/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2007

 * 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 <cmath>

#include <lemon/bits/base_extender.h>

#include <lemon/bits/graph_extender.h>

#include <lemon/bits/invalid.h>

#include <lemon/bits/utility.h>

///\ingroup graphs

///\file

///\brief FullGraph and FullUGraph classes.

namespace lemon {

  class FullGraphBase {

    int _nodeNum;

    int _edgeNum;

  public:

    typedef FullGraphBase Graph;

    class Node;

    class Edge;

  protected:

    FullGraphBase() {}

    void construct(int n) { _nodeNum = n; _edgeNum = n * n; }

  public:

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    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 { 

      return Edge(*this, u.id, v.id); 

    }

    int nodeNum() const { return _nodeNum; }

    int edgeNum() const { return _edgeNum; }

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

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

    Node source(Edge e) const { return e.id % _nodeNum; }

    Node target(Edge e) const { return e.id / _nodeNum; }

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

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

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

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

    typedef True FindEdgeTag;

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

      return prev.id == -1 ? Edge(*this, u.id, v.id) : INVALID;

    }

    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;

    protected:

      int id;  // _nodeNum * target + source;

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

      Edge(const FullGraphBase& _graph, int source, int target) 

	: id(_graph._nodeNum * target+source) {}

    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& e) const {

      e.id = _edgeNum-1;

    }

    static void next(Edge& e) {

      --e.id;

    }

    void firstOut(Edge& e, const Node& n) const {

      e.id = _edgeNum + n.id - _nodeNum;

    }

    void nextOut(Edge& e) const {

      e.id -= _nodeNum;

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

    }

    void firstIn(Edge& e, const Node& n) const {

      e.id = n.id * _nodeNum;

    }

    void nextIn(Edge& e) const {

      ++e.id;

      if (e.id % _nodeNum == 0) e.id = -1;

    }

  };

  typedef GraphExtender<FullGraphBase> ExtendedFullGraphBase;

  /// \ingroup graphs

  ///

  /// \brief A full graph class.

  ///

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

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

  /// edges or nodes.

  /// Thus it 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.

  /// \sa concepts::Graph.

  ///

  /// \sa FullUGraph

  ///

  /// \author Alpar Juttner

  class FullGraph : public ExtendedFullGraphBase {

  public:

    typedef ExtendedFullGraphBase Parent;

    /// \brief Constructor

    FullGraph() { construct(0); }

    /// \brief Constructor

    ///

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

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

      construct(n);

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

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

    }

    /// \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 ix) const { return Parent::operator()(ix); }

    /// \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 Parent::index(node); }

    /// \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 edges.

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

  };

  class FullUGraphBase {

    int _nodeNum;

    int _edgeNum;

  public:

    typedef FullUGraphBase Graph;

    class Node;

    class Edge;

  protected:

    FullUGraphBase() {}

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

  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 { 

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

    }

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    int nodeNum() const { return _nodeNum; }

    int edgeNum() const { return _edgeNum; }

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

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

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

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

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

    }

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

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

    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& n) const {

      n.id = _nodeNum - 1;

    }

    static void next(Node& n) {

      --n.id;

    }

    void first(Edge& e) const {

      e.id = _edgeNum - 1;

    }

    static void next(Edge& e) {

      --e.id;

    }

    void firstOut(Edge& e, const Node& n) const {      

      int src = n.id;

      int trg = 0;

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

    }

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

    void nextOut(Edge& e) const {

      int src = source(e).id;

      int trg = target(e).id;

      ++trg;

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

    }

    void firstIn(Edge& e, const Node& n) const {

      int src = n.id + 1;

      int trg = n.id;

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

    }

    void nextIn(Edge& e) const {

      int src = source(e).id;

      int trg = target(e).id;

      ++src;

      e.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.

  ///

  ///It also has an

  ///important extra feature that

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

  ///

  /// \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::notifier(Edge()).clear();

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

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

      construct(n);

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

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

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

    }

    /// \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 ix) const { return Parent::operator()(ix); }

    /// \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 Parent::index(node); }

    /// \brief Number of nodes.

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

    /// \brief Number of edges.

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

    /// \brief Number of undirected edges.

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

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

    ///

    /// Returns the edge connects the given nodes.

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

      if (Parent::index(u) > Parent::index(v)) {

        return Parent::direct(Parent::edge(u, v), true);

      } else if (Parent::index(u) == Parent::index(v)) {

        return INVALID;

      } else {

        return Parent::direct(Parent::edge(v, u), false); 

      }

    }

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

    ///

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

    UEdge uEdge(const Node& u, const Node& v) const {

      if (Parent::index(u) > Parent::index(v)) {

        return Parent::edge(u, v);

      } else if (Parent::index(u) == Parent::index(v)) {

        return INVALID;

      } else {

        return Parent::edge(v, u);

      }

    }

  };

  class FullBpUGraphBase {

  protected:

    int _aNodeNum;

    int _bNodeNum;

    int _edgeNum;

  protected:

    FullBpUGraphBase() {}

    void construct(int ann, int bnn) {

      _aNodeNum = ann;

      _bNodeNum = bnn;

      _edgeNum = ann * bnn;

    }

  public:

    class NodeSetError : public LogicError {

    public:

      virtual const char* what() const throw() { 

	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;}

    };

    Node aNode(int ix) const { return Node(ix << 1); }

    Node bNode(int ix) const { return Node((ix << 1) + 1); }

    int aNodeIndex(const Node& node) const { return node.id >> 1; }

    int bNodeIndex(const Node& node) const { return node.id >> 1; }

    UEdge uEdge(const Node& u, const Node& v) const { 

      if (((u.id ^ v.id) & 1) != 1) {

        return UEdge(-1);

      } else if ((u.id & 1) == 0) {

        return UEdge((u.id >> 1) * _bNodeNum + (v.id >> 1));

      } else {

        return UEdge((v.id >> 1) * _bNodeNum + (u.id >> 1));

      }

    }

    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 nodeFromANodeId(int id) {

      return Node(id << 1);

    }

    int maxANodeId() const {

      return _aNodeNum;

    }

    static int bNodeId(const Node& node) {

      return node.id >> 1;

    }

    static Node nodeFromBNodeId(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;

    }

    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 True FindEdgeTag;

    UEdge findUEdge(Node u, Node v, UEdge prev = INVALID) const {

      if (prev.id != -1 || ((u.id ^ v.id) & 1) != 1) {

        return UEdge(-1);

      } else if ((u.id & 1) == 0) {

        return UEdge((u.id >> 1) * _bNodeNum + (v.id >> 1));

      } else {

        return UEdge((v.id >> 1) * _bNodeNum + (u.id >> 1));

      }

    }

  };

  typedef BpUGraphExtender<BidirBpUGraphExtender<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.

  ///

  /// \author Balazs Dezso

  class FullBpUGraph : 

    public ExtendedFullBpUGraphBase {

  public:

    typedef ExtendedFullBpUGraphBase Parent;

    FullBpUGraph() {

      Parent::construct(0, 0);

    }

    FullBpUGraph(int ann, int bnn) {

      Parent::construct(ann, bnn);

    }

    /// \brief Resize the graph

    ///

    /// Resize the graph

    void resize(int n, int m) {

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

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

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

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

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

      construct(n, m);

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

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

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

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

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

    }

    /// \brief Number of nodes.

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

    /// \brief Number of A-nodes.

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

    /// \brief Number of B-nodes.

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

    /// \brief Number of edges.

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

    /// \brief Number of undirected edges.

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

    using Parent::aNode;

    using Parent::bNode;

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

    ///

    /// Returns the A-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 aNodeNum()-1 and the index of

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

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

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

    ///

    /// Returns the B-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 bNodeNum()-1 and the index of

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

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

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

    ///

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

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

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

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

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

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

    ///

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

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

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

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

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

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

    ///

    /// Returns the edge connects the given nodes.

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

      UEdge uedge = Parent::uEdge(u, v);

      if (uedge != INVALID) {

        return Parent::direct(uedge, Parent::aNode(u));

      } else {

        return INVALID;

      }

    }

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

    ///

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

    UEdge uEdge(const Node& u, const Node& v) const {

      return Parent::uEdge(u, v);

    }

  };

} //namespace lemon

#endif //LEMON_FULL_GRAPH_H