/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2006

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

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

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

  * precise terms see the accompanying LICENSE file.

  *

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

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

  * purpose.

  *

  */

 #ifndef LEMON_SMART_GRAPH_H

 #define LEMON_SMART_GRAPH_H

 ///\ingroup graphs

 ///\file

 ///\brief SmartGraph and SmartUGraph classes.

 #include <vector>

 #include <lemon/bits/invalid.h>

 #include <lemon/bits/base_extender.h>

 #include <lemon/bits/graph_extender.h>

 #include <lemon/bits/utility.h>

 #include <lemon/error.h>

 #include <lemon/bits/graph_extender.h>

 namespace lemon {

   class SmartGraph;

   ///Base of SmartGraph

   ///Base of SmartGraph

   ///

   class SmartGraphBase {

   protected:

     struct NodeT 

     {

       int first_in, first_out;      

       NodeT() {}

     };

     struct EdgeT 

     {

       int target, source, next_in, next_out;      

       EdgeT() {}  

     };

     std::vector<NodeT> nodes;

     std::vector<EdgeT> edges;

   public:

     typedef SmartGraphBase Graph;

     class Node;

     class Edge;

   public:

     SmartGraphBase() : nodes(), edges() { }

     SmartGraphBase(const SmartGraphBase &_g) 

       : nodes(_g.nodes), edges(_g.edges) { }

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

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

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

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

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

     Node addNode() {

       int n = nodes.size();     

       nodes.push_back(NodeT());

       nodes[n].first_in = -1;

       nodes[n].first_out = -1;

       return Node(n);

     }

     Edge addEdge(Node u, Node v) {

       int n = edges.size(); 

       edges.push_back(EdgeT());

       edges[n].source = u.id; 

       edges[n].target = v.id;

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

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

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

       return Edge(n);

     }

     void clear() {

       edges.clear();

       nodes.clear();

     }

     Node source(Edge e) const { return Node(edges[e.id].source); }

     Node target(Edge e) const { return Node(edges[e.id].target); }

     static int id(Node v) { return v.id; }

     static int id(Edge e) { return e.id; }

     static Node nodeFromId(int id) { return Node(id);}

     static Edge edgeFromId(int id) { return Edge(id);}

     class Node {

       friend class SmartGraphBase;

       friend class SmartGraph;

     protected:

       int id;

       explicit Node(int _id) : id(_id) {}

     public:

       Node() {}

       Node (Invalid) : id(-1) {}

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

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

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

     };

     class Edge {

       friend class SmartGraphBase;

       friend class SmartGraph;

     protected:

       int id;

       explicit Edge(int _id) : id(_id) {}

     public:

       Edge() { }

       Edge (Invalid) : 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;}

     };

     void first(Node& node) const {

       node.id = nodes.size() - 1;

     }

     static void next(Node& node) {

       --node.id;

     }

     void first(Edge& edge) const {

       edge.id = edges.size() - 1;

     }

     static void next(Edge& edge) {

       --edge.id;

     }

     void firstOut(Edge& edge, const Node& node) const {

       edge.id = nodes[node.id].first_out;

     }

     void nextOut(Edge& edge) const {

       edge.id = edges[edge.id].next_out;

     }

     void firstIn(Edge& edge, const Node& node) const {

       edge.id = nodes[node.id].first_in;

     }

     void nextIn(Edge& edge) const {

       edge.id = edges[edge.id].next_in;

     }

   };

   typedef GraphExtender<SmartGraphBase> ExtendedSmartGraphBase;

   /// \ingroup graphs

   ///A smart graph class.

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

   ///It is also quite memory efficient, but at the price

   ///that <b> it does support only limited (only stack-like)

   ///node and edge deletions</b>.

   ///It conforms to 

   ///the \ref concepts::Graph "Graph concept" with an

   ///important extra feature that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   ///\sa concepts::Graph.

   ///

   ///\author Alpar Juttner

   class SmartGraph : public ExtendedSmartGraphBase {

   public:

     typedef ExtendedSmartGraphBase Parent;

   private:

     ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.

     ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.

     ///

     SmartGraph(const SmartGraph &) : ExtendedSmartGraphBase() {};

     ///\brief Assignment of SmartGraph to another one is \e not allowed.

     ///Use GraphCopy() instead.

     ///Assignment of SmartGraph to another one is \e not allowed.

     ///Use GraphCopy() instead.

     void operator=(const SmartGraph &) {}

   public:

     /// Constructor

     /// Constructor.

     ///

     SmartGraph() {};

     ///Add a new node to the graph.

     /// \return the new node.

     ///

     Node addNode() { return Parent::addNode(); }

     ///Add a new edge to the graph.

     ///Add a new edge to the graph with source node \c s

     ///and target node \c t.

     ///\return the new edge.

     Edge addEdge(const Node& s, const Node& t) { 

       return Parent::addEdge(s, t); 

     }

     ///Clear the graph.

     ///Erase all the nodes and edges from the graph.

     ///

     void clear() {

       Parent::clear();

     }

     ///Split a node.

     ///This function splits a node. First a new node is added to the graph,

     ///then the source of each outgoing edge of \c n is moved to this new node.

     ///If \c connect is \c true (this is the default value), then a new edge

     ///from \c n to the newly created node is also added.

     ///\return The newly created node.

     ///

     ///\note The <tt>Edge</tt>s

     ///referencing a moved edge remain

     ///valid. However <tt>InEdge</tt>'s and <tt>OutEdge</tt>'s

     ///may be invalidated.

     ///\warning This functionality cannot be used together with the Snapshot

     ///feature.

     ///\todo It could be implemented in a bit faster way.

     Node split(Node n, bool connect = true)

     {

       Node b = addNode();

       nodes[b.id].first_out=nodes[n.id].first_out;

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

       for(int i=nodes[b.id].first_out;i!=-1;i++) edges[i].source=b.id;

       if(connect) addEdge(n,b);

       return b;

     }

   public:

     class Snapshot;

   protected:

     void restoreSnapshot(const Snapshot &s)

     {

       while(s.edge_num<edges.size()) {

         Edge edge = edgeFromId(edges.size()-1);

 	Parent::getNotifier(Edge()).erase(edge);

 	nodes[edges.back().source].first_out=edges.back().next_out;

 	nodes[edges.back().target].first_in=edges.back().next_in;

 	edges.pop_back();

       }

       while(s.node_num<nodes.size()) {

         Node node = nodeFromId(nodes.size()-1);

 	Parent::getNotifier(Node()).erase(node);

 	nodes.pop_back();

       }

     }    

   public:

     ///Class to make a snapshot of the graph and to restrore to it later.

     ///Class to make a snapshot of the graph and to restrore to it later.

     ///

     ///The newly added nodes and edges can be removed using the

     ///restore() function.

     ///\note After you restore a state, you cannot restore

     ///a later state, in other word you cannot add again the edges deleted

     ///by restore() using another one Snapshot instance.

     ///

     ///\warning If you do not use correctly the snapshot that can cause

     ///either broken program, invalid state of the graph, valid but

     ///not the restored graph or no change. Because the runtime performance

     ///the validity of the snapshot is not stored.

     class Snapshot 

     {

       SmartGraph *g;

     protected:

       friend class SmartGraph;

       unsigned int node_num;

       unsigned int edge_num;

     public:

       ///Default constructor.

       ///Default constructor.

       ///To actually make a snapshot you must call save().

       ///

       Snapshot() : g(0) {}

       ///Constructor that immediately makes a snapshot

       ///This constructor immediately makes a snapshot of the graph.

       ///\param _g The graph we make a snapshot of.

       Snapshot(SmartGraph &_g) :g(&_g) {

 	node_num=g->nodes.size();

 	edge_num=g->edges.size();

       }

       ///Make a snapshot.

       ///Make a snapshot of the graph.

       ///

       ///This function can be called more than once. In case of a repeated

       ///call, the previous snapshot gets lost.

       ///\param _g The graph we make the snapshot of.

       void save(SmartGraph &_g) 

       {

 	g=&_g;

 	node_num=g->nodes.size();

 	edge_num=g->edges.size();

       }

       ///Undo the changes until a snapshot.

       ///Undo the changes until a snapshot created by save().

       ///

       ///\note After you restored a state, you cannot restore

       ///a later state, in other word you cannot add again the edges deleted

       ///by restore().

       void restore()

       {

 	g->restoreSnapshot(*this);

       }

     };

   };

   class SmartUGraphBase {

   protected:

     struct NodeT {

       int first_out;

     };

     struct EdgeT {

       int target;

       int next_out;

     };

     std::vector<NodeT> nodes;

     std::vector<EdgeT> edges;

     int first_free_edge;

   public:

     typedef SmartUGraphBase Graph;

     class Node;

     class Edge;

     class UEdge;

     class Node {

       friend class SmartUGraphBase;

     protected:

       int id;

       explicit Node(int pid) { id = pid;}

     public:

       Node() {}

       Node (Invalid) { id = -1; }

       bool operator==(const Node& node) const {return id == node.id;}

       bool operator!=(const Node& node) const {return id != node.id;}

       bool operator<(const Node& node) const {return id < node.id;}

     };

     class UEdge {

       friend class SmartUGraphBase;

     protected:

       int id;

       explicit UEdge(int pid) { id = pid;}

     public:

       UEdge() {}

       UEdge (Invalid) { id = -1; }

       bool operator==(const UEdge& edge) const {return id == edge.id;}

       bool operator!=(const UEdge& edge) const {return id != edge.id;}

       bool operator<(const UEdge& edge) const {return id < edge.id;}

     };

     class Edge {

       friend class SmartUGraphBase;

     protected:

       int id;

       explicit Edge(int pid) { id = pid;}

     public:

       operator UEdge() const { return uEdgeFromId(id / 2); }

       Edge() {}

       Edge (Invalid) { id = -1; }

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

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

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

     };

     SmartUGraphBase()

       : nodes(), edges() {}

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

     int maxUEdgeId() const { return edges.size() / 2 - 1; }

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

     Node source(Edge e) const { return Node(edges[e.id ^ 1].target); }

     Node target(Edge e) const { return Node(edges[e.id].target); }

     Node source(UEdge e) const { return Node(edges[2 * e.id].target); }

     Node target(UEdge e) const { return Node(edges[2 * e.id + 1].target); }

     static bool direction(Edge e) {

       return (e.id & 1) == 1;

     }

     static Edge direct(UEdge e, bool d) {

       return Edge(e.id * 2 + (d ? 1 : 0));

     }

     void first(Node& node) const { 

       node.id = nodes.size() - 1;

     }

     void next(Node& node) const {

       --node.id;

     }

     void first(Edge& edge) const { 

       edge.id = edges.size() - 1;

     }

     void next(Edge& edge) const {

       --edge.id;

     }

     void first(UEdge& edge) const { 

       edge.id = edges.size() / 2 - 1;

     }

     void next(UEdge& edge) const {

       --edge.id;

     }

     void firstOut(Edge &edge, const Node& v) const {

       edge.id = nodes[v.id].first_out;

     }

     void nextOut(Edge &edge) const {

       edge.id = edges[edge.id].next_out;

     }

     void firstIn(Edge &edge, const Node& v) const {

       edge.id = ((nodes[v.id].first_out) ^ 1);

       if (edge.id == -2) edge.id = -1;

     }

     void nextIn(Edge &edge) const {

       edge.id = ((edges[edge.id ^ 1].next_out) ^ 1);

       if (edge.id == -2) edge.id = -1;

     }

     void firstInc(UEdge &edge, bool& d, const Node& v) const {

       int de = nodes[v.id].first_out;

       edge.id = de / 2;

       d = ((de & 1) == 1);

     }

     void nextInc(UEdge &edge, bool& d) const {

       int de = (edges[(edge.id * 2) | (d ? 1 : 0)].next_out);

       edge.id = de / 2;

       d = ((de & 1) == 1);

     }

     static int id(Node v) { return v.id; }

     static int id(Edge e) { return e.id; }

     static int id(UEdge e) { return e.id; }

     static Node nodeFromId(int id) { return Node(id);}

     static Edge edgeFromId(int id) { return Edge(id);}

     static UEdge uEdgeFromId(int id) { return UEdge(id);}

     Node addNode() {     

       int n = nodes.size();

       nodes.push_back(NodeT());

       nodes[n].first_out = -1;

       return Node(n);

     }

     UEdge addEdge(Node u, Node v) {

       int n = edges.size();

       edges.push_back(EdgeT());

       edges.push_back(EdgeT());

       edges[n].target = u.id;

       edges[n | 1].target = v.id;

       edges[n].next_out = nodes[v.id].first_out;

       edges[n | 1].next_out = nodes[u.id].first_out;

       nodes[v.id].first_out = n;

       nodes[u.id].first_out = (n | 1);

       return UEdge(n / 2);

     }

     void clear() {

       edges.clear();

       nodes.clear();

     }

   };

   typedef UGraphExtender<SmartUGraphBase> ExtendedSmartUGraphBase;

   /// \ingroup graphs

   ///

   /// \brief A smart undirected graph class.

   ///

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

   /// It is also quite memory efficient, but at the price

   /// that <b> it does support only limited (only stack-like)

   /// node and edge deletions</b>.

   /// Except from this it conforms to 

   /// the \ref concepts::UGraph "UGraph concept".

   ///

   ///It also has an

   ///important extra feature that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   /// \sa concepts::UGraph.

   ///

   class SmartUGraph : public ExtendedSmartUGraphBase {

   private:

     ///SmartUGraph is \e not copy constructible. Use UGraphCopy() instead.

     ///SmartUGraph is \e not copy constructible. Use UGraphCopy() instead.

     ///

     SmartUGraph(const SmartUGraph &) : ExtendedSmartUGraphBase() {};

     ///\brief Assignment of SmartUGraph to another one is \e not allowed.

     ///Use UGraphCopy() instead.

     ///Assignment of SmartUGraph to another one is \e not allowed.

     ///Use UGraphCopy() instead.

     void operator=(const SmartUGraph &) {}

   public:

     typedef ExtendedSmartUGraphBase Parent;

     typedef Parent::OutEdgeIt IncEdgeIt;

     /// Constructor

     /// Constructor.

     ///

     SmartUGraph() {}

     ///Add a new node to the graph.

     /// \return the new node.

     ///

     Node addNode() { return Parent::addNode(); }

     ///Add a new undirected edge to the graph.

     ///Add a new undirected edge to the graph with node \c s

     ///and \c t.

     ///\return the new undirected edge.

     UEdge addEdge(const Node& s, const Node& t) { 

       return Parent::addEdge(s, t); 

     }

     ///Clear the graph.

     ///Erase all the nodes and edges from the graph.

     ///

     void clear() {

       Parent::clear();

     }

   public:

     class Snapshot;

   protected:

     void saveSnapshot(Snapshot &s)

     {

       s.g = this;

       s.node_num = nodes.size();

       s.edge_num = edges.size();

     }

     void restoreSnapshot(const Snapshot &s)

     {

       while(s.edge_num<edges.size()) {

         int n=edges.size()-1;

         UEdge edge=uEdgeFromId(n/2);

 	Parent::getNotifier(UEdge()).erase(edge);

         std::vector<Edge> dir;

         dir.push_back(edgeFromId(n));

         dir.push_back(edgeFromId(n-1));

 	Parent::getNotifier(Edge()).erase(dir);

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

 	nodes[edges[n-1].target].first_out=edges[n-1].next_out;

 	edges.pop_back();

 	edges.pop_back();

       }

       while(s.node_num<nodes.size()) {

         int n=nodes.size()-1;

         Node node = nodeFromId(n);

 	Parent::getNotifier(Node()).erase(node);

 	nodes.pop_back();

       }

     }    

   public:

     ///Class to make a snapshot of the graph and to restrore to it later.

     ///Class to make a snapshot of the graph and to restrore to it later.

     ///

     ///The newly added nodes and edges can be removed using the

     ///restore() function.

     ///

     ///\note After you restore a state, you cannot restore

     ///a later state, in other word you cannot add again the edges deleted

     ///by restore() using another one Snapshot instance.

     ///

     ///\warning If you do not use correctly the snapshot that can cause

     ///either broken program, invalid state of the graph, valid but

     ///not the restored graph or no change. Because the runtime performance

     ///the validity of the snapshot is not stored.

     class Snapshot 

     {

       SmartUGraph *g;

     protected:

       friend class SmartUGraph;

       unsigned int node_num;

       unsigned int edge_num;

     public:

       ///Default constructor.

       ///Default constructor.

       ///To actually make a snapshot you must call save().

       ///

       Snapshot() : g(0) {}

       ///Constructor that immediately makes a snapshot

       ///This constructor immediately makes a snapshot of the graph.

       ///\param _g The graph we make a snapshot of.

       Snapshot(SmartUGraph &g) {

         g.saveSnapshot(*this);

       }

       ///Make a snapshot.

       ///Make a snapshot of the graph.

       ///

       ///This function can be called more than once. In case of a repeated

       ///call, the previous snapshot gets lost.

       ///\param _g The graph we make the snapshot of.

       void save(SmartUGraph &g) 

       {

         g.saveSnapshot(*this);

       }

       ///Undo the changes until a snapshot.

       ///Undo the changes until a snapshot created by save().

       ///

       ///\note After you restored a state, you cannot restore

       ///a later state, in other word you cannot add again the edges deleted

       ///by restore().

       void restore()

       {

         g->restoreSnapshot(*this);

       }

     };

   };

   class SmartBpUGraphBase {

   public:

     class NodeSetError : public LogicError {

     public:

       virtual const char* what() const throw() { 

 	return "lemon::SmartBpUGraph::NodeSetError";

       }

     };

   protected:

     struct NodeT {

       int first;

       NodeT() {}

       NodeT(int _first) : first(_first) {}

     };

     struct UEdgeT {

       int aNode, next_out;

       int bNode, next_in;

     };

     std::vector<NodeT> aNodes;

     std::vector<NodeT> bNodes;

     std::vector<UEdgeT> edges;

   public:

     class Node {

       friend class SmartBpUGraphBase;

     protected:

       int id;

       explicit Node(int _id) : id(_id) {}

     public:

       Node() {}

       Node(Invalid) : id(-1) {}

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

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

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

     };

     class UEdge {

       friend class SmartBpUGraphBase;

     protected:

       int id;

       UEdge(int _id) : id(_id) {}

     public:

       UEdge() {}

       UEdge(Invalid) : id(-1) {}

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

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

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

     };

     void firstANode(Node& node) const {

       node.id = 2 * aNodes.size() - 2;

       if (node.id < 0) node.id = -1; 

     }

     void nextANode(Node& node) const {

       node.id -= 2;

       if (node.id < 0) node.id = -1; 

     }

     void firstBNode(Node& node) const {

       node.id = 2 * bNodes.size() - 1;

     }

     void nextBNode(Node& node) const {

       node.id -= 2;

     }

     void first(Node& node) const {

       if (aNodes.size() > 0) {

 	node.id = 2 * aNodes.size() - 2;

       } else {

 	node.id = 2 * bNodes.size() - 1;

       }

     }

     void next(Node& node) const {

       node.id -= 2;

       if (node.id == -2) {

 	node.id = 2 * bNodes.size() - 1;

       }

     }

     void first(UEdge& edge) const {

       edge.id = edges.size() - 1;

     }

     void next(UEdge& edge) const {

       --edge.id;

     }

     void firstFromANode(UEdge& edge, const Node& node) const {

       LEMON_ASSERT((node.id & 1) == 0, NodeSetError());

       edge.id = aNodes[node.id >> 1].first;

     }

     void nextFromANode(UEdge& edge) const {

       edge.id = edges[edge.id].next_out;

     }

     void firstFromBNode(UEdge& edge, const Node& node) const {

       LEMON_ASSERT((node.id & 1) == 1, NodeSetError());

       edge.id = bNodes[node.id >> 1].first;

     }

     void nextFromBNode(UEdge& edge) const {

       edge.id = edges[edge.id].next_in;

     }

     static int id(const Node& node) {

       return node.id;

     }

     static Node nodeFromId(int id) {

       return Node(id);

     }

     int maxNodeId() const {

       return aNodes.size() > bNodes.size() ?

 	aNodes.size() * 2 - 2 : bNodes.size() * 2 - 1;

     }

     static int id(const UEdge& edge) {

       return edge.id;

     }

     static UEdge uEdgeFromId(int id) {

       return UEdge(id);

     }

     int maxUEdgeId() const {

       return edges.size();

     }

     static int aNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node nodeFromANodeId(int id) {

       return Node(id << 1);

     }

     int maxANodeId() const {

       return aNodes.size();

     }

     static int bNodeId(const Node& node) {

       return node.id >> 1;

     }

     static Node nodeFromBNodeId(int id) {

       return Node((id << 1) + 1);

     }

     int maxBNodeId() const {

       return bNodes.size();

     }

     Node aNode(const UEdge& edge) const {

       return Node(edges[edge.id].aNode);

     }

     Node bNode(const UEdge& edge) const {

       return Node(edges[edge.id].bNode);

     }

     static bool aNode(const Node& node) {

       return (node.id & 1) == 0;

     }

     static bool bNode(const Node& node) {

       return (node.id & 1) == 1;

     }

     Node addANode() {

       NodeT nodeT;

       nodeT.first = -1;

       aNodes.push_back(nodeT);

       return Node(aNodes.size() * 2 - 2);

     }

     Node addBNode() {

       NodeT nodeT;

       nodeT.first = -1;

       bNodes.push_back(nodeT);

       return Node(bNodes.size() * 2 - 1);

     }

     UEdge addEdge(const Node& source, const Node& target) {

       LEMON_ASSERT(((source.id ^ target.id) & 1) == 1, NodeSetError());

       UEdgeT edgeT;

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

 	edgeT.aNode = source.id;

 	edgeT.bNode = target.id;

       } else {

 	edgeT.aNode = target.id;

 	edgeT.bNode = source.id;

       }

       edgeT.next_out = aNodes[edgeT.aNode >> 1].first;

       aNodes[edgeT.aNode >> 1].first = edges.size();

       edgeT.next_in = bNodes[edgeT.bNode >> 1].first;

       bNodes[edgeT.bNode >> 1].first = edges.size();

       edges.push_back(edgeT);

       return UEdge(edges.size() - 1);

     }

     void clear() {

       aNodes.clear();

       bNodes.clear();

       edges.clear();

     }

     typedef True NodeNumTag;

     int nodeNum() const { return aNodes.size() + bNodes.size(); }

     int aNodeNum() const { return aNodes.size(); }

     int bNodeNum() const { return bNodes.size(); }

     typedef True EdgeNumTag;

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

   };

   typedef BpUGraphExtender<BidirBpUGraphExtender<SmartBpUGraphBase> >

   ExtendedSmartBpUGraphBase;

   /// \ingroup graphs

   ///

   /// \brief A smart bipartite undirected graph class.

   ///

   /// This is a simple and fast bipartite undirected graph implementation.

   /// It is also quite memory efficient, but at the price

   /// that <b> it does not support node and edge deletions</b>.

   /// Except from this it conforms to 

   /// the \ref concepts::BpUGraph "BpUGraph concept".

   ///

   ///It also has an

   ///important extra feature that

   ///its maps are real \ref concepts::ReferenceMap "reference map"s.

   ///

   /// \sa concepts::BpUGraph.

   ///

   class SmartBpUGraph : public ExtendedSmartBpUGraphBase {

   private:

     /// \brief SmartBpUGraph is \e not copy constructible.

     ///

     ///SmartBpUGraph is \e not copy constructible.

     SmartBpUGraph(const SmartBpUGraph &) : ExtendedSmartBpUGraphBase() {};

     /// \brief Assignment of SmartBpUGraph to another one is \e not

     /// allowed.

     ///

     /// Assignment of SmartBpUGraph to another one is \e not allowed.

     void operator=(const SmartBpUGraph &) {}

   public:

     typedef ExtendedSmartBpUGraphBase Parent;

     ///Constructor

     ///Constructor.

     ///

     SmartBpUGraph() : ExtendedSmartBpUGraphBase() {}

     ///Add a new ANode to the graph.

     /// \return the new node.

     ///

     Node addANode() { return Parent::addANode(); }

     ///Add a new BNode to the graph.

     /// \return the new node.

     ///

     Node addBNode() { return Parent::addBNode(); }

     ///Add a new undirected edge to the graph.

     ///Add a new undirected edge to the graph with node \c s

     ///and \c t.

     ///\return the new undirected edge.

     UEdge addEdge(const Node& s, const Node& t) { 

       return Parent::addEdge(s, t); 

     }

     ///Clear the graph.

     ///Erase all the nodes and edges from the graph.

     ///

     void clear() {

       Parent::clear();

     }

   public:

     class Snapshot;

   protected:

     void restoreSnapshot(const Snapshot &s)

     {

       while(s.edge_num<edges.size()) {

         UEdge edge = uEdgeFromId(edges.size()-1);

 	Parent::getNotifier(UEdge()).erase(edge);

         std::vector<Edge> dir;

         dir.push_back(Parent::direct(edge, true));

         dir.push_back(Parent::direct(edge, false));

 	Parent::getNotifier(Edge()).erase(dir);

 	aNodes[edges.back().aNode >> 1].first=edges.back().next_out;

 	bNodes[edges.back().bNode >> 1].first=edges.back().next_in;

 	edges.pop_back();

       }

       while(s.anode_num<aNodes.size()) {

         Node node = nodeFromANodeId(aNodes.size() - 1);

 	Parent::getNotifier(ANode()).erase(node);

 	Parent::getNotifier(Node()).erase(node);

 	aNodes.pop_back();

       }

       while(s.bnode_num<bNodes.size()) {

         Node node = nodeFromBNodeId(bNodes.size() - 1);

 	Parent::getNotifier(BNode()).erase(node);

 	Parent::getNotifier(Node()).erase(node);

 	bNodes.pop_back();

       }

     }    

   public:

     ///Class to make a snapshot of the graph and to restrore to it later.

     ///Class to make a snapshot of the graph and to restrore to it later.

     ///

     ///The newly added nodes and edges can be removed using the

     ///restore() function.

     ///

     ///\note After you restore a state, you cannot restore

     ///a later state, in other word you cannot add again the edges deleted

     ///by restore() using another one Snapshot instance.

     ///

     ///\warning If you do not use correctly the snapshot that can cause

     ///either broken program, invalid state of the graph, valid but

     ///not the restored graph or no change. Because the runtime performance

     ///the validity of the snapshot is not stored.

     class Snapshot 

     {

       SmartBpUGraph *g;

     protected:

       friend class SmartBpUGraph;

       unsigned int anode_num;

       unsigned int bnode_num;

       unsigned int edge_num;

     public:

       ///Default constructor.

       ///Default constructor.

       ///To actually make a snapshot you must call save().

       ///

       Snapshot() : g(0) {}

       ///Constructor that immediately makes a snapshot

       ///This constructor immediately makes a snapshot of the graph.

       ///\param _g The graph we make a snapshot of.

       Snapshot(SmartBpUGraph &_g) : g(&_g) {

 	anode_num=g->aNodes.size();

 	bnode_num=g->bNodes.size();

 	edge_num=g->edges.size();

       }

       ///Make a snapshot.

       ///Make a snapshot of the graph.

       ///

       ///This function can be called more than once. In case of a repeated

       ///call, the previous snapshot gets lost.

       ///\param _g The graph we make the snapshot of.

       void save(SmartBpUGraph &_g) 

       {

 	g=&_g;

 	anode_num=g->aNodes.size();

 	bnode_num=g->bNodes.size();

 	edge_num=g->edges.size();

       }

       ///Undo the changes until a snapshot.

       ///Undo the changes until a snapshot created by save().

       ///

       ///\note After you restored a state, you cannot restore

       ///a later state, in other word you cannot add again the edges deleted

       ///by restore().

       void restore()

       {

 	g->restoreSnapshot(*this);

       }

     };

   };

   /// @}  

 } //namespace lemon

 #endif //LEMON_SMART_GRAPH_H