COIN-OR::LEMON - Graph Library

source: lemon/lemon/concepts/graph.h @ 1369:9fd86ec2cb81

Last change on this file since 1369:9fd86ec2cb81 was 1336:0759d974de81, checked in by Gabor Gevay <ggab90@…>, 6 years ago

STL style iterators (#325)

For

  • graph types,
  • graph adaptors,
  • paths,
  • iterable maps,
  • LP rows/cols and
  • active nodes is BellmanFord?
File size: 29.9 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2013
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///\ingroup graph_concepts
20///\file
21///\brief The concept of undirected graphs.
22
23#ifndef LEMON_CONCEPTS_GRAPH_H
24#define LEMON_CONCEPTS_GRAPH_H
25
26#include <lemon/concepts/graph_components.h>
27#include <lemon/concepts/maps.h>
28#include <lemon/concept_check.h>
29#include <lemon/core.h>
30#include <lemon/bits/stl_iterators.h>
31
32namespace lemon {
33  namespace concepts {
34
35    /// \ingroup graph_concepts
36    ///
37    /// \brief Class describing the concept of undirected graphs.
38    ///
39    /// This class describes the common interface of all undirected
40    /// graphs.
41    ///
42    /// Like all concept classes, it only provides an interface
43    /// without any sensible implementation. So any general algorithm for
44    /// undirected graphs should compile with this class, but it will not
45    /// run properly, of course.
46    /// An actual graph implementation like \ref ListGraph or
47    /// \ref SmartGraph may have additional functionality.
48    ///
49    /// The undirected graphs also fulfill the concept of \ref Digraph
50    /// "directed graphs", since each edge can also be regarded as two
51    /// oppositely directed arcs.
52    /// Undirected graphs provide an Edge type for the undirected edges and
53    /// an Arc type for the directed arcs. The Arc type is convertible to
54    /// Edge or inherited from it, i.e. the corresponding edge can be
55    /// obtained from an arc.
56    /// EdgeIt and EdgeMap classes can be used for the edges, while ArcIt
57    /// and ArcMap classes can be used for the arcs (just like in digraphs).
58    /// Both InArcIt and OutArcIt iterates on the same edges but with
59    /// opposite direction. IncEdgeIt also iterates on the same edges
60    /// as OutArcIt and InArcIt, but it is not convertible to Arc,
61    /// only to Edge.
62    ///
63    /// In LEMON, each undirected edge has an inherent orientation.
64    /// Thus it can defined if an arc is forward or backward oriented in
65    /// an undirected graph with respect to this default oriantation of
66    /// the represented edge.
67    /// With the direction() and direct() functions the direction
68    /// of an arc can be obtained and set, respectively.
69    ///
70    /// Only nodes and edges can be added to or removed from an undirected
71    /// graph and the corresponding arcs are added or removed automatically.
72    ///
73    /// \sa Digraph
74    class Graph {
75    private:
76      /// Graphs are \e not copy constructible. Use GraphCopy instead.
77      Graph(const Graph&) {}
78      /// \brief Assignment of a graph to another one is \e not allowed.
79      /// Use GraphCopy instead.
80      void operator=(const Graph&) {}
81
82    public:
83      /// Default constructor.
84      Graph() {}
85
86      /// \brief Undirected graphs should be tagged with \c UndirectedTag.
87      ///
88      /// Undirected graphs should be tagged with \c UndirectedTag.
89      ///
90      /// This tag helps the \c enable_if technics to make compile time
91      /// specializations for undirected graphs.
92      typedef True UndirectedTag;
93
94      /// The node type of the graph
95
96      /// This class identifies a node of the graph. It also serves
97      /// as a base class of the node iterators,
98      /// thus they convert to this type.
99      class Node {
100      public:
101        /// Default constructor
102
103        /// Default constructor.
104        /// \warning It sets the object to an undefined value.
105        Node() { }
106        /// Copy constructor.
107
108        /// Copy constructor.
109        ///
110        Node(const Node&) { }
111
112        /// %Invalid constructor \& conversion.
113
114        /// Initializes the object to be invalid.
115        /// \sa Invalid for more details.
116        Node(Invalid) { }
117        /// Equality operator
118
119        /// Equality operator.
120        ///
121        /// Two iterators are equal if and only if they point to the
122        /// same object or both are \c INVALID.
123        bool operator==(Node) const { return true; }
124
125        /// Inequality operator
126
127        /// Inequality operator.
128        bool operator!=(Node) const { return true; }
129
130        /// Artificial ordering operator.
131
132        /// Artificial ordering operator.
133        ///
134        /// \note This operator only has to define some strict ordering of
135        /// the items; this order has nothing to do with the iteration
136        /// ordering of the items.
137        bool operator<(Node) const { return false; }
138
139      };
140
141      /// Iterator class for the nodes.
142
143      /// This iterator goes through each node of the graph.
144      /// Its usage is quite simple, for example, you can count the number
145      /// of nodes in a graph \c g of type \c %Graph like this:
146      ///\code
147      /// int count=0;
148      /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;
149      ///\endcode
150      class NodeIt : public Node {
151      public:
152        /// Default constructor
153
154        /// Default constructor.
155        /// \warning It sets the iterator to an undefined value.
156        NodeIt() { }
157        /// Copy constructor.
158
159        /// Copy constructor.
160        ///
161        NodeIt(const NodeIt& n) : Node(n) { }
162        /// %Invalid constructor \& conversion.
163
164        /// Initializes the iterator to be invalid.
165        /// \sa Invalid for more details.
166        NodeIt(Invalid) { }
167        /// Sets the iterator to the first node.
168
169        /// Sets the iterator to the first node of the given digraph.
170        ///
171        explicit NodeIt(const Graph&) { }
172        /// Sets the iterator to the given node.
173
174        /// Sets the iterator to the given node of the given digraph.
175        ///
176        NodeIt(const Graph&, const Node&) { }
177        /// Next node.
178
179        /// Assign the iterator to the next node.
180        ///
181        NodeIt& operator++() { return *this; }
182      };
183
184      /// \brief Gets the collection of the nodes of the graph.
185      ///
186      /// This function can be used for iterating on
187      /// the nodes of the graph. It returns a wrapped NodeIt, which looks
188      /// like an STL container (by having begin() and end())
189      /// which you can use in range-based for loops, STL algorithms, etc.
190      /// For example you can write:
191      ///\code
192      /// ListGraph g;
193      /// for(auto v: g.nodes())
194      ///   doSomething(v);
195      ///
196      /// //Using an STL algorithm:
197      /// copy(g.nodes().begin(), g.nodes().end(), vect.begin());
198      ///\endcode
199      LemonRangeWrapper1<NodeIt, Graph> nodes() const {
200        return LemonRangeWrapper1<NodeIt, Graph>(*this);
201      }
202
203
204      /// The edge type of the graph
205
206      /// This class identifies an edge of the graph. It also serves
207      /// as a base class of the edge iterators,
208      /// thus they will convert to this type.
209      class Edge {
210      public:
211        /// Default constructor
212
213        /// Default constructor.
214        /// \warning It sets the object to an undefined value.
215        Edge() { }
216        /// Copy constructor.
217
218        /// Copy constructor.
219        ///
220        Edge(const Edge&) { }
221        /// %Invalid constructor \& conversion.
222
223        /// Initializes the object to be invalid.
224        /// \sa Invalid for more details.
225        Edge(Invalid) { }
226        /// Equality operator
227
228        /// Equality operator.
229        ///
230        /// Two iterators are equal if and only if they point to the
231        /// same object or both are \c INVALID.
232        bool operator==(Edge) const { return true; }
233        /// Inequality operator
234
235        /// Inequality operator.
236        bool operator!=(Edge) const { return true; }
237
238        /// Artificial ordering operator.
239
240        /// Artificial ordering operator.
241        ///
242        /// \note This operator only has to define some strict ordering of
243        /// the edges; this order has nothing to do with the iteration
244        /// ordering of the edges.
245        bool operator<(Edge) const { return false; }
246      };
247
248      /// Iterator class for the edges.
249
250      /// This iterator goes through each edge of the graph.
251      /// Its usage is quite simple, for example, you can count the number
252      /// of edges in a graph \c g of type \c %Graph as follows:
253      ///\code
254      /// int count=0;
255      /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;
256      ///\endcode
257      class EdgeIt : public Edge {
258      public:
259        /// Default constructor
260
261        /// Default constructor.
262        /// \warning It sets the iterator to an undefined value.
263        EdgeIt() { }
264        /// Copy constructor.
265
266        /// Copy constructor.
267        ///
268        EdgeIt(const EdgeIt& e) : Edge(e) { }
269        /// %Invalid constructor \& conversion.
270
271        /// Initializes the iterator to be invalid.
272        /// \sa Invalid for more details.
273        EdgeIt(Invalid) { }
274        /// Sets the iterator to the first edge.
275
276        /// Sets the iterator to the first edge of the given graph.
277        ///
278        explicit EdgeIt(const Graph&) { }
279        /// Sets the iterator to the given edge.
280
281        /// Sets the iterator to the given edge of the given graph.
282        ///
283        EdgeIt(const Graph&, const Edge&) { }
284        /// Next edge
285
286        /// Assign the iterator to the next edge.
287        ///
288        EdgeIt& operator++() { return *this; }
289      };
290
291      /// \brief Gets the collection of the edges of the graph.
292      ///
293      /// This function can be used for iterating on the
294      /// edges of the graph. It returns a wrapped
295      /// EdgeIt, which looks like an STL container
296      /// (by having begin() and end()) which you can use in range-based
297      /// for loops, STL algorithms, etc.
298      /// For example you can write:
299      ///\code
300      /// ListGraph g;
301      /// for(auto e: g.edges())
302      ///   doSomething(e);
303      ///
304      /// //Using an STL algorithm:
305      /// copy(g.edges().begin(), g.edges().end(), vect.begin());
306      ///\endcode
307      LemonRangeWrapper1<EdgeIt, Graph> edges() const {
308        return LemonRangeWrapper1<EdgeIt, Graph>(*this);
309      }
310
311
312      /// Iterator class for the incident edges of a node.
313
314      /// This iterator goes trough the incident undirected edges
315      /// of a certain node of a graph.
316      /// Its usage is quite simple, for example, you can compute the
317      /// degree (i.e. the number of incident edges) of a node \c n
318      /// in a graph \c g of type \c %Graph as follows.
319      ///
320      ///\code
321      /// int count=0;
322      /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;
323      ///\endcode
324      ///
325      /// \warning Loop edges will be iterated twice.
326      class IncEdgeIt : public Edge {
327      public:
328        /// Default constructor
329
330        /// Default constructor.
331        /// \warning It sets the iterator to an undefined value.
332        IncEdgeIt() { }
333        /// Copy constructor.
334
335        /// Copy constructor.
336        ///
337        IncEdgeIt(const IncEdgeIt& e) : Edge(e) { }
338        /// %Invalid constructor \& conversion.
339
340        /// Initializes the iterator to be invalid.
341        /// \sa Invalid for more details.
342        IncEdgeIt(Invalid) { }
343        /// Sets the iterator to the first incident edge.
344
345        /// Sets the iterator to the first incident edge of the given node.
346        ///
347        IncEdgeIt(const Graph&, const Node&) { }
348        /// Sets the iterator to the given edge.
349
350        /// Sets the iterator to the given edge of the given graph.
351        ///
352        IncEdgeIt(const Graph&, const Edge&) { }
353        /// Next incident edge
354
355        /// Assign the iterator to the next incident edge
356        /// of the corresponding node.
357        IncEdgeIt& operator++() { return *this; }
358      };
359
360      /// \brief Gets the collection of the incident undirected edges
361      ///  of a certain node of the graph.
362      ///
363      /// This function can be used for iterating on the
364      /// incident undirected edges of a certain node of the graph.
365      /// It returns a wrapped
366      /// IncEdgeIt, which looks like an STL container
367      /// (by having begin() and end()) which you can use in range-based
368      /// for loops, STL algorithms, etc.
369      /// For example if g is a Graph and u is a Node, you can write:
370      ///\code
371      /// for(auto e: g.incEdges(u))
372      ///   doSomething(e);
373      ///
374      /// //Using an STL algorithm:
375      /// copy(g.incEdges(u).begin(), g.incEdges(u).end(), vect.begin());
376      ///\endcode
377      LemonRangeWrapper2<IncEdgeIt, Graph, Node> incEdges(const Node& u) const {
378        return LemonRangeWrapper2<IncEdgeIt, Graph, Node>(*this, u);
379      }
380
381
382      /// The arc type of the graph
383
384      /// This class identifies a directed arc of the graph. It also serves
385      /// as a base class of the arc iterators,
386      /// thus they will convert to this type.
387      class Arc {
388      public:
389        /// Default constructor
390
391        /// Default constructor.
392        /// \warning It sets the object to an undefined value.
393        Arc() { }
394        /// Copy constructor.
395
396        /// Copy constructor.
397        ///
398        Arc(const Arc&) { }
399        /// %Invalid constructor \& conversion.
400
401        /// Initializes the object to be invalid.
402        /// \sa Invalid for more details.
403        Arc(Invalid) { }
404        /// Equality operator
405
406        /// Equality operator.
407        ///
408        /// Two iterators are equal if and only if they point to the
409        /// same object or both are \c INVALID.
410        bool operator==(Arc) const { return true; }
411        /// Inequality operator
412
413        /// Inequality operator.
414        bool operator!=(Arc) const { return true; }
415
416        /// Artificial ordering operator.
417
418        /// Artificial ordering operator.
419        ///
420        /// \note This operator only has to define some strict ordering of
421        /// the arcs; this order has nothing to do with the iteration
422        /// ordering of the arcs.
423        bool operator<(Arc) const { return false; }
424
425        /// Converison to \c Edge
426
427        /// Converison to \c Edge.
428        ///
429        operator Edge() const { return Edge(); }
430      };
431
432      /// Iterator class for the arcs.
433
434      /// This iterator goes through each directed arc of the graph.
435      /// Its usage is quite simple, for example, you can count the number
436      /// of arcs in a graph \c g of type \c %Graph as follows:
437      ///\code
438      /// int count=0;
439      /// for(Graph::ArcIt a(g); a!=INVALID; ++a) ++count;
440      ///\endcode
441      class ArcIt : public Arc {
442      public:
443        /// Default constructor
444
445        /// Default constructor.
446        /// \warning It sets the iterator to an undefined value.
447        ArcIt() { }
448        /// Copy constructor.
449
450        /// Copy constructor.
451        ///
452        ArcIt(const ArcIt& e) : Arc(e) { }
453        /// %Invalid constructor \& conversion.
454
455        /// Initializes the iterator to be invalid.
456        /// \sa Invalid for more details.
457        ArcIt(Invalid) { }
458        /// Sets the iterator to the first arc.
459
460        /// Sets the iterator to the first arc of the given graph.
461        ///
462        explicit ArcIt(const Graph &g) {
463          ::lemon::ignore_unused_variable_warning(g);
464        }
465        /// Sets the iterator to the given arc.
466
467        /// Sets the iterator to the given arc of the given graph.
468        ///
469        ArcIt(const Graph&, const Arc&) { }
470        /// Next arc
471
472        /// Assign the iterator to the next arc.
473        ///
474        ArcIt& operator++() { return *this; }
475      };
476
477      /// \brief Gets the collection of the directed arcs of the graph.
478      ///
479      /// This function can be used for iterating on the
480      /// arcs of the graph. It returns a wrapped
481      /// ArcIt, which looks like an STL container
482      /// (by having begin() and end()) which you can use in range-based
483      /// for loops, STL algorithms, etc.
484      /// For example you can write:
485      ///\code
486      /// ListGraph g;
487      /// for(auto a: g.arcs())
488      ///   doSomething(a);
489      ///
490      /// //Using an STL algorithm:
491      /// copy(g.arcs().begin(), g.arcs().end(), vect.begin());
492      ///\endcode
493      LemonRangeWrapper1<ArcIt, Graph> arcs() const {
494        return LemonRangeWrapper1<ArcIt, Graph>(*this);
495      }
496
497
498      /// Iterator class for the outgoing arcs of a node.
499
500      /// This iterator goes trough the \e outgoing directed arcs of a
501      /// certain node of a graph.
502      /// Its usage is quite simple, for example, you can count the number
503      /// of outgoing arcs of a node \c n
504      /// in a graph \c g of type \c %Graph as follows.
505      ///\code
506      /// int count=0;
507      /// for (Digraph::OutArcIt a(g, n); a!=INVALID; ++a) ++count;
508      ///\endcode
509      class OutArcIt : public Arc {
510      public:
511        /// Default constructor
512
513        /// Default constructor.
514        /// \warning It sets the iterator to an undefined value.
515        OutArcIt() { }
516        /// Copy constructor.
517
518        /// Copy constructor.
519        ///
520        OutArcIt(const OutArcIt& e) : Arc(e) { }
521        /// %Invalid constructor \& conversion.
522
523        /// Initializes the iterator to be invalid.
524        /// \sa Invalid for more details.
525        OutArcIt(Invalid) { }
526        /// Sets the iterator to the first outgoing arc.
527
528        /// Sets the iterator to the first outgoing arc of the given node.
529        ///
530        OutArcIt(const Graph& n, const Node& g) {
531          ::lemon::ignore_unused_variable_warning(n);
532          ::lemon::ignore_unused_variable_warning(g);
533        }
534        /// Sets the iterator to the given arc.
535
536        /// Sets the iterator to the given arc of the given graph.
537        ///
538        OutArcIt(const Graph&, const Arc&) { }
539        /// Next outgoing arc
540
541        /// Assign the iterator to the next
542        /// outgoing arc of the corresponding node.
543        OutArcIt& operator++() { return *this; }
544      };
545
546      /// \brief Gets the collection of the outgoing directed arcs of a
547      /// certain node of the graph.
548      ///
549      /// This function can be used for iterating on the
550      /// outgoing arcs of a certain node of the graph. It returns a wrapped
551      /// OutArcIt, which looks like an STL container
552      /// (by having begin() and end()) which you can use in range-based
553      /// for loops, STL algorithms, etc.
554      /// For example if g is a Graph and u is a Node, you can write:
555      ///\code
556      /// for(auto a: g.outArcs(u))
557      ///   doSomething(a);
558      ///
559      /// //Using an STL algorithm:
560      /// copy(g.outArcs(u).begin(), g.outArcs(u).end(), vect.begin());
561      ///\endcode
562      LemonRangeWrapper2<OutArcIt, Graph, Node> outArcs(const Node& u) const {
563        return LemonRangeWrapper2<OutArcIt, Graph, Node>(*this, u);
564      }
565
566
567      /// Iterator class for the incoming arcs of a node.
568
569      /// This iterator goes trough the \e incoming directed arcs of a
570      /// certain node of a graph.
571      /// Its usage is quite simple, for example, you can count the number
572      /// of incoming arcs of a node \c n
573      /// in a graph \c g of type \c %Graph as follows.
574      ///\code
575      /// int count=0;
576      /// for (Digraph::InArcIt a(g, n); a!=INVALID; ++a) ++count;
577      ///\endcode
578      class InArcIt : public Arc {
579      public:
580        /// Default constructor
581
582        /// Default constructor.
583        /// \warning It sets the iterator to an undefined value.
584        InArcIt() { }
585        /// Copy constructor.
586
587        /// Copy constructor.
588        ///
589        InArcIt(const InArcIt& e) : Arc(e) { }
590        /// %Invalid constructor \& conversion.
591
592        /// Initializes the iterator to be invalid.
593        /// \sa Invalid for more details.
594        InArcIt(Invalid) { }
595        /// Sets the iterator to the first incoming arc.
596
597        /// Sets the iterator to the first incoming arc of the given node.
598        ///
599        InArcIt(const Graph& g, const Node& n) {
600          ::lemon::ignore_unused_variable_warning(n);
601          ::lemon::ignore_unused_variable_warning(g);
602        }
603        /// Sets the iterator to the given arc.
604
605        /// Sets the iterator to the given arc of the given graph.
606        ///
607        InArcIt(const Graph&, const Arc&) { }
608        /// Next incoming arc
609
610        /// Assign the iterator to the next
611        /// incoming arc of the corresponding node.
612        InArcIt& operator++() { return *this; }
613      };
614
615      /// \brief Gets the collection of the incoming directed arcs of
616      /// a certain node of the graph.
617      ///
618      /// This function can be used for iterating on the
619      /// incoming directed arcs of a certain node of the graph. It returns
620      /// a wrapped InArcIt, which looks like an STL container
621      /// (by having begin() and end()) which you can use in range-based
622      /// for loops, STL algorithms, etc.
623      /// For example if g is a Graph and u is a Node, you can write:
624      ///\code
625      /// for(auto a: g.inArcs(u))
626      ///   doSomething(a);
627      ///
628      /// //Using an STL algorithm:
629      /// copy(g.inArcs(u).begin(), g.inArcs(u).end(), vect.begin());
630      ///\endcode
631      LemonRangeWrapper2<InArcIt, Graph, Node> inArcs(const Node& u) const {
632        return LemonRangeWrapper2<InArcIt, Graph, Node>(*this, u);
633      }
634
635      /// \brief Standard graph map type for the nodes.
636      ///
637      /// Standard graph map type for the nodes.
638      /// It conforms to the ReferenceMap concept.
639      template<class T>
640      class NodeMap : public ReferenceMap<Node, T, T&, const T&>
641      {
642      public:
643
644        /// Constructor
645        explicit NodeMap(const Graph&) { }
646        /// Constructor with given initial value
647        NodeMap(const Graph&, T) { }
648
649      private:
650        ///Copy constructor
651        NodeMap(const NodeMap& nm) :
652          ReferenceMap<Node, T, T&, const T&>(nm) { }
653        ///Assignment operator
654        template <typename CMap>
655        NodeMap& operator=(const CMap&) {
656          checkConcept<ReadMap<Node, T>, CMap>();
657          return *this;
658        }
659      };
660
661      /// \brief Standard graph map type for the arcs.
662      ///
663      /// Standard graph map type for the arcs.
664      /// It conforms to the ReferenceMap concept.
665      template<class T>
666      class ArcMap : public ReferenceMap<Arc, T, T&, const T&>
667      {
668      public:
669
670        /// Constructor
671        explicit ArcMap(const Graph&) { }
672        /// Constructor with given initial value
673        ArcMap(const Graph&, T) { }
674
675      private:
676        ///Copy constructor
677        ArcMap(const ArcMap& em) :
678          ReferenceMap<Arc, T, T&, const T&>(em) { }
679        ///Assignment operator
680        template <typename CMap>
681        ArcMap& operator=(const CMap&) {
682          checkConcept<ReadMap<Arc, T>, CMap>();
683          return *this;
684        }
685      };
686
687      /// \brief Standard graph map type for the edges.
688      ///
689      /// Standard graph map type for the edges.
690      /// It conforms to the ReferenceMap concept.
691      template<class T>
692      class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>
693      {
694      public:
695
696        /// Constructor
697        explicit EdgeMap(const Graph&) { }
698        /// Constructor with given initial value
699        EdgeMap(const Graph&, T) { }
700
701      private:
702        ///Copy constructor
703        EdgeMap(const EdgeMap& em) :
704          ReferenceMap<Edge, T, T&, const T&>(em) {}
705        ///Assignment operator
706        template <typename CMap>
707        EdgeMap& operator=(const CMap&) {
708          checkConcept<ReadMap<Edge, T>, CMap>();
709          return *this;
710        }
711      };
712
713      /// \brief The first node of the edge.
714      ///
715      /// Returns the first node of the given edge.
716      ///
717      /// Edges don't have source and target nodes, however, methods
718      /// u() and v() are used to query the two end-nodes of an edge.
719      /// The orientation of an edge that arises this way is called
720      /// the inherent direction, it is used to define the default
721      /// direction for the corresponding arcs.
722      /// \sa v()
723      /// \sa direction()
724      Node u(Edge) const { return INVALID; }
725
726      /// \brief The second node of the edge.
727      ///
728      /// Returns the second node of the given edge.
729      ///
730      /// Edges don't have source and target nodes, however, methods
731      /// u() and v() are used to query the two end-nodes of an edge.
732      /// The orientation of an edge that arises this way is called
733      /// the inherent direction, it is used to define the default
734      /// direction for the corresponding arcs.
735      /// \sa u()
736      /// \sa direction()
737      Node v(Edge) const { return INVALID; }
738
739      /// \brief The source node of the arc.
740      ///
741      /// Returns the source node of the given arc.
742      Node source(Arc) const { return INVALID; }
743
744      /// \brief The target node of the arc.
745      ///
746      /// Returns the target node of the given arc.
747      Node target(Arc) const { return INVALID; }
748
749      /// \brief The ID of the node.
750      ///
751      /// Returns the ID of the given node.
752      int id(Node) const { return -1; }
753
754      /// \brief The ID of the edge.
755      ///
756      /// Returns the ID of the given edge.
757      int id(Edge) const { return -1; }
758
759      /// \brief The ID of the arc.
760      ///
761      /// Returns the ID of the given arc.
762      int id(Arc) const { return -1; }
763
764      /// \brief The node with the given ID.
765      ///
766      /// Returns the node with the given ID.
767      /// \pre The argument should be a valid node ID in the graph.
768      Node nodeFromId(int) const { return INVALID; }
769
770      /// \brief The edge with the given ID.
771      ///
772      /// Returns the edge with the given ID.
773      /// \pre The argument should be a valid edge ID in the graph.
774      Edge edgeFromId(int) const { return INVALID; }
775
776      /// \brief The arc with the given ID.
777      ///
778      /// Returns the arc with the given ID.
779      /// \pre The argument should be a valid arc ID in the graph.
780      Arc arcFromId(int) const { return INVALID; }
781
782      /// \brief An upper bound on the node IDs.
783      ///
784      /// Returns an upper bound on the node IDs.
785      int maxNodeId() const { return -1; }
786
787      /// \brief An upper bound on the edge IDs.
788      ///
789      /// Returns an upper bound on the edge IDs.
790      int maxEdgeId() const { return -1; }
791
792      /// \brief An upper bound on the arc IDs.
793      ///
794      /// Returns an upper bound on the arc IDs.
795      int maxArcId() const { return -1; }
796
797      /// \brief The direction of the arc.
798      ///
799      /// Returns \c true if the direction of the given arc is the same as
800      /// the inherent orientation of the represented edge.
801      bool direction(Arc) const { return true; }
802
803      /// \brief Direct the edge.
804      ///
805      /// Direct the given edge. The returned arc
806      /// represents the given edge and its direction comes
807      /// from the bool parameter. If it is \c true, then the direction
808      /// of the arc is the same as the inherent orientation of the edge.
809      Arc direct(Edge, bool) const {
810        return INVALID;
811      }
812
813      /// \brief Direct the edge.
814      ///
815      /// Direct the given edge. The returned arc represents the given
816      /// edge and its source node is the given node.
817      Arc direct(Edge, Node) const {
818        return INVALID;
819      }
820
821      /// \brief The oppositely directed arc.
822      ///
823      /// Returns the oppositely directed arc representing the same edge.
824      Arc oppositeArc(Arc) const { return INVALID; }
825
826      /// \brief The opposite node on the edge.
827      ///
828      /// Returns the opposite node on the given edge.
829      Node oppositeNode(Node, Edge) const { return INVALID; }
830
831      void first(Node&) const {}
832      void next(Node&) const {}
833
834      void first(Edge&) const {}
835      void next(Edge&) const {}
836
837      void first(Arc&) const {}
838      void next(Arc&) const {}
839
840      void firstOut(Arc&, Node) const {}
841      void nextOut(Arc&) const {}
842
843      void firstIn(Arc&, Node) const {}
844      void nextIn(Arc&) const {}
845
846      void firstInc(Edge &, bool &, const Node &) const {}
847      void nextInc(Edge &, bool &) const {}
848
849      // The second parameter is dummy.
850      Node fromId(int, Node) const { return INVALID; }
851      // The second parameter is dummy.
852      Edge fromId(int, Edge) const { return INVALID; }
853      // The second parameter is dummy.
854      Arc fromId(int, Arc) const { return INVALID; }
855
856      // Dummy parameter.
857      int maxId(Node) const { return -1; }
858      // Dummy parameter.
859      int maxId(Edge) const { return -1; }
860      // Dummy parameter.
861      int maxId(Arc) const { return -1; }
862
863      /// \brief The base node of the iterator.
864      ///
865      /// Returns the base node of the given incident edge iterator.
866      Node baseNode(IncEdgeIt) const { return INVALID; }
867
868      /// \brief The running node of the iterator.
869      ///
870      /// Returns the running node of the given incident edge iterator.
871      Node runningNode(IncEdgeIt) const { return INVALID; }
872
873      /// \brief The base node of the iterator.
874      ///
875      /// Returns the base node of the given outgoing arc iterator
876      /// (i.e. the source node of the corresponding arc).
877      Node baseNode(OutArcIt) const { return INVALID; }
878
879      /// \brief The running node of the iterator.
880      ///
881      /// Returns the running node of the given outgoing arc iterator
882      /// (i.e. the target node of the corresponding arc).
883      Node runningNode(OutArcIt) const { return INVALID; }
884
885      /// \brief The base node of the iterator.
886      ///
887      /// Returns the base node of the given incoming arc iterator
888      /// (i.e. the target node of the corresponding arc).
889      Node baseNode(InArcIt) const { return INVALID; }
890
891      /// \brief The running node of the iterator.
892      ///
893      /// Returns the running node of the given incoming arc iterator
894      /// (i.e. the source node of the corresponding arc).
895      Node runningNode(InArcIt) const { return INVALID; }
896
897      template <typename _Graph>
898      struct Constraints {
899        void constraints() {
900          checkConcept<BaseGraphComponent, _Graph>();
901          checkConcept<IterableGraphComponent<>, _Graph>();
902          checkConcept<IDableGraphComponent<>, _Graph>();
903          checkConcept<MappableGraphComponent<>, _Graph>();
904        }
905      };
906
907    };
908
909  }
910
911}
912
913#endif
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