/* -*- C++ -*-

 * src/hugo/list_graph.h - Part of HUGOlib, 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 HUGO_LIST_GRAPH_H

#define HUGO_LIST_GRAPH_H

///\ingroup graphs

///\file

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

#include <vector>

#include <climits>

#include <hugo/invalid.h>

#include <hugo/map_registry.h>

#include <hugo/array_map.h>

#include <hugo/map_defines.h>

namespace hugo {

/// \addtogroup graphs

/// @{

  ///A list graph class.

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

  ///

  ///It conforms to the

  ///\ref skeleton::ErasableGraph "ErasableGraph" concept.

  ///\sa skeleton::ErasableGraph.

  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;

    };

    //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;

    };

    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;

  public:

    typedef ListGraph Graph;

    class Node;

    class Edge;

  public:

    class NodeIt;

    class EdgeIt;

    class OutEdgeIt;

    class InEdgeIt;

    // Create map registries.

    CREATE_MAP_REGISTRIES;

    // Create node and edge maps.

    CREATE_MAPS(ArrayMap);

  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) {}

    ///Number of nodes.

    int nodeNum() const { return nodes.size(); }

    ///Number of edges.

    int edgeNum() const { return edges.size(); }

    ///Set the expected maximum 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); };

    /// Maximum node ID.

    /// Maximum node ID.

    ///\sa id(Node)

    int maxNodeId() const { return nodes.size()-1; } 

    /// Maximum edge ID.

    /// Maximum edge ID.

    ///\sa id(Edge)

    int maxEdgeId() const { return edges.size()-1; }

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

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

    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; }

    /// 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.n; }

    /// 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.n; }

    /// Adds a new node to the graph.

    /// \warning It adds the new node to the front of the list.

    /// (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;

    }

    /// 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) 

    {

      int e = (prev.n==-1)? nodes[u.n].first_out : edges[prev.n].next_out;

      while(e!=-1 && edges[e].tail!=v.n) e = edges[e].next_out;

      prev.n=e;

      return prev;

    }

  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;

      edge_maps.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);

      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) { eraseEdge(e.n); }

    void clear() {

      edge_maps.clear();

      edges.clear();

      node_maps.clear();

      nodes.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); 

      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;}

      //      ///Validity check

      //      operator bool() { return n!=-1; }

    };

    class NodeIt : public Node {

      const ListGraph *G;

      friend class ListGraph;

    public:

      NodeIt() : Node() { }

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

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

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

      NodeIt &operator++() {

	n=G->nodes[n].next; 

	return *this; 

      }

      //      ///Validity check

      //      operator bool() { return Node::operator bool(); }      

    };

    class Edge {

      friend class ListGraph;

      template <typename T> friend class EdgeMap;

      friend class SymListGraph;

      friend class Node;

      friend class NodeIt;

    protected:

      int n;

      friend int ListGraph::id(Edge e);

    public:

      /// An Edge with id \c n.

      /// \bug It should be

      /// obtained by a member function of the Graph.

      Edge(int nn) {n=nn;}

      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;}

      //      ///Validity check

      //      operator bool() { return n!=-1; }

   };

    class EdgeIt : public Edge {

      const ListGraph *G;

      friend class ListGraph;

    public:

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

      	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(const ListGraph& _G, Edge e) : Edge(e), G(&_G) { }

      EdgeIt() : Edge() { }

      EdgeIt &operator++() {

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

	else {

	  int nn;

	  for(nn=G->nodes[G->edges[n].head].next;

	      nn!=-1 && G->nodes[nn].first_in == -1;

	      nn = G->nodes[nn].next) ;

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

	}

	return *this;

      }

      //      ///Validity check

      //      operator bool() { return Edge::operator bool(); }      

    };

    class OutEdgeIt : public Edge {

      const ListGraph *G;

      friend class ListGraph;

    public: 

      OutEdgeIt() : Edge() { }

      OutEdgeIt(const ListGraph& _G, Edge e) : Edge(e), G(&_G) { }

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

      OutEdgeIt(const ListGraph& _G,const Node v)

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

      OutEdgeIt &operator++() { n=G->edges[n].next_out; return *this; }

      //      ///Validity check

      //      operator bool() { return Edge::operator bool(); }      

    };

    class InEdgeIt : public Edge {

      const ListGraph *G;

      friend class ListGraph;

    public: 

      InEdgeIt() : Edge() { }

      InEdgeIt(const ListGraph& _G, Edge e) : Edge(e), G(&_G) { }

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

      InEdgeIt(const ListGraph& _G,Node v)

	: Edge(_G.nodes[v.n].first_in), G(&_G) { }

      InEdgeIt &operator++() { n=G->edges[n].next_in; return *this; }

      //      ///Validity check

      //      operator bool() { return Edge::operator bool(); }      

    };

  };

  ///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 Graph::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.

  /*  

  class SymListGraph : public ListGraph

  {

  public:

    typedef SymListGraph Graph;

    // Create symmetric map registry.

    CREATE_SYM_EDGE_MAP_REGISTRY;

    // Create symmetric edge map.

    CREATE_SYM_EDGE_MAP(ArrayMap);

    SymListGraph() : ListGraph() { }

    SymListGraph(const ListGraph &_g) : ListGraph(_g) { }

    ///Adds a pair of oppositely directed edges to the graph.

    Edge addEdge(Node u, Node v)

    {

      Edge e = ListGraph::addEdge(u,v);

      Edge f = ListGraph::addEdge(v,u);

      sym_edge_maps.add(e);

      sym_edge_maps.add(f);

      return e;

    }

    void erase(Node n) { ListGraph::erase(n);}

    ///The oppositely directed edge.

    ///Returns the oppositely directed

    ///pair of the edge \c e.

    static Edge opposite(Edge e)

    {

      Edge f;

      f.n = e.n - 2*(e.n%2) + 1;

      return f;

    }

    ///Removes a pair of oppositely directed edges to the graph.

    void erase(Edge e) {

      Edge f = opposite(e);

      sym_edge_maps.erase(e);

      sym_edge_maps.erase(f);

      ListGraph::erase(f);

      ListGraph::erase(e);

    }    

    };*/

  class SymListGraph : public ListGraph {

    typedef ListGraph Parent;

  public:

    typedef SymListGraph Graph;

    typedef ListGraph::Node Node;

    typedef ListGraph::NodeIt NodeIt;

    class SymEdge;

    class SymEdgeIt;

    class Edge;

    class EdgeIt;

    class OutEdgeIt;

    class InEdgeIt;

    template <typename Value>

    class NodeMap : public Parent::NodeMap<Value> {      

    public:

      NodeMap(const SymListGraph& g) 

	: SymListGraph::Parent::NodeMap<Value>(g) {}

      NodeMap(const SymListGraph& g, Value v) 

	: SymListGraph::Parent::NodeMap<Value>(g, v) {}

      template<typename TT> 

      NodeMap(const NodeMap<TT>& copy) 

	: SymListGraph::Parent::NodeMap<Value>(copy) { }            

    };

    template <typename Value>

    class SymEdgeMap : public Parent::EdgeMap<Value> {

    public:

      typedef SymEdge KeyType;

      SymEdgeMap(const SymListGraph& g) 

	: SymListGraph::Parent::EdgeMap<Value>(g) {}

      SymEdgeMap(const SymListGraph& g, Value v) 

	: SymListGraph::Parent::EdgeMap<Value>(g, v) {}

      template<typename TT> 

      SymEdgeMap(const SymEdgeMap<TT>& copy) 

	: SymListGraph::Parent::EdgeMap<Value>(copy) { }

    };

    // Create edge map registry.

    CREATE_EDGE_MAP_REGISTRY;

    // Create edge maps.

    CREATE_EDGE_MAP(ArrayMap);

    class Edge {

      friend class SymListGraph;

      friend class SymListGraph::EdgeIt;

      friend class SymListGraph::OutEdgeIt;

      friend class SymListGraph::InEdgeIt;

    protected:

      int id;

      Edge(int pid) { id = pid; }

    public:

      /// An Edge with id \c n.

      Edge() { }

      Edge (Invalid) { id = -1; }

      operator SymEdge(){ return SymEdge(id >> 1);}

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

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

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

      //      ///Validity check

      //      operator bool() { return n!=-1; }

    };

    class SymEdge : public ListGraph::Edge {

      friend class SymListGraph;

      friend class SymListGraph::Edge;

      typedef ListGraph::Edge Parent;

    protected:      

      SymEdge(int pid) : Parent(pid) {}

    public:

      SymEdge() { }

      SymEdge(const ListGraph::Edge& i) : Parent(i) {} 

      SymEdge (Invalid) : Parent(INVALID) {}

    };

    class OutEdgeIt {

      Parent::OutEdgeIt out;

      Parent::InEdgeIt in;      

    public: 

      OutEdgeIt() {}

      OutEdgeIt(const SymListGraph& g, Edge e) { 

	if (e.id & 1 == 0) {	

	  out = Parent::OutEdgeIt(g, SymEdge(e));

	  in = Parent::InEdgeIt(g, g.tail(e));

	} else {

	  out = Parent::OutEdgeIt(INVALID);

	  in = Parent::InEdgeIt(g, SymEdge(e));

	}

      }

      OutEdgeIt (Invalid i) : out(INVALID), in(INVALID) { }

      OutEdgeIt(const SymListGraph& g, const Node v)

	: out(g, v), in(g, v) {}

      OutEdgeIt &operator++() { 

	if (out != INVALID) {

	  ++out;

	} else {

	  ++in;

	}

	return *this; 

      }

      operator Edge() const {

	if (out == INVALID && in == INVALID) return INVALID;

	return out != INVALID ? forward(out) : backward(in);

      }

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

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

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

    };

    class InEdgeIt {

      Parent::OutEdgeIt out;

      Parent::InEdgeIt in;      

    public: 

      InEdgeIt() {}

      InEdgeIt(const SymListGraph& g, Edge e) { 

	if (e.id & 1 == 0) {	

	  out = Parent::OutEdgeIt(g, SymEdge(e));

	  in = Parent::InEdgeIt(g, g.tail(e));

	} else {

	  out = Parent::OutEdgeIt(INVALID);

	  in = Parent::InEdgeIt(g, SymEdge(e));

	}

      }

      InEdgeIt (Invalid i) : out(INVALID), in(INVALID) { }

      InEdgeIt(const SymListGraph& g, const Node v)

	: out(g, v), in(g, v) {}

      InEdgeIt &operator++() { 

	if (out != INVALID) {

	  ++out;

	} else {

	  ++in;

	}

	return *this; 

      }

      operator Edge() const {

	if (out == INVALID && in == INVALID) return INVALID;

	return out != INVALID ? backward(out) : forward(in);

      }

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

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

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

    };

    class SymEdgeIt : public Parent::EdgeIt {

    public:

      SymEdgeIt() {}

      SymEdgeIt(const SymListGraph& g) 

	: SymListGraph::Parent::EdgeIt(g) {}

      SymEdgeIt(const SymListGraph& g, SymEdge e) 

	: SymListGraph::Parent::EdgeIt(g, e) {}

      SymEdgeIt(Invalid i) 

	: SymListGraph::Parent::EdgeIt(INVALID) {}

      SymEdgeIt& operator++() {

	SymListGraph::Parent::EdgeIt::operator++();

	return *this;

      }

      operator SymEdge() const {

	return SymEdge

	  (static_cast<const SymListGraph::Parent::EdgeIt&>(*this));

      }

      bool operator==(const SymEdge i) const {return SymEdge(*this) == i;}

      bool operator!=(const SymEdge i) const {return SymEdge(*this) != i;}

      bool operator<(const SymEdge i) const {return SymEdge(*this) < i;}

    };

    class EdgeIt {

      SymEdgeIt it;

      bool fw;

    public:

      EdgeIt(const SymListGraph& g) : it(g), fw(true) {}

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

      EdgeIt(const SymListGraph& g, Edge e) 

	: it(g, SymEdge(e)), fw(id(e) & 1 == 0) { }

      EdgeIt() { }

      EdgeIt& operator++() {

	fw = !fw;

	if (fw) ++it;

	return *this;

      }

      operator Edge() const {

	if (it == INVALID) return INVALID;

	return fw ? forward(it) : backward(it);

      }

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

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

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

    };

    ///Number of nodes.

    int nodeNum() const { return Parent::nodeNum(); }

    ///Number of edges.

    int edgeNum() const { return 2*Parent::edgeNum(); }

    ///Number of symmetric edges.

    int symEdgeNum() const { return Parent::edgeNum(); }

    ///Set the expected maximum 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 reserveSymEdge(int n) { Parent::reserveEdge(n); };

    /// Maximum node ID.

    /// Maximum node ID.

    ///\sa id(Node)

    int maxNodeId() const { return Parent::maxNodeId(); } 

    /// Maximum edge ID.

    /// Maximum edge ID.

    ///\sa id(Edge)

    int maxEdgeId() const { return 2*Parent::maxEdgeId(); }

    /// Maximum symmetric edge ID.

    /// Maximum symmetric edge ID.

    ///\sa id(SymEdge)

    int maxSymEdgeId() const { return Parent::maxEdgeId(); }

    Node tail(Edge e) const { 

      return e.id & 1 == 0 ? 

	Parent::tail(SymEdge(e)) : Parent::head(SymEdge(e)); 

    }

    Node head(Edge e) const { 

      return e.id & 1 == 0 ? 

	Parent::head(SymEdge(e)) : Parent::tail(SymEdge(e)); 

    }

    Node tail(SymEdge e) const { 

      return Parent::tail(e); 

    }

    Node head(SymEdge e) const { 

      return Parent::head(e); 

    }

    NodeIt& first(NodeIt& v) const { 

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

    EdgeIt& first(EdgeIt& e) const { 

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

    SymEdgeIt& first(SymEdgeIt& e) const {

      e=SymEdgeIt(*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; }

    /// 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 Parent::id(v); }

    /// 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; }

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

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

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

    ///

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

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

    static int id(SymEdge e) { return Parent::id(e); }

    /// Adds a new node to the graph.

    /// \warning It adds the new node to the front of the list.

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

    Node addNode() {

      return Parent::addNode();

    }

    SymEdge addEdge(Node u, Node v) {

      SymEdge se = Parent::addEdge(u, v);

      edge_maps.add(forward(se));

      edge_maps.add(backward(se));

      return se;

    }

    /// 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) 

    {     

      if (prev == INVALID || id(prev) & 1 == 0) {

	SymEdge se = Parent::findEdge(u, v, SymEdge(prev));

	if (se != INVALID) return forward(se);

      } else {

	SymEdge se = Parent::findEdge(v, u, SymEdge(prev));

	if (se != INVALID) return backward(se);	

      }

      return INVALID;

    }

    /// Finds an symmetric edge between two nodes.

    /// Finds an symmetric 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.

//     SymEdge findEdge(Node u, Node v, SymEdge prev = INVALID) 

//     {     

//       if (prev == INVALID || id(prev) & 1 == 0) {

// 	SymEdge se = Parent::findEdge(u, v, SymEdge(prev));

// 	if (se != INVALID) return se;

//       } else {

// 	SymEdge se = Parent::findEdge(v, u, SymEdge(prev));

// 	if (se != INVALID) return se;	

//       }

//       return INVALID;

//     }

  public:

    void erase(Node n) {      

      for (OutEdgeIt it(*this, n); it != INVALID; ++it) {

	edge_maps.erase(it);

	edge_maps.erase(opposite(it));

      }

      Parent::erase(n);

    }

    void erase(SymEdge e) { 

      edge_maps.erase(forward(e));

      edge_maps.erase(backward(e));

      Parent::erase(e); 

    };

    void clear() {

      edge_maps.clear();

      Parent::clear();

    }

    static Edge opposite(Edge e) {

      return Edge(id(e) ^ 1);

    }

    static Edge forward(SymEdge e) {

      return Edge(id(e) << 1);

    }

    static Edge backward(SymEdge e) {

      return Edge((id(e) << 1) & 1);

    }

  };

  ///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 \ref skeleton::ExtendableGraph "ExtendableGraph" concept

  ///with the exception that you cannot

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

  ///always \ref INVALID.

  ///\sa skeleton::ExtendableGraph

  ///\sa 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;

  public:

    typedef NodeSet Graph;

    class Node;

    class Edge;

  public:

    class NodeIt;

    class EdgeIt;

    class OutEdgeIt;

    class InEdgeIt;

    // Create node map registry.

    CREATE_NODE_MAP_REGISTRY;

    // Create node maps.

    CREATE_NODE_MAP(ArrayMap);

    /// Creating empty map structure for edges.

    template <typename Value>

    class EdgeMap {

    public:

      EdgeMap(const Graph&) {}

      EdgeMap(const Graph&, const Value&) {}

      EdgeMap(const EdgeMap&) {}

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

      EdgeMap& operator=(const EdgeMap&) {}

      template <typename CMap> EdgeMap& operator=(const CMap&) {}

      class ConstIterator {

      public:

	bool operator==(const ConstIterator&) {return true;}

	bool operator!=(const ConstIterator&) {return false;}

      };

      typedef ConstIterator Iterator;

      Iterator begin() { return Iterator();}

      Iterator end() { return Iterator();}

      ConstIterator begin() const { return ConstIterator();}

      ConstIterator end() const { return ConstIterator();}

    };

  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) {}

    ///Number of nodes.

    int nodeNum() const { return nodes.size(); }

    ///Number of edges.

    int edgeNum() const { return 0; }

    /// Maximum node ID.

    /// Maximum node ID.

    ///\sa id(Node)

    int maxNodeId() const { return nodes.size()-1; }

    /// Maximum edge ID.

    /// Maximum edge ID.

    ///\sa id(Edge)

    int maxEdgeId() const { return 0; }

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

    Node head(Edge 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; }