class SmartBpGraphBase {

   protected:

     struct NodeT {

       int first_out;

       int partition_next;

       int partition_index;

       bool red;

     };

     struct ArcT {

       int target;

       int next_out;

     };

     std::vector<NodeT> nodes;

     std::vector<ArcT> arcs;

     int first_red, first_blue;

   public:

     typedef SmartBpGraphBase Graph;

     class Node;

     class Arc;

     class Edge;

     class Node {

       friend class SmartBpGraphBase;

     protected:

       int _id;

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

     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 SmartBpGraphBase;

     protected:

       int _id;

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

     public:

       Edge() {}

       Edge (Invalid) { _id = -1; }

       bool operator==(const Edge& arc) const {return _id == arc._id;}

       bool operator!=(const Edge& arc) const {return _id != arc._id;}

       bool operator<(const Edge& arc) const {return _id < arc._id;}

     };

     class Arc {

       friend class SmartBpGraphBase;

     protected:

       int _id;

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

     public:

       operator Edge() const {

         return _id != -1 ? edgeFromId(_id / 2) : INVALID;

       }

       Arc() {}

       Arc (Invalid) { _id = -1; }

       bool operator==(const Arc& arc) const {return _id == arc._id;}

       bool operator!=(const Arc& arc) const {return _id != arc._id;}

       bool operator<(const Arc& arc) const {return _id < arc._id;}

     };

     SmartBpGraphBase()

       : nodes(), arcs(), first_red(-1), first_blue(-1) {}

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

     typedef True ArcNumTag;

     int nodeNum() const { return nodes.size(); }

     int redNum() const {

       return first_red == -1 ? 0 : nodes[first_red].partition_index + 1;

     }

     int blueNum() const {

       return first_blue == -1 ? 0 : nodes[first_blue].partition_index + 1;

     }

     int edgeNum() const { return arcs.size() / 2; }

     int arcNum() const { return arcs.size(); }

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

     int maxRedId() const {

       return first_red == -1 ? -1 : nodes[first_red].partition_index;

     }

     int maxBlueId() const {

       return first_blue == -1 ? -1 : nodes[first_blue].partition_index;

     }

     int maxEdgeId() const { return arcs.size() / 2 - 1; }

     int maxArcId() const { return arcs.size()-1; }

     bool red(Node n) const { return nodes[n._id].red; }

     bool blue(Node n) const { return !nodes[n._id].red; }

     Node source(Arc a) const { return Node(arcs[a._id ^ 1].target); }

     Node target(Arc a) const { return Node(arcs[a._id].target); }

     Node redNode(Edge e) const { return Node(arcs[2 * e._id].target); }

     Node blueNode(Edge e) const { return Node(arcs[2 * e._id + 1].target); }

     Node u(Edge e) const { return redNode(e); }

     Node v(Edge e) const { return blueNode(e); }

     static bool direction(Arc a) {

       return (a._id & 1) == 1;

     }

     static Arc direct(Edge e, bool d) {

       return Arc(e._id * 2 + (d ? 1 : 0));

     }

     void first(Node& node) const {

       node._id = nodes.size() - 1;

     }

     static void next(Node& node) {

       --node._id;

     }

     void firstRed(Node& node) const {

       node._id = first_red;

     }

     void nextRed(Node& node) const {

       node._id = nodes[node._id].partition_next;

     }

     void firstBlue(Node& node) const {

       node._id = first_blue;

     }

     void nextBlue(Node& node) const {

       node._id = nodes[node._id].partition_next;

     }

     void first(Arc& arc) const {

       arc._id = arcs.size() - 1;

     }

     static void next(Arc& arc) {

       --arc._id;

     }

     void first(Edge& arc) const {

       arc._id = arcs.size() / 2 - 1;

     }

     static void next(Edge& arc) {

       --arc._id;

     }

     void firstOut(Arc &arc, const Node& v) const {

       arc._id = nodes[v._id].first_out;

     }

     void nextOut(Arc &arc) const {

       arc._id = arcs[arc._id].next_out;

     }

     void firstIn(Arc &arc, const Node& v) const {

       arc._id = ((nodes[v._id].first_out) ^ 1);

       if (arc._id == -2) arc._id = -1;

     }

     void nextIn(Arc &arc) const {

       arc._id = ((arcs[arc._id ^ 1].next_out) ^ 1);

       if (arc._id == -2) arc._id = -1;

     }

     void firstInc(Edge &arc, bool& d, const Node& v) const {

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

       if (de != -1) {

         arc._id = de / 2;

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

       } else {

         arc._id = -1;

         d = true;

       }

     }

     void nextInc(Edge &arc, bool& d) const {

       int de = (arcs[(arc._id * 2) | (d ? 1 : 0)].next_out);

       if (de != -1) {

         arc._id = de / 2;

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

       } else {

         arc._id = -1;

         d = true;

       }

     }

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

     int redId(Node v) const {

       LEMON_DEBUG(nodes[v._id].red, "Node has to be red");

       return nodes[v._id].partition_index;

     }

     int blueId(Node v) const {

       LEMON_DEBUG(nodes[v._id].red, "Node has to be blue");

       return nodes[v._id].partition_index;

     }

     static int id(Arc e) { return e._id; }

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

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

     static Arc arcFromId(int id) { return Arc(id);}

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

     bool valid(Node n) const {

       return n._id >= 0 && n._id < static_cast<int>(nodes.size());

     }

     bool valid(Arc a) const {

       return a._id >= 0 && a._id < static_cast<int>(arcs.size());

     }

     bool valid(Edge e) const {

       return e._id >= 0 && 2 * e._id < static_cast<int>(arcs.size());

     }

     Node addRedNode() {

       int n = nodes.size();

       nodes.push_back(NodeT());

       nodes[n].first_out = -1;

       nodes[n].red = true;

       if (first_red == -1) {

         nodes[n].partition_index = 0;

       } else {

         nodes[n].partition_index = nodes[first_red].partition_index + 1;

       }

       nodes[n].partition_next = first_red;

       first_red = n;

       return Node(n);

     }

     Node addBlueNode() {

       int n = nodes.size();

       nodes.push_back(NodeT());

       nodes[n].first_out = -1;

       nodes[n].red = false;

       if (first_blue == -1) {

         nodes[n].partition_index = 0;

       } else {

         nodes[n].partition_index = nodes[first_blue].partition_index + 1;

       }

       nodes[n].partition_next = first_blue;

       first_blue = n;

       return Node(n);

     }

     Edge addEdge(Node u, Node v) {

       int n = arcs.size();

       arcs.push_back(ArcT());

       arcs.push_back(ArcT());

       arcs[n].target = u._id;

       arcs[n | 1].target = v._id;

       arcs[n].next_out = nodes[v._id].first_out;

       nodes[v._id].first_out = n;

       arcs[n | 1].next_out = nodes[u._id].first_out;

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

       return Edge(n / 2);

     }

     void clear() {

       arcs.clear();

       nodes.clear();

       first_red = -1;

       first_blue = -1;

     }

   };

   typedef BpGraphExtender<SmartBpGraphBase> ExtendedSmartBpGraphBase;

   /// \ingroup graphs

   ///

   /// \brief A smart undirected graph class.

   ///

   /// \ref SmartBpGraph is a simple and fast graph implementation.

   /// It is also quite memory efficient but at the price

   /// that it does not support node and edge deletion

   /// (except for the Snapshot feature).

   ///

   /// This type fully conforms to the \ref concepts::Graph "Graph concept"

   /// and it also provides some additional functionalities.

   /// Most of its member functions and nested classes are documented

   /// only in the concept class.

   ///

   /// This class provides constant time counting for nodes, edges and arcs.

   ///

   /// \sa concepts::Graph

   /// \sa SmartDigraph

   class SmartBpGraph : public ExtendedSmartBpGraphBase {

     typedef ExtendedSmartBpGraphBase Parent;

   private:

     /// Graphs are \e not copy constructible. Use GraphCopy instead.

     SmartBpGraph(const SmartBpGraph &) : ExtendedSmartBpGraphBase() {};

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

     /// Use GraphCopy instead.

     void operator=(const SmartBpGraph &) {}

   public:

     /// Constructor

     /// Constructor.

     ///

     SmartBpGraph() {}

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

     ///

     /// This function adds a red new node to the graph.

     /// \return The new node.

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

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

     ///

     /// This function adds a blue new node to the graph.

     /// \return The new node.

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

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

     ///

     /// This function adds a new edge to the graph between nodes

     /// \c u and \c v with inherent orientation from node \c u to

     /// node \c v.

     /// \return The new edge.

     Edge addEdge(Node red, Node blue) {

       LEMON_DEBUG(Parent::red(red) && Parent::blue(blue),

                   "Edge has to be formed by a red and a blue nodes");

       return Parent::addEdge(red, blue);

     }

     /// \brief Node validity check

     ///

     /// This function gives back \c true if the given node is valid,

     /// i.e. it is a real node of the graph.

     ///

     /// \warning A removed node (using Snapshot) could become valid again

     /// if new nodes are added to the graph.

     bool valid(Node n) const { return Parent::valid(n); }

     /// \brief Edge validity check

     ///

     /// This function gives back \c true if the given edge is valid,

     /// i.e. it is a real edge of the graph.

     ///

     /// \warning A removed edge (using Snapshot) could become valid again

     /// if new edges are added to the graph.

     bool valid(Edge e) const { return Parent::valid(e); }

     /// \brief Arc validity check

     ///

     /// This function gives back \c true if the given arc is valid,

     /// i.e. it is a real arc of the graph.

     ///

     /// \warning A removed arc (using Snapshot) could become valid again

     /// if new edges are added to the graph.

     bool valid(Arc a) const { return Parent::valid(a); }

     ///Clear the graph.

     ///This function erases all nodes and arcs from the graph.

     ///

     void clear() {

       Parent::clear();

     }

     /// Reserve memory for nodes.

     /// Using this function, it is possible to avoid superfluous memory

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

     /// be 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); };

     /// Reserve memory for edges.

     /// Using this function, it is possible to avoid superfluous memory

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

     /// be 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) { arcs.reserve(2 * m); };

   public:

     class Snapshot;

   protected:

     void saveSnapshot(Snapshot &s)

     {

       s._graph = this;

       s.node_num = nodes.size();

       s.arc_num = arcs.size();

     }

     void restoreSnapshot(const Snapshot &s)

     {

       while(s.arc_num<arcs.size()) {

         int n=arcs.size()-1;

         Edge arc=edgeFromId(n/2);

         Parent::notifier(Edge()).erase(arc);

         std::vector<Arc> dir;

         dir.push_back(arcFromId(n));

         dir.push_back(arcFromId(n-1));

         Parent::notifier(Arc()).erase(dir);

         nodes[arcs[n-1].target].first_out=arcs[n].next_out;

         nodes[arcs[n].target].first_out=arcs[n-1].next_out;

         arcs.pop_back();

         arcs.pop_back();

       }

       while(s.node_num<nodes.size()) {

         int n=nodes.size()-1;

         Node node = nodeFromId(n);

         if (Parent::red(node)) {

           first_red = nodes[n].partition_next;

           Parent::notifier(RedNode()).erase(node);          

         } else {

           first_blue = nodes[n].partition_next;

           Parent::notifier(BlueNode()).erase(node);

         }

         Parent::notifier(Node()).erase(node);

         nodes.pop_back();

       }

     }

   public:

     ///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. This is the only way for deleting nodes and/or

     ///edges from a SmartBpGraph structure.

     ///

     ///\note After a state is restored, you cannot restore a later state,

     ///i.e. you cannot add the removed nodes and edges again using

     ///another Snapshot instance.

     ///

     ///\warning The validity of the snapshot is not stored due to

     ///performance reasons. If you do not use the snapshot correctly,

     ///it can cause broken program, invalid or not restored state of

     ///the graph or no change.

     class Snapshot

     {

       SmartBpGraph *_graph;

     protected:

       friend class SmartBpGraph;

       unsigned int node_num;

       unsigned int arc_num;

     public:

       ///Default constructor.

       ///Default constructor.

       ///You have to call save() to actually make a snapshot.

       Snapshot() : _graph(0) {}

       ///Constructor that immediately makes a snapshot

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

       ///

       Snapshot(SmartBpGraph &gr) {

         gr.saveSnapshot(*this);

       }

       ///Make a snapshot.

       ///This function makes a snapshot of the given graph.

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

       ///call, the previous snapshot gets lost.

       void save(SmartBpGraph &gr)

       {

         gr.saveSnapshot(*this);

       }

       ///Undo the changes until the last snapshot.

       ///This function undos the changes until the last snapshot

       ///created by save() or Snapshot(SmartBpGraph&).

       void restore()

       {

         _graph->restoreSnapshot(*this);

       }

     };

   };