COIN-OR::LEMON - Graph Library

source: lemon/lemon/list_graph.h @ 785:456fa5bc3256

Last change on this file since 785:456fa5bc3256 was 785:456fa5bc3256, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Much better implementation for node splitting (#311)
in ListDigraph?. This solution is the same as the one that
is used in SmartDigraph?. It is much faster and does not
invalidate any iterator like the former implementation.

File size: 43.7 KB
Line 
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) 2003-2009
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_LIST_GRAPH_H
20#define LEMON_LIST_GRAPH_H
21
22///\ingroup graphs
23///\file
24///\brief ListDigraph and ListGraph classes.
25
26#include <lemon/core.h>
27#include <lemon/error.h>
28#include <lemon/bits/graph_extender.h>
29
30#include <vector>
31#include <list>
32
33namespace lemon {
34
35  class ListDigraph;
36
37  class ListDigraphBase {
38
39  protected:
40    struct NodeT {
41      int first_in, first_out;
42      int prev, next;
43    };
44
45    struct ArcT {
46      int target, source;
47      int prev_in, prev_out;
48      int next_in, next_out;
49    };
50
51    std::vector<NodeT> nodes;
52
53    int first_node;
54
55    int first_free_node;
56
57    std::vector<ArcT> arcs;
58
59    int first_free_arc;
60
61  public:
62
63    typedef ListDigraphBase Digraph;
64
65    class Node {
66      friend class ListDigraphBase;
67      friend class ListDigraph;
68    protected:
69
70      int id;
71      explicit Node(int pid) { id = pid;}
72
73    public:
74      Node() {}
75      Node (Invalid) { id = -1; }
76      bool operator==(const Node& node) const {return id == node.id;}
77      bool operator!=(const Node& node) const {return id != node.id;}
78      bool operator<(const Node& node) const {return id < node.id;}
79    };
80
81    class Arc {
82      friend class ListDigraphBase;
83      friend class ListDigraph;
84    protected:
85
86      int id;
87      explicit Arc(int pid) { id = pid;}
88
89    public:
90      Arc() {}
91      Arc (Invalid) { id = -1; }
92      bool operator==(const Arc& arc) const {return id == arc.id;}
93      bool operator!=(const Arc& arc) const {return id != arc.id;}
94      bool operator<(const Arc& arc) const {return id < arc.id;}
95    };
96
97
98
99    ListDigraphBase()
100      : nodes(), first_node(-1),
101        first_free_node(-1), arcs(), first_free_arc(-1) {}
102
103
104    int maxNodeId() const { return nodes.size()-1; }
105    int maxArcId() const { return arcs.size()-1; }
106
107    Node source(Arc e) const { return Node(arcs[e.id].source); }
108    Node target(Arc e) const { return Node(arcs[e.id].target); }
109
110
111    void first(Node& node) const {
112      node.id = first_node;
113    }
114
115    void next(Node& node) const {
116      node.id = nodes[node.id].next;
117    }
118
119
120    void first(Arc& arc) const {
121      int n;
122      for(n = first_node;
123          n!=-1 && nodes[n].first_in == -1;
124          n = nodes[n].next) {}
125      arc.id = (n == -1) ? -1 : nodes[n].first_in;
126    }
127
128    void next(Arc& arc) const {
129      if (arcs[arc.id].next_in != -1) {
130        arc.id = arcs[arc.id].next_in;
131      } else {
132        int n;
133        for(n = nodes[arcs[arc.id].target].next;
134            n!=-1 && nodes[n].first_in == -1;
135            n = nodes[n].next) {}
136        arc.id = (n == -1) ? -1 : nodes[n].first_in;
137      }
138    }
139
140    void firstOut(Arc &e, const Node& v) const {
141      e.id = nodes[v.id].first_out;
142    }
143    void nextOut(Arc &e) const {
144      e.id=arcs[e.id].next_out;
145    }
146
147    void firstIn(Arc &e, const Node& v) const {
148      e.id = nodes[v.id].first_in;
149    }
150    void nextIn(Arc &e) const {
151      e.id=arcs[e.id].next_in;
152    }
153
154
155    static int id(Node v) { return v.id; }
156    static int id(Arc e) { return e.id; }
157
158    static Node nodeFromId(int id) { return Node(id);}
159    static Arc arcFromId(int id) { return Arc(id);}
160
161    bool valid(Node n) const {
162      return n.id >= 0 && n.id < static_cast<int>(nodes.size()) &&
163        nodes[n.id].prev != -2;
164    }
165
166    bool valid(Arc a) const {
167      return a.id >= 0 && a.id < static_cast<int>(arcs.size()) &&
168        arcs[a.id].prev_in != -2;
169    }
170
171    Node addNode() {
172      int n;
173
174      if(first_free_node==-1) {
175        n = nodes.size();
176        nodes.push_back(NodeT());
177      } else {
178        n = first_free_node;
179        first_free_node = nodes[n].next;
180      }
181
182      nodes[n].next = first_node;
183      if(first_node != -1) nodes[first_node].prev = n;
184      first_node = n;
185      nodes[n].prev = -1;
186
187      nodes[n].first_in = nodes[n].first_out = -1;
188
189      return Node(n);
190    }
191
192    Arc addArc(Node u, Node v) {
193      int n;
194
195      if (first_free_arc == -1) {
196        n = arcs.size();
197        arcs.push_back(ArcT());
198      } else {
199        n = first_free_arc;
200        first_free_arc = arcs[n].next_in;
201      }
202
203      arcs[n].source = u.id;
204      arcs[n].target = v.id;
205
206      arcs[n].next_out = nodes[u.id].first_out;
207      if(nodes[u.id].first_out != -1) {
208        arcs[nodes[u.id].first_out].prev_out = n;
209      }
210
211      arcs[n].next_in = nodes[v.id].first_in;
212      if(nodes[v.id].first_in != -1) {
213        arcs[nodes[v.id].first_in].prev_in = n;
214      }
215
216      arcs[n].prev_in = arcs[n].prev_out = -1;
217
218      nodes[u.id].first_out = nodes[v.id].first_in = n;
219
220      return Arc(n);
221    }
222
223    void erase(const Node& node) {
224      int n = node.id;
225
226      if(nodes[n].next != -1) {
227        nodes[nodes[n].next].prev = nodes[n].prev;
228      }
229
230      if(nodes[n].prev != -1) {
231        nodes[nodes[n].prev].next = nodes[n].next;
232      } else {
233        first_node = nodes[n].next;
234      }
235
236      nodes[n].next = first_free_node;
237      first_free_node = n;
238      nodes[n].prev = -2;
239
240    }
241
242    void erase(const Arc& arc) {
243      int n = arc.id;
244
245      if(arcs[n].next_in!=-1) {
246        arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;
247      }
248
249      if(arcs[n].prev_in!=-1) {
250        arcs[arcs[n].prev_in].next_in = arcs[n].next_in;
251      } else {
252        nodes[arcs[n].target].first_in = arcs[n].next_in;
253      }
254
255
256      if(arcs[n].next_out!=-1) {
257        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
258      }
259
260      if(arcs[n].prev_out!=-1) {
261        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
262      } else {
263        nodes[arcs[n].source].first_out = arcs[n].next_out;
264      }
265
266      arcs[n].next_in = first_free_arc;
267      first_free_arc = n;
268      arcs[n].prev_in = -2;
269    }
270
271    void clear() {
272      arcs.clear();
273      nodes.clear();
274      first_node = first_free_node = first_free_arc = -1;
275    }
276
277  protected:
278    void changeTarget(Arc e, Node n)
279    {
280      if(arcs[e.id].next_in != -1)
281        arcs[arcs[e.id].next_in].prev_in = arcs[e.id].prev_in;
282      if(arcs[e.id].prev_in != -1)
283        arcs[arcs[e.id].prev_in].next_in = arcs[e.id].next_in;
284      else nodes[arcs[e.id].target].first_in = arcs[e.id].next_in;
285      if (nodes[n.id].first_in != -1) {
286        arcs[nodes[n.id].first_in].prev_in = e.id;
287      }
288      arcs[e.id].target = n.id;
289      arcs[e.id].prev_in = -1;
290      arcs[e.id].next_in = nodes[n.id].first_in;
291      nodes[n.id].first_in = e.id;
292    }
293    void changeSource(Arc e, Node n)
294    {
295      if(arcs[e.id].next_out != -1)
296        arcs[arcs[e.id].next_out].prev_out = arcs[e.id].prev_out;
297      if(arcs[e.id].prev_out != -1)
298        arcs[arcs[e.id].prev_out].next_out = arcs[e.id].next_out;
299      else nodes[arcs[e.id].source].first_out = arcs[e.id].next_out;
300      if (nodes[n.id].first_out != -1) {
301        arcs[nodes[n.id].first_out].prev_out = e.id;
302      }
303      arcs[e.id].source = n.id;
304      arcs[e.id].prev_out = -1;
305      arcs[e.id].next_out = nodes[n.id].first_out;
306      nodes[n.id].first_out = e.id;
307    }
308
309  };
310
311  typedef DigraphExtender<ListDigraphBase> ExtendedListDigraphBase;
312
313  /// \addtogroup graphs
314  /// @{
315
316  ///A general directed graph structure.
317
318  ///\ref ListDigraph is a versatile and fast directed graph
319  ///implementation based on linked lists that are stored in
320  ///\c std::vector structures.
321  ///
322  ///This type fully conforms to the \ref concepts::Digraph "Digraph concept"
323  ///and it also provides several useful additional functionalities.
324  ///Most of its member functions and nested classes are documented
325  ///only in the concept class.
326  ///
327  ///\sa concepts::Digraph
328  ///\sa ListGraph
329  class ListDigraph : public ExtendedListDigraphBase {
330    typedef ExtendedListDigraphBase Parent;
331
332  private:
333    /// Digraphs are \e not copy constructible. Use DigraphCopy instead.
334    ListDigraph(const ListDigraph &) :ExtendedListDigraphBase() {};
335    /// \brief Assignment of a digraph to another one is \e not allowed.
336    /// Use DigraphCopy instead.
337    void operator=(const ListDigraph &) {}
338  public:
339
340    /// Constructor
341
342    /// Constructor.
343    ///
344    ListDigraph() {}
345
346    ///Add a new node to the digraph.
347
348    ///This function adds a new node to the digraph.
349    ///\return The new node.
350    Node addNode() { return Parent::addNode(); }
351
352    ///Add a new arc to the digraph.
353
354    ///This function adds a new arc to the digraph with source node \c s
355    ///and target node \c t.
356    ///\return The new arc.
357    Arc addArc(Node s, Node t) {
358      return Parent::addArc(s, t);
359    }
360
361    ///\brief Erase a node from the digraph.
362    ///
363    ///This function erases the given node from the digraph.
364    void erase(Node n) { Parent::erase(n); }
365
366    ///\brief Erase an arc from the digraph.
367    ///
368    ///This function erases the given arc from the digraph.
369    void erase(Arc a) { Parent::erase(a); }
370
371    /// Node validity check
372
373    /// This function gives back \c true if the given node is valid,
374    /// i.e. it is a real node of the digraph.
375    ///
376    /// \warning A removed node could become valid again if new nodes are
377    /// added to the digraph.
378    bool valid(Node n) const { return Parent::valid(n); }
379
380    /// Arc validity check
381
382    /// This function gives back \c true if the given arc is valid,
383    /// i.e. it is a real arc of the digraph.
384    ///
385    /// \warning A removed arc could become valid again if new arcs are
386    /// added to the digraph.
387    bool valid(Arc a) const { return Parent::valid(a); }
388
389    /// Change the target node of an arc
390
391    /// This function changes the target node of the given arc \c a to \c n.
392    ///
393    ///\note \c ArcIt and \c OutArcIt iterators referencing the changed
394    ///arc remain valid, however \c InArcIt iterators are invalidated.
395    ///
396    ///\warning This functionality cannot be used together with the Snapshot
397    ///feature.
398    void changeTarget(Arc a, Node n) {
399      Parent::changeTarget(a,n);
400    }
401    /// Change the source node of an arc
402
403    /// This function changes the source node of the given arc \c a to \c n.
404    ///
405    ///\note \c InArcIt iterators referencing the changed arc remain
406    ///valid, however \c ArcIt and \c OutArcIt iterators are invalidated.
407    ///
408    ///\warning This functionality cannot be used together with the Snapshot
409    ///feature.
410    void changeSource(Arc a, Node n) {
411      Parent::changeSource(a,n);
412    }
413
414    /// Reverse the direction of an arc.
415
416    /// This function reverses the direction of the given arc.
417    ///\note \c ArcIt, \c OutArcIt and \c InArcIt iterators referencing
418    ///the changed arc are invalidated.
419    ///
420    ///\warning This functionality cannot be used together with the Snapshot
421    ///feature.
422    void reverseArc(Arc a) {
423      Node t=target(a);
424      changeTarget(a,source(a));
425      changeSource(a,t);
426    }
427
428    ///Contract two nodes.
429
430    ///This function contracts the given two nodes.
431    ///Node \c v is removed, but instead of deleting its
432    ///incident arcs, they are joined to node \c u.
433    ///If the last parameter \c r is \c true (this is the default value),
434    ///then the newly created loops are removed.
435    ///
436    ///\note The moved arcs are joined to node \c u using changeSource()
437    ///or changeTarget(), thus \c ArcIt and \c OutArcIt iterators are
438    ///invalidated for the outgoing arcs of node \c v and \c InArcIt
439    ///iterators are invalidated for the incomming arcs of \c v.
440    ///Moreover all iterators referencing node \c v or the removed
441    ///loops are also invalidated. Other iterators remain valid.
442    ///
443    ///\warning This functionality cannot be used together with the Snapshot
444    ///feature.
445    void contract(Node u, Node v, bool r = true)
446    {
447      for(OutArcIt e(*this,v);e!=INVALID;) {
448        OutArcIt f=e;
449        ++f;
450        if(r && target(e)==u) erase(e);
451        else changeSource(e,u);
452        e=f;
453      }
454      for(InArcIt e(*this,v);e!=INVALID;) {
455        InArcIt f=e;
456        ++f;
457        if(r && source(e)==u) erase(e);
458        else changeTarget(e,u);
459        e=f;
460      }
461      erase(v);
462    }
463
464    ///Split a node.
465
466    ///This function splits the given node. First, a new node is added
467    ///to the digraph, then the source of each outgoing arc of node \c n
468    ///is moved to this new node.
469    ///If the second parameter \c connect is \c true (this is the default
470    ///value), then a new arc from node \c n to the newly created node
471    ///is also added.
472    ///\return The newly created node.
473    ///
474    ///\note All iterators remain valid.
475    ///
476    ///\warning This functionality cannot be used together with the
477    ///Snapshot feature.
478    Node split(Node n, bool connect = true) {
479      Node b = addNode();
480      nodes[b.id].first_out=nodes[n.id].first_out;
481      nodes[n.id].first_out=-1;
482      for(int i=nodes[b.id].first_out; i!=-1; i=arcs[i].next_out) {
483        arcs[i].source=b.id;
484      }
485      if (connect) addArc(n,b);
486      return b;
487    }
488
489    ///Split an arc.
490
491    ///This function splits the given arc. First, a new node \c v is
492    ///added to the digraph, then the target node of the original arc
493    ///is set to \c v. Finally, an arc from \c v to the original target
494    ///is added.
495    ///\return The newly created node.
496    ///
497    ///\note \c InArcIt iterators referencing the original arc are
498    ///invalidated. Other iterators remain valid.
499    ///
500    ///\warning This functionality cannot be used together with the
501    ///Snapshot feature.
502    Node split(Arc a) {
503      Node v = addNode();
504      addArc(v,target(a));
505      changeTarget(a,v);
506      return v;
507    }
508
509    ///Clear the digraph.
510
511    ///This function erases all nodes and arcs from the digraph.
512    ///
513    void clear() {
514      Parent::clear();
515    }
516
517    /// Reserve memory for nodes.
518
519    /// Using this function, it is possible to avoid superfluous memory
520    /// allocation: if you know that the digraph you want to build will
521    /// be large (e.g. it will contain millions of nodes and/or arcs),
522    /// then it is worth reserving space for this amount before starting
523    /// to build the digraph.
524    /// \sa reserveArc()
525    void reserveNode(int n) { nodes.reserve(n); };
526
527    /// Reserve memory for arcs.
528
529    /// Using this function, it is possible to avoid superfluous memory
530    /// allocation: if you know that the digraph you want to build will
531    /// be large (e.g. it will contain millions of nodes and/or arcs),
532    /// then it is worth reserving space for this amount before starting
533    /// to build the digraph.
534    /// \sa reserveNode()
535    void reserveArc(int m) { arcs.reserve(m); };
536
537    /// \brief Class to make a snapshot of the digraph and restore
538    /// it later.
539    ///
540    /// Class to make a snapshot of the digraph and restore it later.
541    ///
542    /// The newly added nodes and arcs can be removed using the
543    /// restore() function.
544    ///
545    /// \note After a state is restored, you cannot restore a later state,
546    /// i.e. you cannot add the removed nodes and arcs again using
547    /// another Snapshot instance.
548    ///
549    /// \warning Node and arc deletions and other modifications (e.g.
550    /// reversing, contracting, splitting arcs or nodes) cannot be
551    /// restored. These events invalidate the snapshot.
552    /// However the arcs and nodes that were added to the digraph after
553    /// making the current snapshot can be removed without invalidating it.
554    class Snapshot {
555    protected:
556
557      typedef Parent::NodeNotifier NodeNotifier;
558
559      class NodeObserverProxy : public NodeNotifier::ObserverBase {
560      public:
561
562        NodeObserverProxy(Snapshot& _snapshot)
563          : snapshot(_snapshot) {}
564
565        using NodeNotifier::ObserverBase::attach;
566        using NodeNotifier::ObserverBase::detach;
567        using NodeNotifier::ObserverBase::attached;
568
569      protected:
570
571        virtual void add(const Node& node) {
572          snapshot.addNode(node);
573        }
574        virtual void add(const std::vector<Node>& nodes) {
575          for (int i = nodes.size() - 1; i >= 0; ++i) {
576            snapshot.addNode(nodes[i]);
577          }
578        }
579        virtual void erase(const Node& node) {
580          snapshot.eraseNode(node);
581        }
582        virtual void erase(const std::vector<Node>& nodes) {
583          for (int i = 0; i < int(nodes.size()); ++i) {
584            snapshot.eraseNode(nodes[i]);
585          }
586        }
587        virtual void build() {
588          Node node;
589          std::vector<Node> nodes;
590          for (notifier()->first(node); node != INVALID;
591               notifier()->next(node)) {
592            nodes.push_back(node);
593          }
594          for (int i = nodes.size() - 1; i >= 0; --i) {
595            snapshot.addNode(nodes[i]);
596          }
597        }
598        virtual void clear() {
599          Node node;
600          for (notifier()->first(node); node != INVALID;
601               notifier()->next(node)) {
602            snapshot.eraseNode(node);
603          }
604        }
605
606        Snapshot& snapshot;
607      };
608
609      class ArcObserverProxy : public ArcNotifier::ObserverBase {
610      public:
611
612        ArcObserverProxy(Snapshot& _snapshot)
613          : snapshot(_snapshot) {}
614
615        using ArcNotifier::ObserverBase::attach;
616        using ArcNotifier::ObserverBase::detach;
617        using ArcNotifier::ObserverBase::attached;
618
619      protected:
620
621        virtual void add(const Arc& arc) {
622          snapshot.addArc(arc);
623        }
624        virtual void add(const std::vector<Arc>& arcs) {
625          for (int i = arcs.size() - 1; i >= 0; ++i) {
626            snapshot.addArc(arcs[i]);
627          }
628        }
629        virtual void erase(const Arc& arc) {
630          snapshot.eraseArc(arc);
631        }
632        virtual void erase(const std::vector<Arc>& arcs) {
633          for (int i = 0; i < int(arcs.size()); ++i) {
634            snapshot.eraseArc(arcs[i]);
635          }
636        }
637        virtual void build() {
638          Arc arc;
639          std::vector<Arc> arcs;
640          for (notifier()->first(arc); arc != INVALID;
641               notifier()->next(arc)) {
642            arcs.push_back(arc);
643          }
644          for (int i = arcs.size() - 1; i >= 0; --i) {
645            snapshot.addArc(arcs[i]);
646          }
647        }
648        virtual void clear() {
649          Arc arc;
650          for (notifier()->first(arc); arc != INVALID;
651               notifier()->next(arc)) {
652            snapshot.eraseArc(arc);
653          }
654        }
655
656        Snapshot& snapshot;
657      };
658
659      ListDigraph *digraph;
660
661      NodeObserverProxy node_observer_proxy;
662      ArcObserverProxy arc_observer_proxy;
663
664      std::list<Node> added_nodes;
665      std::list<Arc> added_arcs;
666
667
668      void addNode(const Node& node) {
669        added_nodes.push_front(node);
670      }
671      void eraseNode(const Node& node) {
672        std::list<Node>::iterator it =
673          std::find(added_nodes.begin(), added_nodes.end(), node);
674        if (it == added_nodes.end()) {
675          clear();
676          arc_observer_proxy.detach();
677          throw NodeNotifier::ImmediateDetach();
678        } else {
679          added_nodes.erase(it);
680        }
681      }
682
683      void addArc(const Arc& arc) {
684        added_arcs.push_front(arc);
685      }
686      void eraseArc(const Arc& arc) {
687        std::list<Arc>::iterator it =
688          std::find(added_arcs.begin(), added_arcs.end(), arc);
689        if (it == added_arcs.end()) {
690          clear();
691          node_observer_proxy.detach();
692          throw ArcNotifier::ImmediateDetach();
693        } else {
694          added_arcs.erase(it);
695        }
696      }
697
698      void attach(ListDigraph &_digraph) {
699        digraph = &_digraph;
700        node_observer_proxy.attach(digraph->notifier(Node()));
701        arc_observer_proxy.attach(digraph->notifier(Arc()));
702      }
703
704      void detach() {
705        node_observer_proxy.detach();
706        arc_observer_proxy.detach();
707      }
708
709      bool attached() const {
710        return node_observer_proxy.attached();
711      }
712
713      void clear() {
714        added_nodes.clear();
715        added_arcs.clear();
716      }
717
718    public:
719
720      /// \brief Default constructor.
721      ///
722      /// Default constructor.
723      /// You have to call save() to actually make a snapshot.
724      Snapshot()
725        : digraph(0), node_observer_proxy(*this),
726          arc_observer_proxy(*this) {}
727
728      /// \brief Constructor that immediately makes a snapshot.
729      ///
730      /// This constructor immediately makes a snapshot of the given digraph.
731      Snapshot(ListDigraph &gr)
732        : node_observer_proxy(*this),
733          arc_observer_proxy(*this) {
734        attach(gr);
735      }
736
737      /// \brief Make a snapshot.
738      ///
739      /// This function makes a snapshot of the given digraph.
740      /// It can be called more than once. In case of a repeated
741      /// call, the previous snapshot gets lost.
742      void save(ListDigraph &gr) {
743        if (attached()) {
744          detach();
745          clear();
746        }
747        attach(gr);
748      }
749
750      /// \brief Undo the changes until the last snapshot.
751      ///
752      /// This function undos the changes until the last snapshot
753      /// created by save() or Snapshot(ListDigraph&).
754      void restore() {
755        detach();
756        for(std::list<Arc>::iterator it = added_arcs.begin();
757            it != added_arcs.end(); ++it) {
758          digraph->erase(*it);
759        }
760        for(std::list<Node>::iterator it = added_nodes.begin();
761            it != added_nodes.end(); ++it) {
762          digraph->erase(*it);
763        }
764        clear();
765      }
766
767      /// \brief Returns \c true if the snapshot is valid.
768      ///
769      /// This function returns \c true if the snapshot is valid.
770      bool valid() const {
771        return attached();
772      }
773    };
774
775  };
776
777  ///@}
778
779  class ListGraphBase {
780
781  protected:
782
783    struct NodeT {
784      int first_out;
785      int prev, next;
786    };
787
788    struct ArcT {
789      int target;
790      int prev_out, next_out;
791    };
792
793    std::vector<NodeT> nodes;
794
795    int first_node;
796
797    int first_free_node;
798
799    std::vector<ArcT> arcs;
800
801    int first_free_arc;
802
803  public:
804
805    typedef ListGraphBase Graph;
806
807    class Node {
808      friend class ListGraphBase;
809    protected:
810
811      int id;
812      explicit Node(int pid) { id = pid;}
813
814    public:
815      Node() {}
816      Node (Invalid) { id = -1; }
817      bool operator==(const Node& node) const {return id == node.id;}
818      bool operator!=(const Node& node) const {return id != node.id;}
819      bool operator<(const Node& node) const {return id < node.id;}
820    };
821
822    class Edge {
823      friend class ListGraphBase;
824    protected:
825
826      int id;
827      explicit Edge(int pid) { id = pid;}
828
829    public:
830      Edge() {}
831      Edge (Invalid) { id = -1; }
832      bool operator==(const Edge& edge) const {return id == edge.id;}
833      bool operator!=(const Edge& edge) const {return id != edge.id;}
834      bool operator<(const Edge& edge) const {return id < edge.id;}
835    };
836
837    class Arc {
838      friend class ListGraphBase;
839    protected:
840
841      int id;
842      explicit Arc(int pid) { id = pid;}
843
844    public:
845      operator Edge() const {
846        return id != -1 ? edgeFromId(id / 2) : INVALID;
847      }
848
849      Arc() {}
850      Arc (Invalid) { id = -1; }
851      bool operator==(const Arc& arc) const {return id == arc.id;}
852      bool operator!=(const Arc& arc) const {return id != arc.id;}
853      bool operator<(const Arc& arc) const {return id < arc.id;}
854    };
855
856    ListGraphBase()
857      : nodes(), first_node(-1),
858        first_free_node(-1), arcs(), first_free_arc(-1) {}
859
860
861    int maxNodeId() const { return nodes.size()-1; }
862    int maxEdgeId() const { return arcs.size() / 2 - 1; }
863    int maxArcId() const { return arcs.size()-1; }
864
865    Node source(Arc e) const { return Node(arcs[e.id ^ 1].target); }
866    Node target(Arc e) const { return Node(arcs[e.id].target); }
867
868    Node u(Edge e) const { return Node(arcs[2 * e.id].target); }
869    Node v(Edge e) const { return Node(arcs[2 * e.id + 1].target); }
870
871    static bool direction(Arc e) {
872      return (e.id & 1) == 1;
873    }
874
875    static Arc direct(Edge e, bool d) {
876      return Arc(e.id * 2 + (d ? 1 : 0));
877    }
878
879    void first(Node& node) const {
880      node.id = first_node;
881    }
882
883    void next(Node& node) const {
884      node.id = nodes[node.id].next;
885    }
886
887    void first(Arc& e) const {
888      int n = first_node;
889      while (n != -1 && nodes[n].first_out == -1) {
890        n = nodes[n].next;
891      }
892      e.id = (n == -1) ? -1 : nodes[n].first_out;
893    }
894
895    void next(Arc& e) const {
896      if (arcs[e.id].next_out != -1) {
897        e.id = arcs[e.id].next_out;
898      } else {
899        int n = nodes[arcs[e.id ^ 1].target].next;
900        while(n != -1 && nodes[n].first_out == -1) {
901          n = nodes[n].next;
902        }
903        e.id = (n == -1) ? -1 : nodes[n].first_out;
904      }
905    }
906
907    void first(Edge& e) const {
908      int n = first_node;
909      while (n != -1) {
910        e.id = nodes[n].first_out;
911        while ((e.id & 1) != 1) {
912          e.id = arcs[e.id].next_out;
913        }
914        if (e.id != -1) {
915          e.id /= 2;
916          return;
917        }
918        n = nodes[n].next;
919      }
920      e.id = -1;
921    }
922
923    void next(Edge& e) const {
924      int n = arcs[e.id * 2].target;
925      e.id = arcs[(e.id * 2) | 1].next_out;
926      while ((e.id & 1) != 1) {
927        e.id = arcs[e.id].next_out;
928      }
929      if (e.id != -1) {
930        e.id /= 2;
931        return;
932      }
933      n = nodes[n].next;
934      while (n != -1) {
935        e.id = nodes[n].first_out;
936        while ((e.id & 1) != 1) {
937          e.id = arcs[e.id].next_out;
938        }
939        if (e.id != -1) {
940          e.id /= 2;
941          return;
942        }
943        n = nodes[n].next;
944      }
945      e.id = -1;
946    }
947
948    void firstOut(Arc &e, const Node& v) const {
949      e.id = nodes[v.id].first_out;
950    }
951    void nextOut(Arc &e) const {
952      e.id = arcs[e.id].next_out;
953    }
954
955    void firstIn(Arc &e, const Node& v) const {
956      e.id = ((nodes[v.id].first_out) ^ 1);
957      if (e.id == -2) e.id = -1;
958    }
959    void nextIn(Arc &e) const {
960      e.id = ((arcs[e.id ^ 1].next_out) ^ 1);
961      if (e.id == -2) e.id = -1;
962    }
963
964    void firstInc(Edge &e, bool& d, const Node& v) const {
965      int a = nodes[v.id].first_out;
966      if (a != -1 ) {
967        e.id = a / 2;
968        d = ((a & 1) == 1);
969      } else {
970        e.id = -1;
971        d = true;
972      }
973    }
974    void nextInc(Edge &e, bool& d) const {
975      int a = (arcs[(e.id * 2) | (d ? 1 : 0)].next_out);
976      if (a != -1 ) {
977        e.id = a / 2;
978        d = ((a & 1) == 1);
979      } else {
980        e.id = -1;
981        d = true;
982      }
983    }
984
985    static int id(Node v) { return v.id; }
986    static int id(Arc e) { return e.id; }
987    static int id(Edge e) { return e.id; }
988
989    static Node nodeFromId(int id) { return Node(id);}
990    static Arc arcFromId(int id) { return Arc(id);}
991    static Edge edgeFromId(int id) { return Edge(id);}
992
993    bool valid(Node n) const {
994      return n.id >= 0 && n.id < static_cast<int>(nodes.size()) &&
995        nodes[n.id].prev != -2;
996    }
997
998    bool valid(Arc a) const {
999      return a.id >= 0 && a.id < static_cast<int>(arcs.size()) &&
1000        arcs[a.id].prev_out != -2;
1001    }
1002
1003    bool valid(Edge e) const {
1004      return e.id >= 0 && 2 * e.id < static_cast<int>(arcs.size()) &&
1005        arcs[2 * e.id].prev_out != -2;
1006    }
1007
1008    Node addNode() {
1009      int n;
1010
1011      if(first_free_node==-1) {
1012        n = nodes.size();
1013        nodes.push_back(NodeT());
1014      } else {
1015        n = first_free_node;
1016        first_free_node = nodes[n].next;
1017      }
1018
1019      nodes[n].next = first_node;
1020      if (first_node != -1) nodes[first_node].prev = n;
1021      first_node = n;
1022      nodes[n].prev = -1;
1023
1024      nodes[n].first_out = -1;
1025
1026      return Node(n);
1027    }
1028
1029    Edge addEdge(Node u, Node v) {
1030      int n;
1031
1032      if (first_free_arc == -1) {
1033        n = arcs.size();
1034        arcs.push_back(ArcT());
1035        arcs.push_back(ArcT());
1036      } else {
1037        n = first_free_arc;
1038        first_free_arc = arcs[n].next_out;
1039      }
1040
1041      arcs[n].target = u.id;
1042      arcs[n | 1].target = v.id;
1043
1044      arcs[n].next_out = nodes[v.id].first_out;
1045      if (nodes[v.id].first_out != -1) {
1046        arcs[nodes[v.id].first_out].prev_out = n;
1047      }
1048      arcs[n].prev_out = -1;
1049      nodes[v.id].first_out = n;
1050
1051      arcs[n | 1].next_out = nodes[u.id].first_out;
1052      if (nodes[u.id].first_out != -1) {
1053        arcs[nodes[u.id].first_out].prev_out = (n | 1);
1054      }
1055      arcs[n | 1].prev_out = -1;
1056      nodes[u.id].first_out = (n | 1);
1057
1058      return Edge(n / 2);
1059    }
1060
1061    void erase(const Node& node) {
1062      int n = node.id;
1063
1064      if(nodes[n].next != -1) {
1065        nodes[nodes[n].next].prev = nodes[n].prev;
1066      }
1067
1068      if(nodes[n].prev != -1) {
1069        nodes[nodes[n].prev].next = nodes[n].next;
1070      } else {
1071        first_node = nodes[n].next;
1072      }
1073
1074      nodes[n].next = first_free_node;
1075      first_free_node = n;
1076      nodes[n].prev = -2;
1077    }
1078
1079    void erase(const Edge& edge) {
1080      int n = edge.id * 2;
1081
1082      if (arcs[n].next_out != -1) {
1083        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
1084      }
1085
1086      if (arcs[n].prev_out != -1) {
1087        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
1088      } else {
1089        nodes[arcs[n | 1].target].first_out = arcs[n].next_out;
1090      }
1091
1092      if (arcs[n | 1].next_out != -1) {
1093        arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;
1094      }
1095
1096      if (arcs[n | 1].prev_out != -1) {
1097        arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;
1098      } else {
1099        nodes[arcs[n].target].first_out = arcs[n | 1].next_out;
1100      }
1101
1102      arcs[n].next_out = first_free_arc;
1103      first_free_arc = n;
1104      arcs[n].prev_out = -2;
1105      arcs[n | 1].prev_out = -2;
1106
1107    }
1108
1109    void clear() {
1110      arcs.clear();
1111      nodes.clear();
1112      first_node = first_free_node = first_free_arc = -1;
1113    }
1114
1115  protected:
1116
1117    void changeV(Edge e, Node n) {
1118      if(arcs[2 * e.id].next_out != -1) {
1119        arcs[arcs[2 * e.id].next_out].prev_out = arcs[2 * e.id].prev_out;
1120      }
1121      if(arcs[2 * e.id].prev_out != -1) {
1122        arcs[arcs[2 * e.id].prev_out].next_out =
1123          arcs[2 * e.id].next_out;
1124      } else {
1125        nodes[arcs[(2 * e.id) | 1].target].first_out =
1126          arcs[2 * e.id].next_out;
1127      }
1128
1129      if (nodes[n.id].first_out != -1) {
1130        arcs[nodes[n.id].first_out].prev_out = 2 * e.id;
1131      }
1132      arcs[(2 * e.id) | 1].target = n.id;
1133      arcs[2 * e.id].prev_out = -1;
1134      arcs[2 * e.id].next_out = nodes[n.id].first_out;
1135      nodes[n.id].first_out = 2 * e.id;
1136    }
1137
1138    void changeU(Edge e, Node n) {
1139      if(arcs[(2 * e.id) | 1].next_out != -1) {
1140        arcs[arcs[(2 * e.id) | 1].next_out].prev_out =
1141          arcs[(2 * e.id) | 1].prev_out;
1142      }
1143      if(arcs[(2 * e.id) | 1].prev_out != -1) {
1144        arcs[arcs[(2 * e.id) | 1].prev_out].next_out =
1145          arcs[(2 * e.id) | 1].next_out;
1146      } else {
1147        nodes[arcs[2 * e.id].target].first_out =
1148          arcs[(2 * e.id) | 1].next_out;
1149      }
1150
1151      if (nodes[n.id].first_out != -1) {
1152        arcs[nodes[n.id].first_out].prev_out = ((2 * e.id) | 1);
1153      }
1154      arcs[2 * e.id].target = n.id;
1155      arcs[(2 * e.id) | 1].prev_out = -1;
1156      arcs[(2 * e.id) | 1].next_out = nodes[n.id].first_out;
1157      nodes[n.id].first_out = ((2 * e.id) | 1);
1158    }
1159
1160  };
1161
1162  typedef GraphExtender<ListGraphBase> ExtendedListGraphBase;
1163
1164
1165  /// \addtogroup graphs
1166  /// @{
1167
1168  ///A general undirected graph structure.
1169
1170  ///\ref ListGraph is a versatile and fast undirected graph
1171  ///implementation based on linked lists that are stored in
1172  ///\c std::vector structures.
1173  ///
1174  ///This type fully conforms to the \ref concepts::Graph "Graph concept"
1175  ///and it also provides several useful additional functionalities.
1176  ///Most of its member functions and nested classes are documented
1177  ///only in the concept class.
1178  ///
1179  ///\sa concepts::Graph
1180  ///\sa ListDigraph
1181  class ListGraph : public ExtendedListGraphBase {
1182    typedef ExtendedListGraphBase Parent;
1183
1184  private:
1185    /// Graphs are \e not copy constructible. Use GraphCopy instead.
1186    ListGraph(const ListGraph &) :ExtendedListGraphBase()  {};
1187    /// \brief Assignment of a graph to another one is \e not allowed.
1188    /// Use GraphCopy instead.
1189    void operator=(const ListGraph &) {}
1190  public:
1191    /// Constructor
1192
1193    /// Constructor.
1194    ///
1195    ListGraph() {}
1196
1197    typedef Parent::OutArcIt IncEdgeIt;
1198
1199    /// \brief Add a new node to the graph.
1200    ///
1201    /// This function adds a new node to the graph.
1202    /// \return The new node.
1203    Node addNode() { return Parent::addNode(); }
1204
1205    /// \brief Add a new edge to the graph.
1206    ///
1207    /// This function adds a new edge to the graph between nodes
1208    /// \c u and \c v with inherent orientation from node \c u to
1209    /// node \c v.
1210    /// \return The new edge.
1211    Edge addEdge(Node u, Node v) {
1212      return Parent::addEdge(u, v);
1213    }
1214
1215    ///\brief Erase a node from the graph.
1216    ///
1217    /// This function erases the given node from the graph.
1218    void erase(Node n) { Parent::erase(n); }
1219
1220    ///\brief Erase an edge from the graph.
1221    ///
1222    /// This function erases the given edge from the graph.
1223    void erase(Edge e) { Parent::erase(e); }
1224    /// Node validity check
1225
1226    /// This function gives back \c true if the given node is valid,
1227    /// i.e. it is a real node of the graph.
1228    ///
1229    /// \warning A removed node could become valid again if new nodes are
1230    /// added to the graph.
1231    bool valid(Node n) const { return Parent::valid(n); }
1232    /// Edge validity check
1233
1234    /// This function gives back \c true if the given edge is valid,
1235    /// i.e. it is a real edge of the graph.
1236    ///
1237    /// \warning A removed edge could become valid again if new edges are
1238    /// added to the graph.
1239    bool valid(Edge e) const { return Parent::valid(e); }
1240    /// Arc validity check
1241
1242    /// This function gives back \c true if the given arc is valid,
1243    /// i.e. it is a real arc of the graph.
1244    ///
1245    /// \warning A removed arc could become valid again if new edges are
1246    /// added to the graph.
1247    bool valid(Arc a) const { return Parent::valid(a); }
1248
1249    /// \brief Change the first node of an edge.
1250    ///
1251    /// This function changes the first node of the given edge \c e to \c n.
1252    ///
1253    ///\note \c EdgeIt and \c ArcIt iterators referencing the
1254    ///changed edge are invalidated and all other iterators whose
1255    ///base node is the changed node are also invalidated.
1256    ///
1257    ///\warning This functionality cannot be used together with the
1258    ///Snapshot feature.
1259    void changeU(Edge e, Node n) {
1260      Parent::changeU(e,n);
1261    }
1262    /// \brief Change the second node of an edge.
1263    ///
1264    /// This function changes the second node of the given edge \c e to \c n.
1265    ///
1266    ///\note \c EdgeIt iterators referencing the changed edge remain
1267    ///valid, however \c ArcIt iterators referencing the changed edge and
1268    ///all other iterators whose base node is the changed node are also
1269    ///invalidated.
1270    ///
1271    ///\warning This functionality cannot be used together with the
1272    ///Snapshot feature.
1273    void changeV(Edge e, Node n) {
1274      Parent::changeV(e,n);
1275    }
1276
1277    /// \brief Contract two nodes.
1278    ///
1279    /// This function contracts the given two nodes.
1280    /// Node \c b is removed, but instead of deleting
1281    /// its incident edges, they are joined to node \c a.
1282    /// If the last parameter \c r is \c true (this is the default value),
1283    /// then the newly created loops are removed.
1284    ///
1285    /// \note The moved edges are joined to node \c a using changeU()
1286    /// or changeV(), thus all edge and arc iterators whose base node is
1287    /// \c b are invalidated.
1288    /// Moreover all iterators referencing node \c b or the removed
1289    /// loops are also invalidated. Other iterators remain valid.
1290    ///
1291    ///\warning This functionality cannot be used together with the
1292    ///Snapshot feature.
1293    void contract(Node a, Node b, bool r = true) {
1294      for(IncEdgeIt e(*this, b); e!=INVALID;) {
1295        IncEdgeIt f = e; ++f;
1296        if (r && runningNode(e) == a) {
1297          erase(e);
1298        } else if (u(e) == b) {
1299          changeU(e, a);
1300        } else {
1301          changeV(e, a);
1302        }
1303        e = f;
1304      }
1305      erase(b);
1306    }
1307
1308    ///Clear the graph.
1309
1310    ///This function erases all nodes and arcs from the graph.
1311    ///
1312    void clear() {
1313      Parent::clear();
1314    }
1315
1316    /// Reserve memory for nodes.
1317
1318    /// Using this function, it is possible to avoid superfluous memory
1319    /// allocation: if you know that the graph you want to build will
1320    /// be large (e.g. it will contain millions of nodes and/or edges),
1321    /// then it is worth reserving space for this amount before starting
1322    /// to build the graph.
1323    /// \sa reserveEdge()
1324    void reserveNode(int n) { nodes.reserve(n); };
1325
1326    /// Reserve memory for edges.
1327
1328    /// Using this function, it is possible to avoid superfluous memory
1329    /// allocation: if you know that the graph you want to build will
1330    /// be large (e.g. it will contain millions of nodes and/or edges),
1331    /// then it is worth reserving space for this amount before starting
1332    /// to build the graph.
1333    /// \sa reserveNode()
1334    void reserveEdge(int m) { arcs.reserve(2 * m); };
1335
1336    /// \brief Class to make a snapshot of the graph and restore
1337    /// it later.
1338    ///
1339    /// Class to make a snapshot of the graph and restore it later.
1340    ///
1341    /// The newly added nodes and edges can be removed
1342    /// using the restore() function.
1343    ///
1344    /// \note After a state is restored, you cannot restore a later state,
1345    /// i.e. you cannot add the removed nodes and edges again using
1346    /// another Snapshot instance.
1347    ///
1348    /// \warning Node and edge deletions and other modifications
1349    /// (e.g. changing the end-nodes of edges or contracting nodes)
1350    /// cannot be restored. These events invalidate the snapshot.
1351    /// However the edges and nodes that were added to the graph after
1352    /// making the current snapshot can be removed without invalidating it.
1353    class Snapshot {
1354    protected:
1355
1356      typedef Parent::NodeNotifier NodeNotifier;
1357
1358      class NodeObserverProxy : public NodeNotifier::ObserverBase {
1359      public:
1360
1361        NodeObserverProxy(Snapshot& _snapshot)
1362          : snapshot(_snapshot) {}
1363
1364        using NodeNotifier::ObserverBase::attach;
1365        using NodeNotifier::ObserverBase::detach;
1366        using NodeNotifier::ObserverBase::attached;
1367
1368      protected:
1369
1370        virtual void add(const Node& node) {
1371          snapshot.addNode(node);
1372        }
1373        virtual void add(const std::vector<Node>& nodes) {
1374          for (int i = nodes.size() - 1; i >= 0; ++i) {
1375            snapshot.addNode(nodes[i]);
1376          }
1377        }
1378        virtual void erase(const Node& node) {
1379          snapshot.eraseNode(node);
1380        }
1381        virtual void erase(const std::vector<Node>& nodes) {
1382          for (int i = 0; i < int(nodes.size()); ++i) {
1383            snapshot.eraseNode(nodes[i]);
1384          }
1385        }
1386        virtual void build() {
1387          Node node;
1388          std::vector<Node> nodes;
1389          for (notifier()->first(node); node != INVALID;
1390               notifier()->next(node)) {
1391            nodes.push_back(node);
1392          }
1393          for (int i = nodes.size() - 1; i >= 0; --i) {
1394            snapshot.addNode(nodes[i]);
1395          }
1396        }
1397        virtual void clear() {
1398          Node node;
1399          for (notifier()->first(node); node != INVALID;
1400               notifier()->next(node)) {
1401            snapshot.eraseNode(node);
1402          }
1403        }
1404
1405        Snapshot& snapshot;
1406      };
1407
1408      class EdgeObserverProxy : public EdgeNotifier::ObserverBase {
1409      public:
1410
1411        EdgeObserverProxy(Snapshot& _snapshot)
1412          : snapshot(_snapshot) {}
1413
1414        using EdgeNotifier::ObserverBase::attach;
1415        using EdgeNotifier::ObserverBase::detach;
1416        using EdgeNotifier::ObserverBase::attached;
1417
1418      protected:
1419
1420        virtual void add(const Edge& edge) {
1421          snapshot.addEdge(edge);
1422        }
1423        virtual void add(const std::vector<Edge>& edges) {
1424          for (int i = edges.size() - 1; i >= 0; ++i) {
1425            snapshot.addEdge(edges[i]);
1426          }
1427        }
1428        virtual void erase(const Edge& edge) {
1429          snapshot.eraseEdge(edge);
1430        }
1431        virtual void erase(const std::vector<Edge>& edges) {
1432          for (int i = 0; i < int(edges.size()); ++i) {
1433            snapshot.eraseEdge(edges[i]);
1434          }
1435        }
1436        virtual void build() {
1437          Edge edge;
1438          std::vector<Edge> edges;
1439          for (notifier()->first(edge); edge != INVALID;
1440               notifier()->next(edge)) {
1441            edges.push_back(edge);
1442          }
1443          for (int i = edges.size() - 1; i >= 0; --i) {
1444            snapshot.addEdge(edges[i]);
1445          }
1446        }
1447        virtual void clear() {
1448          Edge edge;
1449          for (notifier()->first(edge); edge != INVALID;
1450               notifier()->next(edge)) {
1451            snapshot.eraseEdge(edge);
1452          }
1453        }
1454
1455        Snapshot& snapshot;
1456      };
1457
1458      ListGraph *graph;
1459
1460      NodeObserverProxy node_observer_proxy;
1461      EdgeObserverProxy edge_observer_proxy;
1462
1463      std::list<Node> added_nodes;
1464      std::list<Edge> added_edges;
1465
1466
1467      void addNode(const Node& node) {
1468        added_nodes.push_front(node);
1469      }
1470      void eraseNode(const Node& node) {
1471        std::list<Node>::iterator it =
1472          std::find(added_nodes.begin(), added_nodes.end(), node);
1473        if (it == added_nodes.end()) {
1474          clear();
1475          edge_observer_proxy.detach();
1476          throw NodeNotifier::ImmediateDetach();
1477        } else {
1478          added_nodes.erase(it);
1479        }
1480      }
1481
1482      void addEdge(const Edge& edge) {
1483        added_edges.push_front(edge);
1484      }
1485      void eraseEdge(const Edge& edge) {
1486        std::list<Edge>::iterator it =
1487          std::find(added_edges.begin(), added_edges.end(), edge);
1488        if (it == added_edges.end()) {
1489          clear();
1490          node_observer_proxy.detach();
1491          throw EdgeNotifier::ImmediateDetach();
1492        } else {
1493          added_edges.erase(it);
1494        }
1495      }
1496
1497      void attach(ListGraph &_graph) {
1498        graph = &_graph;
1499        node_observer_proxy.attach(graph->notifier(Node()));
1500        edge_observer_proxy.attach(graph->notifier(Edge()));
1501      }
1502
1503      void detach() {
1504        node_observer_proxy.detach();
1505        edge_observer_proxy.detach();
1506      }
1507
1508      bool attached() const {
1509        return node_observer_proxy.attached();
1510      }
1511
1512      void clear() {
1513        added_nodes.clear();
1514        added_edges.clear();
1515      }
1516
1517    public:
1518
1519      /// \brief Default constructor.
1520      ///
1521      /// Default constructor.
1522      /// You have to call save() to actually make a snapshot.
1523      Snapshot()
1524        : graph(0), node_observer_proxy(*this),
1525          edge_observer_proxy(*this) {}
1526
1527      /// \brief Constructor that immediately makes a snapshot.
1528      ///
1529      /// This constructor immediately makes a snapshot of the given graph.
1530      Snapshot(ListGraph &gr)
1531        : node_observer_proxy(*this),
1532          edge_observer_proxy(*this) {
1533        attach(gr);
1534      }
1535
1536      /// \brief Make a snapshot.
1537      ///
1538      /// This function makes a snapshot of the given graph.
1539      /// It can be called more than once. In case of a repeated
1540      /// call, the previous snapshot gets lost.
1541      void save(ListGraph &gr) {
1542        if (attached()) {
1543          detach();
1544          clear();
1545        }
1546        attach(gr);
1547      }
1548
1549      /// \brief Undo the changes until the last snapshot.
1550      ///
1551      /// This function undos the changes until the last snapshot
1552      /// created by save() or Snapshot(ListGraph&).
1553      void restore() {
1554        detach();
1555        for(std::list<Edge>::iterator it = added_edges.begin();
1556            it != added_edges.end(); ++it) {
1557          graph->erase(*it);
1558        }
1559        for(std::list<Node>::iterator it = added_nodes.begin();
1560            it != added_nodes.end(); ++it) {
1561          graph->erase(*it);
1562        }
1563        clear();
1564      }
1565
1566      /// \brief Returns \c true if the snapshot is valid.
1567      ///
1568      /// This function returns \c true if the snapshot is valid.
1569      bool valid() const {
1570        return attached();
1571      }
1572    };
1573  };
1574
1575  /// @}
1576} //namespace lemon
1577
1578
1579#endif
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