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

 *

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

 *

 * Copyright (C) 2003-2008

 * 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 FullGraph and FullDigraph classes.

namespace lemon {

  class FullDigraphBase {

  public:

    typedef FullDigraphBase Graph;

    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); }

    int index(const Node& node) const { 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 full digraph class.

  ///

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

  /// From each node go arcs to each node (including the source node),

  /// therefore the number of the arcs in the digraph is the square of

  /// the node number. This digraph type is completely static, so you

  /// can neither add nor delete either arcs or nodes, and it needs

  /// constant space in memory.

  ///

  /// This class conforms to the \ref concepts::Digraph "Digraph" concept

  /// and it also has an important extra feature that its maps are

  /// real \ref concepts::ReferenceMap "reference map"s.

  ///

  /// The \c FullDigraph and \c FullGraph classes are very similar,

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

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

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

  /// moreover \c FullGraph does not contain a loop arc for each

  /// node as \c FullDigraph does.

  ///

  /// \sa FullGraph

  class FullDigraph : public ExtendedFullDigraphBase {

  public:

    typedef ExtendedFullDigraphBase Parent;

    /// \brief Constructor

    FullDigraph() { construct(0); }

    /// \brief Constructor

    ///

    /// Constructor.

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

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

    /// \brief Resizes the digraph

    ///

    /// Resizes the digraph. The function will fully destroy and

    /// rebuild the digraph. This cause that the maps of the digraph will

    /// 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 it is a static

    /// digraph its nodes can be indexed with integers from the range

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

    /// \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 it is a static

    /// digraph its nodes can be indexed with integers from the range

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

    /// \sa operator()

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

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

    ///

    /// Returns the arc connecting 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 arcs.

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

  };

  class FullGraphBase {

    int _node_num;

    int _edge_num;

  public:

    typedef FullGraphBase Graph;

    class Node;

    class Arc;

    class Edge;

  protected:

    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); }

    int index(const Node& node) const { 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 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;

    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.

  ///

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

  /// implementation. From each node go edge to each other node,

  /// therefore the number of edges in the graph is \f$n(n-1)/2\f$.

  /// This graph type is completely static, so you can neither

  /// add nor delete either edges or nodes, and it needs constant

  /// space in memory.

  ///

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

  /// and it also has an important extra feature that its maps are

  /// real \ref concepts::ReferenceMap "reference map"s.

  ///

  /// The \c FullGraph and \c FullDigraph classes are very similar,

  /// but there are two differences. While the \c FullDigraph class

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

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

  /// moreover \c FullGraph does not contain a loop arc for each

  /// node as \c FullDigraph does.

  ///

  /// \sa FullDigraph

  class FullGraph : public ExtendedFullGraphBase {

  public:

    typedef ExtendedFullGraphBase Parent;

    /// \brief Constructor

    FullGraph() { construct(0); }

    /// \brief Constructor

    ///

    /// Constructor.

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

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

    /// \brief Resizes the graph

    ///

    /// Resizes the graph. The function will fully destroy and

    /// rebuild 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::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 it is a static

    /// graph its nodes can be indexed with integers from the range

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

    /// \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 it is a static

    /// graph its nodes can be indexed with integers from the range

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

    /// \sa operator()

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

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

    ///

    /// Returns the arc connecting the given nodes.

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

      return Parent::arc(s, t);

    }

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

    ///

    /// Returns the edge connects the given nodes.

    Edge edge(const Node& u, const 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(); }

  };

} //namespace lemon

#endif //LEMON_FULL_GRAPH_H

	lemon/full_graph.h \

#include <lemon/full_graph.h>

void checkFullDigraph(int num) {

  typedef FullDigraph Digraph;

  DIGRAPH_TYPEDEFS(Digraph);

  Digraph G(num);

  checkGraphNodeList(G, num);

  checkGraphArcList(G, num * num);

  for (NodeIt n(G); n != INVALID; ++n) {

    checkGraphOutArcList(G, n, num);

    checkGraphInArcList(G, n, num);

  }

  checkGraphConArcList(G, num * num);

  checkNodeIds(G);

  checkArcIds(G);

  checkGraphNodeMap(G);

  checkGraphArcMap(G);

  for (int i = 0; i < G.nodeNum(); ++i) {

    check(G.index(G(i)) == i, "Wrong index");

  }

  for (NodeIt s(G); s != INVALID; ++s) {

    for (NodeIt t(G); t != INVALID; ++t) {

      Arc a = G.arc(s, t);

      check(G.source(a) == s && G.target(a) == t, "Wrong arc lookup");

    }

  }

}

  { // Checking FullDigraph

    checkConcept<Digraph, FullDigraph>();

  }

  { // Checking FullDigraph

    checkFullDigraph(8);

  }

#include <lemon/full_graph.h>

void checkFullGraph(int num) {

  typedef FullGraph Graph;

  GRAPH_TYPEDEFS(Graph);

  Graph G(num);

  checkGraphNodeList(G, num);

  checkGraphEdgeList(G, num * (num - 1) / 2);

  for (NodeIt n(G); n != INVALID; ++n) {

    checkGraphOutArcList(G, n, num - 1);    

    checkGraphInArcList(G, n, num - 1);    

    checkGraphIncEdgeList(G, n, num - 1);    

  }

  checkGraphConArcList(G, num * (num - 1));

  checkGraphConEdgeList(G, num * (num - 1) / 2);

  checkArcDirections(G);

  checkNodeIds(G);

  checkArcIds(G);

  checkEdgeIds(G);

  checkGraphNodeMap(G);

  checkGraphArcMap(G);

  checkGraphEdgeMap(G);

  for (int i = 0; i < G.nodeNum(); ++i) {

    check(G.index(G(i)) == i, "Wrong index");

  }

  for (NodeIt u(G); u != INVALID; ++u) {

    for (NodeIt v(G); v != INVALID; ++v) {

      Edge e = G.edge(u, v);

      Arc a = G.arc(u, v);

      if (u == v) {

        check(e == INVALID, "Wrong edge lookup");

        check(a == INVALID, "Wrong arc lookup");

      } else {

        check((G.u(e) == u && G.v(e) == v) ||

              (G.u(e) == v && G.v(e) == u), "Wrong edge lookup");

        check(G.source(a) == u && G.target(a) == v, "Wrong arc lookup");

      }

    }

  }

}

  { // Checking FullGraph

    checkConcept<Graph, FullGraph>();

  }

  { // Checking FullGraph   

    checkFullGraph(7);

    checkFullGraph(8);

  }