();

       bNodes.clear();

       edges.clear();

       first_anode = -1;

       first_free_anode = -1;

       first_bnode = -1;

       first_free_bnode = -1;

       first_free_edge = -1;

     }

   };

   typedef BpUGraphExtender< ListBpUGraphBase > ExtendedListBpUGraphBase;

   /// \ingroup graphs

   ///

   /// \brief A smart bipartite undirected graph class.

   ///

   /// This is a bipartite undirected graph implementation.

   /// It is conforms to the \ref concept::ErasableBpUGraph "ErasableBpUGraph" 

   /// concept.

   /// \sa concept::BpUGraph.

   ///

   class ListBpUGraph : public ExtendedListBpUGraphBase {};

   /// @}  

 } //namespace lemon

 #endif