/* -*- 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