lemon/smart_graph.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 06 Oct 2008 11:01:03 +0100
changeset 297 92b193385702
parent 238 79643f6e8c52
child 313 64f8f7cc6168
permissions -rw-r--r--
Merge
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_SMART_GRAPH_H
    20 #define LEMON_SMART_GRAPH_H
    21 
    22 ///\ingroup graphs
    23 ///\file
    24 ///\brief SmartDigraph and SmartGraph classes.
    25 
    26 #include <vector>
    27 
    28 #include <lemon/core.h>
    29 #include <lemon/error.h>
    30 #include <lemon/bits/graph_extender.h>
    31 
    32 namespace lemon {
    33 
    34   class SmartDigraph;
    35   ///Base of SmartDigraph
    36 
    37   ///Base of SmartDigraph
    38   ///
    39   class SmartDigraphBase {
    40   protected:
    41 
    42     struct NodeT
    43     {
    44       int first_in, first_out;
    45       NodeT() {}
    46     };
    47     struct ArcT
    48     {
    49       int target, source, next_in, next_out;
    50       ArcT() {}
    51     };
    52 
    53     std::vector<NodeT> nodes;
    54     std::vector<ArcT> arcs;
    55 
    56   public:
    57 
    58     typedef SmartDigraphBase Graph;
    59 
    60     class Node;
    61     class Arc;
    62 
    63   public:
    64 
    65     SmartDigraphBase() : nodes(), arcs() { }
    66     SmartDigraphBase(const SmartDigraphBase &_g)
    67       : nodes(_g.nodes), arcs(_g.arcs) { }
    68 
    69     typedef True NodeNumTag;
    70     typedef True EdgeNumTag;
    71 
    72     int nodeNum() const { return nodes.size(); }
    73     int arcNum() const { return arcs.size(); }
    74 
    75     int maxNodeId() const { return nodes.size()-1; }
    76     int maxArcId() const { return arcs.size()-1; }
    77 
    78     Node addNode() {
    79       int n = nodes.size();
    80       nodes.push_back(NodeT());
    81       nodes[n].first_in = -1;
    82       nodes[n].first_out = -1;
    83       return Node(n);
    84     }
    85 
    86     Arc addArc(Node u, Node v) {
    87       int n = arcs.size();
    88       arcs.push_back(ArcT());
    89       arcs[n].source = u._id;
    90       arcs[n].target = v._id;
    91       arcs[n].next_out = nodes[u._id].first_out;
    92       arcs[n].next_in = nodes[v._id].first_in;
    93       nodes[u._id].first_out = nodes[v._id].first_in = n;
    94 
    95       return Arc(n);
    96     }
    97 
    98     void clear() {
    99       arcs.clear();
   100       nodes.clear();
   101     }
   102 
   103     Node source(Arc a) const { return Node(arcs[a._id].source); }
   104     Node target(Arc a) const { return Node(arcs[a._id].target); }
   105 
   106     static int id(Node v) { return v._id; }
   107     static int id(Arc a) { return a._id; }
   108 
   109     static Node nodeFromId(int id) { return Node(id);}
   110     static Arc arcFromId(int id) { return Arc(id);}
   111 
   112     bool valid(Node n) const {
   113       return n._id >= 0 && n._id < static_cast<int>(nodes.size());
   114     }
   115     bool valid(Arc a) const {
   116       return a._id >= 0 && a._id < static_cast<int>(arcs.size());
   117     }
   118 
   119     class Node {
   120       friend class SmartDigraphBase;
   121       friend class SmartDigraph;
   122 
   123     protected:
   124       int _id;
   125       explicit Node(int id) : _id(id) {}
   126     public:
   127       Node() {}
   128       Node (Invalid) : _id(-1) {}
   129       bool operator==(const Node i) const {return _id == i._id;}
   130       bool operator!=(const Node i) const {return _id != i._id;}
   131       bool operator<(const Node i) const {return _id < i._id;}
   132     };
   133 
   134 
   135     class Arc {
   136       friend class SmartDigraphBase;
   137       friend class SmartDigraph;
   138 
   139     protected:
   140       int _id;
   141       explicit Arc(int id) : _id(id) {}
   142     public:
   143       Arc() { }
   144       Arc (Invalid) : _id(-1) {}
   145       bool operator==(const Arc i) const {return _id == i._id;}
   146       bool operator!=(const Arc i) const {return _id != i._id;}
   147       bool operator<(const Arc i) const {return _id < i._id;}
   148     };
   149 
   150     void first(Node& node) const {
   151       node._id = nodes.size() - 1;
   152     }
   153 
   154     static void next(Node& node) {
   155       --node._id;
   156     }
   157 
   158     void first(Arc& arc) const {
   159       arc._id = arcs.size() - 1;
   160     }
   161 
   162     static void next(Arc& arc) {
   163       --arc._id;
   164     }
   165 
   166     void firstOut(Arc& arc, const Node& node) const {
   167       arc._id = nodes[node._id].first_out;
   168     }
   169 
   170     void nextOut(Arc& arc) const {
   171       arc._id = arcs[arc._id].next_out;
   172     }
   173 
   174     void firstIn(Arc& arc, const Node& node) const {
   175       arc._id = nodes[node._id].first_in;
   176     }
   177 
   178     void nextIn(Arc& arc) const {
   179       arc._id = arcs[arc._id].next_in;
   180     }
   181 
   182   };
   183 
   184   typedef DigraphExtender<SmartDigraphBase> ExtendedSmartDigraphBase;
   185 
   186   ///\ingroup graphs
   187   ///
   188   ///\brief A smart directed graph class.
   189   ///
   190   ///This is a simple and fast digraph implementation.
   191   ///It is also quite memory efficient, but at the price
   192   ///that <b> it does support only limited (only stack-like)
   193   ///node and arc deletions</b>.
   194   ///It conforms to the \ref concepts::Digraph "Digraph concept" with
   195   ///an important extra feature that its maps are real \ref
   196   ///concepts::ReferenceMap "reference map"s.
   197   ///
   198   ///\sa concepts::Digraph.
   199   class SmartDigraph : public ExtendedSmartDigraphBase {
   200   public:
   201 
   202     typedef ExtendedSmartDigraphBase Parent;
   203 
   204   private:
   205 
   206     ///SmartDigraph is \e not copy constructible. Use DigraphCopy() instead.
   207 
   208     ///SmartDigraph is \e not copy constructible. Use DigraphCopy() instead.
   209     ///
   210     SmartDigraph(const SmartDigraph &) : ExtendedSmartDigraphBase() {};
   211     ///\brief Assignment of SmartDigraph to another one is \e not allowed.
   212     ///Use DigraphCopy() instead.
   213 
   214     ///Assignment of SmartDigraph to another one is \e not allowed.
   215     ///Use DigraphCopy() instead.
   216     void operator=(const SmartDigraph &) {}
   217 
   218   public:
   219 
   220     /// Constructor
   221 
   222     /// Constructor.
   223     ///
   224     SmartDigraph() {};
   225 
   226     ///Add a new node to the digraph.
   227 
   228     /// \return the new node.
   229     ///
   230     Node addNode() { return Parent::addNode(); }
   231 
   232     ///Add a new arc to the digraph.
   233 
   234     ///Add a new arc to the digraph with source node \c s
   235     ///and target node \c t.
   236     ///\return the new arc.
   237     Arc addArc(const Node& s, const Node& t) {
   238       return Parent::addArc(s, t);
   239     }
   240 
   241     /// \brief Using this it is possible to avoid the superfluous memory
   242     /// allocation.
   243 
   244     /// Using this it is possible to avoid the superfluous memory
   245     /// allocation: if you know that the digraph you want to build will
   246     /// be very large (e.g. it will contain millions of nodes and/or arcs)
   247     /// then it is worth reserving space for this amount before starting
   248     /// to build the digraph.
   249     /// \sa reserveArc
   250     void reserveNode(int n) { nodes.reserve(n); };
   251 
   252     /// \brief Using this it is possible to avoid the superfluous memory
   253     /// allocation.
   254 
   255     /// Using this it is possible to avoid the superfluous memory
   256     /// allocation: if you know that the digraph you want to build will
   257     /// be very large (e.g. it will contain millions of nodes and/or arcs)
   258     /// then it is worth reserving space for this amount before starting
   259     /// to build the digraph.
   260     /// \sa reserveNode
   261     void reserveArc(int m) { arcs.reserve(m); };
   262 
   263     /// \brief Node validity check
   264     ///
   265     /// This function gives back true if the given node is valid,
   266     /// ie. it is a real node of the graph.
   267     ///
   268     /// \warning A removed node (using Snapshot) could become valid again
   269     /// when new nodes are added to the graph.
   270     bool valid(Node n) const { return Parent::valid(n); }
   271 
   272     /// \brief Arc validity check
   273     ///
   274     /// This function gives back true if the given arc is valid,
   275     /// ie. it is a real arc of the graph.
   276     ///
   277     /// \warning A removed arc (using Snapshot) could become valid again
   278     /// when new arcs are added to the graph.
   279     bool valid(Arc a) const { return Parent::valid(a); }
   280 
   281     ///Clear the digraph.
   282 
   283     ///Erase all the nodes and arcs from the digraph.
   284     ///
   285     void clear() {
   286       Parent::clear();
   287     }
   288 
   289     ///Split a node.
   290 
   291     ///This function splits a node. First a new node is added to the digraph,
   292     ///then the source of each outgoing arc of \c n is moved to this new node.
   293     ///If \c connect is \c true (this is the default value), then a new arc
   294     ///from \c n to the newly created node is also added.
   295     ///\return The newly created node.
   296     ///
   297     ///\note The <tt>Arc</tt>s
   298     ///referencing a moved arc remain
   299     ///valid. However <tt>InArc</tt>'s and <tt>OutArc</tt>'s
   300     ///may be invalidated.
   301     ///\warning This functionality cannot be used together with the Snapshot
   302     ///feature.
   303     Node split(Node n, bool connect = true)
   304     {
   305       Node b = addNode();
   306       nodes[b._id].first_out=nodes[n._id].first_out;
   307       nodes[n._id].first_out=-1;
   308       for(int i=nodes[b._id].first_out;i!=-1;i++) arcs[i].source=b._id;
   309       if(connect) addArc(n,b);
   310       return b;
   311     }
   312 
   313   public:
   314 
   315     class Snapshot;
   316 
   317   protected:
   318 
   319     void restoreSnapshot(const Snapshot &s)
   320     {
   321       while(s.arc_num<arcs.size()) {
   322         Arc arc = arcFromId(arcs.size()-1);
   323         Parent::notifier(Arc()).erase(arc);
   324         nodes[arcs.back().source].first_out=arcs.back().next_out;
   325         nodes[arcs.back().target].first_in=arcs.back().next_in;
   326         arcs.pop_back();
   327       }
   328       while(s.node_num<nodes.size()) {
   329         Node node = nodeFromId(nodes.size()-1);
   330         Parent::notifier(Node()).erase(node);
   331         nodes.pop_back();
   332       }
   333     }
   334 
   335   public:
   336 
   337     ///Class to make a snapshot of the digraph and to restrore to it later.
   338 
   339     ///Class to make a snapshot of the digraph and to restrore to it later.
   340     ///
   341     ///The newly added nodes and arcs can be removed using the
   342     ///restore() function.
   343     ///\note After you restore a state, you cannot restore
   344     ///a later state, in other word you cannot add again the arcs deleted
   345     ///by restore() using another one Snapshot instance.
   346     ///
   347     ///\warning If you do not use correctly the snapshot that can cause
   348     ///either broken program, invalid state of the digraph, valid but
   349     ///not the restored digraph or no change. Because the runtime performance
   350     ///the validity of the snapshot is not stored.
   351     class Snapshot
   352     {
   353       SmartDigraph *_graph;
   354     protected:
   355       friend class SmartDigraph;
   356       unsigned int node_num;
   357       unsigned int arc_num;
   358     public:
   359       ///Default constructor.
   360 
   361       ///Default constructor.
   362       ///To actually make a snapshot you must call save().
   363       ///
   364       Snapshot() : _graph(0) {}
   365       ///Constructor that immediately makes a snapshot
   366 
   367       ///This constructor immediately makes a snapshot of the digraph.
   368       ///\param _g The digraph we make a snapshot of.
   369       Snapshot(SmartDigraph &graph) : _graph(&graph) {
   370         node_num=_graph->nodes.size();
   371         arc_num=_graph->arcs.size();
   372       }
   373 
   374       ///Make a snapshot.
   375 
   376       ///Make a snapshot of the digraph.
   377       ///
   378       ///This function can be called more than once. In case of a repeated
   379       ///call, the previous snapshot gets lost.
   380       ///\param _g The digraph we make the snapshot of.
   381       void save(SmartDigraph &graph)
   382       {
   383         _graph=&graph;
   384         node_num=_graph->nodes.size();
   385         arc_num=_graph->arcs.size();
   386       }
   387 
   388       ///Undo the changes until a snapshot.
   389 
   390       ///Undo the changes until a snapshot created by save().
   391       ///
   392       ///\note After you restored a state, you cannot restore
   393       ///a later state, in other word you cannot add again the arcs deleted
   394       ///by restore().
   395       void restore()
   396       {
   397         _graph->restoreSnapshot(*this);
   398       }
   399     };
   400   };
   401 
   402 
   403   class SmartGraphBase {
   404 
   405   protected:
   406 
   407     struct NodeT {
   408       int first_out;
   409     };
   410 
   411     struct ArcT {
   412       int target;
   413       int next_out;
   414     };
   415 
   416     std::vector<NodeT> nodes;
   417     std::vector<ArcT> arcs;
   418 
   419     int first_free_arc;
   420 
   421   public:
   422 
   423     typedef SmartGraphBase Digraph;
   424 
   425     class Node;
   426     class Arc;
   427     class Edge;
   428 
   429     class Node {
   430       friend class SmartGraphBase;
   431     protected:
   432 
   433       int _id;
   434       explicit Node(int id) { _id = id;}
   435 
   436     public:
   437       Node() {}
   438       Node (Invalid) { _id = -1; }
   439       bool operator==(const Node& node) const {return _id == node._id;}
   440       bool operator!=(const Node& node) const {return _id != node._id;}
   441       bool operator<(const Node& node) const {return _id < node._id;}
   442     };
   443 
   444     class Edge {
   445       friend class SmartGraphBase;
   446     protected:
   447 
   448       int _id;
   449       explicit Edge(int id) { _id = id;}
   450 
   451     public:
   452       Edge() {}
   453       Edge (Invalid) { _id = -1; }
   454       bool operator==(const Edge& arc) const {return _id == arc._id;}
   455       bool operator!=(const Edge& arc) const {return _id != arc._id;}
   456       bool operator<(const Edge& arc) const {return _id < arc._id;}
   457     };
   458 
   459     class Arc {
   460       friend class SmartGraphBase;
   461     protected:
   462 
   463       int _id;
   464       explicit Arc(int id) { _id = id;}
   465 
   466     public:
   467       operator Edge() const { 
   468         return _id != -1 ? edgeFromId(_id / 2) : INVALID; 
   469       }
   470 
   471       Arc() {}
   472       Arc (Invalid) { _id = -1; }
   473       bool operator==(const Arc& arc) const {return _id == arc._id;}
   474       bool operator!=(const Arc& arc) const {return _id != arc._id;}
   475       bool operator<(const Arc& arc) const {return _id < arc._id;}
   476     };
   477 
   478 
   479 
   480     SmartGraphBase()
   481       : nodes(), arcs() {}
   482 
   483 
   484     int maxNodeId() const { return nodes.size()-1; }
   485     int maxEdgeId() const { return arcs.size() / 2 - 1; }
   486     int maxArcId() const { return arcs.size()-1; }
   487 
   488     Node source(Arc e) const { return Node(arcs[e._id ^ 1].target); }
   489     Node target(Arc e) const { return Node(arcs[e._id].target); }
   490 
   491     Node u(Edge e) const { return Node(arcs[2 * e._id].target); }
   492     Node v(Edge e) const { return Node(arcs[2 * e._id + 1].target); }
   493 
   494     static bool direction(Arc e) {
   495       return (e._id & 1) == 1;
   496     }
   497 
   498     static Arc direct(Edge e, bool d) {
   499       return Arc(e._id * 2 + (d ? 1 : 0));
   500     }
   501 
   502     void first(Node& node) const {
   503       node._id = nodes.size() - 1;
   504     }
   505 
   506     void next(Node& node) const {
   507       --node._id;
   508     }
   509 
   510     void first(Arc& arc) const {
   511       arc._id = arcs.size() - 1;
   512     }
   513 
   514     void next(Arc& arc) const {
   515       --arc._id;
   516     }
   517 
   518     void first(Edge& arc) const {
   519       arc._id = arcs.size() / 2 - 1;
   520     }
   521 
   522     void next(Edge& arc) const {
   523       --arc._id;
   524     }
   525 
   526     void firstOut(Arc &arc, const Node& v) const {
   527       arc._id = nodes[v._id].first_out;
   528     }
   529     void nextOut(Arc &arc) const {
   530       arc._id = arcs[arc._id].next_out;
   531     }
   532 
   533     void firstIn(Arc &arc, const Node& v) const {
   534       arc._id = ((nodes[v._id].first_out) ^ 1);
   535       if (arc._id == -2) arc._id = -1;
   536     }
   537     void nextIn(Arc &arc) const {
   538       arc._id = ((arcs[arc._id ^ 1].next_out) ^ 1);
   539       if (arc._id == -2) arc._id = -1;
   540     }
   541 
   542     void firstInc(Edge &arc, bool& d, const Node& v) const {
   543       int de = nodes[v._id].first_out;
   544       if (de != -1) {
   545         arc._id = de / 2;
   546         d = ((de & 1) == 1);
   547       } else {
   548         arc._id = -1;
   549         d = true;
   550       }
   551     }
   552     void nextInc(Edge &arc, bool& d) const {
   553       int de = (arcs[(arc._id * 2) | (d ? 1 : 0)].next_out);
   554       if (de != -1) {
   555         arc._id = de / 2;
   556         d = ((de & 1) == 1);
   557       } else {
   558         arc._id = -1;
   559         d = true;
   560       }
   561     }
   562 
   563     static int id(Node v) { return v._id; }
   564     static int id(Arc e) { return e._id; }
   565     static int id(Edge e) { return e._id; }
   566 
   567     static Node nodeFromId(int id) { return Node(id);}
   568     static Arc arcFromId(int id) { return Arc(id);}
   569     static Edge edgeFromId(int id) { return Edge(id);}
   570 
   571     bool valid(Node n) const {
   572       return n._id >= 0 && n._id < static_cast<int>(nodes.size());
   573     }
   574     bool valid(Arc a) const {
   575       return a._id >= 0 && a._id < static_cast<int>(arcs.size());
   576     }
   577     bool valid(Edge e) const {
   578       return e._id >= 0 && 2 * e._id < static_cast<int>(arcs.size());
   579     }
   580 
   581     Node addNode() {
   582       int n = nodes.size();
   583       nodes.push_back(NodeT());
   584       nodes[n].first_out = -1;
   585 
   586       return Node(n);
   587     }
   588 
   589     Edge addEdge(Node u, Node v) {
   590       int n = arcs.size();
   591       arcs.push_back(ArcT());
   592       arcs.push_back(ArcT());
   593 
   594       arcs[n].target = u._id;
   595       arcs[n | 1].target = v._id;
   596 
   597       arcs[n].next_out = nodes[v._id].first_out;
   598       nodes[v._id].first_out = n;
   599 
   600       arcs[n | 1].next_out = nodes[u._id].first_out;
   601       nodes[u._id].first_out = (n | 1);
   602 
   603       return Edge(n / 2);
   604     }
   605 
   606     void clear() {
   607       arcs.clear();
   608       nodes.clear();
   609     }
   610 
   611   };
   612 
   613   typedef GraphExtender<SmartGraphBase> ExtendedSmartGraphBase;
   614 
   615   /// \ingroup graphs
   616   ///
   617   /// \brief A smart undirected graph class.
   618   ///
   619   /// This is a simple and fast graph implementation.
   620   /// It is also quite memory efficient, but at the price
   621   /// that <b> it does support only limited (only stack-like)
   622   /// node and arc deletions</b>.
   623   /// Except from this it conforms to
   624   /// the \ref concepts::Graph "Graph concept".
   625   ///
   626   /// It also has an
   627   /// important extra feature that
   628   /// its maps are real \ref concepts::ReferenceMap "reference map"s.
   629   ///
   630   /// \sa concepts::Graph.
   631   ///
   632   class SmartGraph : public ExtendedSmartGraphBase {
   633   private:
   634 
   635     ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.
   636 
   637     ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.
   638     ///
   639     SmartGraph(const SmartGraph &) : ExtendedSmartGraphBase() {};
   640 
   641     ///\brief Assignment of SmartGraph to another one is \e not allowed.
   642     ///Use GraphCopy() instead.
   643 
   644     ///Assignment of SmartGraph to another one is \e not allowed.
   645     ///Use GraphCopy() instead.
   646     void operator=(const SmartGraph &) {}
   647 
   648   public:
   649 
   650     typedef ExtendedSmartGraphBase Parent;
   651 
   652     /// Constructor
   653 
   654     /// Constructor.
   655     ///
   656     SmartGraph() {}
   657 
   658     ///Add a new node to the graph.
   659 
   660     /// \return the new node.
   661     ///
   662     Node addNode() { return Parent::addNode(); }
   663 
   664     ///Add a new edge to the graph.
   665 
   666     ///Add a new edge to the graph with node \c s
   667     ///and \c t.
   668     ///\return the new edge.
   669     Edge addEdge(const Node& s, const Node& t) {
   670       return Parent::addEdge(s, t);
   671     }
   672 
   673     /// \brief Node validity check
   674     ///
   675     /// This function gives back true if the given node is valid,
   676     /// ie. it is a real node of the graph.
   677     ///
   678     /// \warning A removed node (using Snapshot) could become valid again
   679     /// when new nodes are added to the graph.
   680     bool valid(Node n) const { return Parent::valid(n); }
   681 
   682     /// \brief Arc validity check
   683     ///
   684     /// This function gives back true if the given arc is valid,
   685     /// ie. it is a real arc of the graph.
   686     ///
   687     /// \warning A removed arc (using Snapshot) could become valid again
   688     /// when new edges are added to the graph.
   689     bool valid(Arc a) const { return Parent::valid(a); }
   690 
   691     /// \brief Edge validity check
   692     ///
   693     /// This function gives back true if the given edge is valid,
   694     /// ie. it is a real edge of the graph.
   695     ///
   696     /// \warning A removed edge (using Snapshot) could become valid again
   697     /// when new edges are added to the graph.
   698     bool valid(Edge e) const { return Parent::valid(e); }
   699 
   700     ///Clear the graph.
   701 
   702     ///Erase all the nodes and edges from the graph.
   703     ///
   704     void clear() {
   705       Parent::clear();
   706     }
   707 
   708   public:
   709 
   710     class Snapshot;
   711 
   712   protected:
   713 
   714     void saveSnapshot(Snapshot &s)
   715     {
   716       s._graph = this;
   717       s.node_num = nodes.size();
   718       s.arc_num = arcs.size();
   719     }
   720 
   721     void restoreSnapshot(const Snapshot &s)
   722     {
   723       while(s.arc_num<arcs.size()) {
   724         int n=arcs.size()-1;
   725         Edge arc=edgeFromId(n/2);
   726         Parent::notifier(Edge()).erase(arc);
   727         std::vector<Arc> dir;
   728         dir.push_back(arcFromId(n));
   729         dir.push_back(arcFromId(n-1));
   730         Parent::notifier(Arc()).erase(dir);
   731         nodes[arcs[n].target].first_out=arcs[n].next_out;
   732         nodes[arcs[n-1].target].first_out=arcs[n-1].next_out;
   733         arcs.pop_back();
   734         arcs.pop_back();
   735       }
   736       while(s.node_num<nodes.size()) {
   737         int n=nodes.size()-1;
   738         Node node = nodeFromId(n);
   739         Parent::notifier(Node()).erase(node);
   740         nodes.pop_back();
   741       }
   742     }
   743 
   744   public:
   745 
   746     ///Class to make a snapshot of the digraph and to restrore to it later.
   747 
   748     ///Class to make a snapshot of the digraph and to restrore to it later.
   749     ///
   750     ///The newly added nodes and arcs can be removed using the
   751     ///restore() function.
   752     ///
   753     ///\note After you restore a state, you cannot restore
   754     ///a later state, in other word you cannot add again the arcs deleted
   755     ///by restore() using another one Snapshot instance.
   756     ///
   757     ///\warning If you do not use correctly the snapshot that can cause
   758     ///either broken program, invalid state of the digraph, valid but
   759     ///not the restored digraph or no change. Because the runtime performance
   760     ///the validity of the snapshot is not stored.
   761     class Snapshot
   762     {
   763       SmartGraph *_graph;
   764     protected:
   765       friend class SmartGraph;
   766       unsigned int node_num;
   767       unsigned int arc_num;
   768     public:
   769       ///Default constructor.
   770 
   771       ///Default constructor.
   772       ///To actually make a snapshot you must call save().
   773       ///
   774       Snapshot() : _graph(0) {}
   775       ///Constructor that immediately makes a snapshot
   776 
   777       ///This constructor immediately makes a snapshot of the digraph.
   778       ///\param g The digraph we make a snapshot of.
   779       Snapshot(SmartGraph &graph) {
   780         graph.saveSnapshot(*this);
   781       }
   782 
   783       ///Make a snapshot.
   784 
   785       ///Make a snapshot of the graph.
   786       ///
   787       ///This function can be called more than once. In case of a repeated
   788       ///call, the previous snapshot gets lost.
   789       ///\param g The digraph we make the snapshot of.
   790       void save(SmartGraph &graph)
   791       {
   792         graph.saveSnapshot(*this);
   793       }
   794 
   795       ///Undo the changes until a snapshot.
   796 
   797       ///Undo the changes until a snapshot created by save().
   798       ///
   799       ///\note After you restored a state, you cannot restore
   800       ///a later state, in other word you cannot add again the arcs deleted
   801       ///by restore().
   802       void restore()
   803       {
   804         _graph->restoreSnapshot(*this);
   805       }
   806     };
   807   };
   808 
   809 } //namespace lemon
   810 
   811 
   812 #endif //LEMON_SMART_GRAPH_H