lemon/smart_graph.h
author Balazs Dezso <deba@inf.elte.hu>
Mon, 28 Jul 2008 09:29:30 +0200
changeset 234 ad6b8c47bd56
parent 209 765619b7cbb2
child 238 79643f6e8c52
permissions -rw-r--r--
Erase in the documentation of list graphs
     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     ///\todo It could be implemented in a bit faster way.
   304     Node split(Node n, bool connect = true)
   305     {
   306       Node b = addNode();
   307       nodes[b._id].first_out=nodes[n._id].first_out;
   308       nodes[n._id].first_out=-1;
   309       for(int i=nodes[b._id].first_out;i!=-1;i++) arcs[i].source=b._id;
   310       if(connect) addArc(n,b);
   311       return b;
   312     }
   313 
   314   public:
   315 
   316     class Snapshot;
   317 
   318   protected:
   319 
   320     void restoreSnapshot(const Snapshot &s)
   321     {
   322       while(s.arc_num<arcs.size()) {
   323         Arc arc = arcFromId(arcs.size()-1);
   324         Parent::notifier(Arc()).erase(arc);
   325         nodes[arcs.back().source].first_out=arcs.back().next_out;
   326         nodes[arcs.back().target].first_in=arcs.back().next_in;
   327         arcs.pop_back();
   328       }
   329       while(s.node_num<nodes.size()) {
   330         Node node = nodeFromId(nodes.size()-1);
   331         Parent::notifier(Node()).erase(node);
   332         nodes.pop_back();
   333       }
   334     }
   335 
   336   public:
   337 
   338     ///Class to make a snapshot of the digraph and to restrore to it later.
   339 
   340     ///Class to make a snapshot of the digraph and to restrore to it later.
   341     ///
   342     ///The newly added nodes and arcs can be removed using the
   343     ///restore() function.
   344     ///\note After you restore a state, you cannot restore
   345     ///a later state, in other word you cannot add again the arcs deleted
   346     ///by restore() using another one Snapshot instance.
   347     ///
   348     ///\warning If you do not use correctly the snapshot that can cause
   349     ///either broken program, invalid state of the digraph, valid but
   350     ///not the restored digraph or no change. Because the runtime performance
   351     ///the validity of the snapshot is not stored.
   352     class Snapshot
   353     {
   354       SmartDigraph *_graph;
   355     protected:
   356       friend class SmartDigraph;
   357       unsigned int node_num;
   358       unsigned int arc_num;
   359     public:
   360       ///Default constructor.
   361 
   362       ///Default constructor.
   363       ///To actually make a snapshot you must call save().
   364       ///
   365       Snapshot() : _graph(0) {}
   366       ///Constructor that immediately makes a snapshot
   367 
   368       ///This constructor immediately makes a snapshot of the digraph.
   369       ///\param _g The digraph we make a snapshot of.
   370       Snapshot(SmartDigraph &graph) : _graph(&graph) {
   371         node_num=_graph->nodes.size();
   372         arc_num=_graph->arcs.size();
   373       }
   374 
   375       ///Make a snapshot.
   376 
   377       ///Make a snapshot of the digraph.
   378       ///
   379       ///This function can be called more than once. In case of a repeated
   380       ///call, the previous snapshot gets lost.
   381       ///\param _g The digraph we make the snapshot of.
   382       void save(SmartDigraph &graph)
   383       {
   384         _graph=&graph;
   385         node_num=_graph->nodes.size();
   386         arc_num=_graph->arcs.size();
   387       }
   388 
   389       ///Undo the changes until a snapshot.
   390 
   391       ///Undo the changes until a snapshot created by save().
   392       ///
   393       ///\note After you restored a state, you cannot restore
   394       ///a later state, in other word you cannot add again the arcs deleted
   395       ///by restore().
   396       void restore()
   397       {
   398         _graph->restoreSnapshot(*this);
   399       }
   400     };
   401   };
   402 
   403 
   404   class SmartGraphBase {
   405 
   406   protected:
   407 
   408     struct NodeT {
   409       int first_out;
   410     };
   411 
   412     struct ArcT {
   413       int target;
   414       int next_out;
   415     };
   416 
   417     std::vector<NodeT> nodes;
   418     std::vector<ArcT> arcs;
   419 
   420     int first_free_arc;
   421 
   422   public:
   423 
   424     typedef SmartGraphBase Digraph;
   425 
   426     class Node;
   427     class Arc;
   428     class Edge;
   429 
   430     class Node {
   431       friend class SmartGraphBase;
   432     protected:
   433 
   434       int _id;
   435       explicit Node(int id) { _id = id;}
   436 
   437     public:
   438       Node() {}
   439       Node (Invalid) { _id = -1; }
   440       bool operator==(const Node& node) const {return _id == node._id;}
   441       bool operator!=(const Node& node) const {return _id != node._id;}
   442       bool operator<(const Node& node) const {return _id < node._id;}
   443     };
   444 
   445     class Edge {
   446       friend class SmartGraphBase;
   447     protected:
   448 
   449       int _id;
   450       explicit Edge(int id) { _id = id;}
   451 
   452     public:
   453       Edge() {}
   454       Edge (Invalid) { _id = -1; }
   455       bool operator==(const Edge& arc) const {return _id == arc._id;}
   456       bool operator!=(const Edge& arc) const {return _id != arc._id;}
   457       bool operator<(const Edge& arc) const {return _id < arc._id;}
   458     };
   459 
   460     class Arc {
   461       friend class SmartGraphBase;
   462     protected:
   463 
   464       int _id;
   465       explicit Arc(int id) { _id = id;}
   466 
   467     public:
   468       operator Edge() const { return edgeFromId(_id / 2); }
   469 
   470       Arc() {}
   471       Arc (Invalid) { _id = -1; }
   472       bool operator==(const Arc& arc) const {return _id == arc._id;}
   473       bool operator!=(const Arc& arc) const {return _id != arc._id;}
   474       bool operator<(const Arc& arc) const {return _id < arc._id;}
   475     };
   476 
   477 
   478 
   479     SmartGraphBase()
   480       : nodes(), arcs() {}
   481 
   482 
   483     int maxNodeId() const { return nodes.size()-1; }
   484     int maxEdgeId() const { return arcs.size() / 2 - 1; }
   485     int maxArcId() const { return arcs.size()-1; }
   486 
   487     Node source(Arc e) const { return Node(arcs[e._id ^ 1].target); }
   488     Node target(Arc e) const { return Node(arcs[e._id].target); }
   489 
   490     Node u(Edge e) const { return Node(arcs[2 * e._id].target); }
   491     Node v(Edge e) const { return Node(arcs[2 * e._id + 1].target); }
   492 
   493     static bool direction(Arc e) {
   494       return (e._id & 1) == 1;
   495     }
   496 
   497     static Arc direct(Edge e, bool d) {
   498       return Arc(e._id * 2 + (d ? 1 : 0));
   499     }
   500 
   501     void first(Node& node) const {
   502       node._id = nodes.size() - 1;
   503     }
   504 
   505     void next(Node& node) const {
   506       --node._id;
   507     }
   508 
   509     void first(Arc& arc) const {
   510       arc._id = arcs.size() - 1;
   511     }
   512 
   513     void next(Arc& arc) const {
   514       --arc._id;
   515     }
   516 
   517     void first(Edge& arc) const {
   518       arc._id = arcs.size() / 2 - 1;
   519     }
   520 
   521     void next(Edge& arc) const {
   522       --arc._id;
   523     }
   524 
   525     void firstOut(Arc &arc, const Node& v) const {
   526       arc._id = nodes[v._id].first_out;
   527     }
   528     void nextOut(Arc &arc) const {
   529       arc._id = arcs[arc._id].next_out;
   530     }
   531 
   532     void firstIn(Arc &arc, const Node& v) const {
   533       arc._id = ((nodes[v._id].first_out) ^ 1);
   534       if (arc._id == -2) arc._id = -1;
   535     }
   536     void nextIn(Arc &arc) const {
   537       arc._id = ((arcs[arc._id ^ 1].next_out) ^ 1);
   538       if (arc._id == -2) arc._id = -1;
   539     }
   540 
   541     void firstInc(Edge &arc, bool& d, const Node& v) const {
   542       int de = nodes[v._id].first_out;
   543       if (de != -1) {
   544         arc._id = de / 2;
   545         d = ((de & 1) == 1);
   546       } else {
   547         arc._id = -1;
   548         d = true;
   549       }
   550     }
   551     void nextInc(Edge &arc, bool& d) const {
   552       int de = (arcs[(arc._id * 2) | (d ? 1 : 0)].next_out);
   553       if (de != -1) {
   554         arc._id = de / 2;
   555         d = ((de & 1) == 1);
   556       } else {
   557         arc._id = -1;
   558         d = true;
   559       }
   560     }
   561 
   562     static int id(Node v) { return v._id; }
   563     static int id(Arc e) { return e._id; }
   564     static int id(Edge e) { return e._id; }
   565 
   566     static Node nodeFromId(int id) { return Node(id);}
   567     static Arc arcFromId(int id) { return Arc(id);}
   568     static Edge edgeFromId(int id) { return Edge(id);}
   569 
   570     bool valid(Node n) const {
   571       return n._id >= 0 && n._id < static_cast<int>(nodes.size());
   572     }
   573     bool valid(Arc a) const {
   574       return a._id >= 0 && a._id < static_cast<int>(arcs.size());
   575     }
   576     bool valid(Edge e) const {
   577       return e._id >= 0 && 2 * e._id < static_cast<int>(arcs.size());
   578     }
   579 
   580     Node addNode() {
   581       int n = nodes.size();
   582       nodes.push_back(NodeT());
   583       nodes[n].first_out = -1;
   584 
   585       return Node(n);
   586     }
   587 
   588     Edge addEdge(Node u, Node v) {
   589       int n = arcs.size();
   590       arcs.push_back(ArcT());
   591       arcs.push_back(ArcT());
   592 
   593       arcs[n].target = u._id;
   594       arcs[n | 1].target = v._id;
   595 
   596       arcs[n].next_out = nodes[v._id].first_out;
   597       nodes[v._id].first_out = n;
   598 
   599       arcs[n | 1].next_out = nodes[u._id].first_out;
   600       nodes[u._id].first_out = (n | 1);
   601 
   602       return Edge(n / 2);
   603     }
   604 
   605     void clear() {
   606       arcs.clear();
   607       nodes.clear();
   608     }
   609 
   610   };
   611 
   612   typedef GraphExtender<SmartGraphBase> ExtendedSmartGraphBase;
   613 
   614   /// \ingroup graphs
   615   ///
   616   /// \brief A smart undirected graph class.
   617   ///
   618   /// This is a simple and fast graph implementation.
   619   /// It is also quite memory efficient, but at the price
   620   /// that <b> it does support only limited (only stack-like)
   621   /// node and arc deletions</b>.
   622   /// Except from this it conforms to
   623   /// the \ref concepts::Graph "Graph concept".
   624   ///
   625   /// It also has an
   626   /// important extra feature that
   627   /// its maps are real \ref concepts::ReferenceMap "reference map"s.
   628   ///
   629   /// \sa concepts::Graph.
   630   ///
   631   class SmartGraph : public ExtendedSmartGraphBase {
   632   private:
   633 
   634     ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.
   635 
   636     ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.
   637     ///
   638     SmartGraph(const SmartGraph &) : ExtendedSmartGraphBase() {};
   639 
   640     ///\brief Assignment of SmartGraph to another one is \e not allowed.
   641     ///Use GraphCopy() instead.
   642 
   643     ///Assignment of SmartGraph to another one is \e not allowed.
   644     ///Use GraphCopy() instead.
   645     void operator=(const SmartGraph &) {}
   646 
   647   public:
   648 
   649     typedef ExtendedSmartGraphBase Parent;
   650 
   651     /// Constructor
   652 
   653     /// Constructor.
   654     ///
   655     SmartGraph() {}
   656 
   657     ///Add a new node to the graph.
   658 
   659     /// \return the new node.
   660     ///
   661     Node addNode() { return Parent::addNode(); }
   662 
   663     ///Add a new edge to the graph.
   664 
   665     ///Add a new edge to the graph with node \c s
   666     ///and \c t.
   667     ///\return the new edge.
   668     Edge addEdge(const Node& s, const Node& t) {
   669       return Parent::addEdge(s, t);
   670     }
   671 
   672     /// \brief Node validity check
   673     ///
   674     /// This function gives back true if the given node is valid,
   675     /// ie. it is a real node of the graph.
   676     ///
   677     /// \warning A removed node (using Snapshot) could become valid again
   678     /// when new nodes are added to the graph.
   679     bool valid(Node n) const { return Parent::valid(n); }
   680 
   681     /// \brief Arc validity check
   682     ///
   683     /// This function gives back true if the given arc is valid,
   684     /// ie. it is a real arc of the graph.
   685     ///
   686     /// \warning A removed arc (using Snapshot) could become valid again
   687     /// when new edges are added to the graph.
   688     bool valid(Arc a) const { return Parent::valid(a); }
   689 
   690     /// \brief Edge validity check
   691     ///
   692     /// This function gives back true if the given edge is valid,
   693     /// ie. it is a real edge of the graph.
   694     ///
   695     /// \warning A removed edge (using Snapshot) could become valid again
   696     /// when new edges are added to the graph.
   697     bool valid(Edge e) const { return Parent::valid(e); }
   698 
   699     ///Clear the graph.
   700 
   701     ///Erase all the nodes and edges from the graph.
   702     ///
   703     void clear() {
   704       Parent::clear();
   705     }
   706 
   707   public:
   708 
   709     class Snapshot;
   710 
   711   protected:
   712 
   713     void saveSnapshot(Snapshot &s)
   714     {
   715       s._graph = this;
   716       s.node_num = nodes.size();
   717       s.arc_num = arcs.size();
   718     }
   719 
   720     void restoreSnapshot(const Snapshot &s)
   721     {
   722       while(s.arc_num<arcs.size()) {
   723         int n=arcs.size()-1;
   724         Edge arc=edgeFromId(n/2);
   725         Parent::notifier(Edge()).erase(arc);
   726         std::vector<Arc> dir;
   727         dir.push_back(arcFromId(n));
   728         dir.push_back(arcFromId(n-1));
   729         Parent::notifier(Arc()).erase(dir);
   730         nodes[arcs[n].target].first_out=arcs[n].next_out;
   731         nodes[arcs[n-1].target].first_out=arcs[n-1].next_out;
   732         arcs.pop_back();
   733         arcs.pop_back();
   734       }
   735       while(s.node_num<nodes.size()) {
   736         int n=nodes.size()-1;
   737         Node node = nodeFromId(n);
   738         Parent::notifier(Node()).erase(node);
   739         nodes.pop_back();
   740       }
   741     }
   742 
   743   public:
   744 
   745     ///Class to make a snapshot of the digraph and to restrore to it later.
   746 
   747     ///Class to make a snapshot of the digraph and to restrore to it later.
   748     ///
   749     ///The newly added nodes and arcs can be removed using the
   750     ///restore() function.
   751     ///
   752     ///\note After you restore a state, you cannot restore
   753     ///a later state, in other word you cannot add again the arcs deleted
   754     ///by restore() using another one Snapshot instance.
   755     ///
   756     ///\warning If you do not use correctly the snapshot that can cause
   757     ///either broken program, invalid state of the digraph, valid but
   758     ///not the restored digraph or no change. Because the runtime performance
   759     ///the validity of the snapshot is not stored.
   760     class Snapshot
   761     {
   762       SmartGraph *_graph;
   763     protected:
   764       friend class SmartGraph;
   765       unsigned int node_num;
   766       unsigned int arc_num;
   767     public:
   768       ///Default constructor.
   769 
   770       ///Default constructor.
   771       ///To actually make a snapshot you must call save().
   772       ///
   773       Snapshot() : _graph(0) {}
   774       ///Constructor that immediately makes a snapshot
   775 
   776       ///This constructor immediately makes a snapshot of the digraph.
   777       ///\param g The digraph we make a snapshot of.
   778       Snapshot(SmartGraph &graph) {
   779         graph.saveSnapshot(*this);
   780       }
   781 
   782       ///Make a snapshot.
   783 
   784       ///Make a snapshot of the graph.
   785       ///
   786       ///This function can be called more than once. In case of a repeated
   787       ///call, the previous snapshot gets lost.
   788       ///\param g The digraph we make the snapshot of.
   789       void save(SmartGraph &graph)
   790       {
   791         graph.saveSnapshot(*this);
   792       }
   793 
   794       ///Undo the changes until a snapshot.
   795 
   796       ///Undo the changes until a snapshot created by save().
   797       ///
   798       ///\note After you restored a state, you cannot restore
   799       ///a later state, in other word you cannot add again the arcs deleted
   800       ///by restore().
   801       void restore()
   802       {
   803         _graph->restoreSnapshot(*this);
   804       }
   805     };
   806   };
   807 
   808 } //namespace lemon
   809 
   810 
   811 #endif //LEMON_SMART_GRAPH_H