// -*- 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); }