/* -*- C++ -*-

  * src/lemon/list_graph.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Combinatorial Optimization Research Group, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_LIST_GRAPH_H

 #define LEMON_LIST_GRAPH_H

 ///\ingroup graphs

 ///\file

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

 #include <vector>

 #include <climits>

 #include <lemon/invalid.h>

 #include <lemon/map_registry.h>

 #include <lemon/array_map.h>

 #include <lemon/map_defines.h>

 namespace lemon {

 /// \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) {}

     /// \bug In the vector can be hole if a node is erased from the graph.

     ///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 lemon::SymListGraph::SymEdgeMap "SymEdgeMap"

   ///that complements this

   ///feature by

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

   ///\ref lemon::skeleton::StaticGraph::EdgeMap "EdgeMap"

   ///can be used

   ///as well.

   ///

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

   ///using \ref lemon::SymListGraph::opposite() "opposite()" member function.

   ///

   ///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; }

     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 -1; }

     /// 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;

     }

     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

       node_maps.erase(nn);

     }

     Edge findEdge(Node u,Node v, Edge prev = INVALID) 

     {

       return INVALID;

     }

     void clear() {

       node_maps.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); 

       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 {

       const NodeSet *G;

       friend class NodeSet;

     public:

       NodeIt() : Node() { }

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

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

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

       NodeIt &operator++() {

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

 	return *this; 

       }

     };

     class Edge {

     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;}

     };

     class EdgeIt : public Edge {

     public:

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

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

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

       EdgeIt() : Edge() { }

       EdgeIt operator++() { return INVALID; }

     };

     class OutEdgeIt : public Edge {

       friend class NodeSet;

     public: 

       OutEdgeIt() : Edge() { }

       OutEdgeIt(const NodeSet&, Edge) : Edge() { }

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

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

       OutEdgeIt operator++() { return INVALID; }

     };

     class InEdgeIt : public Edge {

       friend class NodeSet;

     public: 

       InEdgeIt() : Edge() { }

       InEdgeIt(const NodeSet&, Edge) : Edge() { }

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

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

       InEdgeIt operator++() { return INVALID; }

     };

   };

   ///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 to the

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

   ///

   ///It conforms to the 

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

   ///\sa skeleton::ExtendableGraph.

   ///\sa NodeSet.

   template<typename GG>

   class EdgeSet {

     typedef GG NodeGraphType;

     NodeGraphType &G;

   public:

     class Node;

     class Edge;

     class OutEdgeIt;

     class InEdgeIt;

     class SymEdge;

     typedef EdgeSet Graph;

     int id(Node v) const; 

     class Node : public NodeGraphType::Node {

       friend class EdgeSet;

       friend class Edge;

       friend class OutEdgeIt;

       friend class InEdgeIt;

       friend class SymEdge;

     public:

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

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

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

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

       NodeIt(const typename NodeGraphType::NodeIt &n)

 	: NodeGraphType::NodeIt(n) {}

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

       NodeIt &operator++()

       { this->NodeGraphType::NodeIt::operator++(); return *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;

   public:

     class Node;

     class Edge;

     class NodeIt;

     class EdgeIt;

     class OutEdgeIt;

     class InEdgeIt;

     // Create edge map registry.

     CREATE_EDGE_MAP_REGISTRY;

     // Create edge maps.

     CREATE_EDGE_MAP(ArrayMap);

     // Import node maps from the NodeGraphType.

     IMPORT_NODE_MAP(NodeGraphType, graph.G, EdgeSet, graph);

   public:

     ///Constructor

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

     ///\param _G the base graph.

     explicit 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.

     explicit EdgeSet(const EdgeSet &_g) 

       : G(_g.G), nodes(_g.G), edges(_g.edges),

 	first_free_edge(_g.first_free_edge) {}

     ///Number of nodes.

     int nodeNum() const { return G.nodeNum(); }

     ///Number of edges.

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

     /// Maximum node ID.

     /// Maximum node ID.

     ///\sa id(Node)

     int maxNodeId() const { return G.maxNodeId(); }

     /// 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. 

     int id(Node v) { return G.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.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

       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].first_out : edges[prev.n].next_out;

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

       //Update dynamic maps

       Edge e; e.n = n;

       edge_maps.erase(e);

     }

   public:

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

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

     void clear() {

       edge_maps.clear();

       edges.clear();

       first_free_edge=-1;

     }

     class Edge {

     public:

       friend class EdgeSet;

       template <typename T> friend class EdgeMap;

       friend class Node;

       friend class NodeIt;

     protected:

       int n;

       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;}

     };

     class EdgeIt : public Edge {

       friend class EdgeSet;

       template <typename T> friend class EdgeMap;

       const EdgeSet *G;

     public:

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

         NodeIt m;

 	for(G->first(m);

 	    m!=INVALID && G->nodes[m].first_in == -1;  ++m);

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

 	this->n = m!=INVALID?-1:G->nodes[m].first_in;

       }

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

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

       EdgeIt() : Edge() { }

       ///.

       ///\bug UNIMPLEMENTED!!!!!

       //

       EdgeIt &operator++() {

 	return *this;

       }

     };

     class OutEdgeIt : public Edge {

       const EdgeSet *G;

       friend class EdgeSet;

     public: 

       OutEdgeIt() : Edge() { }

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

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

       OutEdgeIt(const EdgeSet& _G,const Node v) :

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

       OutEdgeIt &operator++() { 

 	Edge::n = G->edges[Edge::n].next_out;

 	return *this; 

       }

     };

     class InEdgeIt : public Edge {

       const EdgeSet *G;

       friend class EdgeSet;

     public: 

       InEdgeIt() : Edge() { }

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

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

       InEdgeIt(const EdgeSet& _G,Node v)

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

       InEdgeIt &operator++() { 

 	Edge::n = G->edges[Edge::n].next_in; 

 	return *this; 

       }

     };

   };

   template<typename GG>

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

 /// @}  

 } //namespace lemon

 #endif //LEMON_LIST_GRAPH_H