COIN-OR::LEMON - Graph Library

source: lemon-1.0/lemon/list_graph.h @ 244:c30731a37f91

Last change on this file since 244:c30731a37f91 was 212:1ae84dea7d09, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Fix the incorrect tab replacements of unify-sources.sh

File size: 42.4 KB
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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_LIST_GRAPH_H
20#define LEMON_LIST_GRAPH_H
21
22///\ingroup graphs
23///\file
24///\brief ListDigraph, ListGraph classes.
25
26#include <lemon/bits/graph_extender.h>
27
28#include <vector>
29#include <list>
30
31namespace lemon {
32
33  class ListDigraphBase {
34
35  protected:
36    struct NodeT {
37      int first_in, first_out;
38      int prev, next;
39    };
40
41    struct ArcT {
42      int target, source;
43      int prev_in, prev_out;
44      int next_in, next_out;
45    };
46
47    std::vector<NodeT> nodes;
48
49    int first_node;
50
51    int first_free_node;
52
53    std::vector<ArcT> arcs;
54
55    int first_free_arc;
56
57  public:
58
59    typedef ListDigraphBase Digraph;
60
61    class Node {
62      friend class ListDigraphBase;
63    protected:
64
65      int id;
66      explicit Node(int pid) { id = pid;}
67
68    public:
69      Node() {}
70      Node (Invalid) { id = -1; }
71      bool operator==(const Node& node) const {return id == node.id;}
72      bool operator!=(const Node& node) const {return id != node.id;}
73      bool operator<(const Node& node) const {return id < node.id;}
74    };
75
76    class Arc {
77      friend class ListDigraphBase;
78    protected:
79
80      int id;
81      explicit Arc(int pid) { id = pid;}
82
83    public:
84      Arc() {}
85      Arc (Invalid) { id = -1; }
86      bool operator==(const Arc& arc) const {return id == arc.id;}
87      bool operator!=(const Arc& arc) const {return id != arc.id;}
88      bool operator<(const Arc& arc) const {return id < arc.id;}
89    };
90
91
92
93    ListDigraphBase()
94      : nodes(), first_node(-1),
95        first_free_node(-1), arcs(), first_free_arc(-1) {}
96
97
98    int maxNodeId() const { return nodes.size()-1; }
99    int maxArcId() const { return arcs.size()-1; }
100
101    Node source(Arc e) const { return Node(arcs[e.id].source); }
102    Node target(Arc e) const { return Node(arcs[e.id].target); }
103
104
105    void first(Node& node) const {
106      node.id = first_node;
107    }
108
109    void next(Node& node) const {
110      node.id = nodes[node.id].next;
111    }
112
113
114    void first(Arc& arc) const {
115      int n;
116      for(n = first_node;
117          n!=-1 && nodes[n].first_in == -1;
118          n = nodes[n].next) {}
119      arc.id = (n == -1) ? -1 : nodes[n].first_in;
120    }
121
122    void next(Arc& arc) const {
123      if (arcs[arc.id].next_in != -1) {
124        arc.id = arcs[arc.id].next_in;
125      } else {
126        int n;
127        for(n = nodes[arcs[arc.id].target].next;
128            n!=-1 && nodes[n].first_in == -1;
129            n = nodes[n].next) {}
130        arc.id = (n == -1) ? -1 : nodes[n].first_in;
131      }
132    }
133
134    void firstOut(Arc &e, const Node& v) const {
135      e.id = nodes[v.id].first_out;
136    }
137    void nextOut(Arc &e) const {
138      e.id=arcs[e.id].next_out;
139    }
140
141    void firstIn(Arc &e, const Node& v) const {
142      e.id = nodes[v.id].first_in;
143    }
144    void nextIn(Arc &e) const {
145      e.id=arcs[e.id].next_in;
146    }
147
148
149    static int id(Node v) { return v.id; }
150    static int id(Arc e) { return e.id; }
151
152    static Node nodeFromId(int id) { return Node(id);}
153    static Arc arcFromId(int id) { return Arc(id);}
154
155    bool valid(Node n) const {
156      return n.id >= 0 && n.id < static_cast<int>(nodes.size()) &&
157        nodes[n.id].prev != -2;
158    }
159
160    bool valid(Arc a) const {
161      return a.id >= 0 && a.id < static_cast<int>(arcs.size()) &&
162        arcs[a.id].prev_in != -2;
163    }
164
165    Node addNode() {
166      int n;
167
168      if(first_free_node==-1) {
169        n = nodes.size();
170        nodes.push_back(NodeT());
171      } else {
172        n = first_free_node;
173        first_free_node = nodes[n].next;
174      }
175
176      nodes[n].next = first_node;
177      if(first_node != -1) nodes[first_node].prev = n;
178      first_node = n;
179      nodes[n].prev = -1;
180
181      nodes[n].first_in = nodes[n].first_out = -1;
182
183      return Node(n);
184    }
185
186    Arc addArc(Node u, Node v) {
187      int n;
188
189      if (first_free_arc == -1) {
190        n = arcs.size();
191        arcs.push_back(ArcT());
192      } else {
193        n = first_free_arc;
194        first_free_arc = arcs[n].next_in;
195      }
196
197      arcs[n].source = u.id;
198      arcs[n].target = v.id;
199
200      arcs[n].next_out = nodes[u.id].first_out;
201      if(nodes[u.id].first_out != -1) {
202        arcs[nodes[u.id].first_out].prev_out = n;
203      }
204
205      arcs[n].next_in = nodes[v.id].first_in;
206      if(nodes[v.id].first_in != -1) {
207        arcs[nodes[v.id].first_in].prev_in = n;
208      }
209
210      arcs[n].prev_in = arcs[n].prev_out = -1;
211
212      nodes[u.id].first_out = nodes[v.id].first_in = n;
213
214      return Arc(n);
215    }
216
217    void erase(const Node& node) {
218      int n = node.id;
219
220      if(nodes[n].next != -1) {
221        nodes[nodes[n].next].prev = nodes[n].prev;
222      }
223
224      if(nodes[n].prev != -1) {
225        nodes[nodes[n].prev].next = nodes[n].next;
226      } else {
227        first_node = nodes[n].next;
228      }
229
230      nodes[n].next = first_free_node;
231      first_free_node = n;
232      nodes[n].prev = -2;
233
234    }
235
236    void erase(const Arc& arc) {
237      int n = arc.id;
238
239      if(arcs[n].next_in!=-1) {
240        arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;
241      }
242
243      if(arcs[n].prev_in!=-1) {
244        arcs[arcs[n].prev_in].next_in = arcs[n].next_in;
245      } else {
246        nodes[arcs[n].target].first_in = arcs[n].next_in;
247      }
248
249
250      if(arcs[n].next_out!=-1) {
251        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
252      }
253
254      if(arcs[n].prev_out!=-1) {
255        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
256      } else {
257        nodes[arcs[n].source].first_out = arcs[n].next_out;
258      }
259
260      arcs[n].next_in = first_free_arc;
261      first_free_arc = n;
262      arcs[n].prev_in = -2;
263    }
264
265    void clear() {
266      arcs.clear();
267      nodes.clear();
268      first_node = first_free_node = first_free_arc = -1;
269    }
270
271  protected:
272    void changeTarget(Arc e, Node n)
273    {
274      if(arcs[e.id].next_in != -1)
275        arcs[arcs[e.id].next_in].prev_in = arcs[e.id].prev_in;
276      if(arcs[e.id].prev_in != -1)
277        arcs[arcs[e.id].prev_in].next_in = arcs[e.id].next_in;
278      else nodes[arcs[e.id].target].first_in = arcs[e.id].next_in;
279      if (nodes[n.id].first_in != -1) {
280        arcs[nodes[n.id].first_in].prev_in = e.id;
281      }
282      arcs[e.id].target = n.id;
283      arcs[e.id].prev_in = -1;
284      arcs[e.id].next_in = nodes[n.id].first_in;
285      nodes[n.id].first_in = e.id;
286    }
287    void changeSource(Arc e, Node n)
288    {
289      if(arcs[e.id].next_out != -1)
290        arcs[arcs[e.id].next_out].prev_out = arcs[e.id].prev_out;
291      if(arcs[e.id].prev_out != -1)
292        arcs[arcs[e.id].prev_out].next_out = arcs[e.id].next_out;
293      else nodes[arcs[e.id].source].first_out = arcs[e.id].next_out;
294      if (nodes[n.id].first_out != -1) {
295        arcs[nodes[n.id].first_out].prev_out = e.id;
296      }
297      arcs[e.id].source = n.id;
298      arcs[e.id].prev_out = -1;
299      arcs[e.id].next_out = nodes[n.id].first_out;
300      nodes[n.id].first_out = e.id;
301    }
302
303  };
304
305  typedef DigraphExtender<ListDigraphBase> ExtendedListDigraphBase;
306
307  /// \addtogroup graphs
308  /// @{
309
310  ///A general directed graph structure.
311
312  ///\ref ListDigraph is a simple and fast <em>directed graph</em>
313  ///implementation based on static linked lists that are stored in
314  ///\c std::vector structures.
315  ///
316  ///It conforms to the \ref concepts::Digraph "Digraph concept" and it
317  ///also provides several useful additional functionalities.
318  ///Most of the member functions and nested classes are documented
319  ///only in the concept class.
320  ///
321  ///An important extra feature of this digraph implementation is that
322  ///its maps are real \ref concepts::ReferenceMap "reference map"s.
323  ///
324  ///\sa concepts::Digraph
325
326  class ListDigraph : public ExtendedListDigraphBase {
327  private:
328    ///ListDigraph is \e not copy constructible. Use copyDigraph() instead.
329
330    ///ListDigraph is \e not copy constructible. Use copyDigraph() instead.
331    ///
332    ListDigraph(const ListDigraph &) :ExtendedListDigraphBase() {};
333    ///\brief Assignment of ListDigraph to another one is \e not allowed.
334    ///Use copyDigraph() instead.
335
336    ///Assignment of ListDigraph to another one is \e not allowed.
337    ///Use copyDigraph() instead.
338    void operator=(const ListDigraph &) {}
339  public:
340
341    typedef ExtendedListDigraphBase Parent;
342
343    /// Constructor
344
345    /// Constructor.
346    ///
347    ListDigraph() {}
348
349    ///Add a new node to the digraph.
350
351    ///Add a new node to the digraph.
352    ///\return the new node.
353    Node addNode() { return Parent::addNode(); }
354
355    ///Add a new arc to the digraph.
356
357    ///Add a new arc to the digraph with source node \c s
358    ///and target node \c t.
359    ///\return the new arc.
360    Arc addArc(const Node& s, const Node& t) {
361      return Parent::addArc(s, t);
362    }
363
364    /// Node validity check
365
366    /// This function gives back true if the given node is valid,
367    /// ie. it is a real node of the graph.
368    ///
369    /// \warning A Node pointing to a removed item
370    /// could become valid again later if new nodes are
371    /// added to the graph.
372    bool valid(Node n) const { return Parent::valid(n); }
373
374    /// Arc validity check
375
376    /// This function gives back true if the given arc is valid,
377    /// ie. it is a real arc of the graph.
378    ///
379    /// \warning An Arc pointing to a removed item
380    /// could become valid again later if new nodes are
381    /// added to the graph.
382    bool valid(Arc a) const { return Parent::valid(a); }
383
384    /// Change the target of \c e to \c n
385
386    /// Change the target of \c e to \c n
387    ///
388    ///\note The <tt>ArcIt</tt>s and <tt>OutArcIt</tt>s referencing
389    ///the changed arc remain valid. However <tt>InArcIt</tt>s are
390    ///invalidated.
391    ///
392    ///\warning This functionality cannot be used together with the Snapshot
393    ///feature.
394    void changeTarget(Arc e, Node n) {
395      Parent::changeTarget(e,n);
396    }
397    /// Change the source of \c e to \c n
398
399    /// Change the source of \c e to \c n
400    ///
401    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s referencing
402    ///the changed arc remain valid. However <tt>OutArcIt</tt>s are
403    ///invalidated.
404    ///
405    ///\warning This functionality cannot be used together with the Snapshot
406    ///feature.
407    void changeSource(Arc e, Node n) {
408      Parent::changeSource(e,n);
409    }
410
411    /// Invert the direction of an arc.
412
413    ///\note The <tt>ArcIt</tt>s referencing the changed arc remain
414    ///valid. However <tt>OutArcIt</tt>s and <tt>InArcIt</tt>s are
415    ///invalidated.
416    ///
417    ///\warning This functionality cannot be used together with the Snapshot
418    ///feature.
419    void reverseArc(Arc e) {
420      Node t=target(e);
421      changeTarget(e,source(e));
422      changeSource(e,t);
423    }
424
425    /// Reserve memory for nodes.
426
427    /// Using this function it is possible to avoid the superfluous memory
428    /// allocation: if you know that the digraph you want to build will
429    /// be very large (e.g. it will contain millions of nodes and/or arcs)
430    /// then it is worth reserving space for this amount before starting
431    /// to build the digraph.
432    /// \sa reserveArc
433    void reserveNode(int n) { nodes.reserve(n); };
434
435    /// Reserve memory for arcs.
436
437    /// Using this function it is possible to avoid the superfluous memory
438    /// allocation: if you know that the digraph you want to build will
439    /// be very large (e.g. it will contain millions of nodes and/or arcs)
440    /// then it is worth reserving space for this amount before starting
441    /// to build the digraph.
442    /// \sa reserveNode
443    void reserveArc(int m) { arcs.reserve(m); };
444
445    ///Contract two nodes.
446
447    ///This function contracts two nodes.
448    ///Node \p b will be removed but instead of deleting
449    ///incident arcs, they will be joined to \p a.
450    ///The last parameter \p r controls whether to remove loops. \c true
451    ///means that loops will be removed.
452    ///
453    ///\note The <tt>ArcIt</tt>s referencing a moved arc remain
454    ///valid. However <tt>InArcIt</tt>s and <tt>OutArcIt</tt>s
455    ///may be invalidated.
456    ///
457    ///\warning This functionality cannot be used together with the Snapshot
458    ///feature.
459    void contract(Node a, Node b, bool r = true)
460    {
461      for(OutArcIt e(*this,b);e!=INVALID;) {
462        OutArcIt f=e;
463        ++f;
464        if(r && target(e)==a) erase(e);
465        else changeSource(e,a);
466        e=f;
467      }
468      for(InArcIt e(*this,b);e!=INVALID;) {
469        InArcIt f=e;
470        ++f;
471        if(r && source(e)==a) erase(e);
472        else changeTarget(e,a);
473        e=f;
474      }
475      erase(b);
476    }
477
478    ///Split a node.
479
480    ///This function splits a node. First a new node is added to the digraph,
481    ///then the source of each outgoing arc of \c n is moved to this new node.
482    ///If \c connect is \c true (this is the default value), then a new arc
483    ///from \c n to the newly created node is also added.
484    ///\return The newly created node.
485    ///
486    ///\note The <tt>ArcIt</tt>s referencing a moved arc remain
487    ///valid. However <tt>InArcIt</tt>s and <tt>OutArcIt</tt>s may
488    ///be invalidated.
489    ///
490    ///\warning This functionality cannot be used together with the
491    ///Snapshot feature.
492    ///
493    ///\todo It could be implemented in a bit faster way.
494    Node split(Node n, bool connect = true) {
495      Node b = addNode();
496      for(OutArcIt e(*this,n);e!=INVALID;) {
497        OutArcIt f=e;
498        ++f;
499        changeSource(e,b);
500        e=f;
501      }
502      if (connect) addArc(n,b);
503      return b;
504    }
505
506    ///Split an arc.
507
508    ///This function splits an arc. First a new node \c b is added to
509    ///the digraph, then the original arc is re-targeted to \c
510    ///b. Finally an arc from \c b to the original target is added.
511    ///
512    ///\return The newly created node.
513    ///
514    ///\warning This functionality cannot be used together with the
515    ///Snapshot feature.
516    Node split(Arc e) {
517      Node b = addNode();
518      addArc(b,target(e));
519      changeTarget(e,b);
520      return b;
521    }
522
523    /// \brief Class to make a snapshot of the digraph and restore
524    /// it later.
525    ///
526    /// Class to make a snapshot of the digraph and restore it later.
527    ///
528    /// The newly added nodes and arcs can be removed using the
529    /// restore() function.
530    ///
531    /// \warning Arc and node deletions and other modifications (e.g.
532    /// contracting, splitting, reversing arcs or nodes) cannot be
533    /// restored. These events invalidate the snapshot.
534    class Snapshot {
535    protected:
536
537      typedef Parent::NodeNotifier NodeNotifier;
538
539      class NodeObserverProxy : public NodeNotifier::ObserverBase {
540      public:
541
542        NodeObserverProxy(Snapshot& _snapshot)
543          : snapshot(_snapshot) {}
544
545        using NodeNotifier::ObserverBase::attach;
546        using NodeNotifier::ObserverBase::detach;
547        using NodeNotifier::ObserverBase::attached;
548
549      protected:
550
551        virtual void add(const Node& node) {
552          snapshot.addNode(node);
553        }
554        virtual void add(const std::vector<Node>& nodes) {
555          for (int i = nodes.size() - 1; i >= 0; ++i) {
556            snapshot.addNode(nodes[i]);
557          }
558        }
559        virtual void erase(const Node& node) {
560          snapshot.eraseNode(node);
561        }
562        virtual void erase(const std::vector<Node>& nodes) {
563          for (int i = 0; i < int(nodes.size()); ++i) {
564            snapshot.eraseNode(nodes[i]);
565          }
566        }
567        virtual void build() {
568          Node node;
569          std::vector<Node> nodes;
570          for (notifier()->first(node); node != INVALID;
571               notifier()->next(node)) {
572            nodes.push_back(node);
573          }
574          for (int i = nodes.size() - 1; i >= 0; --i) {
575            snapshot.addNode(nodes[i]);
576          }
577        }
578        virtual void clear() {
579          Node node;
580          for (notifier()->first(node); node != INVALID;
581               notifier()->next(node)) {
582            snapshot.eraseNode(node);
583          }
584        }
585
586        Snapshot& snapshot;
587      };
588
589      class ArcObserverProxy : public ArcNotifier::ObserverBase {
590      public:
591
592        ArcObserverProxy(Snapshot& _snapshot)
593          : snapshot(_snapshot) {}
594
595        using ArcNotifier::ObserverBase::attach;
596        using ArcNotifier::ObserverBase::detach;
597        using ArcNotifier::ObserverBase::attached;
598
599      protected:
600
601        virtual void add(const Arc& arc) {
602          snapshot.addArc(arc);
603        }
604        virtual void add(const std::vector<Arc>& arcs) {
605          for (int i = arcs.size() - 1; i >= 0; ++i) {
606            snapshot.addArc(arcs[i]);
607          }
608        }
609        virtual void erase(const Arc& arc) {
610          snapshot.eraseArc(arc);
611        }
612        virtual void erase(const std::vector<Arc>& arcs) {
613          for (int i = 0; i < int(arcs.size()); ++i) {
614            snapshot.eraseArc(arcs[i]);
615          }
616        }
617        virtual void build() {
618          Arc arc;
619          std::vector<Arc> arcs;
620          for (notifier()->first(arc); arc != INVALID;
621               notifier()->next(arc)) {
622            arcs.push_back(arc);
623          }
624          for (int i = arcs.size() - 1; i >= 0; --i) {
625            snapshot.addArc(arcs[i]);
626          }
627        }
628        virtual void clear() {
629          Arc arc;
630          for (notifier()->first(arc); arc != INVALID;
631               notifier()->next(arc)) {
632            snapshot.eraseArc(arc);
633          }
634        }
635
636        Snapshot& snapshot;
637      };
638
639      ListDigraph *digraph;
640
641      NodeObserverProxy node_observer_proxy;
642      ArcObserverProxy arc_observer_proxy;
643
644      std::list<Node> added_nodes;
645      std::list<Arc> added_arcs;
646
647
648      void addNode(const Node& node) {
649        added_nodes.push_front(node);
650      }
651      void eraseNode(const Node& node) {
652        std::list<Node>::iterator it =
653          std::find(added_nodes.begin(), added_nodes.end(), node);
654        if (it == added_nodes.end()) {
655          clear();
656          arc_observer_proxy.detach();
657          throw NodeNotifier::ImmediateDetach();
658        } else {
659          added_nodes.erase(it);
660        }
661      }
662
663      void addArc(const Arc& arc) {
664        added_arcs.push_front(arc);
665      }
666      void eraseArc(const Arc& arc) {
667        std::list<Arc>::iterator it =
668          std::find(added_arcs.begin(), added_arcs.end(), arc);
669        if (it == added_arcs.end()) {
670          clear();
671          node_observer_proxy.detach();
672          throw ArcNotifier::ImmediateDetach();
673        } else {
674          added_arcs.erase(it);
675        }
676      }
677
678      void attach(ListDigraph &_digraph) {
679        digraph = &_digraph;
680        node_observer_proxy.attach(digraph->notifier(Node()));
681        arc_observer_proxy.attach(digraph->notifier(Arc()));
682      }
683
684      void detach() {
685        node_observer_proxy.detach();
686        arc_observer_proxy.detach();
687      }
688
689      bool attached() const {
690        return node_observer_proxy.attached();
691      }
692
693      void clear() {
694        added_nodes.clear();
695        added_arcs.clear();
696      }
697
698    public:
699
700      /// \brief Default constructor.
701      ///
702      /// Default constructor.
703      /// To actually make a snapshot you must call save().
704      Snapshot()
705        : digraph(0), node_observer_proxy(*this),
706          arc_observer_proxy(*this) {}
707
708      /// \brief Constructor that immediately makes a snapshot.
709      ///
710      /// This constructor immediately makes a snapshot of the digraph.
711      /// \param _digraph The digraph we make a snapshot of.
712      Snapshot(ListDigraph &_digraph)
713        : node_observer_proxy(*this),
714          arc_observer_proxy(*this) {
715        attach(_digraph);
716      }
717
718      /// \brief Make a snapshot.
719      ///
720      /// Make a snapshot of the digraph.
721      ///
722      /// This function can be called more than once. In case of a repeated
723      /// call, the previous snapshot gets lost.
724      /// \param _digraph The digraph we make the snapshot of.
725      void save(ListDigraph &_digraph) {
726        if (attached()) {
727          detach();
728          clear();
729        }
730        attach(_digraph);
731      }
732
733      /// \brief Undo the changes until the last snapshot.
734      //
735      /// Undo the changes until the last snapshot created by save().
736      void restore() {
737        detach();
738        for(std::list<Arc>::iterator it = added_arcs.begin();
739            it != added_arcs.end(); ++it) {
740          digraph->erase(*it);
741        }
742        for(std::list<Node>::iterator it = added_nodes.begin();
743            it != added_nodes.end(); ++it) {
744          digraph->erase(*it);
745        }
746        clear();
747      }
748
749      /// \brief Gives back true when the snapshot is valid.
750      ///
751      /// Gives back true when the snapshot is valid.
752      bool valid() const {
753        return attached();
754      }
755    };
756
757  };
758
759  ///@}
760
761  class ListGraphBase {
762
763  protected:
764
765    struct NodeT {
766      int first_out;
767      int prev, next;
768    };
769
770    struct ArcT {
771      int target;
772      int prev_out, next_out;
773    };
774
775    std::vector<NodeT> nodes;
776
777    int first_node;
778
779    int first_free_node;
780
781    std::vector<ArcT> arcs;
782
783    int first_free_arc;
784
785  public:
786
787    typedef ListGraphBase Digraph;
788
789    class Node;
790    class Arc;
791    class Edge;
792
793    class Node {
794      friend class ListGraphBase;
795    protected:
796
797      int id;
798      explicit Node(int pid) { id = pid;}
799
800    public:
801      Node() {}
802      Node (Invalid) { id = -1; }
803      bool operator==(const Node& node) const {return id == node.id;}
804      bool operator!=(const Node& node) const {return id != node.id;}
805      bool operator<(const Node& node) const {return id < node.id;}
806    };
807
808    class Edge {
809      friend class ListGraphBase;
810    protected:
811
812      int id;
813      explicit Edge(int pid) { id = pid;}
814
815    public:
816      Edge() {}
817      Edge (Invalid) { id = -1; }
818      bool operator==(const Edge& edge) const {return id == edge.id;}
819      bool operator!=(const Edge& edge) const {return id != edge.id;}
820      bool operator<(const Edge& edge) const {return id < edge.id;}
821    };
822
823    class Arc {
824      friend class ListGraphBase;
825    protected:
826
827      int id;
828      explicit Arc(int pid) { id = pid;}
829
830    public:
831      operator Edge() const { return edgeFromId(id / 2); }
832
833      Arc() {}
834      Arc (Invalid) { id = -1; }
835      bool operator==(const Arc& arc) const {return id == arc.id;}
836      bool operator!=(const Arc& arc) const {return id != arc.id;}
837      bool operator<(const Arc& arc) const {return id < arc.id;}
838    };
839
840
841
842    ListGraphBase()
843      : nodes(), first_node(-1),
844        first_free_node(-1), arcs(), first_free_arc(-1) {}
845
846
847    int maxNodeId() const { return nodes.size()-1; }
848    int maxEdgeId() const { return arcs.size() / 2 - 1; }
849    int maxArcId() const { return arcs.size()-1; }
850
851    Node source(Arc e) const { return Node(arcs[e.id ^ 1].target); }
852    Node target(Arc e) const { return Node(arcs[e.id].target); }
853
854    Node u(Edge e) const { return Node(arcs[2 * e.id].target); }
855    Node v(Edge e) const { return Node(arcs[2 * e.id + 1].target); }
856
857    static bool direction(Arc e) {
858      return (e.id & 1) == 1;
859    }
860
861    static Arc direct(Edge e, bool d) {
862      return Arc(e.id * 2 + (d ? 1 : 0));
863    }
864
865    void first(Node& node) const {
866      node.id = first_node;
867    }
868
869    void next(Node& node) const {
870      node.id = nodes[node.id].next;
871    }
872
873    void first(Arc& e) const {
874      int n = first_node;
875      while (n != -1 && nodes[n].first_out == -1) {
876        n = nodes[n].next;
877      }
878      e.id = (n == -1) ? -1 : nodes[n].first_out;
879    }
880
881    void next(Arc& e) const {
882      if (arcs[e.id].next_out != -1) {
883        e.id = arcs[e.id].next_out;
884      } else {
885        int n = nodes[arcs[e.id ^ 1].target].next;
886        while(n != -1 && nodes[n].first_out == -1) {
887          n = nodes[n].next;
888        }
889        e.id = (n == -1) ? -1 : nodes[n].first_out;
890      }
891    }
892
893    void first(Edge& e) const {
894      int n = first_node;
895      while (n != -1) {
896        e.id = nodes[n].first_out;
897        while ((e.id & 1) != 1) {
898          e.id = arcs[e.id].next_out;
899        }
900        if (e.id != -1) {
901          e.id /= 2;
902          return;
903        }
904        n = nodes[n].next;
905      }
906      e.id = -1;
907    }
908
909    void next(Edge& e) const {
910      int n = arcs[e.id * 2].target;
911      e.id = arcs[(e.id * 2) | 1].next_out;
912      while ((e.id & 1) != 1) {
913        e.id = arcs[e.id].next_out;
914      }
915      if (e.id != -1) {
916        e.id /= 2;
917        return;
918      }
919      n = nodes[n].next;
920      while (n != -1) {
921        e.id = nodes[n].first_out;
922        while ((e.id & 1) != 1) {
923          e.id = arcs[e.id].next_out;
924        }
925        if (e.id != -1) {
926          e.id /= 2;
927          return;
928        }
929        n = nodes[n].next;
930      }
931      e.id = -1;
932    }
933
934    void firstOut(Arc &e, const Node& v) const {
935      e.id = nodes[v.id].first_out;
936    }
937    void nextOut(Arc &e) const {
938      e.id = arcs[e.id].next_out;
939    }
940
941    void firstIn(Arc &e, const Node& v) const {
942      e.id = ((nodes[v.id].first_out) ^ 1);
943      if (e.id == -2) e.id = -1;
944    }
945    void nextIn(Arc &e) const {
946      e.id = ((arcs[e.id ^ 1].next_out) ^ 1);
947      if (e.id == -2) e.id = -1;
948    }
949
950    void firstInc(Edge &e, bool& d, const Node& v) const {
951      int a = nodes[v.id].first_out;
952      if (a != -1 ) {
953        e.id = a / 2;
954        d = ((a & 1) == 1);
955      } else {
956        e.id = -1;
957        d = true;
958      }
959    }
960    void nextInc(Edge &e, bool& d) const {
961      int a = (arcs[(e.id * 2) | (d ? 1 : 0)].next_out);
962      if (a != -1 ) {
963        e.id = a / 2;
964        d = ((a & 1) == 1);
965      } else {
966        e.id = -1;
967        d = true;
968      }
969    }
970
971    static int id(Node v) { return v.id; }
972    static int id(Arc e) { return e.id; }
973    static int id(Edge e) { return e.id; }
974
975    static Node nodeFromId(int id) { return Node(id);}
976    static Arc arcFromId(int id) { return Arc(id);}
977    static Edge edgeFromId(int id) { return Edge(id);}
978
979    bool valid(Node n) const {
980      return n.id >= 0 && n.id < static_cast<int>(nodes.size()) &&
981        nodes[n.id].prev != -2;
982    }
983
984    bool valid(Arc a) const {
985      return a.id >= 0 && a.id < static_cast<int>(arcs.size()) &&
986        arcs[a.id].prev_out != -2;
987    }
988
989    bool valid(Edge e) const {
990      return e.id >= 0 && 2 * e.id < static_cast<int>(arcs.size()) &&
991        arcs[2 * e.id].prev_out != -2;
992    }
993
994    Node addNode() {
995      int n;
996
997      if(first_free_node==-1) {
998        n = nodes.size();
999        nodes.push_back(NodeT());
1000      } else {
1001        n = first_free_node;
1002        first_free_node = nodes[n].next;
1003      }
1004
1005      nodes[n].next = first_node;
1006      if (first_node != -1) nodes[first_node].prev = n;
1007      first_node = n;
1008      nodes[n].prev = -1;
1009
1010      nodes[n].first_out = -1;
1011
1012      return Node(n);
1013    }
1014
1015    Edge addEdge(Node u, Node v) {
1016      int n;
1017
1018      if (first_free_arc == -1) {
1019        n = arcs.size();
1020        arcs.push_back(ArcT());
1021        arcs.push_back(ArcT());
1022      } else {
1023        n = first_free_arc;
1024        first_free_arc = arcs[n].next_out;
1025      }
1026
1027      arcs[n].target = u.id;
1028      arcs[n | 1].target = v.id;
1029
1030      arcs[n].next_out = nodes[v.id].first_out;
1031      if (nodes[v.id].first_out != -1) {
1032        arcs[nodes[v.id].first_out].prev_out = n;
1033      }
1034      arcs[n].prev_out = -1;
1035      nodes[v.id].first_out = n;
1036
1037      arcs[n | 1].next_out = nodes[u.id].first_out;
1038      if (nodes[u.id].first_out != -1) {
1039        arcs[nodes[u.id].first_out].prev_out = (n | 1);
1040      }
1041      arcs[n | 1].prev_out = -1;
1042      nodes[u.id].first_out = (n | 1);
1043
1044      return Edge(n / 2);
1045    }
1046
1047    void erase(const Node& node) {
1048      int n = node.id;
1049
1050      if(nodes[n].next != -1) {
1051        nodes[nodes[n].next].prev = nodes[n].prev;
1052      }
1053
1054      if(nodes[n].prev != -1) {
1055        nodes[nodes[n].prev].next = nodes[n].next;
1056      } else {
1057        first_node = nodes[n].next;
1058      }
1059
1060      nodes[n].next = first_free_node;
1061      first_free_node = n;
1062      nodes[n].prev = -2;
1063    }
1064
1065    void erase(const Edge& edge) {
1066      int n = edge.id * 2;
1067
1068      if (arcs[n].next_out != -1) {
1069        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
1070      }
1071
1072      if (arcs[n].prev_out != -1) {
1073        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
1074      } else {
1075        nodes[arcs[n | 1].target].first_out = arcs[n].next_out;
1076      }
1077
1078      if (arcs[n | 1].next_out != -1) {
1079        arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;
1080      }
1081
1082      if (arcs[n | 1].prev_out != -1) {
1083        arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;
1084      } else {
1085        nodes[arcs[n].target].first_out = arcs[n | 1].next_out;
1086      }
1087
1088      arcs[n].next_out = first_free_arc;
1089      first_free_arc = n;
1090      arcs[n].prev_out = -2;
1091      arcs[n | 1].prev_out = -2;
1092
1093    }
1094
1095    void clear() {
1096      arcs.clear();
1097      nodes.clear();
1098      first_node = first_free_node = first_free_arc = -1;
1099    }
1100
1101  protected:
1102
1103    void changeTarget(Edge e, Node n) {
1104      if(arcs[2 * e.id].next_out != -1) {
1105        arcs[arcs[2 * e.id].next_out].prev_out = arcs[2 * e.id].prev_out;
1106      }
1107      if(arcs[2 * e.id].prev_out != -1) {
1108        arcs[arcs[2 * e.id].prev_out].next_out =
1109          arcs[2 * e.id].next_out;
1110      } else {
1111        nodes[arcs[(2 * e.id) | 1].target].first_out =
1112          arcs[2 * e.id].next_out;
1113      }
1114
1115      if (nodes[n.id].first_out != -1) {
1116        arcs[nodes[n.id].first_out].prev_out = 2 * e.id;
1117      }
1118      arcs[(2 * e.id) | 1].target = n.id;
1119      arcs[2 * e.id].prev_out = -1;
1120      arcs[2 * e.id].next_out = nodes[n.id].first_out;
1121      nodes[n.id].first_out = 2 * e.id;
1122    }
1123
1124    void changeSource(Edge e, Node n) {
1125      if(arcs[(2 * e.id) | 1].next_out != -1) {
1126        arcs[arcs[(2 * e.id) | 1].next_out].prev_out =
1127          arcs[(2 * e.id) | 1].prev_out;
1128      }
1129      if(arcs[(2 * e.id) | 1].prev_out != -1) {
1130        arcs[arcs[(2 * e.id) | 1].prev_out].next_out =
1131          arcs[(2 * e.id) | 1].next_out;
1132      } else {
1133        nodes[arcs[2 * e.id].target].first_out =
1134          arcs[(2 * e.id) | 1].next_out;
1135      }
1136
1137      if (nodes[n.id].first_out != -1) {
1138        arcs[nodes[n.id].first_out].prev_out = ((2 * e.id) | 1);
1139      }
1140      arcs[2 * e.id].target = n.id;
1141      arcs[(2 * e.id) | 1].prev_out = -1;
1142      arcs[(2 * e.id) | 1].next_out = nodes[n.id].first_out;
1143      nodes[n.id].first_out = ((2 * e.id) | 1);
1144    }
1145
1146  };
1147
1148  typedef GraphExtender<ListGraphBase> ExtendedListGraphBase;
1149
1150
1151  /// \addtogroup graphs
1152  /// @{
1153
1154  ///A general undirected graph structure.
1155
1156  ///\ref ListGraph is a simple and fast <em>undirected graph</em>
1157  ///implementation based on static linked lists that are stored in
1158  ///\c std::vector structures.
1159  ///
1160  ///It conforms to the \ref concepts::Graph "Graph concept" and it
1161  ///also provides several useful additional functionalities.
1162  ///Most of the member functions and nested classes are documented
1163  ///only in the concept class.
1164  ///
1165  ///An important extra feature of this graph implementation is that
1166  ///its maps are real \ref concepts::ReferenceMap "reference map"s.
1167  ///
1168  ///\sa concepts::Graph
1169
1170  class ListGraph : public ExtendedListGraphBase {
1171  private:
1172    ///ListGraph is \e not copy constructible. Use copyGraph() instead.
1173
1174    ///ListGraph is \e not copy constructible. Use copyGraph() instead.
1175    ///
1176    ListGraph(const ListGraph &) :ExtendedListGraphBase()  {};
1177    ///\brief Assignment of ListGraph to another one is \e not allowed.
1178    ///Use copyGraph() instead.
1179
1180    ///Assignment of ListGraph to another one is \e not allowed.
1181    ///Use copyGraph() instead.
1182    void operator=(const ListGraph &) {}
1183  public:
1184    /// Constructor
1185
1186    /// Constructor.
1187    ///
1188    ListGraph() {}
1189
1190    typedef ExtendedListGraphBase Parent;
1191
1192    typedef Parent::OutArcIt IncEdgeIt;
1193
1194    /// \brief Add a new node to the graph.
1195    ///
1196    /// Add a new node to the graph.
1197    /// \return the new node.
1198    Node addNode() { return Parent::addNode(); }
1199
1200    /// \brief Add a new edge to the graph.
1201    ///
1202    /// Add a new edge to the graph with source node \c s
1203    /// and target node \c t.
1204    /// \return the new edge.
1205    Edge addEdge(const Node& s, const Node& t) {
1206      return Parent::addEdge(s, t);
1207    }
1208    /// Node validity check
1209
1210    /// This function gives back true if the given node is valid,
1211    /// ie. it is a real node of the graph.
1212    ///
1213    /// \warning A Node pointing to a removed item
1214    /// could become valid again later if new nodes are
1215    /// added to the graph.
1216    bool valid(Node n) const { return Parent::valid(n); }
1217    /// Arc validity check
1218
1219    /// This function gives back true if the given arc is valid,
1220    /// ie. it is a real arc of the graph.
1221    ///
1222    /// \warning An Arc pointing to a removed item
1223    /// could become valid again later if new edges are
1224    /// added to the graph.
1225    bool valid(Arc a) const { return Parent::valid(a); }
1226    /// Edge validity check
1227
1228    /// This function gives back true if the given edge is valid,
1229    /// ie. it is a real arc of the graph.
1230    ///
1231    /// \warning A Edge pointing to a removed item
1232    /// could become valid again later if new edges are
1233    /// added to the graph.
1234    bool valid(Edge e) const { return Parent::valid(e); }
1235    /// \brief Change the source of \c e to \c n
1236    ///
1237    /// This function changes the source of \c e to \c n.
1238    ///
1239    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s
1240    ///referencing the changed arc remain
1241    ///valid. However <tt>OutArcIt</tt>s are invalidated.
1242    ///
1243    ///\warning This functionality cannot be used together with the
1244    ///Snapshot feature.
1245    void changeSource(Edge e, Node n) {
1246      Parent::changeSource(e,n);
1247    }
1248    /// \brief Change the target of \c e to \c n
1249    ///
1250    /// This function changes the target of \c e to \c n.
1251    ///
1252    /// \note The <tt>ArcIt</tt>s referencing the changed arc remain
1253    /// valid. However the other iterators may be invalidated.
1254    ///
1255    ///\warning This functionality cannot be used together with the
1256    ///Snapshot feature.
1257    void changeTarget(Edge e, Node n) {
1258      Parent::changeTarget(e,n);
1259    }
1260    /// \brief Change the source of \c e to \c n
1261    ///
1262    /// This function changes the source of \c e to \c n.
1263    /// It also changes the proper node of the represented edge.
1264    ///
1265    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s
1266    ///referencing the changed arc remain
1267    ///valid. However <tt>OutArcIt</tt>s are invalidated.
1268    ///
1269    ///\warning This functionality cannot be used together with the
1270    ///Snapshot feature.
1271    void changeSource(Arc e, Node n) {
1272      if (Parent::direction(e)) {
1273        Parent::changeSource(e,n);
1274      } else {
1275        Parent::changeTarget(e,n);
1276      }
1277    }
1278    /// \brief Change the target of \c e to \c n
1279    ///
1280    /// This function changes the target of \c e to \c n.
1281    /// It also changes the proper node of the represented edge.
1282    ///
1283    ///\note The <tt>ArcIt</tt>s and <tt>OutArcIt</tt>s
1284    ///referencing the changed arc remain
1285    ///valid. However <tt>InArcIt</tt>s are invalidated.
1286    ///
1287    ///\warning This functionality cannot be used together with the
1288    ///Snapshot feature.
1289    void changeTarget(Arc e, Node n) {
1290      if (Parent::direction(e)) {
1291        Parent::changeTarget(e,n);
1292      } else {
1293        Parent::changeSource(e,n);
1294      }
1295    }
1296    /// \brief Contract two nodes.
1297    ///
1298    /// This function contracts two nodes.
1299    /// Node \p b will be removed but instead of deleting
1300    /// its neighboring arcs, they will be joined to \p a.
1301    /// The last parameter \p r controls whether to remove loops. \c true
1302    /// means that loops will be removed.
1303    ///
1304    /// \note The <tt>ArcIt</tt>s referencing a moved arc remain
1305    /// valid.
1306    ///
1307    ///\warning This functionality cannot be used together with the
1308    ///Snapshot feature.
1309    void contract(Node a, Node b, bool r = true) {
1310      for(IncEdgeIt e(*this, b); e!=INVALID;) {
1311        IncEdgeIt f = e; ++f;
1312        if (r && runningNode(e) == a) {
1313          erase(e);
1314        } else if (source(e) == b) {
1315          changeSource(e, a);
1316        } else {
1317          changeTarget(e, a);
1318        }
1319        e = f;
1320      }
1321      erase(b);
1322    }
1323
1324
1325    /// \brief Class to make a snapshot of the graph and restore
1326    /// it later.
1327    ///
1328    /// Class to make a snapshot of the graph and restore it later.
1329    ///
1330    /// The newly added nodes and edges can be removed
1331    /// using the restore() function.
1332    ///
1333    /// \warning Edge and node deletions and other modifications
1334    /// (e.g. changing nodes of edges, contracting nodes) cannot be
1335    /// restored. These events invalidate the snapshot.
1336    class Snapshot {
1337    protected:
1338
1339      typedef Parent::NodeNotifier NodeNotifier;
1340
1341      class NodeObserverProxy : public NodeNotifier::ObserverBase {
1342      public:
1343
1344        NodeObserverProxy(Snapshot& _snapshot)
1345          : snapshot(_snapshot) {}
1346
1347        using NodeNotifier::ObserverBase::attach;
1348        using NodeNotifier::ObserverBase::detach;
1349        using NodeNotifier::ObserverBase::attached;
1350
1351      protected:
1352
1353        virtual void add(const Node& node) {
1354          snapshot.addNode(node);
1355        }
1356        virtual void add(const std::vector<Node>& nodes) {
1357          for (int i = nodes.size() - 1; i >= 0; ++i) {
1358            snapshot.addNode(nodes[i]);
1359          }
1360        }
1361        virtual void erase(const Node& node) {
1362          snapshot.eraseNode(node);
1363        }
1364        virtual void erase(const std::vector<Node>& nodes) {
1365          for (int i = 0; i < int(nodes.size()); ++i) {
1366            snapshot.eraseNode(nodes[i]);
1367          }
1368        }
1369        virtual void build() {
1370          Node node;
1371          std::vector<Node> nodes;
1372          for (notifier()->first(node); node != INVALID;
1373               notifier()->next(node)) {
1374            nodes.push_back(node);
1375          }
1376          for (int i = nodes.size() - 1; i >= 0; --i) {
1377            snapshot.addNode(nodes[i]);
1378          }
1379        }
1380        virtual void clear() {
1381          Node node;
1382          for (notifier()->first(node); node != INVALID;
1383               notifier()->next(node)) {
1384            snapshot.eraseNode(node);
1385          }
1386        }
1387
1388        Snapshot& snapshot;
1389      };
1390
1391      class EdgeObserverProxy : public EdgeNotifier::ObserverBase {
1392      public:
1393
1394        EdgeObserverProxy(Snapshot& _snapshot)
1395          : snapshot(_snapshot) {}
1396
1397        using EdgeNotifier::ObserverBase::attach;
1398        using EdgeNotifier::ObserverBase::detach;
1399        using EdgeNotifier::ObserverBase::attached;
1400
1401      protected:
1402
1403        virtual void add(const Edge& edge) {
1404          snapshot.addEdge(edge);
1405        }
1406        virtual void add(const std::vector<Edge>& edges) {
1407          for (int i = edges.size() - 1; i >= 0; ++i) {
1408            snapshot.addEdge(edges[i]);
1409          }
1410        }
1411        virtual void erase(const Edge& edge) {
1412          snapshot.eraseEdge(edge);
1413        }
1414        virtual void erase(const std::vector<Edge>& edges) {
1415          for (int i = 0; i < int(edges.size()); ++i) {
1416            snapshot.eraseEdge(edges[i]);
1417          }
1418        }
1419        virtual void build() {
1420          Edge edge;
1421          std::vector<Edge> edges;
1422          for (notifier()->first(edge); edge != INVALID;
1423               notifier()->next(edge)) {
1424            edges.push_back(edge);
1425          }
1426          for (int i = edges.size() - 1; i >= 0; --i) {
1427            snapshot.addEdge(edges[i]);
1428          }
1429        }
1430        virtual void clear() {
1431          Edge edge;
1432          for (notifier()->first(edge); edge != INVALID;
1433               notifier()->next(edge)) {
1434            snapshot.eraseEdge(edge);
1435          }
1436        }
1437
1438        Snapshot& snapshot;
1439      };
1440
1441      ListGraph *graph;
1442
1443      NodeObserverProxy node_observer_proxy;
1444      EdgeObserverProxy edge_observer_proxy;
1445
1446      std::list<Node> added_nodes;
1447      std::list<Edge> added_edges;
1448
1449
1450      void addNode(const Node& node) {
1451        added_nodes.push_front(node);
1452      }
1453      void eraseNode(const Node& node) {
1454        std::list<Node>::iterator it =
1455          std::find(added_nodes.begin(), added_nodes.end(), node);
1456        if (it == added_nodes.end()) {
1457          clear();
1458          edge_observer_proxy.detach();
1459          throw NodeNotifier::ImmediateDetach();
1460        } else {
1461          added_nodes.erase(it);
1462        }
1463      }
1464
1465      void addEdge(const Edge& edge) {
1466        added_edges.push_front(edge);
1467      }
1468      void eraseEdge(const Edge& edge) {
1469        std::list<Edge>::iterator it =
1470          std::find(added_edges.begin(), added_edges.end(), edge);
1471        if (it == added_edges.end()) {
1472          clear();
1473          node_observer_proxy.detach();
1474          throw EdgeNotifier::ImmediateDetach();
1475        } else {
1476          added_edges.erase(it);
1477        }
1478      }
1479
1480      void attach(ListGraph &_graph) {
1481        graph = &_graph;
1482        node_observer_proxy.attach(graph->notifier(Node()));
1483        edge_observer_proxy.attach(graph->notifier(Edge()));
1484      }
1485
1486      void detach() {
1487        node_observer_proxy.detach();
1488        edge_observer_proxy.detach();
1489      }
1490
1491      bool attached() const {
1492        return node_observer_proxy.attached();
1493      }
1494
1495      void clear() {
1496        added_nodes.clear();
1497        added_edges.clear();
1498      }
1499
1500    public:
1501
1502      /// \brief Default constructor.
1503      ///
1504      /// Default constructor.
1505      /// To actually make a snapshot you must call save().
1506      Snapshot()
1507        : graph(0), node_observer_proxy(*this),
1508          edge_observer_proxy(*this) {}
1509
1510      /// \brief Constructor that immediately makes a snapshot.
1511      ///
1512      /// This constructor immediately makes a snapshot of the graph.
1513      /// \param _graph The graph we make a snapshot of.
1514      Snapshot(ListGraph &_graph)
1515        : node_observer_proxy(*this),
1516          edge_observer_proxy(*this) {
1517        attach(_graph);
1518      }
1519
1520      /// \brief Make a snapshot.
1521      ///
1522      /// Make a snapshot of the graph.
1523      ///
1524      /// This function can be called more than once. In case of a repeated
1525      /// call, the previous snapshot gets lost.
1526      /// \param _graph The graph we make the snapshot of.
1527      void save(ListGraph &_graph) {
1528        if (attached()) {
1529          detach();
1530          clear();
1531        }
1532        attach(_graph);
1533      }
1534
1535      /// \brief Undo the changes until the last snapshot.
1536      //
1537      /// Undo the changes until the last snapshot created by save().
1538      void restore() {
1539        detach();
1540        for(std::list<Edge>::iterator it = added_edges.begin();
1541            it != added_edges.end(); ++it) {
1542          graph->erase(*it);
1543        }
1544        for(std::list<Node>::iterator it = added_nodes.begin();
1545            it != added_nodes.end(); ++it) {
1546          graph->erase(*it);
1547        }
1548        clear();
1549      }
1550
1551      /// \brief Gives back true when the snapshot is valid.
1552      ///
1553      /// Gives back true when the snapshot is valid.
1554      bool valid() const {
1555        return attached();
1556      }
1557    };
1558  };
1559
1560  /// @}
1561} //namespace lemon
1562
1563
1564#endif
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