/* -*- 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 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; }

    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);

      }

    }

    Node redNode(Edge e) const {

      return Node(e._id % _red_num);

    }

    Node blueNode(Edge e) const {

      return Node(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 firstRed(Node& node) const {

      node._id = _red_num - 1;

    }

    static void nextRed(Node& node) {

      --node._id;

    }

    void firstBlue(Node& node) const {

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

      else node._id = _node_num - 1;

    }

    void nextBlue(Node& 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(Node v) { return v._id; }

    int redId(Node v) const {

      LEMON_DEBUG(v._id < _red_num, "Node has to be red");

      return v._id;

    }

    int blueId(Node v) const {

      LEMON_DEBUG(v._id >= _red_num, "Node has to be blue");

      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;

    }

    Node redNode(int index) const {

      return Node(index);

    }

    int redIndex(Node n) const {

      return n._id;

    }

    Node blueNode(int index) const {

      return Node(index + _red_num);

    }

    int blueIndex(Node 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();

    }