/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

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

  *

  * Copyright (C) 2003-2010

  * 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_FULL_GRAPH_H

 #define LEMON_FULL_GRAPH_H

 #include <lemon/core.h>

 #include <lemon/bits/graph_extender.h>

 ///\ingroup graphs

 ///\file

 ///\brief FullDigraph and FullGraph classes.

 namespace lemon {

   class FullDigraphBase {

   public:

     typedef FullDigraphBase Digraph;

     class Node;

     class Arc;

   protected:

     int _node_num;

     int _arc_num;

     FullDigraphBase() {}

     void construct(int n) { _node_num = n; _arc_num = n * n; }

   public:

     typedef True NodeNumTag;

     typedef True ArcNumTag;

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

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

     Arc arc(const Node& s, const Node& t) const {

       return Arc(s._id * _node_num + t._id);

     }

     int nodeNum() const { return _node_num; }

     int arcNum() const { return _arc_num; }

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

     int maxArcId() const { return _arc_num - 1; }

     Node source(Arc arc) const { return arc._id / _node_num; }

     Node target(Arc arc) const { return arc._id % _node_num; }

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

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

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

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

     typedef True FindArcTag;

     Arc findArc(Node s, Node t, Arc prev = INVALID) const {

       return prev == INVALID ? arc(s, t) : INVALID;

     }

     class Node {

       friend class FullDigraphBase;

     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 Arc {

       friend class FullDigraphBase;

     protected:

       int _id;  // _node_num * source + target;

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

     public:

       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;}

     };

     void first(Node& node) const {

       node._id = _node_num - 1;

     }

     static void next(Node& node) {

       --node._id;

     }

     void first(Arc& arc) const {

       arc._id = _arc_num - 1;

     }

     static void next(Arc& arc) {

       --arc._id;

     }

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

       arc._id = (node._id + 1) * _node_num - 1;

     }

     void nextOut(Arc& arc) const {

       if (arc._id % _node_num == 0) arc._id = 0;

       --arc._id;

     }

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

       arc._id = _arc_num + node._id - _node_num;

     }

     void nextIn(Arc& arc) const {

       arc._id -= _node_num;

       if (arc._id < 0) arc._id = -1;

     }

   };

   typedef DigraphExtender<FullDigraphBase> ExtendedFullDigraphBase;

   /// \ingroup graphs

   ///

   /// \brief A directed full graph class.

   ///

   /// FullDigraph is a simple and fast implmenetation of directed full

   /// (complete) graphs. It contains an arc from each node to each node

   /// (including a loop for each node), therefore the number of arcs

   /// is the square of the number of nodes.

   /// This class is completely static and it needs constant memory space.

   /// Thus you can neither add nor delete nodes or arcs, however

   /// the structure can be resized using resize().

   ///

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

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

   /// only in the concept class.

   ///

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

   ///

   /// \note FullDigraph and FullGraph classes are very similar,

   /// but there are two differences. While this class conforms only

   /// to the \ref concepts::Digraph "Digraph" concept, FullGraph

   /// conforms to the \ref concepts::Graph "Graph" concept,

   /// moreover FullGraph does not contain a loop for each

   /// node as this class does.

   ///

   /// \sa FullGraph

   class FullDigraph : public ExtendedFullDigraphBase {

     typedef ExtendedFullDigraphBase Parent;

   public:

     /// \brief Default constructor.

     ///

     /// Default constructor. The number of nodes and arcs will be zero.

     FullDigraph() { construct(0); }

     /// \brief Constructor

     ///

     /// Constructor.

     /// \param n The number of the nodes.

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

     /// \brief Resizes the digraph

     ///

     /// This function resizes the digraph. It fully destroys and

     /// rebuilds the structure, therefore the maps of the digraph will be

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

     void resize(int n) {

       Parent::notifier(Arc()).clear();

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

       construct(n);

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

       Parent::notifier(Arc()).build();

     }

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

     ///

     /// Returns the node with the given index. Since this structure is

     /// completely static, the nodes can be indexed with integers from

     /// the range <tt>[0..nodeNum()-1]</tt>.

     /// The index of a node is the same as its ID.

     /// \sa index()

     Node operator()(int ix) const { return Parent::operator()(ix); }

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

     ///

     /// Returns the index of the given node. Since this structure is

     /// completely static, the nodes can be indexed with integers from

     /// the range <tt>[0..nodeNum()-1]</tt>.

     /// The index of a node is the same as its ID.

     /// \sa operator()()

     static int index(const Node& node) { return Parent::index(node); }

     /// \brief Returns the arc connecting the given nodes.

     ///

     /// Returns the arc connecting the given nodes.

     Arc arc(Node u, Node v) const {

       return Parent::arc(u, v);

     }

     /// \brief Number of nodes.

     int nodeNum() const { return Parent::nodeNum(); }

     /// \brief Number of arcs.

     int arcNum() const { return Parent::arcNum(); }

   };

   class FullGraphBase {

   public:

     typedef FullGraphBase Graph;

     class Node;

     class Arc;

     class Edge;

   protected:

     int _node_num;

     int _edge_num;

     FullGraphBase() {}

     void construct(int n) { _node_num = n; _edge_num = n * (n - 1) / 2; }

     int _uid(int e) const {

       int u = e / _node_num;

       int v = e % _node_num;

       return u < v ? u : _node_num - 2 - u;

     }

     int _vid(int e) const {

       int u = e / _node_num;

       int v = e % _node_num;

       return u < v ? v : _node_num - 1 - v;

     }

     void _uvid(int e, int& u, int& v) const {

       u = e / _node_num;

       v = e % _node_num;

       if  (u >= v) {

         u = _node_num - 2 - u;

         v = _node_num - 1 - v;

       }

     }

     void _stid(int a, int& s, int& t) const {

       if ((a & 1) == 1) {

         _uvid(a >> 1, s, t);

       } else {

         _uvid(a >> 1, t, s);

       }

     }

     int _eid(int u, int v) const {

       if (u < (_node_num - 1) / 2) {

         return u * _node_num + v;

       } else {

         return (_node_num - 1 - u) * _node_num - v - 1;

       }

     }

   public:

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

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

     Edge edge(const Node& u, const Node& v) const {

       if (u._id < v._id) {

         return Edge(_eid(u._id, v._id));

       } else if (u._id != v._id) {

         return Edge(_eid(v._id, u._id));

       } else {

         return INVALID;

       }

     }

     Arc arc(const Node& s, const Node& t) const {

       if (s._id < t._id) {

         return Arc((_eid(s._id, t._id) << 1) | 1);

       } else if (s._id != t._id) {

         return Arc(_eid(t._id, s._id) << 1);

       } else {

         return INVALID;

       }

     }

     typedef True NodeNumTag;

     typedef True ArcNumTag;

     typedef True EdgeNumTag;

     int nodeNum() const { return _node_num; }

     int arcNum() const { return 2 * _edge_num; }

     int edgeNum() const { return _edge_num; }

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

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

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

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

     int maxArcId() const { return 2 * _edge_num-1; }

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

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

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

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

     Node u(Edge edge) const {

       return Node(_uid(edge._id));

     }

     Node v(Edge edge) const {

       return Node(_vid(edge._id));

     }

     Node source(Arc arc) const {

       return Node((arc._id & 1) == 1 ?

                   _uid(arc._id >> 1) : _vid(arc._id >> 1));

     }

     Node target(Arc arc) const {

       return Node((arc._id & 1) == 1 ?

                   _vid(arc._id >> 1) : _uid(arc._id >> 1));

     }

     typedef True FindEdgeTag;

     typedef True FindArcTag;

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

       return prev != INVALID ? INVALID : edge(u, v);

     }

     Arc findArc(Node s, Node t, Arc prev = INVALID) const {

       return prev != INVALID ? INVALID : arc(s, t);

     }

     class Node {

       friend class FullGraphBase;

     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 FullGraphBase;

       friend class Arc;

     protected:

       int _id;

       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;}

     };

     class Arc {

       friend class FullGraphBase;

     protected:

       int _id;

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

     public:

       Arc() { }

       Arc (Invalid) { _id = -1; }

       operator Edge() const { return Edge(_id != -1 ? (_id >> 1) : -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;}

     };

     static bool direction(Arc arc) {

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

     }

     static Arc direct(Edge edge, bool dir) {

       return Arc((edge._id << 1) | (dir ? 1 : 0));

     }

     void first(Node& node) const {

       node._id = _node_num - 1;

     }

     static void next(Node& node) {

       --node._id;

     }

     void first(Arc& arc) const {

       arc._id = (_edge_num << 1) - 1;

     }

     static void next(Arc& arc) {

       --arc._id;

     }

     void first(Edge& edge) const {

       edge._id = _edge_num - 1;

     }

     static void next(Edge& edge) {

       --edge._id;

     }

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

       int s = node._id, t = _node_num - 1;

       if (s < t) {

         arc._id = (_eid(s, t) << 1) | 1;

       } else {

         --t;

         arc._id = (t != -1 ? (_eid(t, s) << 1) : -1);

       }

     }

     void nextOut(Arc& arc) const {

       int s, t;

       _stid(arc._id, s, t);

       --t;

       if (s < t) {

         arc._id = (_eid(s, t) << 1) | 1;

       } else {

         if (s == t) --t;

         arc._id = (t != -1 ? (_eid(t, s) << 1) : -1);

       }

     }

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

       int s = _node_num - 1, t = node._id;

       if (s > t) {

         arc._id = (_eid(t, s) << 1);

       } else {

         --s;

         arc._id = (s != -1 ? (_eid(s, t) << 1) | 1 : -1);

       }

     }

     void nextIn(Arc& arc) const {

       int s, t;

       _stid(arc._id, s, t);

       --s;

       if (s > t) {

         arc._id = (_eid(t, s) << 1);

       } else {

         if (s == t) --s;

         arc._id = (s != -1 ? (_eid(s, t) << 1) | 1 : -1);

       }

     }

     void firstInc(Edge& edge, bool& dir, const Node& node) const {

       int u = node._id, v = _node_num - 1;

       if (u < v) {

         edge._id = _eid(u, v);

         dir = true;

       } else {

         --v;

         edge._id = (v != -1 ? _eid(v, u) : -1);

         dir = false;

       }

     }

     void nextInc(Edge& edge, bool& dir) const {

       int u, v;

       if (dir) {

         _uvid(edge._id, u, v);

         --v;

         if (u < v) {

           edge._id = _eid(u, v);

         } else {

           --v;

           edge._id = (v != -1 ? _eid(v, u) : -1);

           dir = false;

         }

       } else {

         _uvid(edge._id, v, u);

         --v;

         edge._id = (v != -1 ? _eid(v, u) : -1);

       }

     }

   };

   typedef GraphExtender<FullGraphBase> ExtendedFullGraphBase;

   /// \ingroup graphs

   ///

   /// \brief An undirected full graph class.

   ///

   /// FullGraph is a simple and fast implmenetation of undirected full

   /// (complete) graphs. It contains an edge between every distinct pair

   /// of nodes, therefore the number of edges is <tt>n(n-1)/2</tt>.

   /// This class is completely static and it needs constant memory space.

   /// Thus you can neither add nor delete nodes or edges, however

   /// the structure can be resized using resize().

   ///

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

   /// 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.

   ///

   /// \note FullDigraph and FullGraph classes are very similar,

   /// but there are two differences. While FullDigraph

   /// conforms only to the \ref concepts::Digraph "Digraph" concept,

   /// this class conforms to the \ref concepts::Graph "Graph" concept,

   /// moreover this class does not contain a loop for each

   /// node as FullDigraph does.

   ///

   /// \sa FullDigraph

   class FullGraph : public ExtendedFullGraphBase {

     typedef ExtendedFullGraphBase Parent;

   public:

     /// \brief Default constructor.

     ///

     /// Default constructor. The number of nodes and edges will be zero.

     FullGraph() { construct(0); }

     /// \brief Constructor

     ///

     /// Constructor.

     /// \param n The number of the nodes.

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

     /// \brief Resizes the graph

     ///

     /// This function resizes the graph. It fully destroys and

     /// rebuilds the structure, therefore the maps of the graph will be

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

     void resize(int n) {

       Parent::notifier(Arc()).clear();

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

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

       construct(n);

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

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

       Parent::notifier(Arc()).build();

     }

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

     ///

     /// Returns the node with the given index. Since this structure is

     /// completely static, the nodes can be indexed with integers from

     /// the range <tt>[0..nodeNum()-1]</tt>.

     /// The index of a node is the same as its ID.

     /// \sa index()

     Node operator()(int ix) const { return Parent::operator()(ix); }

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

     ///

     /// Returns the index of the given node. Since this structure is

     /// completely static, the nodes can be indexed with integers from

     /// the range <tt>[0..nodeNum()-1]</tt>.

     /// The index of a node is the same as its ID.

     /// \sa operator()()

     static int index(const Node& node) { return Parent::index(node); }

     /// \brief Returns the arc connecting the given nodes.

     ///

     /// Returns the arc connecting the given nodes.

     Arc arc(Node s, Node t) const {

       return Parent::arc(s, t);

     }

     /// \brief Returns the edge connecting the given nodes.

     ///

     /// Returns the edge connecting the given nodes.

     Edge edge(Node u, Node v) const {

       return Parent::edge(u, v);

     }

     /// \brief Number of nodes.

     int nodeNum() const { return Parent::nodeNum(); }

     /// \brief Number of arcs.

     int arcNum() const { return Parent::arcNum(); }

     /// \brief Number of edges.

     int edgeNum() const { return Parent::edgeNum(); }

   };

   class FullBpGraphBase {

   protected:

     int _red_num, _blue_num;

     int _node_num, _edge_num;

   public:

     typedef FullBpGraphBase Graph;

     class Node;

     class Arc;

     class Edge;

     class Node {

       friend class FullBpGraphBase;

     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 RedNode : public Node {

       friend class FullBpGraphBase;

     protected:

       explicit RedNode(int pid) : Node(pid) {}

     public:

       RedNode() {}

       RedNode(const RedNode& node) : Node(node) {}

       RedNode(Invalid) : Node(INVALID){}

     };

     class BlueNode : public Node {

       friend class FullBpGraphBase;

     protected:

       explicit BlueNode(int pid) : Node(pid) {}

     public:

       BlueNode() {}

       BlueNode(const BlueNode& node) : Node(node) {}

       BlueNode(Invalid) : Node(INVALID){}

     };

     class Edge {

       friend class FullBpGraphBase;

     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 FullBpGraphBase;

     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;}

     };

   protected:

     FullBpGraphBase()

       : _red_num(0), _blue_num(0), _node_num(0), _edge_num(0) {}

     void construct(int redNum, int blueNum) {

       _red_num = redNum; _blue_num = blueNum;

       _node_num = redNum + blueNum; _edge_num = redNum * blueNum;

     }

   public:

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

     typedef True ArcNumTag;

     int nodeNum() const { return _node_num; }

     int redNum() const { return _red_num; }

     int blueNum() const { return _blue_num; }

     int edgeNum() const { return _edge_num; }

     int arcNum() const { return 2 * _edge_num; }

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

     int maxRedId() const { return _red_num - 1; }

     int maxBlueId() const { return _blue_num - 1; }

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

     int maxArcId() const { return 2 * _edge_num - 1; }

     bool red(Node n) const { return n._id < _red_num; }

     bool blue(Node n) const { return n._id >= _red_num; }

     static RedNode asRedNodeUnsafe(Node n) { return RedNode(n._id); }

     static BlueNode asBlueNodeUnsafe(Node n) { return BlueNode(n._id); }

     Node source(Arc a) const {

       if (a._id & 1) {

         return Node((a._id >> 1) % _red_num);

       } else {

         return Node((a._id >> 1) / _red_num + _red_num);

       }

     }

     Node target(Arc a) const {

       if (a._id & 1) {

         return Node((a._id >> 1) / _red_num + _red_num);

       } else {

         return Node((a._id >> 1) % _red_num);

       }

     }

     RedNode redNode(Edge e) const {

       return RedNode(e._id % _red_num);

     }

     BlueNode blueNode(Edge e) const {

       return BlueNode(e._id / _red_num + _red_num);

     }

     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 = _node_num - 1;

     }

     static void next(Node& node) {

       --node._id;

     }

     void first(RedNode& node) const {

       node._id = _red_num - 1;

     }

     static void next(RedNode& node) {

       --node._id;

     }

     void first(BlueNode& node) const {

       if (_red_num == _node_num) node._id = -1;

       else node._id = _node_num - 1;

     }

     void next(BlueNode& node) const {

       if (node._id == _red_num) node._id = -1;

       else --node._id;

     }

     void first(Arc& arc) const {

       arc._id = 2 * _edge_num - 1;

     }

     static void next(Arc& arc) {

       --arc._id;

     }

     void first(Edge& arc) const {

       arc._id = _edge_num - 1;

     }

     static void next(Edge& arc) {

       --arc._id;

     }

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

       if (v._id < _red_num) {

         a._id = 2 * (v._id + _red_num * (_blue_num - 1)) + 1;

       } else {

         a._id = 2 * (_red_num - 1 + _red_num * (v._id - _red_num));

       }

     }

     void nextOut(Arc &a) const {

       if (a._id & 1) {

         a._id -= 2 * _red_num;

         if (a._id < 0) a._id = -1;

       } else {

         if (a._id % (2 * _red_num) == 0) a._id = -1;

         else a._id -= 2;

       }

     }

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

       if (v._id < _red_num) {

         a._id = 2 * (v._id + _red_num * (_blue_num - 1));

       } else {

         a._id = 2 * (_red_num - 1 + _red_num * (v._id - _red_num)) + 1;

       }

     }

     void nextIn(Arc &a) const {

       if (a._id & 1) {

         if (a._id % (2 * _red_num) == 1) a._id = -1;

         else a._id -= 2;

       } else {

         a._id -= 2 * _red_num;

         if (a._id < 0) a._id = -1;

       }

     }

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

       if (v._id < _red_num) {

         d = true;

         e._id = v._id + _red_num * (_blue_num - 1);

       } else {

         d = false;

         e._id = _red_num - 1 + _red_num * (v._id - _red_num);

       }

     }

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

       if (d) {

         e._id -= _red_num;

         if (e._id < 0) e._id = -1;

       } else {

         if (e._id % _red_num == 0) e._id = -1;

         else --e._id;

       }

     }

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

     int id(const RedNode& v) const { return v._id; }

     int id(const BlueNode& v) const { return v._id - _red_num; }

     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 < _node_num;

     }

     bool valid(Arc a) const {

       return a._id >= 0 && a._id < 2 * _edge_num;

     }

     bool valid(Edge e) const {

       return e._id >= 0 && e._id < _edge_num;

     }

     RedNode redNode(int index) const {

       return RedNode(index);

     }

     int index(RedNode n) const {

       return n._id;

     }

     BlueNode blueNode(int index) const {

       return BlueNode(index + _red_num);

     }

     int index(BlueNode n) const {

       return n._id - _red_num;

     }

     void clear() {

       _red_num = 0; _blue_num = 0;

       _node_num = 0; _edge_num = 0;

     }

     Edge edge(const Node& u, const Node& v) const { 

       if (u._id < _red_num) {

         if (v._id < _red_num) {

           return Edge(-1);

         } else {

           return Edge(u._id + _red_num * (v._id - _red_num));

         }

       } else {

         if (v._id < _red_num) {

           return Edge(v._id + _red_num * (u._id - _red_num));

         } else {

           return Edge(-1);

         }

       }

     }

     Arc arc(const Node& u, const Node& v) const { 

       if (u._id < _red_num) {

         if (v._id < _red_num) {

           return Arc(-1);

         } else {

           return Arc(2 * (u._id + _red_num * (v._id - _red_num)) + 1);

         }

       } else {

         if (v._id < _red_num) {

           return Arc(2 * (v._id + _red_num * (u._id - _red_num)));

         } else {

           return Arc(-1);

         }

       }

     }

     typedef True FindEdgeTag;

     typedef True FindArcTag;

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

       return prev != INVALID ? INVALID : edge(u, v);

     }

     Arc findArc(Node s, Node t, Arc prev = INVALID) const {

       return prev != INVALID ? INVALID : arc(s, t);

     }

   };

   typedef BpGraphExtender<FullBpGraphBase> ExtendedFullBpGraphBase;

   /// \ingroup graphs

   ///

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

   ///

   /// FullBpGraph is a simple and fast implmenetation of undirected

   /// full bipartite graphs. It contains an edge between every

   /// red-blue pairs of nodes, therefore the number of edges is

   /// <tt>nr*nb</tt>.  This class is completely static and it needs

   /// constant memory space.  Thus you can neither add nor delete

   /// nodes or edges, however the structure can be resized using

   /// resize().

   ///

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

   /// 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 FullGraph

   class FullBpGraph : public ExtendedFullBpGraphBase {

   public:

     typedef ExtendedFullBpGraphBase Parent;

     /// \brief Default constructor.

     ///

     /// Default constructor. The number of nodes and edges will be zero.

     FullBpGraph() { construct(0, 0); }

     /// \brief Constructor

     ///

     /// Constructor.

     /// \param redNum The number of the red nodes.

     /// \param blueNum The number of the blue nodes.

     FullBpGraph(int redNum, int blueNum) { construct(redNum, blueNum); }

     /// \brief Resizes the graph

     ///

     /// This function resizes the graph. It fully destroys and

     /// rebuilds the structure, therefore the maps of the graph will be

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

     void resize(int redNum, int blueNum) {

       Parent::notifier(Arc()).clear();

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

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

       Parent::notifier(BlueNode()).clear();

       Parent::notifier(RedNode()).clear();

       construct(redNum, blueNum);

       Parent::notifier(RedNode()).build();

       Parent::notifier(BlueNode()).build();

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

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

       Parent::notifier(Arc()).build();

     }

     using Parent::redNode;

     using Parent::blueNode;

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

     ///

     /// Returns the red node with the given index. Since this

     /// structure is completely static, the red nodes can be indexed

     /// with integers from the range <tt>[0..redNum()-1]</tt>.

     /// \sa redIndex()

     RedNode redNode(int index) const { return Parent::redNode(index); }

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

     ///

     /// Returns the index of the given red node. Since this structure

     /// is completely static, the red nodes can be indexed with

     /// integers from the range <tt>[0..redNum()-1]</tt>.

     ///

     /// \sa operator()()

     int index(RedNode node) const { return Parent::index(node); }

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

     ///

     /// Returns the blue node with the given index. Since this

     /// structure is completely static, the blue nodes can be indexed

     /// with integers from the range <tt>[0..blueNum()-1]</tt>.

     /// \sa blueIndex()

     BlueNode blueNode(int index) const { return Parent::blueNode(index); }

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

     ///

     /// Returns the index of the given blue node. Since this structure

     /// is completely static, the blue nodes can be indexed with

     /// integers from the range <tt>[0..blueNum()-1]</tt>.

     ///

     /// \sa operator()()

     int index(BlueNode node) const { return Parent::index(node); }

     /// \brief Returns the edge which connects the given nodes.

     ///

     /// Returns the edge which connects the given nodes.

     Edge edge(const Node& u, const Node& v) const {

       return Parent::edge(u, v);

     }

     /// \brief Returns the arc which connects the given nodes.

     ///

     /// Returns the arc which connects the given nodes.

     Arc arc(const Node& u, const Node& v) const {

       return Parent::arc(u, v);

     }

     /// \brief Number of nodes.

     int nodeNum() const { return Parent::nodeNum(); }

     /// \brief Number of red nodes.

     int redNum() const { return Parent::redNum(); }

     /// \brief Number of blue nodes.

     int blueNum() const { return Parent::blueNum(); }

     /// \brief Number of arcs.

     int arcNum() const { return Parent::arcNum(); }

     /// \brief Number of edges.

     int edgeNum() const { return Parent::edgeNum(); }

   };

 } //namespace lemon

 #endif //LEMON_FULL_GRAPH_H