/* -*- C++ -*-

 * lemon/full_graph.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2005 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/iterable_graph_extender.h>

#include <lemon/bits/alteration_notifier.h>

#include <lemon/bits/default_map.h>

#include <lemon/invalid.h>

#include <lemon/utility.h>

///\ingroup graphs

///\file

///\brief FullGraph and SymFullGraph classes.

namespace lemon {

  class FullGraphBase {

    int NodeNum;

    int EdgeNum;

  public:

    typedef FullGraphBase Graph;

    class Node;

    class Edge;

  public:

    FullGraphBase() {}

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

    void construct(int n) { NodeNum = n; EdgeNum = n * n; }

    ///

    //    FullGraphBase(const FullGraphBase &_g)

    //      : NodeNum(_g.nodeNum()), EdgeNum(NodeNum*NodeNum) { }

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    ///Number of nodes.

    int nodeNum() const { return NodeNum; }

    ///Number of edges.

    int edgeNum() const { return EdgeNum; }

    /// Maximum node ID.

    /// Maximum node ID.

    ///\sa id(Node)

    int maxId(Node = INVALID) const { return NodeNum-1; }

    /// Maximum edge ID.

    /// Maximum edge ID.

    ///\sa id(Edge)

    int maxId(Edge = INVALID) const { return EdgeNum-1; }

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

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

    /// Node ID.

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

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

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

    ///

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

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

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

    /// Edge ID.

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

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

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

    ///

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

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

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

    static Node fromId(int id, Node) { return Node(id);}

    static Edge fromId(int id, Edge) { return Edge(id);}

    /// Finds an edge between two nodes.

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

    ///

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

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

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

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

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

    {

      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& edge) const {

      edge.id = EdgeNum-1;

    }

    static void next(Edge& edge) {

      --edge.id;

    }

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

      edge.id = EdgeNum + node.id - NodeNum;

    }

    void nextOut(Edge& edge) const {

      edge.id -= NodeNum;

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

    }

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

      edge.id = node.id * NodeNum;

    }

    void nextIn(Edge& edge) const {

      ++edge.id;

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

    }

  };

  typedef AlterableGraphExtender<FullGraphBase> AlterableFullGraphBase;

  typedef IterableGraphExtender<AlterableFullGraphBase> IterableFullGraphBase;

  typedef DefaultMappableGraphExtender<IterableFullGraphBase> MappableFullGraphBase;

  /// \addtogroup graphs

  /// @{

  ///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 concept::StaticGraph "StaticGraph" concept

  ///\sa concept::StaticGraph.

  ///

  ///\author Alpar Juttner

  class FullGraph : public MappableFullGraphBase {

  public:

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

  };

  ///@}

  // Base graph class for UndirFullGraph.

  class UndirFullGraphBase {

    int NodeNum;

    int EdgeNum;

  public:

    typedef UndirFullGraphBase Graph;

    class Node;

    class Edge;

  public:

    UndirFullGraphBase() {}

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

    void construct(int n) { NodeNum = n; EdgeNum = n * (n - 1) / 2; }

    ///

    //    FullGraphBase(const FullGraphBase &_g)

    //      : NodeNum(_g.nodeNum()), EdgeNum(NodeNum*NodeNum) { }

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    ///Number of nodes.

    int nodeNum() const { return NodeNum; }

    ///Number of edges.

    int edgeNum() const { return EdgeNum; }

    /// Maximum node ID.

    /// Maximum node ID.

    ///\sa id(Node)

    int maxId(Node = INVALID) const { return NodeNum-1; }

    /// Maximum edge ID.

    /// Maximum edge ID.

    ///\sa id(Edge)

    int maxId(Edge = INVALID) const { return EdgeNum-1; }

    Node source(Edge e) const { 

      /// \todo we may do it faster

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

    }

    Node target(Edge e) const { 

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

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

    }

    /// Node ID.

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

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

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

    ///

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

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

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

    /// Edge ID.

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

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

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

    ///

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

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

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

    /// Finds an edge between two nodes.

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

    ///

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

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

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

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

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

    {

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

    }

    class Node {

      friend class UndirFullGraphBase;

    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 UndirFullGraphBase;

    protected:

      int id;  // NodeNum * target + source;

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

      Edge(const UndirFullGraphBase& _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& edge) const {

      edge.id = EdgeNum-1;

    }

    static void next(Edge& edge) {

      --edge.id;

    }

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

      edge.id = node.id != 0 ? node.id * (node.id - 1) / 2 : -1;

    }

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

    void nextOut(Edge& e) const {

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

      int target = e.id - (source) * (source - 1) / 2; 

      ++target;

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

    }

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

      edge.id = node.id * (node.id + 1) / 2 - 1;

    }

    void nextIn(Edge& e) const {

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

      int target = e.id - (source) * (source - 1) / 2; ++target;

      ++source;

      e.id = source < NodeNum ? source * (source - 1) / 2 + target : -1;

    }

  };

  /// \addtogroup graphs

  /// @{

  /// \todo UndirFullGraph from the UndirFullGraphBase

  /// @}  

} //namespace lemon

#endif //LEMON_FULL_GRAPH_H