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::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.

   ///\sa concept::Graph.

   class ListGraph : public ExtendedListGraphBase {

   public:

     typedef ExtendedListGraphBase Parent;

     ///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>Edge</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) { 

       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>Edge</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) { 

       Parent::changeSource(e,n);

     }

     /// Invert the direction of an edge.

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

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

     ///invalidated.

     void reverseEdge(Edge e) {

       Node t=target(e);

       changeTarget(e,source(e));

       changeSource(e,t);

     }

     /// \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

     ///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); };

     /// \brief 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;

     }

     /// \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.

     class Snapshot {

     public:

       class UnsupportedOperation : public LogicError {

       public:

 	virtual const char* exceptionName() const {

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

 	}

       };

     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) {

             if (!snapshot.eraseNode(nodes[i])) break;

           }

         }

         virtual void build() {

           NodeNotifier* notifier = getNotifier();

           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() {

           NodeNotifier* notifier = getNotifier();

           Node node;

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

             if (!snapshot.eraseNode(node)) break;

           }

         }

         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) {

             if (!snapshot.eraseEdge(edges[i])) break;

           }

         }

         virtual void build() {

           EdgeNotifier* notifier = getNotifier();

           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() {

           EdgeNotifier* notifier = getNotifier();

           Edge edge;

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

             if (!snapshot.eraseEdge(edge)) break;

           }

         }

         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);        

       }

       bool eraseNode(const Node& node) {

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

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

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

           clear();

           return false;

         } else {

           added_nodes.erase(it);

           return true;

         }

       }

       void addEdge(const Edge& edge) {

         added_edges.push_front(edge);        

       }

       bool eraseEdge(const Edge& edge) {

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

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

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

           clear();

           return false;

         } else {

           added_edges.erase(it);

           return true;

         }        

       }

       void attach(ListGraph &_graph) {

 	graph = &_graph;

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

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

       }

       void detach() {

 	node_observer_proxy.detach();

 	edge_observer_proxy.detach();

       }

       void clear() {

         detach();

         added_nodes.clear();

         added_edges.clear();        

       }

     public:

       /// \brief Default constructur.

       ///

       /// 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) {

         clear();

         attach(_graph);

       }

       /// \brief 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() {

 	detach();

 	while(!added_edges.empty()) {

 	  graph->erase(added_edges.front());

 	  added_edges.pop_front();

 	}

  	while(!added_nodes.empty()) {

 	  graph->erase(added_nodes.front());

 	  added_nodes.pop_front();

 	}

       }

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

       ///

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

       bool valid() const {

         return node_observer_proxy.attached();

       }

     };

   };

   ///@}

   /**************** 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 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 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) { 

       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>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) { 

       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>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);

     }

   };