/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2008

  * 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) {}

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

     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);}

     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 graph implementation.

   ///

   ///It conforms to the \ref concepts::Graph "Graph concept" and it

   ///also provides several additional useful extra functionalities.

   ///The most of the member functions and nested classes are

   ///documented only in the concept class.

   ///

   ///An important extra feature of this graph implementation is that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   ///\sa concepts::Graph.

   class ListGraph : public ExtendedListGraphBase {

   private:

     ///ListGraph is \e not copy constructible. Use GraphCopy() instead.

     ///ListGraph is \e not copy constructible. Use GraphCopy() instead.

     ///

     ListGraph(const ListGraph &) :ExtendedListGraphBase() {};

     ///\brief Assignment of ListGraph to another one is \e not allowed.

     ///Use GraphCopy() instead.

     ///Assignment of ListGraph to another one is \e not allowed.

     ///Use GraphCopy() instead.

     void operator=(const ListGraph &) {}

   public:

     typedef ExtendedListGraphBase Parent;

     /// Constructor

     /// Constructor.

     ///

     ListGraph() {}

     ///Add a new node to the graph.

     /// \return the new node.

     ///

     Node addNode() { return Parent::addNode(); }

     ///Add a new edge to the graph.

     ///Add a new edge to the graph with source node \c s

     ///and target node \c t.

     ///\return the new edge.

     Edge addEdge(const Node& s, const Node& t) { 

       return Parent::addEdge(s, t); 

     }

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

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

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>OutEdgeIt</tt>s referencing

     ///the changed edge remain valid. However <tt>InEdgeIt</tt>s are

     ///invalidated.

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

     ///feature.

     void changeTarget(Edge e, Node n) { 

       Parent::changeTarget(e,n); 

     }

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

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

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s referencing

     ///the changed edge remain valid. However <tt>OutEdgeIt</tt>s are

     ///invalidated.

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

     ///feature.

     void changeSource(Edge e, Node n) { 

       Parent::changeSource(e,n);

     }

     /// Invert the direction of an edge.

     ///\note The <tt>EdgeIt</tt>s referencing the changed edge remain

     ///valid. However <tt>OutEdgeIt</tt>s and <tt>InEdgeIt</tt>s are

     ///invalidated.

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

     ///feature.

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

     /// be very large (e.g. it will contain millions of nodes and/or edges)

     /// then it is worth reserving space for this amount before starting

     /// to build the graph.

     /// \sa reserveEdge

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

     /// \brief 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

     /// be very large (e.g. it will contain millions of nodes and/or edges)

     /// then it is worth reserving space for this amount before starting

     /// to build the graph.

     /// \sa reserveNode

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

     ///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>EdgeIt</tt>s

     ///referencing a moved edge remain

     ///valid. However <tt>InEdgeIt</tt>s and <tt>OutEdgeIt</tt>s

     ///may be invalidated.

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

     ///feature.

     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>EdgeIt</tt>s referencing a moved edge remain

     ///valid. However <tt>InEdgeIt</tt>s and <tt>OutEdgeIt</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;

     }

     /// \brief Class to make a snapshot of the graph and restore

     /// to 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. This

     /// events invalidate the snapshot. 

     class Snapshot {

     protected:

       typedef Parent::NodeNotifier NodeNotifier;

       class NodeObserverProxy : public NodeNotifier::ObserverBase {

       public:

         NodeObserverProxy(Snapshot& _snapshot)

           : snapshot(_snapshot) {}

         using NodeNotifier::ObserverBase::attach;

         using NodeNotifier::ObserverBase::detach;

         using NodeNotifier::ObserverBase::attached;

       protected:

         virtual void add(const Node& node) {

           snapshot.addNode(node);

         }

         virtual void add(const std::vector<Node>& nodes) {

           for (int i = nodes.size() - 1; i >= 0; ++i) {

             snapshot.addNode(nodes[i]);

           }

         }

         virtual void erase(const Node& node) {

           snapshot.eraseNode(node);

         }

         virtual void erase(const std::vector<Node>& nodes) {

           for (int i = 0; i < int(nodes.size()); ++i) {

             snapshot.eraseNode(nodes[i]);

           }

         }

         virtual void build() {

           Node node;

           std::vector<Node> nodes;

           for (notifier()->first(node); node != INVALID; 

                notifier()->next(node)) {

             nodes.push_back(node);

           }

           for (int i = nodes.size() - 1; i >= 0; --i) {

             snapshot.addNode(nodes[i]);

           }

         }

         virtual void clear() {

           Node node;

           for (notifier()->first(node); node != INVALID; 

                notifier()->next(node)) {

             snapshot.eraseNode(node);

           }

         }

         Snapshot& snapshot;

       };

       class EdgeObserverProxy : public EdgeNotifier::ObserverBase {

       public:

         EdgeObserverProxy(Snapshot& _snapshot)

           : snapshot(_snapshot) {}

         using EdgeNotifier::ObserverBase::attach;

         using EdgeNotifier::ObserverBase::detach;

         using EdgeNotifier::ObserverBase::attached;

       protected:

         virtual void add(const Edge& edge) {

           snapshot.addEdge(edge);

         }

         virtual void add(const std::vector<Edge>& edges) {

           for (int i = edges.size() - 1; i >= 0; ++i) {

             snapshot.addEdge(edges[i]);

           }

         }

         virtual void erase(const Edge& edge) {

           snapshot.eraseEdge(edge);

         }

         virtual void erase(const std::vector<Edge>& edges) {

           for (int i = 0; i < int(edges.size()); ++i) {

             snapshot.eraseEdge(edges[i]);

           }

         }

         virtual void build() {

           Edge edge;

           std::vector<Edge> edges;

           for (notifier()->first(edge); edge != INVALID; 

                notifier()->next(edge)) {

             edges.push_back(edge);

           }

           for (int i = edges.size() - 1; i >= 0; --i) {

             snapshot.addEdge(edges[i]);

           }

         }

         virtual void clear() {

           Edge edge;

           for (notifier()->first(edge); edge != INVALID; 

                notifier()->next(edge)) {

             snapshot.eraseEdge(edge);

           }

         }

         Snapshot& snapshot;

       };

       ListGraph *graph;

       NodeObserverProxy node_observer_proxy;

       EdgeObserverProxy edge_observer_proxy;

       std::list<Node> added_nodes;

       std::list<Edge> added_edges;

       void addNode(const Node& node) {

         added_nodes.push_front(node);        

       }

       void eraseNode(const Node& node) {

         std::list<Node>::iterator it = 

           std::find(added_nodes.begin(), added_nodes.end(), node);

         if (it == added_nodes.end()) {

           clear();

           edge_observer_proxy.detach();

           throw NodeNotifier::ImmediateDetach();

         } else {

           added_nodes.erase(it);

         }

       }

       void addEdge(const Edge& edge) {

         added_edges.push_front(edge);        

       }

       void eraseEdge(const Edge& edge) {

         std::list<Edge>::iterator it = 

           std::find(added_edges.begin(), added_edges.end(), edge);

         if (it == added_edges.end()) {

           clear();

           node_observer_proxy.detach(); 

           throw EdgeNotifier::ImmediateDetach();

         } else {

           added_edges.erase(it);

         }        

       }

       void attach(ListGraph &_graph) {

 	graph = &_graph;

 	node_observer_proxy.attach(graph->notifier(Node()));

         edge_observer_proxy.attach(graph->notifier(Edge()));

       }

       void detach() {

 	node_observer_proxy.detach();

 	edge_observer_proxy.detach();

       }

       bool attached() const {

         return node_observer_proxy.attached();

       }

       void clear() {

         added_nodes.clear();

         added_edges.clear();        

       }

     public:

       /// \brief Default constructor.

       ///

       /// Default constructor.

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

       Snapshot() 

         : graph(0), node_observer_proxy(*this), 

           edge_observer_proxy(*this) {}

       /// \brief Constructor that immediately makes a snapshot.

       ///      

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

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

       Snapshot(ListGraph &_graph) 

         : node_observer_proxy(*this), 

           edge_observer_proxy(*this) {

 	attach(_graph);

       }

       /// \brief 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 _graph The graph we make the snapshot of.

       void save(ListGraph &_graph) {

         if (attached()) {

           detach();

           clear();

         }

         attach(_graph);

       }

       /// \brief Undo the changes until the last snapshot.

       // 

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

       void restore() {

 	detach();

 	for(std::list<Edge>::iterator it = added_edges.begin(); 

             it != added_edges.end(); ++it) {

 	  graph->erase(*it);

 	}

 	for(std::list<Node>::iterator it = added_nodes.begin(); 

             it != added_nodes.end(); ++it) {

 	  graph->erase(*it);

 	}

         clear();

       }

       /// \brief Gives back true when the snapshot is valid.

       ///

       /// Gives back true when the snapshot is valid.

       bool valid() const {

         return attached();

       }

     };

   };

   ///@}

   class ListUGraphBase {

   protected:

     struct NodeT {

       int first_out;

       int prev, next;

     };

     struct EdgeT {

       int target;

       int prev_out, next_out;

     };

     std::vector<NodeT> nodes;

     int first_node;

     int first_free_node;

     std::vector<EdgeT> edges;

     int first_free_edge;

   public:

     typedef ListUGraphBase Graph;

     class Node;

     class Edge;

     class UEdge;

     class Node {

       friend class ListUGraphBase;

     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 UEdge {

       friend class ListUGraphBase;

     protected:

       int id;

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

     public:

       UEdge() {}

       UEdge (Invalid) { id = -1; }

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

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

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

     };

     class Edge {

       friend class ListUGraphBase;

     protected:

       int id;

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

     public:

       operator UEdge() const { return uEdgeFromId(id / 2); }

       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;}

     };

     ListUGraphBase()

       : nodes(), first_node(-1),

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

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

     int maxUEdgeId() const { return edges.size() / 2 - 1; }

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

     Node source(Edge e) const { return Node(edges[e.id ^ 1].target); }

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

     Node source(UEdge e) const { return Node(edges[2 * e.id].target); }

     Node target(UEdge e) const { return Node(edges[2 * e.id + 1].target); }

     static bool direction(Edge e) {

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

     }

     static Edge direct(UEdge e, bool d) {

       return Edge(e.id * 2 + (d ? 1 : 0));

     }

     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 = first_node;

       while (n != -1 && nodes[n].first_out == -1) {

         n = nodes[n].next;

       }

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

     }

     void next(Edge& e) const {

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

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

       } else {

 	int n = nodes[edges[e.id ^ 1].target].next;

         while(n != -1 && nodes[n].first_out == -1) {

           n = nodes[n].next;

         }

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

       }      

     }

     void first(UEdge& e) const { 

       int n = first_node;

       while (n != -1) {

         e.id = nodes[n].first_out;

         while ((e.id & 1) != 1) {

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

         }

         if (e.id != -1) {

           e.id /= 2;

           return;

         } 

         n = nodes[n].next;

       }

       e.id = -1;

     }

     void next(UEdge& e) const {

       int n = edges[e.id * 2].target;

       e.id = edges[(e.id * 2) | 1].next_out;

       while ((e.id & 1) != 1) {

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

       }

       if (e.id != -1) {

         e.id /= 2;

         return;

       } 

       n = nodes[n].next;

       while (n != -1) {

         e.id = nodes[n].first_out;

         while ((e.id & 1) != 1) {

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

         }

         if (e.id != -1) {

           e.id /= 2;

           return;

         } 

         n = nodes[n].next;

       }

       e.id = -1;

     }

     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_out) ^ 1);

       if (e.id == -2) e.id = -1;

     }

     void nextIn(Edge &e) const {

       e.id = ((edges[e.id ^ 1].next_out) ^ 1);

       if (e.id == -2) e.id = -1;

     }

     void firstInc(UEdge &e, bool& d, const Node& v) const {

       int de = nodes[v.id].first_out;

       if (de != -1 ) {

         e.id = de / 2;

         d = ((de & 1) == 1);

       } else {

         e.id = -1;

         d = true;

       }

     }

     void nextInc(UEdge &e, bool& d) const {

       int de = (edges[(e.id * 2) | (d ? 1 : 0)].next_out);

       if (de != -1 ) {

         e.id = de / 2;

         d = ((de & 1) == 1);

       } else {

         e.id = -1;

         d = true;

       }

     }

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

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

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

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

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

     static UEdge uEdgeFromId(int id) { return UEdge(id);}

     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_out = -1;

       return Node(n);

     }

     UEdge addEdge(Node u, Node v) {

       int n;      

       if (first_free_edge == -1) {

 	n = edges.size();

 	edges.push_back(EdgeT());

 	edges.push_back(EdgeT());

       } else {

 	n = first_free_edge;

 	first_free_edge = edges[n].next_out;

       }

       edges[n].target = u.id;

       edges[n | 1].target = v.id;

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

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

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

       }      

       edges[n].prev_out = -1;

       nodes[v.id].first_out = n;

       edges[n | 1].next_out = nodes[u.id].first_out;

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

 	edges[nodes[u.id].first_out].prev_out = (n | 1);

       }

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

       nodes[u.id].first_out = (n | 1);

       return UEdge(n / 2);

     }

     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 UEdge& edge) {

       int n = edge.id * 2;

       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 | 1].target].first_out = edges[n].next_out;

       }

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

 	edges[edges[n | 1].next_out].prev_out = edges[n | 1].prev_out;

       } 

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

 	edges[edges[n | 1].prev_out].next_out = edges[n | 1].next_out;

       } else {

 	nodes[edges[n].target].first_out = edges[n | 1].next_out;

       }

       edges[n].next_out = 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(UEdge e, Node n) {

       if(edges[2 * e.id].next_out != -1) {

 	edges[edges[2 * e.id].next_out].prev_out = edges[2 * e.id].prev_out;

       }

       if(edges[2 * e.id].prev_out != -1) {

 	edges[edges[2 * e.id].prev_out].next_out = 

           edges[2 * e.id].next_out;

       } else {

         nodes[edges[(2 * e.id) | 1].target].first_out = 

           edges[2 * e.id].next_out;

       }

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

 	edges[nodes[n.id].first_out].prev_out = 2 * e.id;

       }

       edges[(2 * e.id) | 1].target = n.id;

       edges[2 * e.id].prev_out = -1;

       edges[2 * e.id].next_out = nodes[n.id].first_out;

       nodes[n.id].first_out = 2 * e.id;

     }

     void changeSource(UEdge e, Node n) {

       if(edges[(2 * e.id) | 1].next_out != -1) {

 	edges[edges[(2 * e.id) | 1].next_out].prev_out = 

           edges[(2 * e.id) | 1].prev_out;

       }

       if(edges[(2 * e.id) | 1].prev_out != -1) {

 	edges[edges[(2 * e.id) | 1].prev_out].next_out = 

           edges[(2 * e.id) | 1].next_out;

       } else {

         nodes[edges[2 * e.id].target].first_out = 

           edges[(2 * e.id) | 1].next_out;

       }

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

 	edges[nodes[n.id].first_out].prev_out = ((2 * e.id) | 1);

       }

       edges[2 * e.id].target = n.id;

       edges[(2 * e.id) | 1].prev_out = -1;

       edges[(2 * e.id) | 1].next_out = nodes[n.id].first_out;

       nodes[n.id].first_out = ((2 * e.id) | 1);

     }

   };

 //   typedef UGraphExtender<UndirGraphExtender<ListGraphBase> > 

 //   ExtendedListUGraphBase;

   typedef UGraphExtender<ListUGraphBase> ExtendedListUGraphBase;

   /// \addtogroup graphs

   /// @{

   ///An undirected list graph class.

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

   ///

   ///An important extra feature of this graph implementation is that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   ///It conforms to the

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

   ///

   ///\sa concepts::UGraph.

   ///

   class ListUGraph : public ExtendedListUGraphBase {

   private:

     ///ListUGraph is \e not copy constructible. Use UGraphCopy() instead.

     ///ListUGraph is \e not copy constructible. Use UGraphCopy() instead.

     ///

     ListUGraph(const ListUGraph &) :ExtendedListUGraphBase()  {};

     ///\brief Assignment of ListUGraph to another one is \e not allowed.

     ///Use UGraphCopy() instead.

     ///Assignment of ListUGraph to another one is \e not allowed.

     ///Use UGraphCopy() instead.

     void operator=(const ListUGraph &) {}

   public:

     /// Constructor

     /// Constructor.

     ///

     ListUGraph() {}

     typedef ExtendedListUGraphBase Parent;

     typedef Parent::OutEdgeIt IncEdgeIt;

     /// \brief Add a new node to the graph.

     ///

     /// \return the new node.

     ///

     Node addNode() { return Parent::addNode(); }

     /// \brief Add a new edge to the graph.

     ///

     /// Add a new edge to the graph with source node \c s

     /// and target node \c t.

     /// \return the new undirected edge.

     UEdge addEdge(const Node& s, const Node& t) { 

       return Parent::addEdge(s, t); 

     }

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

     ///

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

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s

     ///referencing the changed edge remain

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

     void changeSource(UEdge e, Node n) { 

       Parent::changeSource(e,n); 

     }    

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

     ///

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

     ///

     /// \note The <tt>EdgeIt</tt>s referencing the changed edge remain

     /// valid. However the other iterators may be invalidated.

     void changeTarget(UEdge e, Node n) { 

       Parent::changeTarget(e,n); 

     }

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

     ///

     /// Changes the source of \c e to \c n. It changes the proper

     /// node of the represented undirected edge.

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s

     ///referencing the changed edge remain

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

     void changeSource(Edge e, Node n) { 

       if (Parent::direction(e)) {

         Parent::changeSource(e,n);

       } else {

         Parent::changeTarget(e,n);

       } 

     }

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

     ///

     /// Changes the target of \c e to \c n. It changes the proper

     /// node of the represented undirected edge.

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>OutEdgeIt</tt>s

     ///referencing the changed edge remain

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

     void changeTarget(Edge e, Node n) { 

       if (Parent::direction(e)) {

         Parent::changeTarget(e,n);

       } else {

         Parent::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>EdgeIt</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);

     }

     /// \brief Class to make a snapshot of the graph and restore

     /// to it later.

     ///

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

     /// later.

     ///

     /// The newly added nodes and undirected edges can be removed

     /// using the restore() function.

     ///

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

     /// events invalidate the snapshot. 

     class Snapshot {

     protected:

       typedef Parent::NodeNotifier NodeNotifier;

       class NodeObserverProxy : public NodeNotifier::ObserverBase {

       public:

         NodeObserverProxy(Snapshot& _snapshot)

           : snapshot(_snapshot) {}

         using NodeNotifier::ObserverBase::attach;

         using NodeNotifier::ObserverBase::detach;

         using NodeNotifier::ObserverBase::attached;

       protected:

         virtual void add(const Node& node) {

           snapshot.addNode(node);

         }

         virtual void add(const std::vector<Node>& nodes) {

           for (int i = nodes.size() - 1; i >= 0; ++i) {

             snapshot.addNode(nodes[i]);

           }

         }

         virtual void erase(const Node& node) {

           snapshot.eraseNode(node);

         }

         virtual void erase(const std::vector<Node>& nodes) {

           for (int i = 0; i < int(nodes.size()); ++i) {

             snapshot.eraseNode(nodes[i]);

           }

         }

         virtual void build() {

           Node node;

           std::vector<Node> nodes;

           for (notifier()->first(node); node != INVALID; 

                notifier()->next(node)) {

             nodes.push_back(node);

           }

           for (int i = nodes.size() - 1; i >= 0; --i) {

             snapshot.addNode(nodes[i]);

           }

         }

         virtual void clear() {

           Node node;

           for (notifier()->first(node); node != INVALID; 

                notifier()->next(node)) {

             snapshot.eraseNode(node);

           }

         }

         Snapshot& snapshot;

       };

       class UEdgeObserverProxy : public UEdgeNotifier::ObserverBase {

       public:

         UEdgeObserverProxy(Snapshot& _snapshot)

           : snapshot(_snapshot) {}

         using UEdgeNotifier::ObserverBase::attach;

         using UEdgeNotifier::ObserverBase::detach;

         using UEdgeNotifier::ObserverBase::attached;

       protected:

         virtual void add(const UEdge& edge) {

           snapshot.addUEdge(edge);

         }

         virtual void add(const std::vector<UEdge>& edges) {

           for (int i = edges.size() - 1; i >= 0; ++i) {

             snapshot.addUEdge(edges[i]);

           }

         }

         virtual void erase(const UEdge& edge) {

           snapshot.eraseUEdge(edge);

         }

         virtual void erase(const std::vector<UEdge>& edges) {

           for (int i = 0; i < int(edges.size()); ++i) {

             snapshot.eraseUEdge(edges[i]);

           }

         }

         virtual void build() {

           UEdge edge;

           std::vector<UEdge> edges;

           for (notifier()->first(edge); edge != INVALID; 

                notifier()->next(edge)) {

             edges.push_back(edge);

           }

           for (int i = edges.size() - 1; i >= 0; --i) {

             snapshot.addUEdge(edges[i]);

           }

         }

         virtual void clear() {

           UEdge edge;

           for (notifier()->first(edge); edge != INVALID; 

                notifier()->next(edge)) {

             snapshot.eraseUEdge(edge);

           }

         }

         Snapshot& snapshot;

       };

       ListUGraph *graph;

       NodeObserverProxy node_observer_proxy;

       UEdgeObserverProxy edge_observer_proxy;

       std::list<Node> added_nodes;

       std::list<UEdge> added_edges;

       void addNode(const Node& node) {

         added_nodes.push_front(node);        

       }

       void eraseNode(const Node& node) {

         std::list<Node>::iterator it = 

           std::find(added_nodes.begin(), added_nodes.end(), node);

         if (it == added_nodes.end()) {

           clear();

           edge_observer_proxy.detach();

           throw NodeNotifier::ImmediateDetach();

         } else {

           added_nodes.erase(it);

         }

       }

       void addUEdge(const UEdge& edge) {

         added_edges.push_front(edge);        

       }

       void eraseUEdge(const UEdge& edge) {

         std::list<UEdge>::iterator it = 

           std::find(added_edges.begin(), added_edges.end(), edge);

         if (it == added_edges.end()) {

           clear();

           node_observer_proxy.detach();

           throw UEdgeNotifier::ImmediateDetach();

         } else {

           added_edges.erase(it);

         }        

       }

       void attach(ListUGraph &_graph) {

 	graph = &_graph;

 	node_observer_proxy.attach(graph->notifier(Node()));

         edge_observer_proxy.attach(graph->notifier(UEdge()));

       }

       void detach() {

 	node_observer_proxy.detach();

 	edge_observer_proxy.detach();

       }

       bool attached() const {

         return node_observer_proxy.attached();

       }

       void clear() {

         added_nodes.clear();

         added_edges.clear();        

       }

     public:

       /// \brief Default constructor.

       ///

       /// Default constructor.

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

       Snapshot() 

         : graph(0), node_observer_proxy(*this), 

           edge_observer_proxy(*this) {}

       /// \brief Constructor that immediately makes a snapshot.

       ///      

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

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

       Snapshot(ListUGraph &_graph) 

         : node_observer_proxy(*this), 

           edge_observer_proxy(*this) {

 	attach(_graph);

       }

       /// \brief 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 _graph The graph we make the snapshot of.

       void save(ListUGraph &_graph) {

         if (attached()) {

           detach();

           clear();

         }

         attach(_graph);

       }

       /// \brief Undo the changes until the last snapshot.

       // 

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

       void restore() {

 	detach();

 	for(std::list<UEdge>::iterator it = added_edges.begin(); 

             it != added_edges.end(); ++it) {

 	  graph->erase(*it);

 	}

 	for(std::list<Node>::iterator it = added_nodes.begin(); 

             it != added_nodes.end(); ++it) {

 	  graph->erase(*it);

 	}

         clear();

       }

       /// \brief Gives back true when the snapshot is valid.

       ///

       /// Gives back true when the snapshot is valid.

       bool valid() const {

         return attached();

       }

     };

   };

   class ListBpUGraphBase {

   public:

     class NodeSetError : public LogicError {

     public:

       virtual const char* what() const throw() { 

 	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 aid = first_anode;

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

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

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

       }

       if (aid != -1) {

         edge.id = aNodes[aid].first_edge;

       } else {

         edge.id = -1;

       }

     }

     void next(UEdge& edge) const {

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

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

       if (edge.id == -1) {

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

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

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

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

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

         }

         if (aid != -1) {

           edge.id = aNodes[aid].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 nodeFromANodeId(int id) {

       return Node(id << 1);

     }

     int maxANodeId() const {

       return aNodes.size();

     }

     static int bNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node nodeFromBNodeId(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 aid;

       if (first_free_anode == -1) {

         aid = aNodes.size();

         aNodes.push_back(NodeT());

       } else {

         aid = first_free_anode;

         first_free_anode = aNodes[first_free_anode].next;

       }

       if (first_anode != -1) {

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

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

       } else {

         aNodes[aid].next = -1;

       }

       aNodes[aid].prev = -1;

       first_anode = aid;

       aNodes[aid].first_edge = -1;

       return Node(aid << 1);

     }

     Node addBNode() {

       int bid;

       if (first_free_bnode == -1) {

         bid = bNodes.size();

         bNodes.push_back(NodeT());

       } else {

         bid = first_free_bnode;

         first_free_bnode = bNodes[first_free_bnode].next;

       }

       if (first_bnode != -1) {

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

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

       } else {

         bNodes[bid].next = -1;

       }

       bNodes[bid].prev = -1;

       first_bnode = bid;

       bNodes[bid].first_edge = -1;

       return Node((bid << 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 aid = node.id >> 1;

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

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

         } else {

           first_anode = 

             aNodes[aid].next != -1 ? aNodes[aid].next >> 1 : -1;

         }

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

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

         }

         aNodes[aid].next = first_free_anode;

         first_free_anode = aid;

       } else {

         int bid = node.id >> 1;

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

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

         } else {

           first_bnode = 

             bNodes[bid].next != -1 ? bNodes[bid].next >> 1 : -1;

         }

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

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

         }

         bNodes[bid].next = first_free_bnode;

         first_free_bnode = bid;

       }

     }

     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;

     }

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

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

       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 (aNodes[node.id >> 1].first_edge != -1) {

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

       }

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

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

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

       edges[edge.id].aNode = node.id;

     } 

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

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

       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;  

       }

       if (bNodes[node.id >> 1].first_edge != -1) {

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

       }

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

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

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

       edges[edge.id].bNode = node.id;

     } 

   };

   typedef BpUGraphExtender<BidirBpUGraphExtender<ListBpUGraphBase> > 

   ExtendedListBpUGraphBase;

   /// \ingroup graphs

   ///

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

   ///

   /// This is a bipartite undirected graph implementation.

   /// It is conforms to the \ref concepts::BpUGraph "BpUGraph concept".

   ///

   ///An important extra feature of this graph implementation is that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   /// \sa concepts::BpUGraph.

   ///

   class ListBpUGraph : public ExtendedListBpUGraphBase {

     /// \brief ListBpUGraph is \e not copy constructible.

     ///

     ///ListBpUGraph is \e not copy constructible.

     ListBpUGraph(const ListBpUGraph &) :ExtendedListBpUGraphBase()  {};

     /// \brief Assignment of ListBpUGraph to another one is \e not

     /// allowed.

     ///

     /// Assignment of ListBpUGraph to another one is \e not allowed.

     void operator=(const ListBpUGraph &) {}

   public:

     /// \brief Constructor

     ///    

     /// Constructor.

     ///

     ListBpUGraph() {}

     typedef ExtendedListBpUGraphBase Parent;

     /// \brief Add a new ANode to the graph.

     ///

     /// \return the new node.

     ///

     Node addANode() { return Parent::addANode(); }

     /// \brief Add a new BNode to the graph.

     ///

     /// \return the new node.

     ///

     Node addBNode() { return Parent::addBNode(); }

     /// \brief Add a new edge to the graph.

     ///

     /// Add a new edge to the graph with an ANode and a BNode.

     /// \return the new undirected edge.

     UEdge addEdge(const Node& s, const Node& t) { 

       return Parent::addEdge(s, t); 

     }

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

     ///

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

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s referencing

     ///the changed edge remain valid. However <tt>OutEdgeIt</tt>s are

     ///invalidated.

     void changeANode(UEdge e, Node n) { 

       Parent::changeANode(e,n); 

     }

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

     ///

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

     ///

     /// \note The <tt>EdgeIt</tt>s and <tt>OutEdgeIt</tt>s

     /// referencing the changed edge remain

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

     void changeBNode(UEdge e, Node n) { 

       Parent::changeBNode(e,n); 

     }

     /// \brief Changes the source(ANode) of \c e to \c n

     ///

     /// Changes the source(ANode) of \c e to \c n

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s referencing

     ///the changed edge remain valid. However <tt>OutEdgeIt</tt>s are

     ///invalidated.

     void changeSource(UEdge e, Node n) { 

       Parent::changeANode(e,n); 

     }

     /// \brief Changes the target(BNode) of \c e to \c n

     ///

     /// Changes the target(BNode) of \c e to \c n

     ///

     /// \note The <tt>EdgeIt</tt>s and <tt>OutEdgeIt</tt>s

     /// referencing the changed edge remain

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

     void changeTarget(UEdge e, Node n) { 

       Parent::changeBNode(e,n); 

     }

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

     ///

     /// Changes the source of \c e to \c n. It changes the proper

     /// node of the represented undirected edge.

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s

     ///referencing the changed edge remain

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

     void changeSource(Edge e, Node n) { 

       if (Parent::direction(e)) {

         Parent::changeANode(e,n);

       } else {

         Parent::changeBNode(e,n);

       } 

     }

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

     ///

     /// Changes the target of \c e to \c n. It changes the proper

     /// node of the represented undirected edge.

     ///

     ///\note The <tt>EdgeIt</tt>s and <tt>OutEdgeIt</tt>s

     ///referencing the changed edge remain

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

     void changeTarget(Edge e, Node n) { 

       if (Parent::direction(e)) {

         Parent::changeBNode(e,n);

       } else {

         Parent::changeANode(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 two nodes

     /// should be from the same nodeset, of course.

     ///

     /// \note The <tt>EdgeIt</tt>s referencing a moved edge remain

     /// valid.

     void contract(const Node& a, const Node& b) {

       LEMON_ASSERT(Parent::aNode(a) == Parent::aNode(b), NodeSetError());

       if (Parent::aNode(a)) {

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

           IncEdgeIt f = e; ++f;

           changeSource(e, a);

           e = f;

         }

       } else {

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

           IncEdgeIt f = e; ++f;

           changeTarget(e, a);

           e = f;

         }

       }

       erase(b);

     }

     /// \brief Class to make a snapshot of the graph and restore

     /// to it later.

     ///

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

     /// later.

     ///

     /// The newly added nodes and undirected edges can be removed

     /// using the restore() function.

     ///

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

     /// events invalidate the snapshot. 

     class Snapshot {

     protected:

       typedef Parent::NodeNotifier NodeNotifier;

       class NodeObserverProxy : public NodeNotifier::ObserverBase {

       public:

         NodeObserverProxy(Snapshot& _snapshot)

           : snapshot(_snapshot) {}

         using NodeNotifier::ObserverBase::attach;

         using NodeNotifier::ObserverBase::detach;

         using NodeNotifier::ObserverBase::attached;

       protected:

         virtual void add(const Node& node) {

           snapshot.addNode(node);

         }

         virtual void add(const std::vector<Node>& nodes) {

           for (int i = nodes.size() - 1; i >= 0; ++i) {

             snapshot.addNode(nodes[i]);

           }

         }

         virtual void erase(const Node& node) {

           snapshot.eraseNode(node);

         }

         virtual void erase(const std::vector<Node>& nodes) {

           for (int i = 0; i < int(nodes.size()); ++i) {

             snapshot.eraseNode(nodes[i]);

           }

         }

         virtual void build() {

           Node node;

           std::vector<Node> nodes;

           for (notifier()->first(node); node != INVALID; 

                notifier()->next(node)) {

             nodes.push_back(node);

           }

           for (int i = nodes.size() - 1; i >= 0; --i) {

             snapshot.addNode(nodes[i]);

           }

         }

         virtual void clear() {

           Node node;

           for (notifier()->first(node); node != INVALID; 

                notifier()->next(node)) {

             snapshot.eraseNode(node);

           }

         }

         Snapshot& snapshot;

       };

       class UEdgeObserverProxy : public UEdgeNotifier::ObserverBase {

       public:

         UEdgeObserverProxy(Snapshot& _snapshot)

           : snapshot(_snapshot) {}

         using UEdgeNotifier::ObserverBase::attach;

         using UEdgeNotifier::ObserverBase::detach;

         using UEdgeNotifier::ObserverBase::attached;

       protected:

         virtual void add(const UEdge& edge) {

           snapshot.addUEdge(edge);

         }

         virtual void add(const std::vector<UEdge>& edges) {

           for (int i = edges.size() - 1; i >= 0; ++i) {

             snapshot.addUEdge(edges[i]);

           }

         }

         virtual void erase(const UEdge& edge) {

           snapshot.eraseUEdge(edge);

         }

         virtual void erase(const std::vector<UEdge>& edges) {

           for (int i = 0; i < int(edges.size()); ++i) {

             snapshot.eraseUEdge(edges[i]);

           }

         }

         virtual void build() {

           UEdge edge;

           std::vector<UEdge> edges;

           for (notifier()->first(edge); edge != INVALID; 

                notifier()->next(edge)) {

             edges.push_back(edge);

           }

           for (int i = edges.size() - 1; i >= 0; --i) {

             snapshot.addUEdge(edges[i]);

           }

         }

         virtual void clear() {

           UEdge edge;

           for (notifier()->first(edge); edge != INVALID; 

                notifier()->next(edge)) {

             snapshot.eraseUEdge(edge);

           }

         }

         Snapshot& snapshot;

       };

       ListBpUGraph *graph;

       NodeObserverProxy node_observer_proxy;

       UEdgeObserverProxy edge_observer_proxy;

       std::list<Node> added_nodes;

       std::list<UEdge> added_edges;

       void addNode(const Node& node) {

         added_nodes.push_front(node);        

       }

       void eraseNode(const Node& node) {

         std::list<Node>::iterator it = 

           std::find(added_nodes.begin(), added_nodes.end(), node);

         if (it == added_nodes.end()) {

           clear();

           edge_observer_proxy.detach();

           throw NodeNotifier::ImmediateDetach();

         } else {

           added_nodes.erase(it);

         }

       }

       void addUEdge(const UEdge& edge) {

         added_edges.push_front(edge);        

       }

       void eraseUEdge(const UEdge& edge) {

         std::list<UEdge>::iterator it = 

           std::find(added_edges.begin(), added_edges.end(), edge);

         if (it == added_edges.end()) {

           clear();

           node_observer_proxy.detach();

           throw UEdgeNotifier::ImmediateDetach();

         } else {

           added_edges.erase(it);

         }        

       }

       void attach(ListBpUGraph &_graph) {

 	graph = &_graph;

 	node_observer_proxy.attach(graph->notifier(Node()));

         edge_observer_proxy.attach(graph->notifier(UEdge()));

       }

       void detach() {

 	node_observer_proxy.detach();

 	edge_observer_proxy.detach();

       }

       bool attached() const {

         return node_observer_proxy.attached();

       }

       void clear() {

         added_nodes.clear();

         added_edges.clear();        

       }

     public:

       /// \brief Default constructor.

       ///

       /// Default constructor.

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

       Snapshot() 

         : graph(0), node_observer_proxy(*this), 

           edge_observer_proxy(*this) {}

       /// \brief Constructor that immediately makes a snapshot.

       ///      

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

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

       Snapshot(ListBpUGraph &_graph) 

         : node_observer_proxy(*this), 

           edge_observer_proxy(*this) {

 	attach(_graph);

       }

       /// \brief 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 _graph The graph we make the snapshot of.

       void save(ListBpUGraph &_graph) {

         if (attached()) {

           detach();

           clear();

         }

         attach(_graph);

       }

       /// \brief Undo the changes until the last snapshot.

       // 

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

       void restore() {

 	detach();

 	for(std::list<UEdge>::iterator it = added_edges.begin(); 

             it != added_edges.end(); ++it) {

 	  graph->erase(*it);

 	}

 	for(std::list<Node>::iterator it = added_nodes.begin(); 

             it != added_nodes.end(); ++it) {

 	  graph->erase(*it);

 	}

         clear();

       }

       /// \brief Gives back true when the snapshot is valid.

       ///

       /// Gives back true when the snapshot is valid.

       bool valid() const {

         return attached();

       }

     };

   };

   /// @}  

 } //namespace lemon

 #endif