/* -*- C++ -*-
 * src/lemon/full_graph.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, 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/iterable_graph_extender.h>
#include <lemon/alteration_observer_registry.h>
#include <lemon/default_map.h>

#include <lemon/invalid.h>
#include <lemon/utility.h>


///\ingroup graphs
///\file
///\brief FullGraph and SymFullGraph classes.


namespace lemon {

/// \addtogroup graphs
/// @{

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

    /// 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 * head + tail;

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

      Edge(const FullGraphBase& _graph, int tail, int head) 
	: id(_graph.NodeNum * head+tail) {}
    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;

  ///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 tail(Edge e) const { 
      /// \todo we may do it faster
      return ((int)sqrt((double)(1 + 8 * e.id)) + 1) / 2; 
    }

    Node head(Edge e) const { 
      int tail = ((int)sqrt((double)(1 + 8 * e.id)) + 1) / 2;;
      return e.id - (tail) * (tail - 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 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 * head + tail;

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

      Edge(const FullGraphBase& _graph, int tail, int head) 
	: id(_graph.NodeNum * head+tail) {}
    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& edge) const {
      int tail = ((int)sqrt((double)(1 + 8 * e.id)) + 1) / 2;;
      int head = e.id - (tail) * (tail - 1) / 2; 
      ++head;
      return head < tail ? tail * (tail - 1) / 2 + head : -1;
    }

    void firstIn(Edge& edge, const Node& node) const {
      edge.id = node.id * (node.id + 1) / 2 - 1;
    }
    
    void nextIn(Edge& edge) const {
      int tail = ((int)sqrt((double)(1 + 8 * e.id)) + 1) / 2;;
      int head = e.id - (tail) * (tail - 1) / 2; ++head;
      ++tail;
      return tail < nodeNum ? tail * (tail - 1) / 2 + head : -1;
    }

  };

  /// \todo UndirFullGraph from the UndirFullGraphBase

  

  /// @}  

} //namespace lemon


#endif //LEMON_FULL_GRAPH_H