#include <lemon/bits/base_extender.h>

   /// \brief Base of the FullUGrpah.

   ///

   /// Base of the FullUGrpah.

   class FullUGraphBase {

     int _nodeNum;

     int _edgeNum;

   public:

     typedef FullUGraphBase Graph;

     class Node;

     class Edge;

   public:

     FullUGraphBase() {}

     ///Creates a full graph with \c n nodes.

     void construct(int n) { _nodeNum = n; _edgeNum = n * (n - 1) / 2; }

     /// \brief Returns the node with the given index.

     ///

     /// Returns the node with the given index. Because it is a

     /// static size graph the node's of the graph can be indiced

     /// by the range from 0 to \e nodeNum()-1 and the index of

     /// the node can accessed by the \e index() member.

     Node operator()(int index) const { return Node(index); }

     /// \brief Returns the index of the node.

     ///

     /// Returns the index of the node. Because it is a

     /// static size graph the node's of the graph can be indiced

     /// by the range from 0 to \e nodeNum()-1 and the index of

     /// the node can accessed by the \e index() member.

     int index(const Node& node) const { return node.id; }

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

     ///Number of nodes.

     int nodeNum() const { return _nodeNum; }

     ///Number of edges.

     int edgeNum() const { return _edgeNum; }

     /// Maximum node ID.

     /// Maximum node ID.

     ///\sa id(Node)

     int maxNodeId() const { return _nodeNum-1; }

     /// Maximum edge ID.

     /// Maximum edge ID.

     ///\sa id(Edge)

     int maxEdgeId() const { return _edgeNum-1; }

     /// \brief Returns the node from its \c id.

     ///

     /// Returns the node from its \c id. If there is not node

     /// with the given id the effect of the function is undefinied.

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

     /// \brief Returns the edge from its \c id.

     ///

     /// Returns the edge from its \c id. If there is not edge

     /// with the given id the effect of the function is undefinied.

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

     Node source(Edge e) const { 

       /// \todo we may do it faster

       return Node(((int)sqrt((double)(1 + 8 * e.id)) + 1) / 2);

     }

     Node target(Edge e) const { 

       int source = ((int)sqrt((double)(1 + 8 * e.id)) + 1) / 2;;

       return Node(e.id - (source) * (source - 1) / 2);

     }

     /// \brief Node ID.

     ///

     /// The ID of a valid Node is a nonnegative integer not greater than

     /// \ref maxNodeId(). The range of the ID's is not surely continuous

     /// and the greatest node ID can be actually less then \ref maxNodeId().

     ///

     /// The ID of the \ref INVALID node is -1.

     /// \return The ID of the node \c v. 

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

     /// \brief Edge ID.

     ///

     /// The ID of a valid Edge is a nonnegative integer not greater than

     /// \ref maxEdgeId(). The range of the ID's is not surely continuous

     /// and the greatest edge ID can be actually less then \ref maxEdgeId().

     ///

     /// The ID of the \ref INVALID edge is -1.

     ///\return The ID of the edge \c e. 

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

     /// \brief Finds an edge between two nodes.

     ///

     /// Finds an edge from node \c u to node \c v.

     ///

     /// If \c prev is \ref INVALID (this is the default value), then

     /// It finds the first edge from \c u to \c v. Otherwise it looks for

     /// the next edge from \c u to \c v after \c prev.

     /// \return The found edge or INVALID if there is no such an edge.

     Edge findEdge(Node u, Node v, Edge prev = INVALID) const {

       if (prev.id != -1 || u.id <= v.id) return Edge(-1);

       return Edge(u.id * (u.id - 1) / 2 + v.id);

     }

     typedef True FindEdgeTag;

     class Node {

       friend class FullUGraphBase;

     protected:

       int id;

       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 FullUGraphBase;

     protected:

       int id;  // _nodeNum * target + source;

       Edge(int _id) : id(_id) {}

     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;}

     };

     void first(Node& node) const {

       node.id = _nodeNum - 1;

     }

     static void next(Node& node) {

       --node.id;

     }

     void first(Edge& edge) const {

       edge.id = _edgeNum - 1;

     }

     static void next(Edge& edge) {

       --edge.id;

     }

     void firstOut(Edge& edge, const Node& node) const {      

       int src = node.id;

       int trg = 0;

       edge.id = (trg < src ? src * (src - 1) / 2 + trg : -1);

     }

     /// \todo with specialized iterators we can make faster iterating

     void nextOut(Edge& edge) const {

       int src = source(edge).id;

       int trg = target(edge).id;

       ++trg;

       edge.id = (trg < src ? src * (src - 1) / 2 + trg : -1);

     }

     void firstIn(Edge& edge, const Node& node) const {

       int src = node.id + 1;

       int trg = node.id;

       edge.id = (src < _nodeNum ? src * (src - 1) / 2 + trg : -1);

     }

     void nextIn(Edge& edge) const {

       int src = source(edge).id;

       int trg = target(edge).id;

       ++src;

       edge.id = (src < _nodeNum ? src * (src - 1) / 2 + trg : -1);

     }

   };

   typedef UGraphExtender<UndirGraphExtender<FullUGraphBase> > 

   ExtendedFullUGraphBase;

   /// \ingroup graphs

   ///

   /// \brief An undirected full graph class.

   ///

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

   /// It is completely static, so you can neither add nor delete either

   /// edges or nodes.

   ///

   /// The main difference beetween the \e FullGraph and \e FullUGraph class

   /// is that this class conforms to the undirected graph concept and

   /// it does not contain the loop edges.

   ///

   /// \sa FullUGraphBase

   /// \sa FullGraph

   ///

   /// \author Balazs Dezso

   class FullUGraph : public ExtendedFullUGraphBase {

   public:

     typedef ExtendedFullUGraphBase Parent;

     /// \brief Constructor

     FullUGraph() { construct(0); }

     /// \brief Constructor

     FullUGraph(int n) { construct(n); }

     /// \brief Resize the graph

     ///

     /// Resize the graph. The function will fully destroy and build the graph.

     /// This cause that the maps of the graph will reallocated

     /// automatically and the previous values will be lost.

     void resize(int n) {

       Parent::getNotifier(Edge()).clear();

       Parent::getNotifier(UEdge()).clear();

       Parent::getNotifier(Node()).clear();

       construct(n);

       Parent::getNotifier(Node()).build();

       Parent::getNotifier(UEdge()).build();

       Parent::getNotifier(Edge()).build();

     }

   };

   class FullBpUGraphBase {

   protected:

     int _aNodeNum;

     int _bNodeNum;

     int _edgeNum;

   public:

     class NodeSetError : public LogicError {

       virtual const char* exceptionName() const { 

 	return "lemon::FullBpUGraph::NodeSetError";

       }

     };

     class Node {

       friend class FullBpUGraphBase;

     protected:

       int id;

       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 FullBpUGraphBase;

     protected:

       int id;

       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;}

     };

     void construct(int aNodeNum, int bNodeNum) {

       _aNodeNum = aNodeNum;

       _bNodeNum = bNodeNum;

       _edgeNum = aNodeNum * bNodeNum;

     }

     void firstANode(Node& node) const {

       node.id = 2 * _aNodeNum - 2;

       if (node.id < 0) node.id = -1; 

     }

     void nextANode(Node& node) const {

       node.id -= 2;

       if (node.id < 0) node.id = -1; 

     }

     void firstBNode(Node& node) const {

       node.id = 2 * _bNodeNum - 1;

     }

     void nextBNode(Node& node) const {

       node.id -= 2;

     }

     void first(Node& node) const {

       if (_aNodeNum > 0) {

 	node.id = 2 * _aNodeNum - 2;

       } else {

 	node.id = 2 * _bNodeNum - 1;

       }

     }

     void next(Node& node) const {

       node.id -= 2;

       if (node.id == -2) {

 	node.id = 2 * _bNodeNum - 1;

       }

     }

     void first(UEdge& edge) const {

       edge.id = _edgeNum - 1;

     }

     void next(UEdge& edge) const {

       --edge.id;

     }

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

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

       edge.id = (node.id >> 1) * _bNodeNum;

     }

     void nextFromANode(UEdge& edge) const {

       ++(edge.id);

       if (edge.id % _bNodeNum == 0) edge.id = -1;

     }

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

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

       edge.id = (node.id >> 1);

     }

     void nextFromBNode(UEdge& edge) const {

       edge.id += _bNodeNum;

       if (edge.id >= _edgeNum) edge.id = -1;

     }

     static int id(const Node& node) {

       return node.id;

     }

     static Node nodeFromId(int id) {

       return Node(id);

     }

     int maxNodeId() const {

       return _aNodeNum > _bNodeNum ? 

 	_aNodeNum * 2 - 2 : _bNodeNum * 2 - 1;

     }

     static int id(const UEdge& edge) {

       return edge.id;

     }

     static UEdge uEdgeFromId(int id) {

       return UEdge(id);

     }

     int maxUEdgeId() const {

       return _edgeNum - 1;

     }

     static int aNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node fromANodeId(int id) {

       return Node(id << 1);

     }

     int maxANodeId() const {

       return _aNodeNum;

     }

     static int bNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node fromBNodeId(int id) {

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

     }

     int maxBNodeId() const {

       return _bNodeNum;

     }

     Node aNode(const UEdge& edge) const {

       return Node((edge.id / _bNodeNum) << 1);

     }

     Node bNode(const UEdge& edge) const {

       return Node(((edge.id % _bNodeNum) << 1) + 1);

     }

     static bool aNode(const Node& node) {

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

     }

     static bool bNode(const Node& node) {

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

     }

     static Node aNode(int index) {

       return Node(index << 1);

     }

     static Node bNode(int index) {

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

     }

     typedef True NodeNumTag;

     int nodeNum() const { return _aNodeNum + _bNodeNum; }

     int aNodeNum() const { return _aNodeNum; }

     int bNodeNum() const { return _bNodeNum; }

     typedef True EdgeNumTag;

     int uEdgeNum() const { return _edgeNum; }

   };

   typedef BpUGraphExtender<FullBpUGraphBase> ExtendedFullBpUGraphBase;

   /// \ingroup graphs

   ///

   /// \brief An undirected full bipartite graph class.

   ///

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

   /// It is completely static, so you can neither add nor delete either

   /// edges or nodes.

   ///

   /// \sa FullUGraphBase

   /// \sa FullGraph

   ///

   /// \author Balazs Dezso

   class FullBpUGraph : 

     public ExtendedFullBpUGraphBase {

   public:

     typedef ExtendedFullBpUGraphBase Parent;

     FullBpUGraph() {

       Parent::construct(0, 0);

     }

     FullBpUGraph(int aNodeNum, int bNodeNum) {

       Parent::construct(aNodeNum, bNodeNum);

     }

     /// \brief Resize the graph

     ///

     void resize(int n, int m) {

       Parent::getNotifier(Edge()).clear();

       Parent::getNotifier(UEdge()).clear();

       Parent::getNotifier(Node()).clear();

       Parent::getNotifier(ANode()).clear();

       Parent::getNotifier(BNode()).clear();

       construct(n, m);

       Parent::getNotifier(ANode()).build();

       Parent::getNotifier(BNode()).build();

       Parent::getNotifier(Node()).build();

       Parent::getNotifier(UEdge()).build();

       Parent::getNotifier(Edge()).build();

     }

   };