COIN-OR::LEMON - Graph Library

source: lemon/lemon/list_graph.h @ 1270:dceba191c00d

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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) 2003-2013
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_out == -1;
124          n = nodes[n].next) {}
125      arc.id = (n == -1) ? -1 : nodes[n].first_out;
126    }
127
128    void next(Arc& arc) const {
129      if (arcs[arc.id].next_out != -1) {
130        arc.id = arcs[arc.id].next_out;
131      } else {
132        int n;
133        for(n = nodes[arcs[arc.id].source].next;
134            n != -1 && nodes[n].first_out == -1;
135            n = nodes[n].next) {}
136        arc.id = (n == -1) ? -1 : nodes[n].first_out;
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  ///This class provides only linear time counting for nodes and arcs.
328  ///
329  ///\sa concepts::Digraph
330  ///\sa ListGraph
331  class ListDigraph : public ExtendedListDigraphBase {
332    typedef ExtendedListDigraphBase Parent;
333
334  private:
335    /// Digraphs are \e not copy constructible. Use DigraphCopy instead.
336    ListDigraph(const ListDigraph &) :ExtendedListDigraphBase() {};
337    /// \brief Assignment of a digraph to another one is \e not allowed.
338    /// Use DigraphCopy instead.
339    void operator=(const ListDigraph &) {}
340  public:
341
342    /// Constructor
343
344    /// Constructor.
345    ///
346    ListDigraph() {}
347
348    ///Add a new node to the digraph.
349
350    ///This function adds a new node to the digraph.
351    ///\return The new node.
352    Node addNode() { return Parent::addNode(); }
353
354    ///Add a new arc to the digraph.
355
356    ///This function adds a new arc to the digraph with source node \c s
357    ///and target node \c t.
358    ///\return The new arc.
359    Arc addArc(Node s, Node t) {
360      return Parent::addArc(s, t);
361    }
362
363    ///\brief Erase a node from the digraph.
364    ///
365    ///This function erases the given node along with its outgoing and
366    ///incoming arcs from the digraph.
367    ///
368    ///\note All iterators referencing the removed node or the connected
369    ///arcs are invalidated, of course.
370    void erase(Node n) { Parent::erase(n); }
371
372    ///\brief Erase an arc from the digraph.
373    ///
374    ///This function erases the given arc from the digraph.
375    ///
376    ///\note All iterators referencing the removed arc are invalidated,
377    ///of course.
378    void erase(Arc a) { Parent::erase(a); }
379
380    /// Node validity check
381
382    /// This function gives back \c true if the given node is valid,
383    /// i.e. it is a real node of the digraph.
384    ///
385    /// \warning A removed node could become valid again if new nodes are
386    /// added to the digraph.
387    bool valid(Node n) const { return Parent::valid(n); }
388
389    /// Arc validity check
390
391    /// This function gives back \c true if the given arc is valid,
392    /// i.e. it is a real arc of the digraph.
393    ///
394    /// \warning A removed arc could become valid again if new arcs are
395    /// added to the digraph.
396    bool valid(Arc a) const { return Parent::valid(a); }
397
398    /// Change the target node of an arc
399
400    /// This function changes the target node of the given arc \c a to \c n.
401    ///
402    ///\note \c ArcIt and \c OutArcIt iterators referencing the changed
403    ///arc remain valid, but \c InArcIt iterators are invalidated.
404    ///
405    ///\warning This functionality cannot be used together with the Snapshot
406    ///feature.
407    void changeTarget(Arc a, Node n) {
408      Parent::changeTarget(a,n);
409    }
410    /// Change the source node of an arc
411
412    /// This function changes the source node of the given arc \c a to \c n.
413    ///
414    ///\note \c InArcIt iterators referencing the changed arc remain
415    ///valid, but \c ArcIt and \c OutArcIt iterators are invalidated.
416    ///
417    ///\warning This functionality cannot be used together with the Snapshot
418    ///feature.
419    void changeSource(Arc a, Node n) {
420      Parent::changeSource(a,n);
421    }
422
423    /// Reverse the direction of an arc.
424
425    /// This function reverses the direction of the given arc.
426    ///\note \c ArcIt, \c OutArcIt and \c InArcIt iterators referencing
427    ///the changed arc are invalidated.
428    ///
429    ///\warning This functionality cannot be used together with the Snapshot
430    ///feature.
431    void reverseArc(Arc a) {
432      Node t=target(a);
433      changeTarget(a,source(a));
434      changeSource(a,t);
435    }
436
437    ///Contract two nodes.
438
439    ///This function contracts the given two nodes.
440    ///Node \c v is removed, but instead of deleting its
441    ///incident arcs, they are joined to node \c u.
442    ///If the last parameter \c r is \c true (this is the default value),
443    ///then the newly created loops are removed.
444    ///
445    ///\note The moved arcs are joined to node \c u using changeSource()
446    ///or changeTarget(), thus \c ArcIt and \c OutArcIt iterators are
447    ///invalidated for the outgoing arcs of node \c v and \c InArcIt
448    ///iterators are invalidated for the incoming arcs of \c v.
449    ///Moreover all iterators referencing node \c v or the removed
450    ///loops are also invalidated. Other iterators remain valid.
451    ///
452    ///\warning This functionality cannot be used together with the Snapshot
453    ///feature.
454    void contract(Node u, Node v, bool r = true)
455    {
456      for(OutArcIt e(*this,v);e!=INVALID;) {
457        OutArcIt f=e;
458        ++f;
459        if(r && target(e)==u) erase(e);
460        else changeSource(e,u);
461        e=f;
462      }
463      for(InArcIt e(*this,v);e!=INVALID;) {
464        InArcIt f=e;
465        ++f;
466        if(r && source(e)==u) erase(e);
467        else changeTarget(e,u);
468        e=f;
469      }
470      erase(v);
471    }
472
473    ///Split a node.
474
475    ///This function splits the given node. First, a new node is added
476    ///to the digraph, then the source of each outgoing arc of node \c n
477    ///is moved to this new node.
478    ///If the second parameter \c connect is \c true (this is the default
479    ///value), then a new arc from node \c n to the newly created node
480    ///is also added.
481    ///\return The newly created node.
482    ///
483    ///\note All iterators remain valid.
484    ///
485    ///\warning This functionality cannot be used together with the
486    ///Snapshot feature.
487    Node split(Node n, bool connect = true) {
488      Node b = addNode();
489      nodes[b.id].first_out=nodes[n.id].first_out;
490      nodes[n.id].first_out=-1;
491      for(int i=nodes[b.id].first_out; i!=-1; i=arcs[i].next_out) {
492        arcs[i].source=b.id;
493      }
494      if (connect) addArc(n,b);
495      return b;
496    }
497
498    ///Split an arc.
499
500    ///This function splits the given arc. First, a new node \c v is
501    ///added to the digraph, then the target node of the original arc
502    ///is set to \c v. Finally, an arc from \c v to the original target
503    ///is added.
504    ///\return The newly created node.
505    ///
506    ///\note \c InArcIt iterators referencing the original arc are
507    ///invalidated. Other iterators remain valid.
508    ///
509    ///\warning This functionality cannot be used together with the
510    ///Snapshot feature.
511    Node split(Arc a) {
512      Node v = addNode();
513      addArc(v,target(a));
514      changeTarget(a,v);
515      return v;
516    }
517
518    ///Clear the digraph.
519
520    ///This function erases all nodes and arcs from the digraph.
521    ///
522    ///\note All iterators of the digraph are invalidated, of course.
523    void clear() {
524      Parent::clear();
525    }
526
527    /// Reserve memory for nodes.
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 reserveArc()
535    void reserveNode(int n) { nodes.reserve(n); };
536
537    /// Reserve memory for arcs.
538
539    /// Using this function, it is possible to avoid superfluous memory
540    /// allocation: if you know that the digraph you want to build will
541    /// be large (e.g. it will contain millions of nodes and/or arcs),
542    /// then it is worth reserving space for this amount before starting
543    /// to build the digraph.
544    /// \sa reserveNode()
545    void reserveArc(int m) { arcs.reserve(m); };
546
547    /// \brief Class to make a snapshot of the digraph and restore
548    /// it later.
549    ///
550    /// Class to make a snapshot of the digraph and restore it later.
551    ///
552    /// The newly added nodes and arcs can be removed using the
553    /// restore() function.
554    ///
555    /// \note After a state is restored, you cannot restore a later state,
556    /// i.e. you cannot add the removed nodes and arcs again using
557    /// another Snapshot instance.
558    ///
559    /// \warning Node and arc deletions and other modifications (e.g.
560    /// reversing, contracting, splitting arcs or nodes) cannot be
561    /// restored. These events invalidate the snapshot.
562    /// However, the arcs and nodes that were added to the digraph after
563    /// making the current snapshot can be removed without invalidating it.
564    class Snapshot {
565    protected:
566
567      typedef Parent::NodeNotifier NodeNotifier;
568
569      class NodeObserverProxy : public NodeNotifier::ObserverBase {
570      public:
571
572        NodeObserverProxy(Snapshot& _snapshot)
573          : snapshot(_snapshot) {}
574
575        using NodeNotifier::ObserverBase::attach;
576        using NodeNotifier::ObserverBase::detach;
577        using NodeNotifier::ObserverBase::attached;
578
579      protected:
580
581        virtual void add(const Node& node) {
582          snapshot.addNode(node);
583        }
584        virtual void add(const std::vector<Node>& nodes) {
585          for (int i = nodes.size() - 1; i >= 0; ++i) {
586            snapshot.addNode(nodes[i]);
587          }
588        }
589        virtual void erase(const Node& node) {
590          snapshot.eraseNode(node);
591        }
592        virtual void erase(const std::vector<Node>& nodes) {
593          for (int i = 0; i < int(nodes.size()); ++i) {
594            snapshot.eraseNode(nodes[i]);
595          }
596        }
597        virtual void build() {
598          Node node;
599          std::vector<Node> nodes;
600          for (notifier()->first(node); node != INVALID;
601               notifier()->next(node)) {
602            nodes.push_back(node);
603          }
604          for (int i = nodes.size() - 1; i >= 0; --i) {
605            snapshot.addNode(nodes[i]);
606          }
607        }
608        virtual void clear() {
609          Node node;
610          for (notifier()->first(node); node != INVALID;
611               notifier()->next(node)) {
612            snapshot.eraseNode(node);
613          }
614        }
615
616        Snapshot& snapshot;
617      };
618
619      class ArcObserverProxy : public ArcNotifier::ObserverBase {
620      public:
621
622        ArcObserverProxy(Snapshot& _snapshot)
623          : snapshot(_snapshot) {}
624
625        using ArcNotifier::ObserverBase::attach;
626        using ArcNotifier::ObserverBase::detach;
627        using ArcNotifier::ObserverBase::attached;
628
629      protected:
630
631        virtual void add(const Arc& arc) {
632          snapshot.addArc(arc);
633        }
634        virtual void add(const std::vector<Arc>& arcs) {
635          for (int i = arcs.size() - 1; i >= 0; ++i) {
636            snapshot.addArc(arcs[i]);
637          }
638        }
639        virtual void erase(const Arc& arc) {
640          snapshot.eraseArc(arc);
641        }
642        virtual void erase(const std::vector<Arc>& arcs) {
643          for (int i = 0; i < int(arcs.size()); ++i) {
644            snapshot.eraseArc(arcs[i]);
645          }
646        }
647        virtual void build() {
648          Arc arc;
649          std::vector<Arc> arcs;
650          for (notifier()->first(arc); arc != INVALID;
651               notifier()->next(arc)) {
652            arcs.push_back(arc);
653          }
654          for (int i = arcs.size() - 1; i >= 0; --i) {
655            snapshot.addArc(arcs[i]);
656          }
657        }
658        virtual void clear() {
659          Arc arc;
660          for (notifier()->first(arc); arc != INVALID;
661               notifier()->next(arc)) {
662            snapshot.eraseArc(arc);
663          }
664        }
665
666        Snapshot& snapshot;
667      };
668
669      ListDigraph *digraph;
670
671      NodeObserverProxy node_observer_proxy;
672      ArcObserverProxy arc_observer_proxy;
673
674      std::list<Node> added_nodes;
675      std::list<Arc> added_arcs;
676
677
678      void addNode(const Node& node) {
679        added_nodes.push_front(node);
680      }
681      void eraseNode(const Node& node) {
682        std::list<Node>::iterator it =
683          std::find(added_nodes.begin(), added_nodes.end(), node);
684        if (it == added_nodes.end()) {
685          clear();
686          arc_observer_proxy.detach();
687          throw NodeNotifier::ImmediateDetach();
688        } else {
689          added_nodes.erase(it);
690        }
691      }
692
693      void addArc(const Arc& arc) {
694        added_arcs.push_front(arc);
695      }
696      void eraseArc(const Arc& arc) {
697        std::list<Arc>::iterator it =
698          std::find(added_arcs.begin(), added_arcs.end(), arc);
699        if (it == added_arcs.end()) {
700          clear();
701          node_observer_proxy.detach();
702          throw ArcNotifier::ImmediateDetach();
703        } else {
704          added_arcs.erase(it);
705        }
706      }
707
708      void attach(ListDigraph &_digraph) {
709        digraph = &_digraph;
710        node_observer_proxy.attach(digraph->notifier(Node()));
711        arc_observer_proxy.attach(digraph->notifier(Arc()));
712      }
713
714      void detach() {
715        node_observer_proxy.detach();
716        arc_observer_proxy.detach();
717      }
718
719      bool attached() const {
720        return node_observer_proxy.attached();
721      }
722
723      void clear() {
724        added_nodes.clear();
725        added_arcs.clear();
726      }
727
728    public:
729
730      /// \brief Default constructor.
731      ///
732      /// Default constructor.
733      /// You have to call save() to actually make a snapshot.
734      Snapshot()
735        : digraph(0), node_observer_proxy(*this),
736          arc_observer_proxy(*this) {}
737
738      /// \brief Constructor that immediately makes a snapshot.
739      ///
740      /// This constructor immediately makes a snapshot of the given digraph.
741      Snapshot(ListDigraph &gr)
742        : node_observer_proxy(*this),
743          arc_observer_proxy(*this) {
744        attach(gr);
745      }
746
747      /// \brief Make a snapshot.
748      ///
749      /// This function makes a snapshot of the given digraph.
750      /// It can be called more than once. In case of a repeated
751      /// call, the previous snapshot gets lost.
752      void save(ListDigraph &gr) {
753        if (attached()) {
754          detach();
755          clear();
756        }
757        attach(gr);
758      }
759
760      /// \brief Undo the changes until the last snapshot.
761      ///
762      /// This function undos the changes until the last snapshot
763      /// created by save() or Snapshot(ListDigraph&).
764      ///
765      /// \warning This method invalidates the snapshot, i.e. repeated
766      /// restoring is not supported unless you call save() again.
767      void restore() {
768        detach();
769        for(std::list<Arc>::iterator it = added_arcs.begin();
770            it != added_arcs.end(); ++it) {
771          digraph->erase(*it);
772        }
773        for(std::list<Node>::iterator it = added_nodes.begin();
774            it != added_nodes.end(); ++it) {
775          digraph->erase(*it);
776        }
777        clear();
778      }
779
780      /// \brief Returns \c true if the snapshot is valid.
781      ///
782      /// This function returns \c true if the snapshot is valid.
783      bool valid() const {
784        return attached();
785      }
786    };
787
788  };
789
790  ///@}
791
792  class ListGraphBase {
793
794  protected:
795
796    struct NodeT {
797      int first_out;
798      int prev, next;
799    };
800
801    struct ArcT {
802      int target;
803      int prev_out, next_out;
804    };
805
806    std::vector<NodeT> nodes;
807
808    int first_node;
809
810    int first_free_node;
811
812    std::vector<ArcT> arcs;
813
814    int first_free_arc;
815
816  public:
817
818    typedef ListGraphBase Graph;
819
820    class Node {
821      friend class ListGraphBase;
822    protected:
823
824      int id;
825      explicit Node(int pid) { id = pid;}
826
827    public:
828      Node() {}
829      Node (Invalid) { id = -1; }
830      bool operator==(const Node& node) const {return id == node.id;}
831      bool operator!=(const Node& node) const {return id != node.id;}
832      bool operator<(const Node& node) const {return id < node.id;}
833    };
834
835    class Edge {
836      friend class ListGraphBase;
837    protected:
838
839      int id;
840      explicit Edge(int pid) { id = pid;}
841
842    public:
843      Edge() {}
844      Edge (Invalid) { id = -1; }
845      bool operator==(const Edge& edge) const {return id == edge.id;}
846      bool operator!=(const Edge& edge) const {return id != edge.id;}
847      bool operator<(const Edge& edge) const {return id < edge.id;}
848    };
849
850    class Arc {
851      friend class ListGraphBase;
852    protected:
853
854      int id;
855      explicit Arc(int pid) { id = pid;}
856
857    public:
858      operator Edge() const {
859        return id != -1 ? edgeFromId(id / 2) : INVALID;
860      }
861
862      Arc() {}
863      Arc (Invalid) { id = -1; }
864      bool operator==(const Arc& arc) const {return id == arc.id;}
865      bool operator!=(const Arc& arc) const {return id != arc.id;}
866      bool operator<(const Arc& arc) const {return id < arc.id;}
867    };
868
869    ListGraphBase()
870      : nodes(), first_node(-1),
871        first_free_node(-1), arcs(), first_free_arc(-1) {}
872
873
874    int maxNodeId() const { return nodes.size()-1; }
875    int maxEdgeId() const { return arcs.size() / 2 - 1; }
876    int maxArcId() const { return arcs.size()-1; }
877
878    Node source(Arc e) const { return Node(arcs[e.id ^ 1].target); }
879    Node target(Arc e) const { return Node(arcs[e.id].target); }
880
881    Node u(Edge e) const { return Node(arcs[2 * e.id].target); }
882    Node v(Edge e) const { return Node(arcs[2 * e.id + 1].target); }
883
884    static bool direction(Arc e) {
885      return (e.id & 1) == 1;
886    }
887
888    static Arc direct(Edge e, bool d) {
889      return Arc(e.id * 2 + (d ? 1 : 0));
890    }
891
892    void first(Node& node) const {
893      node.id = first_node;
894    }
895
896    void next(Node& node) const {
897      node.id = nodes[node.id].next;
898    }
899
900    void first(Arc& e) const {
901      int n = first_node;
902      while (n != -1 && nodes[n].first_out == -1) {
903        n = nodes[n].next;
904      }
905      e.id = (n == -1) ? -1 : nodes[n].first_out;
906    }
907
908    void next(Arc& e) const {
909      if (arcs[e.id].next_out != -1) {
910        e.id = arcs[e.id].next_out;
911      } else {
912        int n = nodes[arcs[e.id ^ 1].target].next;
913        while(n != -1 && nodes[n].first_out == -1) {
914          n = nodes[n].next;
915        }
916        e.id = (n == -1) ? -1 : nodes[n].first_out;
917      }
918    }
919
920    void first(Edge& e) const {
921      int n = first_node;
922      while (n != -1) {
923        e.id = nodes[n].first_out;
924        while ((e.id & 1) != 1) {
925          e.id = arcs[e.id].next_out;
926        }
927        if (e.id != -1) {
928          e.id /= 2;
929          return;
930        }
931        n = nodes[n].next;
932      }
933      e.id = -1;
934    }
935
936    void next(Edge& e) const {
937      int n = arcs[e.id * 2].target;
938      e.id = arcs[(e.id * 2) | 1].next_out;
939      while ((e.id & 1) != 1) {
940        e.id = arcs[e.id].next_out;
941      }
942      if (e.id != -1) {
943        e.id /= 2;
944        return;
945      }
946      n = nodes[n].next;
947      while (n != -1) {
948        e.id = nodes[n].first_out;
949        while ((e.id & 1) != 1) {
950          e.id = arcs[e.id].next_out;
951        }
952        if (e.id != -1) {
953          e.id /= 2;
954          return;
955        }
956        n = nodes[n].next;
957      }
958      e.id = -1;
959    }
960
961    void firstOut(Arc &e, const Node& v) const {
962      e.id = nodes[v.id].first_out;
963    }
964    void nextOut(Arc &e) const {
965      e.id = arcs[e.id].next_out;
966    }
967
968    void firstIn(Arc &e, const Node& v) const {
969      e.id = ((nodes[v.id].first_out) ^ 1);
970      if (e.id == -2) e.id = -1;
971    }
972    void nextIn(Arc &e) const {
973      e.id = ((arcs[e.id ^ 1].next_out) ^ 1);
974      if (e.id == -2) e.id = -1;
975    }
976
977    void firstInc(Edge &e, bool& d, const Node& v) const {
978      int a = nodes[v.id].first_out;
979      if (a != -1 ) {
980        e.id = a / 2;
981        d = ((a & 1) == 1);
982      } else {
983        e.id = -1;
984        d = true;
985      }
986    }
987    void nextInc(Edge &e, bool& d) const {
988      int a = (arcs[(e.id * 2) | (d ? 1 : 0)].next_out);
989      if (a != -1 ) {
990        e.id = a / 2;
991        d = ((a & 1) == 1);
992      } else {
993        e.id = -1;
994        d = true;
995      }
996    }
997
998    static int id(Node v) { return v.id; }
999    static int id(Arc e) { return e.id; }
1000    static int id(Edge e) { return e.id; }
1001
1002    static Node nodeFromId(int id) { return Node(id);}
1003    static Arc arcFromId(int id) { return Arc(id);}
1004    static Edge edgeFromId(int id) { return Edge(id);}
1005
1006    bool valid(Node n) const {
1007      return n.id >= 0 && n.id < static_cast<int>(nodes.size()) &&
1008        nodes[n.id].prev != -2;
1009    }
1010
1011    bool valid(Arc a) const {
1012      return a.id >= 0 && a.id < static_cast<int>(arcs.size()) &&
1013        arcs[a.id].prev_out != -2;
1014    }
1015
1016    bool valid(Edge e) const {
1017      return e.id >= 0 && 2 * e.id < static_cast<int>(arcs.size()) &&
1018        arcs[2 * e.id].prev_out != -2;
1019    }
1020
1021    Node addNode() {
1022      int n;
1023
1024      if(first_free_node==-1) {
1025        n = nodes.size();
1026        nodes.push_back(NodeT());
1027      } else {
1028        n = first_free_node;
1029        first_free_node = nodes[n].next;
1030      }
1031
1032      nodes[n].next = first_node;
1033      if (first_node != -1) nodes[first_node].prev = n;
1034      first_node = n;
1035      nodes[n].prev = -1;
1036
1037      nodes[n].first_out = -1;
1038
1039      return Node(n);
1040    }
1041
1042    Edge addEdge(Node u, Node v) {
1043      int n;
1044
1045      if (first_free_arc == -1) {
1046        n = arcs.size();
1047        arcs.push_back(ArcT());
1048        arcs.push_back(ArcT());
1049      } else {
1050        n = first_free_arc;
1051        first_free_arc = arcs[n].next_out;
1052      }
1053
1054      arcs[n].target = u.id;
1055      arcs[n | 1].target = v.id;
1056
1057      arcs[n].next_out = nodes[v.id].first_out;
1058      if (nodes[v.id].first_out != -1) {
1059        arcs[nodes[v.id].first_out].prev_out = n;
1060      }
1061      arcs[n].prev_out = -1;
1062      nodes[v.id].first_out = n;
1063
1064      arcs[n | 1].next_out = nodes[u.id].first_out;
1065      if (nodes[u.id].first_out != -1) {
1066        arcs[nodes[u.id].first_out].prev_out = (n | 1);
1067      }
1068      arcs[n | 1].prev_out = -1;
1069      nodes[u.id].first_out = (n | 1);
1070
1071      return Edge(n / 2);
1072    }
1073
1074    void erase(const Node& node) {
1075      int n = node.id;
1076
1077      if(nodes[n].next != -1) {
1078        nodes[nodes[n].next].prev = nodes[n].prev;
1079      }
1080
1081      if(nodes[n].prev != -1) {
1082        nodes[nodes[n].prev].next = nodes[n].next;
1083      } else {
1084        first_node = nodes[n].next;
1085      }
1086
1087      nodes[n].next = first_free_node;
1088      first_free_node = n;
1089      nodes[n].prev = -2;
1090    }
1091
1092    void erase(const Edge& edge) {
1093      int n = edge.id * 2;
1094
1095      if (arcs[n].next_out != -1) {
1096        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
1097      }
1098
1099      if (arcs[n].prev_out != -1) {
1100        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
1101      } else {
1102        nodes[arcs[n | 1].target].first_out = arcs[n].next_out;
1103      }
1104
1105      if (arcs[n | 1].next_out != -1) {
1106        arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;
1107      }
1108
1109      if (arcs[n | 1].prev_out != -1) {
1110        arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;
1111      } else {
1112        nodes[arcs[n].target].first_out = arcs[n | 1].next_out;
1113      }
1114
1115      arcs[n].next_out = first_free_arc;
1116      first_free_arc = n;
1117      arcs[n].prev_out = -2;
1118      arcs[n | 1].prev_out = -2;
1119
1120    }
1121
1122    void clear() {
1123      arcs.clear();
1124      nodes.clear();
1125      first_node = first_free_node = first_free_arc = -1;
1126    }
1127
1128  protected:
1129
1130    void changeV(Edge e, Node n) {
1131      if(arcs[2 * e.id].next_out != -1) {
1132        arcs[arcs[2 * e.id].next_out].prev_out = arcs[2 * e.id].prev_out;
1133      }
1134      if(arcs[2 * e.id].prev_out != -1) {
1135        arcs[arcs[2 * e.id].prev_out].next_out =
1136          arcs[2 * e.id].next_out;
1137      } else {
1138        nodes[arcs[(2 * e.id) | 1].target].first_out =
1139          arcs[2 * e.id].next_out;
1140      }
1141
1142      if (nodes[n.id].first_out != -1) {
1143        arcs[nodes[n.id].first_out].prev_out = 2 * e.id;
1144      }
1145      arcs[(2 * e.id) | 1].target = n.id;
1146      arcs[2 * e.id].prev_out = -1;
1147      arcs[2 * e.id].next_out = nodes[n.id].first_out;
1148      nodes[n.id].first_out = 2 * e.id;
1149    }
1150
1151    void changeU(Edge e, Node n) {
1152      if(arcs[(2 * e.id) | 1].next_out != -1) {
1153        arcs[arcs[(2 * e.id) | 1].next_out].prev_out =
1154          arcs[(2 * e.id) | 1].prev_out;
1155      }
1156      if(arcs[(2 * e.id) | 1].prev_out != -1) {
1157        arcs[arcs[(2 * e.id) | 1].prev_out].next_out =
1158          arcs[(2 * e.id) | 1].next_out;
1159      } else {
1160        nodes[arcs[2 * e.id].target].first_out =
1161          arcs[(2 * e.id) | 1].next_out;
1162      }
1163
1164      if (nodes[n.id].first_out != -1) {
1165        arcs[nodes[n.id].first_out].prev_out = ((2 * e.id) | 1);
1166      }
1167      arcs[2 * e.id].target = n.id;
1168      arcs[(2 * e.id) | 1].prev_out = -1;
1169      arcs[(2 * e.id) | 1].next_out = nodes[n.id].first_out;
1170      nodes[n.id].first_out = ((2 * e.id) | 1);
1171    }
1172
1173  };
1174
1175  typedef GraphExtender<ListGraphBase> ExtendedListGraphBase;
1176
1177
1178  /// \addtogroup graphs
1179  /// @{
1180
1181  ///A general undirected graph structure.
1182
1183  ///\ref ListGraph is a versatile and fast undirected graph
1184  ///implementation based on linked lists that are stored in
1185  ///\c std::vector structures.
1186  ///
1187  ///This type fully conforms to the \ref concepts::Graph "Graph concept"
1188  ///and it also provides several useful additional functionalities.
1189  ///Most of its member functions and nested classes are documented
1190  ///only in the concept class.
1191  ///
1192  ///This class provides only linear time counting for nodes, edges and arcs.
1193  ///
1194  ///\sa concepts::Graph
1195  ///\sa ListDigraph
1196  class ListGraph : public ExtendedListGraphBase {
1197    typedef ExtendedListGraphBase Parent;
1198
1199  private:
1200    /// Graphs are \e not copy constructible. Use GraphCopy instead.
1201    ListGraph(const ListGraph &) :ExtendedListGraphBase()  {};
1202    /// \brief Assignment of a graph to another one is \e not allowed.
1203    /// Use GraphCopy instead.
1204    void operator=(const ListGraph &) {}
1205  public:
1206    /// Constructor
1207
1208    /// Constructor.
1209    ///
1210    ListGraph() {}
1211
1212    typedef Parent::OutArcIt IncEdgeIt;
1213
1214    /// \brief Add a new node to the graph.
1215    ///
1216    /// This function adds a new node to the graph.
1217    /// \return The new node.
1218    Node addNode() { return Parent::addNode(); }
1219
1220    /// \brief Add a new edge to the graph.
1221    ///
1222    /// This function adds a new edge to the graph between nodes
1223    /// \c u and \c v with inherent orientation from node \c u to
1224    /// node \c v.
1225    /// \return The new edge.
1226    Edge addEdge(Node u, Node v) {
1227      return Parent::addEdge(u, v);
1228    }
1229
1230    ///\brief Erase a node from the graph.
1231    ///
1232    /// This function erases the given node along with its incident arcs
1233    /// from the graph.
1234    ///
1235    /// \note All iterators referencing the removed node or the incident
1236    /// edges are invalidated, of course.
1237    void erase(Node n) { Parent::erase(n); }
1238
1239    ///\brief Erase an edge from the graph.
1240    ///
1241    /// This function erases the given edge from the graph.
1242    ///
1243    /// \note All iterators referencing the removed edge are invalidated,
1244    /// of course.
1245    void erase(Edge e) { Parent::erase(e); }
1246    /// Node validity check
1247
1248    /// This function gives back \c true if the given node is valid,
1249    /// i.e. it is a real node of the graph.
1250    ///
1251    /// \warning A removed node could become valid again if new nodes are
1252    /// added to the graph.
1253    bool valid(Node n) const { return Parent::valid(n); }
1254    /// Edge validity check
1255
1256    /// This function gives back \c true if the given edge is valid,
1257    /// i.e. it is a real edge of the graph.
1258    ///
1259    /// \warning A removed edge could become valid again if new edges are
1260    /// added to the graph.
1261    bool valid(Edge e) const { return Parent::valid(e); }
1262    /// Arc validity check
1263
1264    /// This function gives back \c true if the given arc is valid,
1265    /// i.e. it is a real arc of the graph.
1266    ///
1267    /// \warning A removed arc could become valid again if new edges are
1268    /// added to the graph.
1269    bool valid(Arc a) const { return Parent::valid(a); }
1270
1271    /// \brief Change the first node of an edge.
1272    ///
1273    /// This function changes the first node of the given edge \c e to \c n.
1274    ///
1275    ///\note \c EdgeIt and \c ArcIt iterators referencing the
1276    ///changed edge are invalidated and all other iterators whose
1277    ///base node is the changed node are also invalidated.
1278    ///
1279    ///\warning This functionality cannot be used together with the
1280    ///Snapshot feature.
1281    void changeU(Edge e, Node n) {
1282      Parent::changeU(e,n);
1283    }
1284    /// \brief Change the second node of an edge.
1285    ///
1286    /// This function changes the second node of the given edge \c e to \c n.
1287    ///
1288    ///\note \c EdgeIt iterators referencing the changed edge remain
1289    ///valid, but \c ArcIt iterators referencing the changed edge and
1290    ///all other iterators whose base node is the changed node are also
1291    ///invalidated.
1292    ///
1293    ///\warning This functionality cannot be used together with the
1294    ///Snapshot feature.
1295    void changeV(Edge e, Node n) {
1296      Parent::changeV(e,n);
1297    }
1298
1299    /// \brief Contract two nodes.
1300    ///
1301    /// This function contracts the given two nodes.
1302    /// Node \c b is removed, but instead of deleting
1303    /// its incident edges, they are joined to node \c a.
1304    /// If the last parameter \c r is \c true (this is the default value),
1305    /// then the newly created loops are removed.
1306    ///
1307    /// \note The moved edges are joined to node \c a using changeU()
1308    /// or changeV(), thus all edge and arc iterators whose base node is
1309    /// \c b are invalidated.
1310    /// Moreover all iterators referencing node \c b or the removed
1311    /// loops are also invalidated. Other iterators remain valid.
1312    ///
1313    ///\warning This functionality cannot be used together with the
1314    ///Snapshot feature.
1315    void contract(Node a, Node b, bool r = true) {
1316      for(IncEdgeIt e(*this, b); e!=INVALID;) {
1317        IncEdgeIt f = e; ++f;
1318        if (r && runningNode(e) == a) {
1319          erase(e);
1320        } else if (u(e) == b) {
1321          changeU(e, a);
1322        } else {
1323          changeV(e, a);
1324        }
1325        e = f;
1326      }
1327      erase(b);
1328    }
1329
1330    ///Clear the graph.
1331
1332    ///This function erases all nodes and arcs from the graph.
1333    ///
1334    ///\note All iterators of the graph are invalidated, of course.
1335    void clear() {
1336      Parent::clear();
1337    }
1338
1339    /// Reserve memory for nodes.
1340
1341    /// Using this function, it is possible to avoid superfluous memory
1342    /// allocation: if you know that the graph you want to build will
1343    /// be large (e.g. it will contain millions of nodes and/or edges),
1344    /// then it is worth reserving space for this amount before starting
1345    /// to build the graph.
1346    /// \sa reserveEdge()
1347    void reserveNode(int n) { nodes.reserve(n); };
1348
1349    /// Reserve memory for edges.
1350
1351    /// Using this function, it is possible to avoid superfluous memory
1352    /// allocation: if you know that the graph you want to build will
1353    /// be large (e.g. it will contain millions of nodes and/or edges),
1354    /// then it is worth reserving space for this amount before starting
1355    /// to build the graph.
1356    /// \sa reserveNode()
1357    void reserveEdge(int m) { arcs.reserve(2 * m); };
1358
1359    /// \brief Class to make a snapshot of the graph and restore
1360    /// it later.
1361    ///
1362    /// Class to make a snapshot of the graph and restore it later.
1363    ///
1364    /// The newly added nodes and edges can be removed
1365    /// using the restore() function.
1366    ///
1367    /// \note After a state is restored, you cannot restore a later state,
1368    /// i.e. you cannot add the removed nodes and edges again using
1369    /// another Snapshot instance.
1370    ///
1371    /// \warning Node and edge deletions and other modifications
1372    /// (e.g. changing the end-nodes of edges or contracting nodes)
1373    /// cannot be restored. These events invalidate the snapshot.
1374    /// However, the edges and nodes that were added to the graph after
1375    /// making the current snapshot can be removed without invalidating it.
1376    class Snapshot {
1377    protected:
1378
1379      typedef Parent::NodeNotifier NodeNotifier;
1380
1381      class NodeObserverProxy : public NodeNotifier::ObserverBase {
1382      public:
1383
1384        NodeObserverProxy(Snapshot& _snapshot)
1385          : snapshot(_snapshot) {}
1386
1387        using NodeNotifier::ObserverBase::attach;
1388        using NodeNotifier::ObserverBase::detach;
1389        using NodeNotifier::ObserverBase::attached;
1390
1391      protected:
1392
1393        virtual void add(const Node& node) {
1394          snapshot.addNode(node);
1395        }
1396        virtual void add(const std::vector<Node>& nodes) {
1397          for (int i = nodes.size() - 1; i >= 0; ++i) {
1398            snapshot.addNode(nodes[i]);
1399          }
1400        }
1401        virtual void erase(const Node& node) {
1402          snapshot.eraseNode(node);
1403        }
1404        virtual void erase(const std::vector<Node>& nodes) {
1405          for (int i = 0; i < int(nodes.size()); ++i) {
1406            snapshot.eraseNode(nodes[i]);
1407          }
1408        }
1409        virtual void build() {
1410          Node node;
1411          std::vector<Node> nodes;
1412          for (notifier()->first(node); node != INVALID;
1413               notifier()->next(node)) {
1414            nodes.push_back(node);
1415          }
1416          for (int i = nodes.size() - 1; i >= 0; --i) {
1417            snapshot.addNode(nodes[i]);
1418          }
1419        }
1420        virtual void clear() {
1421          Node node;
1422          for (notifier()->first(node); node != INVALID;
1423               notifier()->next(node)) {
1424            snapshot.eraseNode(node);
1425          }
1426        }
1427
1428        Snapshot& snapshot;
1429      };
1430
1431      class EdgeObserverProxy : public EdgeNotifier::ObserverBase {
1432      public:
1433
1434        EdgeObserverProxy(Snapshot& _snapshot)
1435          : snapshot(_snapshot) {}
1436
1437        using EdgeNotifier::ObserverBase::attach;
1438        using EdgeNotifier::ObserverBase::detach;
1439        using EdgeNotifier::ObserverBase::attached;
1440
1441      protected:
1442
1443        virtual void add(const Edge& edge) {
1444          snapshot.addEdge(edge);
1445        }
1446        virtual void add(const std::vector<Edge>& edges) {
1447          for (int i = edges.size() - 1; i >= 0; ++i) {
1448            snapshot.addEdge(edges[i]);
1449          }
1450        }
1451        virtual void erase(const Edge& edge) {
1452          snapshot.eraseEdge(edge);
1453        }
1454        virtual void erase(const std::vector<Edge>& edges) {
1455          for (int i = 0; i < int(edges.size()); ++i) {
1456            snapshot.eraseEdge(edges[i]);
1457          }
1458        }
1459        virtual void build() {
1460          Edge edge;
1461          std::vector<Edge> edges;
1462          for (notifier()->first(edge); edge != INVALID;
1463               notifier()->next(edge)) {
1464            edges.push_back(edge);
1465          }
1466          for (int i = edges.size() - 1; i >= 0; --i) {
1467            snapshot.addEdge(edges[i]);
1468          }
1469        }
1470        virtual void clear() {
1471          Edge edge;
1472          for (notifier()->first(edge); edge != INVALID;
1473               notifier()->next(edge)) {
1474            snapshot.eraseEdge(edge);
1475          }
1476        }
1477
1478        Snapshot& snapshot;
1479      };
1480
1481      ListGraph *graph;
1482
1483      NodeObserverProxy node_observer_proxy;
1484      EdgeObserverProxy edge_observer_proxy;
1485
1486      std::list<Node> added_nodes;
1487      std::list<Edge> added_edges;
1488
1489
1490      void addNode(const Node& node) {
1491        added_nodes.push_front(node);
1492      }
1493      void eraseNode(const Node& node) {
1494        std::list<Node>::iterator it =
1495          std::find(added_nodes.begin(), added_nodes.end(), node);
1496        if (it == added_nodes.end()) {
1497          clear();
1498          edge_observer_proxy.detach();
1499          throw NodeNotifier::ImmediateDetach();
1500        } else {
1501          added_nodes.erase(it);
1502        }
1503      }
1504
1505      void addEdge(const Edge& edge) {
1506        added_edges.push_front(edge);
1507      }
1508      void eraseEdge(const Edge& edge) {
1509        std::list<Edge>::iterator it =
1510          std::find(added_edges.begin(), added_edges.end(), edge);
1511        if (it == added_edges.end()) {
1512          clear();
1513          node_observer_proxy.detach();
1514          throw EdgeNotifier::ImmediateDetach();
1515        } else {
1516          added_edges.erase(it);
1517        }
1518      }
1519
1520      void attach(ListGraph &_graph) {
1521        graph = &_graph;
1522        node_observer_proxy.attach(graph->notifier(Node()));
1523        edge_observer_proxy.attach(graph->notifier(Edge()));
1524      }
1525
1526      void detach() {
1527        node_observer_proxy.detach();
1528        edge_observer_proxy.detach();
1529      }
1530
1531      bool attached() const {
1532        return node_observer_proxy.attached();
1533      }
1534
1535      void clear() {
1536        added_nodes.clear();
1537        added_edges.clear();
1538      }
1539
1540    public:
1541
1542      /// \brief Default constructor.
1543      ///
1544      /// Default constructor.
1545      /// You have to call save() to actually make a snapshot.
1546      Snapshot()
1547        : graph(0), node_observer_proxy(*this),
1548          edge_observer_proxy(*this) {}
1549
1550      /// \brief Constructor that immediately makes a snapshot.
1551      ///
1552      /// This constructor immediately makes a snapshot of the given graph.
1553      Snapshot(ListGraph &gr)
1554        : node_observer_proxy(*this),
1555          edge_observer_proxy(*this) {
1556        attach(gr);
1557      }
1558
1559      /// \brief Make a snapshot.
1560      ///
1561      /// This function makes a snapshot of the given graph.
1562      /// It can be called more than once. In case of a repeated
1563      /// call, the previous snapshot gets lost.
1564      void save(ListGraph &gr) {
1565        if (attached()) {
1566          detach();
1567          clear();
1568        }
1569        attach(gr);
1570      }
1571
1572      /// \brief Undo the changes until the last snapshot.
1573      ///
1574      /// This function undos the changes until the last snapshot
1575      /// created by save() or Snapshot(ListGraph&).
1576      ///
1577      /// \warning This method invalidates the snapshot, i.e. repeated
1578      /// restoring is not supported unless you call save() again.
1579      void restore() {
1580        detach();
1581        for(std::list<Edge>::iterator it = added_edges.begin();
1582            it != added_edges.end(); ++it) {
1583          graph->erase(*it);
1584        }
1585        for(std::list<Node>::iterator it = added_nodes.begin();
1586            it != added_nodes.end(); ++it) {
1587          graph->erase(*it);
1588        }
1589        clear();
1590      }
1591
1592      /// \brief Returns \c true if the snapshot is valid.
1593      ///
1594      /// This function returns \c true if the snapshot is valid.
1595      bool valid() const {
1596        return attached();
1597      }
1598    };
1599  };
1600
1601  /// @}
1602
1603  class ListBpGraphBase {
1604
1605  protected:
1606
1607    struct NodeT {
1608      int first_out;
1609      int prev, next;
1610      int partition_prev, partition_next;
1611      int partition_index;
1612      bool red;
1613    };
1614
1615    struct ArcT {
1616      int target;
1617      int prev_out, next_out;
1618    };
1619
1620    std::vector<NodeT> nodes;
1621
1622    int first_node, first_red, first_blue;
1623    int max_red, max_blue;
1624
1625    int first_free_red, first_free_blue;
1626
1627    std::vector<ArcT> arcs;
1628
1629    int first_free_arc;
1630
1631  public:
1632
1633    typedef ListBpGraphBase BpGraph;
1634
1635    class Node {
1636      friend class ListBpGraphBase;
1637    protected:
1638
1639      int id;
1640      explicit Node(int pid) { id = pid;}
1641
1642    public:
1643      Node() {}
1644      Node (Invalid) { id = -1; }
1645      bool operator==(const Node& node) const {return id == node.id;}
1646      bool operator!=(const Node& node) const {return id != node.id;}
1647      bool operator<(const Node& node) const {return id < node.id;}
1648    };
1649
1650    class RedNode : public Node {
1651      friend class ListBpGraphBase;
1652    protected:
1653
1654      explicit RedNode(int pid) : Node(pid) {}
1655
1656    public:
1657      RedNode() {}
1658      RedNode(const RedNode& node) : Node(node) {}
1659      RedNode(Invalid) : Node(INVALID){}
1660    };
1661
1662    class BlueNode : public Node {
1663      friend class ListBpGraphBase;
1664    protected:
1665
1666      explicit BlueNode(int pid) : Node(pid) {}
1667
1668    public:
1669      BlueNode() {}
1670      BlueNode(const BlueNode& node) : Node(node) {}
1671      BlueNode(Invalid) : Node(INVALID){}
1672    };
1673
1674    class Edge {
1675      friend class ListBpGraphBase;
1676    protected:
1677
1678      int id;
1679      explicit Edge(int pid) { id = pid;}
1680
1681    public:
1682      Edge() {}
1683      Edge (Invalid) { id = -1; }
1684      bool operator==(const Edge& edge) const {return id == edge.id;}
1685      bool operator!=(const Edge& edge) const {return id != edge.id;}
1686      bool operator<(const Edge& edge) const {return id < edge.id;}
1687    };
1688
1689    class Arc {
1690      friend class ListBpGraphBase;
1691    protected:
1692
1693      int id;
1694      explicit Arc(int pid) { id = pid;}
1695
1696    public:
1697      operator Edge() const {
1698        return id != -1 ? edgeFromId(id / 2) : INVALID;
1699      }
1700
1701      Arc() {}
1702      Arc (Invalid) { id = -1; }
1703      bool operator==(const Arc& arc) const {return id == arc.id;}
1704      bool operator!=(const Arc& arc) const {return id != arc.id;}
1705      bool operator<(const Arc& arc) const {return id < arc.id;}
1706    };
1707
1708    ListBpGraphBase()
1709      : nodes(), first_node(-1),
1710        first_red(-1), first_blue(-1),
1711        max_red(-1), max_blue(-1),
1712        first_free_red(-1), first_free_blue(-1),
1713        arcs(), first_free_arc(-1) {}
1714
1715
1716    bool red(Node n) const { return nodes[n.id].red; }
1717    bool blue(Node n) const { return !nodes[n.id].red; }
1718
1719    static RedNode asRedNodeUnsafe(Node n) { return RedNode(n.id); }
1720    static BlueNode asBlueNodeUnsafe(Node n) { return BlueNode(n.id); }
1721
1722    int maxNodeId() const { return nodes.size()-1; }
1723    int maxRedId() const { return max_red; }
1724    int maxBlueId() const { return max_blue; }
1725    int maxEdgeId() const { return arcs.size() / 2 - 1; }
1726    int maxArcId() const { return arcs.size()-1; }
1727
1728    Node source(Arc e) const { return Node(arcs[e.id ^ 1].target); }
1729    Node target(Arc e) const { return Node(arcs[e.id].target); }
1730
1731    RedNode redNode(Edge e) const {
1732      return RedNode(arcs[2 * e.id].target);
1733    }
1734    BlueNode blueNode(Edge e) const {
1735      return BlueNode(arcs[2 * e.id + 1].target);
1736    }
1737
1738    static bool direction(Arc e) {
1739      return (e.id & 1) == 1;
1740    }
1741
1742    static Arc direct(Edge e, bool d) {
1743      return Arc(e.id * 2 + (d ? 1 : 0));
1744    }
1745
1746    void first(Node& node) const {
1747      node.id = first_node;
1748    }
1749
1750    void next(Node& node) const {
1751      node.id = nodes[node.id].next;
1752    }
1753
1754    void first(RedNode& node) const {
1755      node.id = first_red;
1756    }
1757
1758    void next(RedNode& node) const {
1759      node.id = nodes[node.id].partition_next;
1760    }
1761
1762    void first(BlueNode& node) const {
1763      node.id = first_blue;
1764    }
1765
1766    void next(BlueNode& node) const {
1767      node.id = nodes[node.id].partition_next;
1768    }
1769
1770    void first(Arc& e) const {
1771      int n = first_node;
1772      while (n != -1 && nodes[n].first_out == -1) {
1773        n = nodes[n].next;
1774      }
1775      e.id = (n == -1) ? -1 : nodes[n].first_out;
1776    }
1777
1778    void next(Arc& e) const {
1779      if (arcs[e.id].next_out != -1) {
1780        e.id = arcs[e.id].next_out;
1781      } else {
1782        int n = nodes[arcs[e.id ^ 1].target].next;
1783        while(n != -1 && nodes[n].first_out == -1) {
1784          n = nodes[n].next;
1785        }
1786        e.id = (n == -1) ? -1 : nodes[n].first_out;
1787      }
1788    }
1789
1790    void first(Edge& e) const {
1791      int n = first_node;
1792      while (n != -1) {
1793        e.id = nodes[n].first_out;
1794        while ((e.id & 1) != 1) {
1795          e.id = arcs[e.id].next_out;
1796        }
1797        if (e.id != -1) {
1798          e.id /= 2;
1799          return;
1800        }
1801        n = nodes[n].next;
1802      }
1803      e.id = -1;
1804    }
1805
1806    void next(Edge& e) const {
1807      int n = arcs[e.id * 2].target;
1808      e.id = arcs[(e.id * 2) | 1].next_out;
1809      while ((e.id & 1) != 1) {
1810        e.id = arcs[e.id].next_out;
1811      }
1812      if (e.id != -1) {
1813        e.id /= 2;
1814        return;
1815      }
1816      n = nodes[n].next;
1817      while (n != -1) {
1818        e.id = nodes[n].first_out;
1819        while ((e.id & 1) != 1) {
1820          e.id = arcs[e.id].next_out;
1821        }
1822        if (e.id != -1) {
1823          e.id /= 2;
1824          return;
1825        }
1826        n = nodes[n].next;
1827      }
1828      e.id = -1;
1829    }
1830
1831    void firstOut(Arc &e, const Node& v) const {
1832      e.id = nodes[v.id].first_out;
1833    }
1834    void nextOut(Arc &e) const {
1835      e.id = arcs[e.id].next_out;
1836    }
1837
1838    void firstIn(Arc &e, const Node& v) const {
1839      e.id = ((nodes[v.id].first_out) ^ 1);
1840      if (e.id == -2) e.id = -1;
1841    }
1842    void nextIn(Arc &e) const {
1843      e.id = ((arcs[e.id ^ 1].next_out) ^ 1);
1844      if (e.id == -2) e.id = -1;
1845    }
1846
1847    void firstInc(Edge &e, bool& d, const Node& v) const {
1848      int a = nodes[v.id].first_out;
1849      if (a != -1 ) {
1850        e.id = a / 2;
1851        d = ((a & 1) == 1);
1852      } else {
1853        e.id = -1;
1854        d = true;
1855      }
1856    }
1857    void nextInc(Edge &e, bool& d) const {
1858      int a = (arcs[(e.id * 2) | (d ? 1 : 0)].next_out);
1859      if (a != -1 ) {
1860        e.id = a / 2;
1861        d = ((a & 1) == 1);
1862      } else {
1863        e.id = -1;
1864        d = true;
1865      }
1866    }
1867
1868    static int id(Node v) { return v.id; }
1869    int id(RedNode v) const { return nodes[v.id].partition_index; }
1870    int id(BlueNode v) const { return nodes[v.id].partition_index; }
1871    static int id(Arc e) { return e.id; }
1872    static int id(Edge e) { return e.id; }
1873
1874    static Node nodeFromId(int id) { return Node(id);}
1875    static Arc arcFromId(int id) { return Arc(id);}
1876    static Edge edgeFromId(int id) { return Edge(id);}
1877
1878    bool valid(Node n) const {
1879      return n.id >= 0 && n.id < static_cast<int>(nodes.size()) &&
1880        nodes[n.id].prev != -2;
1881    }
1882
1883    bool valid(Arc a) const {
1884      return a.id >= 0 && a.id < static_cast<int>(arcs.size()) &&
1885        arcs[a.id].prev_out != -2;
1886    }
1887
1888    bool valid(Edge e) const {
1889      return e.id >= 0 && 2 * e.id < static_cast<int>(arcs.size()) &&
1890        arcs[2 * e.id].prev_out != -2;
1891    }
1892
1893    RedNode addRedNode() {
1894      int n;
1895
1896      if(first_free_red==-1) {
1897        n = nodes.size();
1898        nodes.push_back(NodeT());
1899        nodes[n].partition_index = ++max_red;
1900        nodes[n].red = true;
1901      } else {
1902        n = first_free_red;
1903        first_free_red = nodes[n].next;
1904      }
1905
1906      nodes[n].next = first_node;
1907      if (first_node != -1) nodes[first_node].prev = n;
1908      first_node = n;
1909      nodes[n].prev = -1;
1910
1911      nodes[n].partition_next = first_red;
1912      if (first_red != -1) nodes[first_red].partition_prev = n;
1913      first_red = n;
1914      nodes[n].partition_prev = -1;
1915
1916      nodes[n].first_out = -1;
1917
1918      return RedNode(n);
1919    }
1920
1921    BlueNode addBlueNode() {
1922      int n;
1923
1924      if(first_free_blue==-1) {
1925        n = nodes.size();
1926        nodes.push_back(NodeT());
1927        nodes[n].partition_index = ++max_blue;
1928        nodes[n].red = false;
1929      } else {
1930        n = first_free_blue;
1931        first_free_blue = nodes[n].next;
1932      }
1933
1934      nodes[n].next = first_node;
1935      if (first_node != -1) nodes[first_node].prev = n;
1936      first_node = n;
1937      nodes[n].prev = -1;
1938
1939      nodes[n].partition_next = first_blue;
1940      if (first_blue != -1) nodes[first_blue].partition_prev = n;
1941      first_blue = n;
1942      nodes[n].partition_prev = -1;
1943
1944      nodes[n].first_out = -1;
1945
1946      return BlueNode(n);
1947    }
1948
1949    Edge addEdge(Node u, Node v) {
1950      int n;
1951
1952      if (first_free_arc == -1) {
1953        n = arcs.size();
1954        arcs.push_back(ArcT());
1955        arcs.push_back(ArcT());
1956      } else {
1957        n = first_free_arc;
1958        first_free_arc = arcs[n].next_out;
1959      }
1960
1961      arcs[n].target = u.id;
1962      arcs[n | 1].target = v.id;
1963
1964      arcs[n].next_out = nodes[v.id].first_out;
1965      if (nodes[v.id].first_out != -1) {
1966        arcs[nodes[v.id].first_out].prev_out = n;
1967      }
1968      arcs[n].prev_out = -1;
1969      nodes[v.id].first_out = n;
1970
1971      arcs[n | 1].next_out = nodes[u.id].first_out;
1972      if (nodes[u.id].first_out != -1) {
1973        arcs[nodes[u.id].first_out].prev_out = (n | 1);
1974      }
1975      arcs[n | 1].prev_out = -1;
1976      nodes[u.id].first_out = (n | 1);
1977
1978      return Edge(n / 2);
1979    }
1980
1981    void erase(const Node& node) {
1982      int n = node.id;
1983
1984      if(nodes[n].next != -1) {
1985        nodes[nodes[n].next].prev = nodes[n].prev;
1986      }
1987
1988      if(nodes[n].prev != -1) {
1989        nodes[nodes[n].prev].next = nodes[n].next;
1990      } else {
1991        first_node = nodes[n].next;
1992      }
1993
1994      if (nodes[n].partition_next != -1) {
1995        nodes[nodes[n].partition_next].partition_prev = nodes[n].partition_prev;
1996      }
1997
1998      if (nodes[n].partition_prev != -1) {
1999        nodes[nodes[n].partition_prev].partition_next = nodes[n].partition_next;
2000      } else {
2001        if (nodes[n].red) {
2002          first_red = nodes[n].partition_next;
2003        } else {
2004          first_blue = nodes[n].partition_next;
2005        }
2006      }
2007
2008      if (nodes[n].red) {
2009        nodes[n].next = first_free_red;
2010        first_free_red = n;
2011      } else {
2012        nodes[n].next = first_free_blue;
2013        first_free_blue = n;
2014      }
2015      nodes[n].prev = -2;
2016    }
2017
2018    void erase(const Edge& edge) {
2019      int n = edge.id * 2;
2020
2021      if (arcs[n].next_out != -1) {
2022        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;
2023      }
2024
2025      if (arcs[n].prev_out != -1) {
2026        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;
2027      } else {
2028        nodes[arcs[n | 1].target].first_out = arcs[n].next_out;
2029      }
2030
2031      if (arcs[n | 1].next_out != -1) {
2032        arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;
2033      }
2034
2035      if (arcs[n | 1].prev_out != -1) {
2036        arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;
2037      } else {
2038        nodes[arcs[n].target].first_out = arcs[n | 1].next_out;
2039      }
2040
2041      arcs[n].next_out = first_free_arc;
2042      first_free_arc = n;
2043      arcs[n].prev_out = -2;
2044      arcs[n | 1].prev_out = -2;
2045
2046    }
2047
2048    void clear() {
2049      arcs.clear();
2050      nodes.clear();
2051      first_node = first_free_arc = first_red = first_blue =
2052        max_red = max_blue = first_free_red = first_free_blue = -1;
2053    }
2054
2055  protected:
2056
2057    void changeRed(Edge e, RedNode n) {
2058      if(arcs[(2 * e.id) | 1].next_out != -1) {
2059        arcs[arcs[(2 * e.id) | 1].next_out].prev_out =
2060          arcs[(2 * e.id) | 1].prev_out;
2061      }
2062      if(arcs[(2 * e.id) | 1].prev_out != -1) {
2063        arcs[arcs[(2 * e.id) | 1].prev_out].next_out =
2064          arcs[(2 * e.id) | 1].next_out;
2065      } else {
2066        nodes[arcs[2 * e.id].target].first_out =
2067          arcs[(2 * e.id) | 1].next_out;
2068      }
2069
2070      if (nodes[n.id].first_out != -1) {
2071        arcs[nodes[n.id].first_out].prev_out = ((2 * e.id) | 1);
2072      }
2073      arcs[2 * e.id].target = n.id;
2074      arcs[(2 * e.id) | 1].prev_out = -1;
2075      arcs[(2 * e.id) | 1].next_out = nodes[n.id].first_out;
2076      nodes[n.id].first_out = ((2 * e.id) | 1);
2077    }
2078
2079    void changeBlue(Edge e, BlueNode n) {
2080       if(arcs[2 * e.id].next_out != -1) {
2081        arcs[arcs[2 * e.id].next_out].prev_out = arcs[2 * e.id].prev_out;
2082      }
2083      if(arcs[2 * e.id].prev_out != -1) {
2084        arcs[arcs[2 * e.id].prev_out].next_out =
2085          arcs[2 * e.id].next_out;
2086      } else {
2087        nodes[arcs[(2 * e.id) | 1].target].first_out =
2088          arcs[2 * e.id].next_out;
2089      }
2090
2091      if (nodes[n.id].first_out != -1) {
2092        arcs[nodes[n.id].first_out].prev_out = 2 * e.id;
2093      }
2094      arcs[(2 * e.id) | 1].target = n.id;
2095      arcs[2 * e.id].prev_out = -1;
2096      arcs[2 * e.id].next_out = nodes[n.id].first_out;
2097      nodes[n.id].first_out = 2 * e.id;
2098    }
2099
2100  };
2101
2102  typedef BpGraphExtender<ListBpGraphBase> ExtendedListBpGraphBase;
2103
2104
2105  /// \addtogroup graphs
2106  /// @{
2107
2108  ///A general undirected graph structure.
2109
2110  ///\ref ListBpGraph is a versatile and fast undirected graph
2111  ///implementation based on linked lists that are stored in
2112  ///\c std::vector structures.
2113  ///
2114  ///This type fully conforms to the \ref concepts::BpGraph "BpGraph concept"
2115  ///and it also provides several useful additional functionalities.
2116  ///Most of its member functions and nested classes are documented
2117  ///only in the concept class.
2118  ///
2119  ///This class provides only linear time counting for nodes, edges and arcs.
2120  ///
2121  ///\sa concepts::BpGraph
2122  ///\sa ListDigraph
2123  class ListBpGraph : public ExtendedListBpGraphBase {
2124    typedef ExtendedListBpGraphBase Parent;
2125
2126  private:
2127    /// BpGraphs are \e not copy constructible. Use BpGraphCopy instead.
2128    ListBpGraph(const ListBpGraph &) :ExtendedListBpGraphBase()  {};
2129    /// \brief Assignment of a graph to another one is \e not allowed.
2130    /// Use BpGraphCopy instead.
2131    void operator=(const ListBpGraph &) {}
2132  public:
2133    /// Constructor
2134
2135    /// Constructor.
2136    ///
2137    ListBpGraph() {}
2138
2139    typedef Parent::OutArcIt IncEdgeIt;
2140
2141    /// \brief Add a new red node to the graph.
2142    ///
2143    /// This function adds a red new node to the graph.
2144    /// \return The new node.
2145    RedNode addRedNode() { return Parent::addRedNode(); }
2146
2147    /// \brief Add a new blue node to the graph.
2148    ///
2149    /// This function adds a blue new node to the graph.
2150    /// \return The new node.
2151    BlueNode addBlueNode() { return Parent::addBlueNode(); }
2152
2153    /// \brief Add a new edge to the graph.
2154    ///
2155    /// This function adds a new edge to the graph between nodes
2156    /// \c u and \c v with inherent orientation from node \c u to
2157    /// node \c v.
2158    /// \return The new edge.
2159    Edge addEdge(RedNode u, BlueNode v) {
2160      return Parent::addEdge(u, v);
2161    }
2162    Edge addEdge(BlueNode v, RedNode u) {
2163      return Parent::addEdge(u, v);
2164    }
2165
2166    ///\brief Erase a node from the graph.
2167    ///
2168    /// This function erases the given node along with its incident arcs
2169    /// from the graph.
2170    ///
2171    /// \note All iterators referencing the removed node or the incident
2172    /// edges are invalidated, of course.
2173    void erase(Node n) { Parent::erase(n); }
2174
2175    ///\brief Erase an edge from the graph.
2176    ///
2177    /// This function erases the given edge from the graph.
2178    ///
2179    /// \note All iterators referencing the removed edge are invalidated,
2180    /// of course.
2181    void erase(Edge e) { Parent::erase(e); }
2182    /// Node validity check
2183
2184    /// This function gives back \c true if the given node is valid,
2185    /// i.e. it is a real node of the graph.
2186    ///
2187    /// \warning A removed node could become valid again if new nodes are
2188    /// added to the graph.
2189    bool valid(Node n) const { return Parent::valid(n); }
2190    /// Edge validity check
2191
2192    /// This function gives back \c true if the given edge is valid,
2193    /// i.e. it is a real edge of the graph.
2194    ///
2195    /// \warning A removed edge could become valid again if new edges are
2196    /// added to the graph.
2197    bool valid(Edge e) const { return Parent::valid(e); }
2198    /// Arc validity check
2199
2200    /// This function gives back \c true if the given arc is valid,
2201    /// i.e. it is a real arc of the graph.
2202    ///
2203    /// \warning A removed arc could become valid again if new edges are
2204    /// added to the graph.
2205    bool valid(Arc a) const { return Parent::valid(a); }
2206
2207    /// \brief Change the red node of an edge.
2208    ///
2209    /// This function changes the red node of the given edge \c e to \c n.
2210    ///
2211    ///\note \c EdgeIt and \c ArcIt iterators referencing the
2212    ///changed edge are invalidated and all other iterators whose
2213    ///base node is the changed node are also invalidated.
2214    ///
2215    ///\warning This functionality cannot be used together with the
2216    ///Snapshot feature.
2217    void changeRed(Edge e, RedNode n) {
2218      Parent::changeRed(e, n);
2219    }
2220    /// \brief Change the blue node of an edge.
2221    ///
2222    /// This function changes the blue node of the given edge \c e to \c n.
2223    ///
2224    ///\note \c EdgeIt iterators referencing the changed edge remain
2225    ///valid, but \c ArcIt iterators referencing the changed edge and
2226    ///all other iterators whose base node is the changed node are also
2227    ///invalidated.
2228    ///
2229    ///\warning This functionality cannot be used together with the
2230    ///Snapshot feature.
2231    void changeBlue(Edge e, BlueNode n) {
2232      Parent::changeBlue(e, n);
2233    }
2234
2235    ///Clear the graph.
2236
2237    ///This function erases all nodes and arcs from the graph.
2238    ///
2239    ///\note All iterators of the graph are invalidated, of course.
2240    void clear() {
2241      Parent::clear();
2242    }
2243
2244    /// Reserve memory for nodes.
2245
2246    /// Using this function, it is possible to avoid superfluous memory
2247    /// allocation: if you know that the graph you want to build will
2248    /// be large (e.g. it will contain millions of nodes and/or edges),
2249    /// then it is worth reserving space for this amount before starting
2250    /// to build the graph.
2251    /// \sa reserveEdge()
2252    void reserveNode(int n) { nodes.reserve(n); };
2253
2254    /// Reserve memory for edges.
2255
2256    /// Using this function, it is possible to avoid superfluous memory
2257    /// allocation: if you know that the graph you want to build will
2258    /// be large (e.g. it will contain millions of nodes and/or edges),
2259    /// then it is worth reserving space for this amount before starting
2260    /// to build the graph.
2261    /// \sa reserveNode()
2262    void reserveEdge(int m) { arcs.reserve(2 * m); };
2263
2264    /// \brief Class to make a snapshot of the graph and restore
2265    /// it later.
2266    ///
2267    /// Class to make a snapshot of the graph and restore it later.
2268    ///
2269    /// The newly added nodes and edges can be removed
2270    /// using the restore() function.
2271    ///
2272    /// \note After a state is restored, you cannot restore a later state,
2273    /// i.e. you cannot add the removed nodes and edges again using
2274    /// another Snapshot instance.
2275    ///
2276    /// \warning Node and edge deletions and other modifications
2277    /// (e.g. changing the end-nodes of edges or contracting nodes)
2278    /// cannot be restored. These events invalidate the snapshot.
2279    /// However, the edges and nodes that were added to the graph after
2280    /// making the current snapshot can be removed without invalidating it.
2281    class Snapshot {
2282    protected:
2283
2284      typedef Parent::NodeNotifier NodeNotifier;
2285
2286      class NodeObserverProxy : public NodeNotifier::ObserverBase {
2287      public:
2288
2289        NodeObserverProxy(Snapshot& _snapshot)
2290          : snapshot(_snapshot) {}
2291
2292        using NodeNotifier::ObserverBase::attach;
2293        using NodeNotifier::ObserverBase::detach;
2294        using NodeNotifier::ObserverBase::attached;
2295
2296      protected:
2297
2298        virtual void add(const Node& node) {
2299          snapshot.addNode(node);
2300        }
2301        virtual void add(const std::vector<Node>& nodes) {
2302          for (int i = nodes.size() - 1; i >= 0; ++i) {
2303            snapshot.addNode(nodes[i]);
2304          }
2305        }
2306        virtual void erase(const Node& node) {
2307          snapshot.eraseNode(node);
2308        }
2309        virtual void erase(const std::vector<Node>& nodes) {
2310          for (int i = 0; i < int(nodes.size()); ++i) {
2311            snapshot.eraseNode(nodes[i]);
2312          }
2313        }
2314        virtual void build() {
2315          Node node;
2316          std::vector<Node> nodes;
2317          for (notifier()->first(node); node != INVALID;
2318               notifier()->next(node)) {
2319            nodes.push_back(node);
2320          }
2321          for (int i = nodes.size() - 1; i >= 0; --i) {
2322            snapshot.addNode(nodes[i]);
2323          }
2324        }
2325        virtual void clear() {
2326          Node node;
2327          for (notifier()->first(node); node != INVALID;
2328               notifier()->next(node)) {
2329            snapshot.eraseNode(node);
2330          }
2331        }
2332
2333        Snapshot& snapshot;
2334      };
2335
2336      class EdgeObserverProxy : public EdgeNotifier::ObserverBase {
2337      public:
2338
2339        EdgeObserverProxy(Snapshot& _snapshot)
2340          : snapshot(_snapshot) {}
2341
2342        using EdgeNotifier::ObserverBase::attach;
2343        using EdgeNotifier::ObserverBase::detach;
2344        using EdgeNotifier::ObserverBase::attached;
2345
2346      protected:
2347
2348        virtual void add(const Edge& edge) {
2349          snapshot.addEdge(edge);
2350        }
2351        virtual void add(const std::vector<Edge>& edges) {
2352          for (int i = edges.size() - 1; i >= 0; ++i) {
2353            snapshot.addEdge(edges[i]);
2354          }
2355        }
2356        virtual void erase(const Edge& edge) {
2357          snapshot.eraseEdge(edge);
2358        }
2359        virtual void erase(const std::vector<Edge>& edges) {
2360          for (int i = 0; i < int(edges.size()); ++i) {
2361            snapshot.eraseEdge(edges[i]);
2362          }
2363        }
2364        virtual void build() {
2365          Edge edge;
2366          std::vector<Edge> edges;
2367          for (notifier()->first(edge); edge != INVALID;
2368               notifier()->next(edge)) {
2369            edges.push_back(edge);
2370          }
2371          for (int i = edges.size() - 1; i >= 0; --i) {
2372            snapshot.addEdge(edges[i]);
2373          }
2374        }
2375        virtual void clear() {
2376          Edge edge;
2377          for (notifier()->first(edge); edge != INVALID;
2378               notifier()->next(edge)) {
2379            snapshot.eraseEdge(edge);
2380          }
2381        }
2382
2383        Snapshot& snapshot;
2384      };
2385
2386      ListBpGraph *graph;
2387
2388      NodeObserverProxy node_observer_proxy;
2389      EdgeObserverProxy edge_observer_proxy;
2390
2391      std::list<Node> added_nodes;
2392      std::list<Edge> added_edges;
2393
2394
2395      void addNode(const Node& node) {
2396        added_nodes.push_front(node);
2397      }
2398      void eraseNode(const Node& node) {
2399        std::list<Node>::iterator it =
2400          std::find(added_nodes.begin(), added_nodes.end(), node);
2401        if (it == added_nodes.end()) {
2402          clear();
2403          edge_observer_proxy.detach();
2404          throw NodeNotifier::ImmediateDetach();
2405        } else {
2406          added_nodes.erase(it);
2407        }
2408      }
2409
2410      void addEdge(const Edge& edge) {
2411        added_edges.push_front(edge);
2412      }
2413      void eraseEdge(const Edge& edge) {
2414        std::list<Edge>::iterator it =
2415          std::find(added_edges.begin(), added_edges.end(), edge);
2416        if (it == added_edges.end()) {
2417          clear();
2418          node_observer_proxy.detach();
2419          throw EdgeNotifier::ImmediateDetach();
2420        } else {
2421          added_edges.erase(it);
2422        }
2423      }
2424
2425      void attach(ListBpGraph &_graph) {
2426        graph = &_graph;
2427        node_observer_proxy.attach(graph->notifier(Node()));
2428        edge_observer_proxy.attach(graph->notifier(Edge()));
2429      }
2430
2431      void detach() {
2432        node_observer_proxy.detach();
2433        edge_observer_proxy.detach();
2434      }
2435
2436      bool attached() const {
2437        return node_observer_proxy.attached();
2438      }
2439
2440      void clear() {
2441        added_nodes.clear();
2442        added_edges.clear();
2443      }
2444
2445    public:
2446
2447      /// \brief Default constructor.
2448      ///
2449      /// Default constructor.
2450      /// You have to call save() to actually make a snapshot.
2451      Snapshot()
2452        : graph(0), node_observer_proxy(*this),
2453          edge_observer_proxy(*this) {}
2454
2455      /// \brief Constructor that immediately makes a snapshot.
2456      ///
2457      /// This constructor immediately makes a snapshot of the given graph.
2458      Snapshot(ListBpGraph &gr)
2459        : node_observer_proxy(*this),
2460          edge_observer_proxy(*this) {
2461        attach(gr);
2462      }
2463
2464      /// \brief Make a snapshot.
2465      ///
2466      /// This function makes a snapshot of the given graph.
2467      /// It can be called more than once. In case of a repeated
2468      /// call, the previous snapshot gets lost.
2469      void save(ListBpGraph &gr) {
2470        if (attached()) {
2471          detach();
2472          clear();
2473        }
2474        attach(gr);
2475      }
2476
2477      /// \brief Undo the changes until the last snapshot.
2478      ///
2479      /// This function undos the changes until the last snapshot
2480      /// created by save() or Snapshot(ListBpGraph&).
2481      ///
2482      /// \warning This method invalidates the snapshot, i.e. repeated
2483      /// restoring is not supported unless you call save() again.
2484      void restore() {
2485        detach();
2486        for(std::list<Edge>::iterator it = added_edges.begin();
2487            it != added_edges.end(); ++it) {
2488          graph->erase(*it);
2489        }
2490        for(std::list<Node>::iterator it = added_nodes.begin();
2491            it != added_nodes.end(); ++it) {
2492          graph->erase(*it);
2493        }
2494        clear();
2495      }
2496
2497      /// \brief Returns \c true if the snapshot is valid.
2498      ///
2499      /// This function returns \c true if the snapshot is valid.
2500      bool valid() const {
2501        return attached();
2502      }
2503    };
2504  };
2505
2506  /// @}
2507} //namespace lemon
2508
2509
2510#endif
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