// -*- mode:C++ -*-

 #ifndef HUGO_LIST_GRAPH_H

 #define HUGO_LIST_GRAPH_H

 ///\ingroup graphs

 ///\file

 ///\brief ListGraph, SymListGraph, NodeSet and EdgeSet classes.

 #include <vector>

 #include <climits>

 #include "invalid.h"

 #include "vector_map_factory.h"

 #include "map_registry.h"

 #include "map_defines.h"

 namespace hugo {

 /// \addtogroup graphs

 /// @{

   ///A list graph class.

   ///This is a simple and fast erasable graph implementation.

   ///

   ///It conforms to the graph interface documented under

   ///the description of \ref GraphSkeleton.

   ///\sa \ref GraphSkeleton.

   class ListGraph {

     //Nodes are double linked.

     //The free nodes are only single linked using the "next" field.

     struct NodeT 

     {

       int first_in,first_out;

       int prev, next;

       //      NodeT() {}

     };

     //Edges are double linked.

     //The free edges are only single linked using the "next_in" field.

     struct EdgeT 

     {

       int head, tail;

       int prev_in, prev_out;

       int next_in, next_out;

       //FIXME: is this necessary?

       //      EdgeT() : next_in(-1), next_out(-1) prev_in(-1), prev_out(-1) {}  

     };

     std::vector<NodeT> nodes;

     //The first node

     int first_node;

     //The first free node

     int first_free_node;

     std::vector<EdgeT> edges;

     //The first free edge

     int first_free_edge;

   protected:

   public:

     class Node;

     class Edge;

     typedef ListGraph Graph;

   public:

     class NodeIt;

     class EdgeIt;

     class OutEdgeIt;

     class InEdgeIt;

     CREATE_MAP_REGISTRIES;

     CREATE_MAPS(VectorMapFactory);

   public:

     ListGraph() : nodes(), first_node(-1),

 		  first_free_node(-1), edges(), first_free_edge(-1) {}

     ListGraph(const ListGraph &_g) : nodes(_g.nodes), first_node(_g.first_node),

 				     first_free_node(_g.first_free_node),

 				     edges(_g.edges),

 				     first_free_edge(_g.first_free_edge) {}

     int nodeNum() const { return nodes.size(); }  //FIXME: What is this?

     int edgeNum() const { return edges.size(); }  //FIXME: What is this?

     ///Set the expected number of edges

     ///With this function, it is possible to set the expected number of edges.

     ///The use of this fasten the building of the graph and makes

     ///it possible to avoid the superfluous memory allocation.

     void reserveEdge(int n) { edges.reserve(n); };

     ///\bug This function does something different than

     ///its name would suggests...

     int maxNodeId() const { return nodes.size(); }  //FIXME: What is this?

     ///\bug This function does something different than

     ///its name would suggests...

     int maxEdgeId() const { return edges.size(); }  //FIXME: What is this?

     Node tail(Edge e) const { return edges[e.n].tail; }

     Node head(Edge e) const { return edges[e.n].head; }

     Node aNode(OutEdgeIt e) const { return edges[e.n].tail; }

     Node aNode(InEdgeIt e) const { return edges[e.n].head; }

     Node bNode(OutEdgeIt e) const { return edges[e.n].head; }

     Node bNode(InEdgeIt e) const { return edges[e.n].tail; }

     NodeIt& first(NodeIt& v) const { 

       v=NodeIt(*this); return v; }

     EdgeIt& first(EdgeIt& e) const { 

       e=EdgeIt(*this); return e; }

     OutEdgeIt& first(OutEdgeIt& e, const Node v) const { 

       e=OutEdgeIt(*this,v); return e; }

     InEdgeIt& first(InEdgeIt& e, const Node v) const { 

       e=InEdgeIt(*this,v); return e; }

 //     template< typename It >

 //     It first() const { It e; first(e); return e; }

 //     template< typename It >

 //     It first(Node v) const { It e; first(e,v); return e; }

     bool valid(Edge e) const { return e.n!=-1; }

     bool valid(Node n) const { return n.n!=-1; }

     void setInvalid(Edge &e) { e.n=-1; }

     void setInvalid(Node &n) { n.n=-1; }

     template <typename It> It getNext(It it) const

     { It tmp(it); return next(tmp); }

     NodeIt& next(NodeIt& it) const { 

       it.n=nodes[it.n].next; 

       return it; 

     }

     OutEdgeIt& next(OutEdgeIt& it) const

     { it.n=edges[it.n].next_out; return it; }

     InEdgeIt& next(InEdgeIt& it) const

     { it.n=edges[it.n].next_in; return it; }

     EdgeIt& next(EdgeIt& it) const {

       if(edges[it.n].next_in!=-1) { 

 	it.n=edges[it.n].next_in;

       }

       else {

 	int n;

 	for(n=nodes[edges[it.n].head].next;

 	    n!=-1 && nodes[n].first_in == -1;

 	    n = nodes[n].next) ;

 	it.n = (n==-1)?-1:nodes[n].first_in;

       }

       return it;

     }

     int id(Node v) const { return v.n; }

     int id(Edge e) const { return e.n; }

     /// Adds a new node to the graph.

     /// \todo It adds the nodes in a reversed order.

     /// (i.e. the lastly added node becomes the first.)

     Node addNode() {

       int n;

       if(first_free_node==-1)

 	{

 	  n = nodes.size();

 	  nodes.push_back(NodeT());

 	}

       else {

 	n = first_free_node;

 	first_free_node = nodes[n].next;

       }

       nodes[n].next = first_node;

       if(first_node != -1) nodes[first_node].prev = n;

       first_node = n;

       nodes[n].prev = -1;

       nodes[n].first_in = nodes[n].first_out = -1;

       Node nn; nn.n=n;

       //Update dynamic maps

       node_maps.add(nn);

       return nn;

     }

     Edge addEdge(Node u, Node v) {

       int n;

       if(first_free_edge==-1)

 	{

 	  n = edges.size();

 	  edges.push_back(EdgeT());

 	}

       else {

 	n = first_free_edge;

 	first_free_edge = edges[n].next_in;

       }

       edges[n].tail = u.n; edges[n].head = v.n;

       edges[n].next_out = nodes[u.n].first_out;

       if(nodes[u.n].first_out != -1) edges[nodes[u.n].first_out].prev_out = n;

       edges[n].next_in = nodes[v.n].first_in;

       if(nodes[v.n].first_in != -1) edges[nodes[v.n].first_in].prev_in = n;

       edges[n].prev_in = edges[n].prev_out = -1;

       nodes[u.n].first_out = nodes[v.n].first_in = n;

       Edge e; e.n=n;

       //Update dynamic maps

       edge_maps.add(e);

       return e;

     }

   private:

     void eraseEdge(int n) {

       if(edges[n].next_in!=-1)

 	edges[edges[n].next_in].prev_in = edges[n].prev_in;

       if(edges[n].prev_in!=-1)

 	edges[edges[n].prev_in].next_in = edges[n].next_in;

       else nodes[edges[n].head].first_in = edges[n].next_in;

       if(edges[n].next_out!=-1)

 	edges[edges[n].next_out].prev_out = edges[n].prev_out;

       if(edges[n].prev_out!=-1)

 	edges[edges[n].prev_out].next_out = edges[n].next_out;

       else nodes[edges[n].tail].first_out = edges[n].next_out;

       edges[n].next_in = first_free_edge;

       first_free_edge = n;      

       //Update dynamic maps

       Edge e; e.n=n;

     }

   public:

     void erase(Node nn) {

       int n=nn.n;

       int m;

       while((m=nodes[n].first_in)!=-1) eraseEdge(m);

       while((m=nodes[n].first_out)!=-1) eraseEdge(m);

       if(nodes[n].next != -1) nodes[nodes[n].next].prev = nodes[n].prev;

       if(nodes[n].prev != -1) nodes[nodes[n].prev].next = nodes[n].next;

       else first_node = nodes[n].next;

       nodes[n].next = first_free_node;

       first_free_node = n;

       //Update dynamic maps

       node_maps.erase(nn);

      }

     void erase(Edge e) { 

       edge_maps.erase(e);

       eraseEdge(e.n); 

     }

     ///\bug Dynamic maps must be updated!

     ///

     void clear() {

       nodes.clear();edges.clear();

       first_node=first_free_node=first_free_edge=-1;

     }

     class Node {

       friend class ListGraph;

       template <typename T> friend class NodeMap;

       friend class Edge;

       friend class OutEdgeIt;

       friend class InEdgeIt;

       friend class SymEdge;

     protected:

       int n;

       friend int ListGraph::id(Node v) const; 

       Node(int nn) {n=nn;}

     public:

       Node() {}

       Node (Invalid) { n=-1; }

       bool operator==(const Node i) const {return n==i.n;}

       bool operator!=(const Node i) const {return n!=i.n;}

       bool operator<(const Node i) const {return n<i.n;}

     };

     class NodeIt : public Node {

       friend class ListGraph;

     public:

       NodeIt() : Node() { }

       NodeIt(Invalid i) : Node(i) { }

       NodeIt(const ListGraph& G) : Node(G.first_node) { }

       ///\todo Undocumented conversion Node -\> NodeIt.

       NodeIt(const ListGraph& G, const Node &n) : Node(n) { }

     };

     class Edge {

       friend class ListGraph;

       template <typename T> friend class EdgeMap;

       //template <typename T> friend class SymListGraph::SymEdgeMap;      

       //friend Edge SymListGraph::opposite(Edge) const;

       friend class Node;

       friend class NodeIt;

     protected:

       int n;

       friend int ListGraph::id(Edge e) const;

       Edge(int nn) {n=nn;}

     public:

       Edge() { }

       Edge (Invalid) { n=-1; }

       bool operator==(const Edge i) const {return n==i.n;}

       bool operator!=(const Edge i) const {return n!=i.n;}

       bool operator<(const Edge i) const {return n<i.n;}

       ///\bug This is a workaround until somebody tells me how to

       ///make class \c SymListGraph::SymEdgeMap friend of Edge

       int &idref() {return n;}

       const int &idref() const {return n;}

     };

     class EdgeIt : public Edge {

       friend class ListGraph;

     public:

       EdgeIt(const ListGraph& G) : Edge() {

       	int m;

 	for(m=G.first_node;

 	    m!=-1 && G.nodes[m].first_in == -1; m = G.nodes[m].next);

 	n = (m==-1)?-1:G.nodes[m].first_in;

       }

       EdgeIt (Invalid i) : Edge(i) { }

       EdgeIt() : Edge() { }

       ///\bug This is a workaround until somebody tells me how to

       ///make class \c SymListGraph::SymEdgeMap friend of Edge

       int &idref() {return n;}

     };

     class OutEdgeIt : public Edge {

       friend class ListGraph;

     public: 

       OutEdgeIt() : Edge() { }

       OutEdgeIt (Invalid i) : Edge(i) { }

       OutEdgeIt(const ListGraph& G,const Node v)

 	: Edge(G.nodes[v.n].first_out) {}

     };

     class InEdgeIt : public Edge {

       friend class ListGraph;

     public: 

       InEdgeIt() : Edge() { }

       InEdgeIt (Invalid i) : Edge(i) { }

       InEdgeIt(const ListGraph& G,Node v) :Edge(G.nodes[v.n].first_in) {}

     };

   };

   ///Graph for bidirectional edges.

   ///The purpose of this graph structure is to handle graphs

   ///having bidirectional edges. Here the function \c addEdge(u,v) adds a pair

   ///of oppositely directed edges.

   ///There is a new edge map type called

   ///\ref SymListGraph::SymEdgeMap "SymEdgeMap"

   ///that complements this

   ///feature by

   ///storing shared values for the edge pairs. The usual

   ///\ref GraphSkeleton::EdgeMap "EdgeMap"

   ///can be used

   ///as well.

   ///

   ///The oppositely directed edge can also be obtained easily

   ///using \ref opposite.

   ///

   ///Here erase(Edge) deletes a pair of edges.

   ///

   ///\todo this date structure need some reconsiderations. Maybe it

   ///should be implemented independently from ListGraph.

   };

   ///A graph class containing only nodes.

   ///This class implements a graph structure without edges.

   ///The most useful application of this class is to be the node set of an

   ///\ref EdgeSet class.

   ///

   ///It conforms to the graph interface documented under

   ///the description of \ref GraphSkeleton with the exception that you cannot

   ///add (or delete) edges. The usual edge iterators are exists, but they are

   ///always \ref INVALID.

   ///\sa \ref GraphSkeleton

   ///\sa \ref EdgeSet

   class NodeSet {

     //Nodes are double linked.

     //The free nodes are only single linked using the "next" field.

     struct NodeT 

     {

       int first_in,first_out;

       int prev, next;

       //      NodeT() {}

     };

     std::vector<NodeT> nodes;

     //The first node

     int first_node;

     //The first free node

     int first_free_node;

   protected:

     template <typename Key> class DynMapBase

     {

     protected:

       const NodeSet* G; 

     public:

       virtual void add(const Key k) = 0;

       virtual void erase(const Key k) = 0;

       DynMapBase(const NodeSet &_G) : G(&_G) {}

       virtual ~DynMapBase() {}

       friend class NodeSet;

     };

   public:

     template <typename T> class EdgeMap;

     template <typename T> class NodeMap;

     class Node;

     class Edge;

     //  protected:

     // HELPME:

   protected:

     ///\bug It must be public because of SymEdgeMap.

     ///

     mutable std::vector<DynMapBase<Node> * > dyn_node_maps;

     //mutable std::vector<DynMapBase<Edge> * > dyn_edge_maps;

   public:

     class NodeIt;

     class EdgeIt;

     class OutEdgeIt;

     class InEdgeIt;

     template <typename T> class NodeMap;

     template <typename T> class EdgeMap;

   public:

     ///Default constructor

     NodeSet() : nodes(), first_node(-1),

 		  first_free_node(-1) {}

     ///Copy constructor

     NodeSet(const NodeSet &_g) : nodes(_g.nodes), first_node(_g.first_node),

 				     first_free_node(_g.first_free_node) {}

     ~NodeSet()

     {

       for(std::vector<DynMapBase<Node> * >::iterator i=dyn_node_maps.begin();

 	  i!=dyn_node_maps.end(); ++i) (**i).G=NULL;

       //for(std::vector<DynMapBase<Edge> * >::iterator i=dyn_edge_maps.begin();

       //	  i!=dyn_edge_maps.end(); ++i) (**i).G=NULL;

     }

     int nodeNum() const { return nodes.size(); }  //FIXME: What is this?

     int edgeNum() const { return 0; }  //FIXME: What is this?

     ///\bug This function does something different than

     ///its name would suggests...

     int maxNodeId() const { return nodes.size(); }  //FIXME: What is this?

     ///\bug This function does something different than

     ///its name would suggests...

     int maxEdgeId() const { return 0; }  //FIXME: What is this?

     Node tail(Edge e) const { return INVALID; }

     Node head(Edge e) const { return INVALID; }

     Node aNode(OutEdgeIt e) const { return INVALID; }

     Node aNode(InEdgeIt e) const { return INVALID; }

     Node bNode(OutEdgeIt e) const { return INVALID; }

     Node bNode(InEdgeIt e) const { return INVALID; }

     NodeIt& first(NodeIt& v) const { 

       v=NodeIt(*this); return v; }

     EdgeIt& first(EdgeIt& e) const { 

       e=EdgeIt(*this); return e; }

     OutEdgeIt& first(OutEdgeIt& e, const Node v) const { 

       e=OutEdgeIt(*this,v); return e; }

     InEdgeIt& first(InEdgeIt& e, const Node v) const { 

       e=InEdgeIt(*this,v); return e; }

 //     template< typename It >

 //     It first() const { It e; first(e); return e; }

 //     template< typename It >

 //     It first(Node v) const { It e; first(e,v); return e; }

     bool valid(Edge e) const { return false; }

     bool valid(Node n) const { return n.n!=-1; }

     void setInvalid(Edge &e) { }

     void setInvalid(Node &n) { n.n=-1; }

     template <typename It> It getNext(It it) const

     { It tmp(it); return next(tmp); }

     NodeIt& next(NodeIt& it) const { 

       it.n=nodes[it.n].next; 

       return it; 

     }

     OutEdgeIt& next(OutEdgeIt& it) const { return it; }

     InEdgeIt& next(InEdgeIt& it) const { return it; }

     EdgeIt& next(EdgeIt& it) const { return it; }

     int id(Node v) const { return v.n; }

     int id(Edge e) const { return -1; }

     /// Adds a new node to the graph.

     /// \todo It adds the nodes in a reversed order.

     /// (i.e. the lastly added node becomes the first.)

     Node addNode() {

       int n;

       if(first_free_node==-1)

 	{

 	  n = nodes.size();

 	  nodes.push_back(NodeT());

 	}

       else {

 	n = first_free_node;

 	first_free_node = nodes[n].next;

       }

       nodes[n].next = first_node;

       if(first_node != -1) nodes[first_node].prev = n;

       first_node = n;

       nodes[n].prev = -1;

       nodes[n].first_in = nodes[n].first_out = -1;

       Node nn; nn.n=n;

       //Update dynamic maps

       for(std::vector<DynMapBase<Node> * >::iterator i=dyn_node_maps.begin();

 	  i!=dyn_node_maps.end(); ++i) (**i).add(nn);

       return nn;

     }

     void erase(Node nn) {

       int n=nn.n;

       if(nodes[n].next != -1) nodes[nodes[n].next].prev = nodes[n].prev;

       if(nodes[n].prev != -1) nodes[nodes[n].prev].next = nodes[n].next;

       else first_node = nodes[n].next;

       nodes[n].next = first_free_node;

       first_free_node = n;

       //Update dynamic maps

       for(std::vector<DynMapBase<Node> * >::iterator i=dyn_node_maps.begin();

 	  i!=dyn_node_maps.end(); ++i) (**i).erase(nn);

     }

     ///\bug Dynamic maps must be updated!

     ///

     void clear() {

       nodes.clear();

       first_node = first_free_node = -1;

     }

     class Node {

       friend class NodeSet;

       template <typename T> friend class NodeMap;

       friend class Edge;

       friend class OutEdgeIt;

       friend class InEdgeIt;

     protected:

       int n;

       friend int NodeSet::id(Node v) const; 

       Node(int nn) {n=nn;}

     public:

       Node() {}

       Node (Invalid i) { n=-1; }

       bool operator==(const Node i) const {return n==i.n;}

       bool operator!=(const Node i) const {return n!=i.n;}

       bool operator<(const Node i) const {return n<i.n;}

     };

     class NodeIt : public Node {

       friend class NodeSet;

     public:

       NodeIt() : Node() { }

       NodeIt(Invalid i) : Node(i) { }

       NodeIt(const NodeSet& G) : Node(G.first_node) { }

       ///\todo Undocumented conversion Node -\> NodeIt.

       NodeIt(const NodeSet& G, const Node &n) : Node(n) { }

     };

     class Edge {

       //friend class NodeSet;

       //template <typename T> friend class EdgeMap;

       //template <typename T> friend class SymNodeSet::SymEdgeMap;      

       //friend Edge SymNodeSet::opposite(Edge) const;

       //      friend class Node;

       //      friend class NodeIt;

     protected:

       //friend int NodeSet::id(Edge e) const;

       //      Edge(int nn) {}

     public:

       Edge() { }

       Edge (Invalid) { }

       bool operator==(const Edge i) const {return true;}

       bool operator!=(const Edge i) const {return false;}

       bool operator<(const Edge i) const {return false;}

       ///\bug This is a workaround until somebody tells me how to

       ///make class \c SymNodeSet::SymEdgeMap friend of Edge

       //      int idref() {return -1;}

       //      int idref() const {return -1;}

     };

     class EdgeIt : public Edge {

       //friend class NodeSet;

     public:

       EdgeIt(const NodeSet& G) : Edge() { }

       EdgeIt (Invalid i) : Edge(i) { }

       EdgeIt() : Edge() { }

       ///\bug This is a workaround until somebody tells me how to

       ///make class \c SymNodeSet::SymEdgeMap friend of Edge

       //      int idref() {return -1;}

     };

     class OutEdgeIt : public Edge {

       friend class NodeSet;

     public: 

       OutEdgeIt() : Edge() { }

       OutEdgeIt (Invalid i) : Edge(i) { }

       OutEdgeIt(const NodeSet& G,const Node v)	: Edge() {}

     };

     class InEdgeIt : public Edge {

       friend class NodeSet;

     public: 

       InEdgeIt() : Edge() { }

       InEdgeIt (Invalid i) : Edge(i) { }

       InEdgeIt(const NodeSet& G,Node v) :Edge() {}

     };

     template <typename T> class NodeMap : public DynMapBase<Node>

     {

       std::vector<T> container;

     public:

       typedef T ValueType;

       typedef Node KeyType;

       NodeMap(const NodeSet &_G) :

 	DynMapBase<Node>(_G), container(_G.maxNodeId())

       {

 	G->dyn_node_maps.push_back(this);

       }

       NodeMap(const NodeSet &_G,const T &t) :

 	DynMapBase<Node>(_G), container(_G.maxNodeId(),t)

       {

 	G->dyn_node_maps.push_back(this);

       }

       NodeMap(const NodeMap<T> &m) :

  	DynMapBase<Node>(*m.G), container(m.container)

       {

  	G->dyn_node_maps.push_back(this);

       }

       template<typename TT> friend class NodeMap;

       ///\todo It can copy between different types.

       ///

       template<typename TT> NodeMap(const NodeMap<TT> &m) :

 	DynMapBase<Node>(*m.G), container(m.container.size())

       {

 	G->dyn_node_maps.push_back(this);

 	typename std::vector<TT>::const_iterator i;

 	for(typename std::vector<TT>::const_iterator i=m.container.begin();

 	    i!=m.container.end();

 	    i++)

 	  container.push_back(*i);

       }

       ~NodeMap()

       {

 	if(G) {

 	  std::vector<DynMapBase<Node>* >::iterator i;

 	  for(i=G->dyn_node_maps.begin();

 	      i!=G->dyn_node_maps.end() && *i!=this; ++i) ;

 	  //if(*i==this) G->dyn_node_maps.erase(i); //FIXME: Way too slow...

 	  //A better way to do that: (Is this really important?)

 	  if(*i==this) {

 	    *i=G->dyn_node_maps.back();

 	    G->dyn_node_maps.pop_back();

 	  }

 	}

       }

       void add(const Node k) 

       {

 	if(k.n>=int(container.size())) container.resize(k.n+1);

       }

       void erase(const Node) { }

       void set(Node n, T a) { container[n.n]=a; }

       //'T& operator[](Node n)' would be wrong here

       typename std::vector<T>::reference

       operator[](Node n) { return container[n.n]; }

       //'const T& operator[](Node n)' would be wrong here

       typename std::vector<T>::const_reference 

       operator[](Node n) const { return container[n.n]; }

       ///\warning There is no safety check at all!

       ///Using operator = between maps attached to different graph may

       ///cause serious problem.

       ///\todo Is this really so?

       ///\todo It can copy between different types.

       const NodeMap<T>& operator=(const NodeMap<T> &m)

       {

 	container = m.container;

 	return *this;

       }

       template<typename TT>

       const NodeMap<T>& operator=(const NodeMap<TT> &m)

       {

 	std::copy(m.container.begin(), m.container.end(), container.begin());

 	return *this;

       }

       void update() {}    //Useless for Dynamic Maps

       void update(T a) {}  //Useless for Dynamic Maps

     };

     template <typename T> class EdgeMap

     {

     public:

       typedef T ValueType;

       typedef Edge KeyType;

       EdgeMap(const NodeSet &) { }

       EdgeMap(const NodeSet &,const T &) { }

       EdgeMap(const EdgeMap<T> &) { }

       //      template<typename TT> friend class EdgeMap;

       ///\todo It can copy between different types.

       ///

       template<typename TT> EdgeMap(const EdgeMap<TT> &) { }

       ~EdgeMap() { }

       void add(const Edge  ) { }

       void erase(const Edge) { }

       void set(Edge, T) { }

       //T get(Edge n) const { return container[n.n]; }

       ValueType &operator[](Edge) { return *((T*)(NULL)); }

       const ValueType &operator[](Edge) const { return *((T*)(NULL)); }

       const EdgeMap<T>& operator=(const EdgeMap<T> &) { return *this; }

       template<typename TT>

       const EdgeMap<T>& operator=(const EdgeMap<TT> &m) { return *this; }

       void update() {}

       void update(T a) {}

     };

   };

   ///Graph structure using a node set of another graph.

   ///This structure can be used to establish another graph over a node set

   /// of an existing one. The node iterator will go through the nodes of the

   /// original graph, and the NodeMap's of both graphs will convert to

   /// each other.

   ///

   ///\warning Adding or deleting nodes from the graph is not safe if an

   ///\ref EdgeSet is currently attached to it!

   ///

   ///\todo Make it possible to add/delete edges from the base graph

   ///(and from \ref EdgeSet, as well)

   ///

   ///\param GG The type of the graph which shares its node set with this class.

   ///Its interface must conform with \ref GraphSkeleton.

   ///

   ///It conforms to the graph interface documented under

   ///the description of \ref GraphSkeleton.

   ///\sa \ref GraphSkeleton.

   ///\sa \ref NodeSet.

   template<typename GG>

   class EdgeSet {

     typedef GG NodeGraphType;

     NodeGraphType &G;

   public:

     class Node;

     int id(Node v) const; 

     class Node : public NodeGraphType::Node {

       friend class EdgeSet;

       //      template <typename T> friend class NodeMap;

       friend class Edge;

       friend class OutEdgeIt;

       friend class InEdgeIt;

       friend class SymEdge;

     public:

       friend int EdgeSet::id(Node v) const; 

       //      Node(int nn) {n=nn;}

     public:

       Node() : NodeGraphType::Node() {}

       Node (Invalid i) : NodeGraphType::Node(i) {}

       Node(const typename NodeGraphType::Node &n) : NodeGraphType::Node(n) {}

     };

     class NodeIt : public NodeGraphType::NodeIt {

       friend class EdgeSet;

     public:

       NodeIt() : NodeGraphType::NodeIt() { }

       NodeIt (Invalid i) : NodeGraphType::NodeIt(i) {}

       NodeIt(const EdgeSet& _G) : NodeGraphType::NodeIt(_G.G) { }

       NodeIt(const typename NodeGraphType::NodeIt &n)

 	: NodeGraphType::NodeIt(n) {}

       ///\todo Undocumented conversion Node -\> NodeIt.

       NodeIt(const EdgeSet& _G, const Node &n)

 	: NodeGraphType::NodeIt(_G.G,n) { }

       operator Node() { return Node(*this);}

     };

   private:

     //Edges are double linked.

     //The free edges are only single linked using the "next_in" field.

     struct NodeT 

     {

       int first_in,first_out;

       NodeT() : first_in(-1), first_out(-1) { }

     };

     struct EdgeT 

     {

       Node head, tail;

       int prev_in, prev_out;

       int next_in, next_out;

     };

     typename NodeGraphType::template NodeMap<NodeT> nodes;

     std::vector<EdgeT> edges;

     //The first free edge

     int first_free_edge;

   protected:

     template <typename Key> class DynMapBase

     {

     protected:

       const EdgeSet* G; 

     public:

       virtual void add(const Key k) = 0;

       virtual void erase(const Key k) = 0;

       DynMapBase(const EdgeSet &_G) : G(&_G) {}

       virtual ~DynMapBase() {}

       friend class EdgeSet;

     };

   public:

     //template <typename T> class NodeMap;

     template <typename T> class EdgeMap;

     class Node;

     class Edge;

     //  protected:

     // HELPME:

   protected:

     // mutable std::vector<DynMapBase<Node> * > dyn_node_maps;

     ///\bug It must be public because of SymEdgeMap.

     ///

     mutable std::vector<DynMapBase<Edge> * > dyn_edge_maps;

   public:

     class NodeIt;

     class EdgeIt;

     class OutEdgeIt;

     class InEdgeIt;

     template <typename T> class NodeMap;

     template <typename T> class EdgeMap;

   public:

     ///Constructor

     ///Construates a new graph based on the nodeset of an existing one.

     ///\param _G the base graph.

     ///\todo It looks like a copy constructor, but it isn't.

     EdgeSet(NodeGraphType &_G) : G(_G),

 				 nodes(_G), edges(),

 				 first_free_edge(-1) { }

     ///Copy constructor

     ///Makes a copy of an EdgeSet.

     ///It will be based on the same graph.

     EdgeSet(const EdgeSet &_g) : G(_g.G), nodes(_g.G), edges(_g.edges),

 				 first_free_edge(_g.first_free_edge) { }

     ~EdgeSet()

     {

       // for(std::vector<DynMapBase<Node> * >::iterator i=dyn_node_maps.begin();

       //  i!=dyn_node_maps.end(); ++i) (**i).G=NULL;

       for(typename std::vector<DynMapBase<Edge> * >::iterator

 	    i=dyn_edge_maps.begin();

 	  i!=dyn_edge_maps.end(); ++i) (**i).G=NULL;

     }

     int nodeNum() const { return G.nodeNum(); }  //FIXME: What is this?

     int edgeNum() const { return edges.size(); }  //FIXME: What is this?

     ///\bug This function does something different than

     ///its name would suggests...

     int maxNodeId() const { return G.maxNodeId(); }  //FIXME: What is this?

     ///\bug This function does something different than

     ///its name would suggests...

     int maxEdgeId() const { return edges.size(); }  //FIXME: What is this?

     Node tail(Edge e) const { return edges[e.n].tail; }

     Node head(Edge e) const { return edges[e.n].head; }

     Node aNode(OutEdgeIt e) const { return edges[e.n].tail; }

     Node aNode(InEdgeIt e) const { return edges[e.n].head; }

     Node bNode(OutEdgeIt e) const { return edges[e.n].head; }

     Node bNode(InEdgeIt e) const { return edges[e.n].tail; }

     NodeIt& first(NodeIt& v) const { 

       v=NodeIt(*this); return v; }

     EdgeIt& first(EdgeIt& e) const { 

       e=EdgeIt(*this); return e; }

     OutEdgeIt& first(OutEdgeIt& e, const Node v) const { 

       e=OutEdgeIt(*this,v); return e; }

     InEdgeIt& first(InEdgeIt& e, const Node v) const { 

       e=InEdgeIt(*this,v); return e; }

 //     template< typename It >

 //     It first() const { It e; first(e); return e; }

 //     template< typename It >

 //     It first(Node v) const { It e; first(e,v); return e; }

     bool valid(Edge e) const { return e.n!=-1; }

     bool valid(Node n) const { return G.valid(n); }

     void setInvalid(Edge &e) { e.n=-1; }

     void setInvalid(Node &n) { G.setInvalid(n); }

     template <typename It> It getNext(It it) const

     { It tmp(it); return next(tmp); }

     NodeIt& next(NodeIt& it) const { G.next(it); return it; }

     OutEdgeIt& next(OutEdgeIt& it) const

     { it.n=edges[it.n].next_out; return it; }

     InEdgeIt& next(InEdgeIt& it) const

     { it.n=edges[it.n].next_in; return it; }

     EdgeIt& next(EdgeIt& it) const {

       if(edges[it.n].next_in!=-1) { 

 	it.n=edges[it.n].next_in;

       }

       else {

 	NodeIt n(*this,edges[it.n].head);

 	for(n=next(n);

 	    valid(n) && nodes[n].first_in == -1;

 	    next(n)) ;

 	it.n = (valid(n))?-1:nodes[n].first_in;

       }

       return it;

     }

     int id(Edge e) const { return e.n; }

     /// Adds a new node to the graph.

     Node addNode() { return G.addNode(); }

     Edge addEdge(Node u, Node v) {

       int n;

       if(first_free_edge==-1)

 	{

 	  n = edges.size();

 	  edges.push_back(EdgeT());

 	}

       else {

 	n = first_free_edge;

 	first_free_edge = edges[n].next_in;

       }

       edges[n].tail = u; edges[n].head = v;

       edges[n].next_out = nodes[u].first_out;

       if(nodes[u].first_out != -1) edges[nodes[u].first_out].prev_out = n;

       edges[n].next_in = nodes[v].first_in;

       if(nodes[v].first_in != -1) edges[nodes[v].first_in].prev_in = n;

       edges[n].prev_in = edges[n].prev_out = -1;

       nodes[u].first_out = nodes[v].first_in = n;

       Edge e; e.n=n;

       //Update dynamic maps

       for(typename std::vector<DynMapBase<Edge> * >::iterator

 	    i=dyn_edge_maps.begin();

 	  i!=dyn_edge_maps.end(); ++i) (**i).add(e);

       return e;

     }

   private:

     void eraseEdge(int n) {

       if(edges[n].next_in!=-1)

 	edges[edges[n].next_in].prev_in = edges[n].prev_in;

       if(edges[n].prev_in!=-1)

 	edges[edges[n].prev_in].next_in = edges[n].next_in;

       else nodes[edges[n].head].first_in = edges[n].next_in;

       if(edges[n].next_out!=-1)

 	edges[edges[n].next_out].prev_out = edges[n].prev_out;

       if(edges[n].prev_out!=-1)

 	edges[edges[n].prev_out].next_out = edges[n].next_out;

       else nodes[edges[n].tail].first_out = edges[n].next_out;

       edges[n].next_in = first_free_edge;

       first_free_edge = -1;      

       //Update dynamic maps

       Edge e; e.n=n;

       for(typename std::vector<DynMapBase<Edge> * >::iterator

 	    i=dyn_edge_maps.begin();

 	  i!=dyn_edge_maps.end(); ++i) (**i).erase(e);

     }

   public:

 //     void erase(Node nn) {

 //       int n=nn.n;

 //       int m;

 //       while((m=nodes[n].first_in)!=-1) eraseEdge(m);

 //       while((m=nodes[n].first_out)!=-1) eraseEdge(m);

 //     }

     void erase(Edge e) { eraseEdge(e.n); }

     ///Clear all edges. (Doesn't clear the nodes!)

     void clear() {

       edges.clear();

       first_free_edge=-1;

     }

 //     //\bug Dynamic maps must be updated!

 //     //

 //     void clear() {

 //       nodes.clear();edges.clear();

 //       first_node=first_free_node=first_free_edge=-1;

 //     }

   public:

     template <typename T> class EdgeMap;

     ///

     class Edge {

     public:

       friend class EdgeSet;

       template <typename T> friend class EdgeMap;

       friend class Node;

       friend class NodeIt;

     public:

       ///\bug It shoud be at least protected

       ///

       int n;

     protected:

       friend int EdgeSet::id(Edge e) const;

       Edge(int nn) {n=nn;}

     public:

       Edge() { }

       Edge (Invalid) { n=-1; }

       bool operator==(const Edge i) const {return n==i.n;}

       bool operator!=(const Edge i) const {return n!=i.n;}

       bool operator<(const Edge i) const {return n<i.n;}

       ///\bug This is a workaround until somebody tells me how to

       ///make class \c SymEdgeSet::SymEdgeMap friend of Edge

       int &idref() {return n;}

       const int &idref() const {return n;}

     };

     class EdgeIt : public Edge {

       friend class EdgeSet;

       template <typename T> friend class EdgeMap;

     public:

       EdgeIt(const EdgeSet& G) : Edge() {

 	//      	typename NodeGraphType::Node m;

         NodeIt m;

 	for(G.first(m);

 	    G.valid(m) && G.nodes[m].first_in == -1;  G.next(m));

 	//AJJAJ! This is a non sense!!!!!!!

 	this->n = G.valid(m)?-1:G.nodes[m].first_in;

       }

       EdgeIt (Invalid i) : Edge(i) { }

       EdgeIt() : Edge() { }

       ///\bug This is a workaround until somebody tells me how to

       ///make class \c SymEdgeSet::SymEdgeMap friend of Edge

       int &idref() {return this->n;}

     };

     class OutEdgeIt : public Edge {

       friend class EdgeSet;

     public: 

       OutEdgeIt() : Edge() { }

       OutEdgeIt (Invalid i) : Edge(i) { }

       OutEdgeIt(const EdgeSet& G,const Node v) : Edge(G.nodes[v].first_out) { }

     };

     class InEdgeIt : public Edge {

       friend class EdgeSet;

     public: 

       InEdgeIt() : Edge() { }

       InEdgeIt (Invalid i) : Edge(i) { }

       InEdgeIt(const EdgeSet& G,Node v) :Edge(G.nodes[v].first_in) { }

     };

     template <typename T> class NodeMap : 

       public NodeGraphType::template NodeMap<T>

     {

       //This is a must, the constructors need it.

       typedef typename NodeGraphType::template NodeMap<T> ParentNodeMap;

     public:

       NodeMap(const EdgeSet &_G) : ParentNodeMap(_G.G) { }

       NodeMap(const EdgeSet &_G,const T &t) : ParentNodeMap(_G.G,t) { }

       //It is unnecessary

       NodeMap(const typename NodeGraphType::template NodeMap<T> &m) :

 	ParentNodeMap(m) { }

       ///\todo It can copy between different types.

       ///

       template<typename TT>

       NodeMap(const typename NodeGraphType::template NodeMap<TT> &m)

 	: ParentNodeMap(m) { }

     };

     ///

     template <typename T> class EdgeMap : public DynMapBase<Edge>

     {

     protected:

     public:

       ///\bug It should be at least protected

       ///

       std::vector<T> container;

     public:

       typedef T ValueType;

       typedef Edge KeyType;

       EdgeMap(const EdgeSet &_G) :

 	DynMapBase<Edge>(_G), container(_G.maxEdgeId())

       {

 	//FIXME: What if there are empty Id's?

 	//FIXME: Can I use 'this' in a constructor?

 	G->dyn_edge_maps.push_back(this);

       }

       EdgeMap(const EdgeSet &_G,const T &t) :

 	DynMapBase<Edge>(_G), container(_G.maxEdgeId(),t)

       {

 	G->dyn_edge_maps.push_back(this);

       } 

       EdgeMap(const EdgeMap<T> &m) :

  	DynMapBase<Edge>(*m.G), container(m.container)

       {

  	G->dyn_edge_maps.push_back(this);

       }

       template<typename TT> friend class EdgeMap;

       ///\todo It can copy between different types.

       ///

       template<typename TT> EdgeMap(const EdgeMap<TT> &m) :

 	DynMapBase<Edge>(*m.G), container(m.container.size())

       {

 	G->dyn_edge_maps.push_back(this);

 	typename std::vector<TT>::const_iterator i;

 	for(typename std::vector<TT>::const_iterator i=m.container.begin();

 	    i!=m.container.end();

 	    i++)

 	  container.push_back(*i);

       }

       ~EdgeMap()

       {

 	if(G) {

 	  typename std::vector<DynMapBase<Edge>* >::iterator i;

 	  for(i=G->dyn_edge_maps.begin();

 	      i!=G->dyn_edge_maps.end() && *i!=this; ++i) ;

 	  //if(*i==this) G->dyn_edge_maps.erase(i); //Way too slow...

 	  //A better way to do that: (Is this really important?)

 	  if(*i==this) {

 	    *i=G->dyn_edge_maps.back();

 	    G->dyn_edge_maps.pop_back();

 	  }

 	}

       }

       void add(const Edge k) 

       {

 	if(k.n>=int(container.size())) container.resize(k.n+1);

       }

       void erase(const Edge) { }

       ///\bug This doesn't work. Why?

       ///      void set(Edge n, T a) { container[n.n]=a; }

       void set(Edge n, T a) { container[G->id(n)]=a; }

       //T get(Edge n) const { return container[n.n]; }

       typename std::vector<T>::reference

       ///\bug This doesn't work. Why?

       ///      operator[](Edge n) { return container[n.n]; }

       operator[](Edge n) { return container[G->id(n)]; }

       typename std::vector<T>::const_reference

       ///\bug This doesn't work. Why?

       ///      operator[](Edge n) const { return container[n.n]; }

       operator[](Edge n) const { return container[G->id(n)]; }

       ///\warning There is no safety check at all!

       ///Using operator = between maps attached to different graph may

       ///cause serious problem.

       ///\todo Is this really so?

       ///\todo It can copy between different types.

       const EdgeMap<T>& operator=(const EdgeMap<T> &m)

       {

 	container = m.container;

 	return *this;

       }

       template<typename TT> friend class EdgeMap;

       template<typename TT>

       const EdgeMap<T>& operator=(const EdgeMap<TT> &m)

       {

 	std::copy(m.container.begin(), m.container.end(), container.begin());

 	return *this;

       }

       void update() {}    //Useless for DynMaps

       void update(T a) {}  //Useless for DynMaps

     };

   };

   template<typename GG>

   inline int EdgeSet<GG>::id(Node v) const { return G.id(v); }

 /// @}  

 } //namespace hugo

 #endif //HUGO_LIST_GRAPH_H