COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/core.h @ 981:2c2e8df67ddc

1.2
Last change on this file since 981:2c2e8df67ddc was 981:2c2e8df67ddc, checked in by Alpar Juttner <alpar@…>, 6 years ago

Merge further fixes #470 to branch 1.2

File size: 59.4 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) 2003-2010
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_CORE_H
20#define LEMON_CORE_H
21
22#include <vector>
23#include <algorithm>
24
25#include <lemon/config.h>
26#include <lemon/bits/enable_if.h>
27#include <lemon/bits/traits.h>
28#include <lemon/assert.h>
29
30// Disable the following warnings when compiling with MSVC:
31// C4250: 'class1' : inherits 'class2::member' via dominance
32// C4355: 'this' : used in base member initializer list
33// C4503: 'function' : decorated name length exceeded, name was truncated
34// C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)
35// C4996: 'function': was declared deprecated
36#ifdef _MSC_VER
37#pragma warning( disable : 4250 4355 4503 4800 4996 )
38#endif
39
40#ifdef __GNUC__
41#define GCC_VERSION (__GNUC__ * 10000                   \
42                     + __GNUC_MINOR__ * 100             \
43                     + __GNUC_PATCHLEVEL__)
44#endif
45
46#if GCC_VERSION >= 40800
47// Needed by the [DI]GRAPH_TYPEDEFS marcos for gcc 4.8
48#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
49#endif
50
51///\file
52///\brief LEMON core utilities.
53///
54///This header file contains core utilities for LEMON.
55///It is automatically included by all graph types, therefore it usually
56///do not have to be included directly.
57
58namespace lemon {
59
60  /// \brief Dummy type to make it easier to create invalid iterators.
61  ///
62  /// Dummy type to make it easier to create invalid iterators.
63  /// See \ref INVALID for the usage.
64  struct Invalid {
65  public:
66    bool operator==(Invalid) { return true;  }
67    bool operator!=(Invalid) { return false; }
68    bool operator< (Invalid) { return false; }
69  };
70
71  /// \brief Invalid iterators.
72  ///
73  /// \ref Invalid is a global type that converts to each iterator
74  /// in such a way that the value of the target iterator will be invalid.
75#ifdef LEMON_ONLY_TEMPLATES
76  const Invalid INVALID = Invalid();
77#else
78  extern const Invalid INVALID;
79#endif
80
81  /// \addtogroup gutils
82  /// @{
83
84  ///Create convenience typedefs for the digraph types and iterators
85
86  ///This \c \#define creates convenient type definitions for the following
87  ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
88  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
89  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
90  ///
91  ///\note If the graph type is a dependent type, ie. the graph type depend
92  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
93  ///macro.
94#define DIGRAPH_TYPEDEFS(Digraph)                                       \
95  typedef Digraph::Node Node;                                           \
96  typedef Digraph::NodeIt NodeIt;                                       \
97  typedef Digraph::Arc Arc;                                             \
98  typedef Digraph::ArcIt ArcIt;                                         \
99  typedef Digraph::InArcIt InArcIt;                                     \
100  typedef Digraph::OutArcIt OutArcIt;                                   \
101  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
102  typedef Digraph::NodeMap<int> IntNodeMap;                             \
103  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
104  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
105  typedef Digraph::ArcMap<int> IntArcMap;                               \
106  typedef Digraph::ArcMap<double> DoubleArcMap
107
108  ///Create convenience typedefs for the digraph types and iterators
109
110  ///\see DIGRAPH_TYPEDEFS
111  ///
112  ///\note Use this macro, if the graph type is a dependent type,
113  ///ie. the graph type depend on a template parameter.
114#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
115  typedef typename Digraph::Node Node;                                  \
116  typedef typename Digraph::NodeIt NodeIt;                              \
117  typedef typename Digraph::Arc Arc;                                    \
118  typedef typename Digraph::ArcIt ArcIt;                                \
119  typedef typename Digraph::InArcIt InArcIt;                            \
120  typedef typename Digraph::OutArcIt OutArcIt;                          \
121  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
122  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
123  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
124  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
125  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
126  typedef typename Digraph::template ArcMap<double> DoubleArcMap
127
128  ///Create convenience typedefs for the graph types and iterators
129
130  ///This \c \#define creates the same convenient type definitions as defined
131  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
132  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
133  ///\c DoubleEdgeMap.
134  ///
135  ///\note If the graph type is a dependent type, ie. the graph type depend
136  ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
137  ///macro.
138#define GRAPH_TYPEDEFS(Graph)                                           \
139  DIGRAPH_TYPEDEFS(Graph);                                              \
140  typedef Graph::Edge Edge;                                             \
141  typedef Graph::EdgeIt EdgeIt;                                         \
142  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
143  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
144  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
145  typedef Graph::EdgeMap<double> DoubleEdgeMap
146
147  ///Create convenience typedefs for the graph types and iterators
148
149  ///\see GRAPH_TYPEDEFS
150  ///
151  ///\note Use this macro, if the graph type is a dependent type,
152  ///ie. the graph type depend on a template parameter.
153#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
154  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
155  typedef typename Graph::Edge Edge;                                    \
156  typedef typename Graph::EdgeIt EdgeIt;                                \
157  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
158  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
159  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
160  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
161
162  /// \brief Function to count the items in a graph.
163  ///
164  /// This function counts the items (nodes, arcs etc.) in a graph.
165  /// The complexity of the function is linear because
166  /// it iterates on all of the items.
167  template <typename Graph, typename Item>
168  inline int countItems(const Graph& g) {
169    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
170    int num = 0;
171    for (ItemIt it(g); it != INVALID; ++it) {
172      ++num;
173    }
174    return num;
175  }
176
177  // Node counting:
178
179  namespace _core_bits {
180
181    template <typename Graph, typename Enable = void>
182    struct CountNodesSelector {
183      static int count(const Graph &g) {
184        return countItems<Graph, typename Graph::Node>(g);
185      }
186    };
187
188    template <typename Graph>
189    struct CountNodesSelector<
190      Graph, typename
191      enable_if<typename Graph::NodeNumTag, void>::type>
192    {
193      static int count(const Graph &g) {
194        return g.nodeNum();
195      }
196    };
197  }
198
199  /// \brief Function to count the nodes in the graph.
200  ///
201  /// This function counts the nodes in the graph.
202  /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
203  /// graph structures it is specialized to run in <em>O</em>(1).
204  ///
205  /// \note If the graph contains a \c nodeNum() member function and a
206  /// \c NodeNumTag tag then this function calls directly the member
207  /// function to query the cardinality of the node set.
208  template <typename Graph>
209  inline int countNodes(const Graph& g) {
210    return _core_bits::CountNodesSelector<Graph>::count(g);
211  }
212
213  // Arc counting:
214
215  namespace _core_bits {
216
217    template <typename Graph, typename Enable = void>
218    struct CountArcsSelector {
219      static int count(const Graph &g) {
220        return countItems<Graph, typename Graph::Arc>(g);
221      }
222    };
223
224    template <typename Graph>
225    struct CountArcsSelector<
226      Graph,
227      typename enable_if<typename Graph::ArcNumTag, void>::type>
228    {
229      static int count(const Graph &g) {
230        return g.arcNum();
231      }
232    };
233  }
234
235  /// \brief Function to count the arcs in the graph.
236  ///
237  /// This function counts the arcs in the graph.
238  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
239  /// graph structures it is specialized to run in <em>O</em>(1).
240  ///
241  /// \note If the graph contains a \c arcNum() member function and a
242  /// \c ArcNumTag tag then this function calls directly the member
243  /// function to query the cardinality of the arc set.
244  template <typename Graph>
245  inline int countArcs(const Graph& g) {
246    return _core_bits::CountArcsSelector<Graph>::count(g);
247  }
248
249  // Edge counting:
250
251  namespace _core_bits {
252
253    template <typename Graph, typename Enable = void>
254    struct CountEdgesSelector {
255      static int count(const Graph &g) {
256        return countItems<Graph, typename Graph::Edge>(g);
257      }
258    };
259
260    template <typename Graph>
261    struct CountEdgesSelector<
262      Graph,
263      typename enable_if<typename Graph::EdgeNumTag, void>::type>
264    {
265      static int count(const Graph &g) {
266        return g.edgeNum();
267      }
268    };
269  }
270
271  /// \brief Function to count the edges in the graph.
272  ///
273  /// This function counts the edges in the graph.
274  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
275  /// graph structures it is specialized to run in <em>O</em>(1).
276  ///
277  /// \note If the graph contains a \c edgeNum() member function and a
278  /// \c EdgeNumTag tag then this function calls directly the member
279  /// function to query the cardinality of the edge set.
280  template <typename Graph>
281  inline int countEdges(const Graph& g) {
282    return _core_bits::CountEdgesSelector<Graph>::count(g);
283
284  }
285
286
287  template <typename Graph, typename DegIt>
288  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
289    int num = 0;
290    for (DegIt it(_g, _n); it != INVALID; ++it) {
291      ++num;
292    }
293    return num;
294  }
295
296  /// \brief Function to count the number of the out-arcs from node \c n.
297  ///
298  /// This function counts the number of the out-arcs from node \c n
299  /// in the graph \c g.
300  template <typename Graph>
301  inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
302    return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
303  }
304
305  /// \brief Function to count the number of the in-arcs to node \c n.
306  ///
307  /// This function counts the number of the in-arcs to node \c n
308  /// in the graph \c g.
309  template <typename Graph>
310  inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
311    return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
312  }
313
314  /// \brief Function to count the number of the inc-edges to node \c n.
315  ///
316  /// This function counts the number of the inc-edges to node \c n
317  /// in the undirected graph \c g.
318  template <typename Graph>
319  inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
320    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
321  }
322
323  namespace _core_bits {
324
325    template <typename Digraph, typename Item, typename RefMap>
326    class MapCopyBase {
327    public:
328      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
329
330      virtual ~MapCopyBase() {}
331    };
332
333    template <typename Digraph, typename Item, typename RefMap,
334              typename FromMap, typename ToMap>
335    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
336    public:
337
338      MapCopy(const FromMap& map, ToMap& tmap)
339        : _map(map), _tmap(tmap) {}
340
341      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
342        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
343        for (ItemIt it(digraph); it != INVALID; ++it) {
344          _tmap.set(refMap[it], _map[it]);
345        }
346      }
347
348    private:
349      const FromMap& _map;
350      ToMap& _tmap;
351    };
352
353    template <typename Digraph, typename Item, typename RefMap, typename It>
354    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
355    public:
356
357      ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
358
359      virtual void copy(const Digraph&, const RefMap& refMap) {
360        _it = refMap[_item];
361      }
362
363    private:
364      Item _item;
365      It& _it;
366    };
367
368    template <typename Digraph, typename Item, typename RefMap, typename Ref>
369    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
370    public:
371
372      RefCopy(Ref& map) : _map(map) {}
373
374      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
375        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
376        for (ItemIt it(digraph); it != INVALID; ++it) {
377          _map.set(it, refMap[it]);
378        }
379      }
380
381    private:
382      Ref& _map;
383    };
384
385    template <typename Digraph, typename Item, typename RefMap,
386              typename CrossRef>
387    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
388    public:
389
390      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
391
392      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
393        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
394        for (ItemIt it(digraph); it != INVALID; ++it) {
395          _cmap.set(refMap[it], it);
396        }
397      }
398
399    private:
400      CrossRef& _cmap;
401    };
402
403    template <typename Digraph, typename Enable = void>
404    struct DigraphCopySelector {
405      template <typename From, typename NodeRefMap, typename ArcRefMap>
406      static void copy(const From& from, Digraph &to,
407                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
408        to.clear();
409        for (typename From::NodeIt it(from); it != INVALID; ++it) {
410          nodeRefMap[it] = to.addNode();
411        }
412        for (typename From::ArcIt it(from); it != INVALID; ++it) {
413          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
414                                    nodeRefMap[from.target(it)]);
415        }
416      }
417    };
418
419    template <typename Digraph>
420    struct DigraphCopySelector<
421      Digraph,
422      typename enable_if<typename Digraph::BuildTag, void>::type>
423    {
424      template <typename From, typename NodeRefMap, typename ArcRefMap>
425      static void copy(const From& from, Digraph &to,
426                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
427        to.build(from, nodeRefMap, arcRefMap);
428      }
429    };
430
431    template <typename Graph, typename Enable = void>
432    struct GraphCopySelector {
433      template <typename From, typename NodeRefMap, typename EdgeRefMap>
434      static void copy(const From& from, Graph &to,
435                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
436        to.clear();
437        for (typename From::NodeIt it(from); it != INVALID; ++it) {
438          nodeRefMap[it] = to.addNode();
439        }
440        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
441          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
442                                      nodeRefMap[from.v(it)]);
443        }
444      }
445    };
446
447    template <typename Graph>
448    struct GraphCopySelector<
449      Graph,
450      typename enable_if<typename Graph::BuildTag, void>::type>
451    {
452      template <typename From, typename NodeRefMap, typename EdgeRefMap>
453      static void copy(const From& from, Graph &to,
454                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
455        to.build(from, nodeRefMap, edgeRefMap);
456      }
457    };
458
459  }
460
461  /// \brief Class to copy a digraph.
462  ///
463  /// Class to copy a digraph to another digraph (duplicate a digraph). The
464  /// simplest way of using it is through the \c digraphCopy() function.
465  ///
466  /// This class not only make a copy of a digraph, but it can create
467  /// references and cross references between the nodes and arcs of
468  /// the two digraphs, and it can copy maps to use with the newly created
469  /// digraph.
470  ///
471  /// To make a copy from a digraph, first an instance of DigraphCopy
472  /// should be created, then the data belongs to the digraph should
473  /// assigned to copy. In the end, the \c run() member should be
474  /// called.
475  ///
476  /// The next code copies a digraph with several data:
477  ///\code
478  ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
479  ///  // Create references for the nodes
480  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
481  ///  cg.nodeRef(nr);
482  ///  // Create cross references (inverse) for the arcs
483  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
484  ///  cg.arcCrossRef(acr);
485  ///  // Copy an arc map
486  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
487  ///  NewGraph::ArcMap<double> namap(new_graph);
488  ///  cg.arcMap(oamap, namap);
489  ///  // Copy a node
490  ///  OrigGraph::Node on;
491  ///  NewGraph::Node nn;
492  ///  cg.node(on, nn);
493  ///  // Execute copying
494  ///  cg.run();
495  ///\endcode
496  template <typename From, typename To>
497  class DigraphCopy {
498  private:
499
500    typedef typename From::Node Node;
501    typedef typename From::NodeIt NodeIt;
502    typedef typename From::Arc Arc;
503    typedef typename From::ArcIt ArcIt;
504
505    typedef typename To::Node TNode;
506    typedef typename To::Arc TArc;
507
508    typedef typename From::template NodeMap<TNode> NodeRefMap;
509    typedef typename From::template ArcMap<TArc> ArcRefMap;
510
511  public:
512
513    /// \brief Constructor of DigraphCopy.
514    ///
515    /// Constructor of DigraphCopy for copying the content of the
516    /// \c from digraph into the \c to digraph.
517    DigraphCopy(const From& from, To& to)
518      : _from(from), _to(to) {}
519
520    /// \brief Destructor of DigraphCopy
521    ///
522    /// Destructor of DigraphCopy.
523    ~DigraphCopy() {
524      for (int i = 0; i < int(_node_maps.size()); ++i) {
525        delete _node_maps[i];
526      }
527      for (int i = 0; i < int(_arc_maps.size()); ++i) {
528        delete _arc_maps[i];
529      }
530
531    }
532
533    /// \brief Copy the node references into the given map.
534    ///
535    /// This function copies the node references into the given map.
536    /// The parameter should be a map, whose key type is the Node type of
537    /// the source digraph, while the value type is the Node type of the
538    /// destination digraph.
539    template <typename NodeRef>
540    DigraphCopy& nodeRef(NodeRef& map) {
541      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
542                           NodeRefMap, NodeRef>(map));
543      return *this;
544    }
545
546    /// \brief Copy the node cross references into the given map.
547    ///
548    /// This function copies the node cross references (reverse references)
549    /// into the given map. The parameter should be a map, whose key type
550    /// is the Node type of the destination digraph, while the value type is
551    /// the Node type of the source digraph.
552    template <typename NodeCrossRef>
553    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
554      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
555                           NodeRefMap, NodeCrossRef>(map));
556      return *this;
557    }
558
559    /// \brief Make a copy of the given node map.
560    ///
561    /// This function makes a copy of the given node map for the newly
562    /// created digraph.
563    /// The key type of the new map \c tmap should be the Node type of the
564    /// destination digraph, and the key type of the original map \c map
565    /// should be the Node type of the source digraph.
566    template <typename FromMap, typename ToMap>
567    DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
568      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
569                           NodeRefMap, FromMap, ToMap>(map, tmap));
570      return *this;
571    }
572
573    /// \brief Make a copy of the given node.
574    ///
575    /// This function makes a copy of the given node.
576    DigraphCopy& node(const Node& node, TNode& tnode) {
577      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
578                           NodeRefMap, TNode>(node, tnode));
579      return *this;
580    }
581
582    /// \brief Copy the arc references into the given map.
583    ///
584    /// This function copies the arc references into the given map.
585    /// The parameter should be a map, whose key type is the Arc type of
586    /// the source digraph, while the value type is the Arc type of the
587    /// destination digraph.
588    template <typename ArcRef>
589    DigraphCopy& arcRef(ArcRef& map) {
590      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
591                          ArcRefMap, ArcRef>(map));
592      return *this;
593    }
594
595    /// \brief Copy the arc cross references into the given map.
596    ///
597    /// This function copies the arc cross references (reverse references)
598    /// into the given map. The parameter should be a map, whose key type
599    /// is the Arc type of the destination digraph, while the value type is
600    /// the Arc type of the source digraph.
601    template <typename ArcCrossRef>
602    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
603      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
604                          ArcRefMap, ArcCrossRef>(map));
605      return *this;
606    }
607
608    /// \brief Make a copy of the given arc map.
609    ///
610    /// This function makes a copy of the given arc map for the newly
611    /// created digraph.
612    /// The key type of the new map \c tmap should be the Arc type of the
613    /// destination digraph, and the key type of the original map \c map
614    /// should be the Arc type of the source digraph.
615    template <typename FromMap, typename ToMap>
616    DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
617      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
618                          ArcRefMap, FromMap, ToMap>(map, tmap));
619      return *this;
620    }
621
622    /// \brief Make a copy of the given arc.
623    ///
624    /// This function makes a copy of the given arc.
625    DigraphCopy& arc(const Arc& arc, TArc& tarc) {
626      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
627                          ArcRefMap, TArc>(arc, tarc));
628      return *this;
629    }
630
631    /// \brief Execute copying.
632    ///
633    /// This function executes the copying of the digraph along with the
634    /// copying of the assigned data.
635    void run() {
636      NodeRefMap nodeRefMap(_from);
637      ArcRefMap arcRefMap(_from);
638      _core_bits::DigraphCopySelector<To>::
639        copy(_from, _to, nodeRefMap, arcRefMap);
640      for (int i = 0; i < int(_node_maps.size()); ++i) {
641        _node_maps[i]->copy(_from, nodeRefMap);
642      }
643      for (int i = 0; i < int(_arc_maps.size()); ++i) {
644        _arc_maps[i]->copy(_from, arcRefMap);
645      }
646    }
647
648  protected:
649
650    const From& _from;
651    To& _to;
652
653    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
654      _node_maps;
655
656    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
657      _arc_maps;
658
659  };
660
661  /// \brief Copy a digraph to another digraph.
662  ///
663  /// This function copies a digraph to another digraph.
664  /// The complete usage of it is detailed in the DigraphCopy class, but
665  /// a short example shows a basic work:
666  ///\code
667  /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
668  ///\endcode
669  ///
670  /// After the copy the \c nr map will contain the mapping from the
671  /// nodes of the \c from digraph to the nodes of the \c to digraph and
672  /// \c acr will contain the mapping from the arcs of the \c to digraph
673  /// to the arcs of the \c from digraph.
674  ///
675  /// \see DigraphCopy
676  template <typename From, typename To>
677  DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
678    return DigraphCopy<From, To>(from, to);
679  }
680
681  /// \brief Class to copy a graph.
682  ///
683  /// Class to copy a graph to another graph (duplicate a graph). The
684  /// simplest way of using it is through the \c graphCopy() function.
685  ///
686  /// This class not only make a copy of a graph, but it can create
687  /// references and cross references between the nodes, edges and arcs of
688  /// the two graphs, and it can copy maps for using with the newly created
689  /// graph.
690  ///
691  /// To make a copy from a graph, first an instance of GraphCopy
692  /// should be created, then the data belongs to the graph should
693  /// assigned to copy. In the end, the \c run() member should be
694  /// called.
695  ///
696  /// The next code copies a graph with several data:
697  ///\code
698  ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
699  ///  // Create references for the nodes
700  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
701  ///  cg.nodeRef(nr);
702  ///  // Create cross references (inverse) for the edges
703  ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
704  ///  cg.edgeCrossRef(ecr);
705  ///  // Copy an edge map
706  ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
707  ///  NewGraph::EdgeMap<double> nemap(new_graph);
708  ///  cg.edgeMap(oemap, nemap);
709  ///  // Copy a node
710  ///  OrigGraph::Node on;
711  ///  NewGraph::Node nn;
712  ///  cg.node(on, nn);
713  ///  // Execute copying
714  ///  cg.run();
715  ///\endcode
716  template <typename From, typename To>
717  class GraphCopy {
718  private:
719
720    typedef typename From::Node Node;
721    typedef typename From::NodeIt NodeIt;
722    typedef typename From::Arc Arc;
723    typedef typename From::ArcIt ArcIt;
724    typedef typename From::Edge Edge;
725    typedef typename From::EdgeIt EdgeIt;
726
727    typedef typename To::Node TNode;
728    typedef typename To::Arc TArc;
729    typedef typename To::Edge TEdge;
730
731    typedef typename From::template NodeMap<TNode> NodeRefMap;
732    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
733
734    struct ArcRefMap {
735      ArcRefMap(const From& from, const To& to,
736                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
737        : _from(from), _to(to),
738          _edge_ref(edge_ref), _node_ref(node_ref) {}
739
740      typedef typename From::Arc Key;
741      typedef typename To::Arc Value;
742
743      Value operator[](const Key& key) const {
744        bool forward = _from.u(key) != _from.v(key) ?
745          _node_ref[_from.source(key)] ==
746          _to.source(_to.direct(_edge_ref[key], true)) :
747          _from.direction(key);
748        return _to.direct(_edge_ref[key], forward);
749      }
750
751      const From& _from;
752      const To& _to;
753      const EdgeRefMap& _edge_ref;
754      const NodeRefMap& _node_ref;
755    };
756
757  public:
758
759    /// \brief Constructor of GraphCopy.
760    ///
761    /// Constructor of GraphCopy for copying the content of the
762    /// \c from graph into the \c to graph.
763    GraphCopy(const From& from, To& to)
764      : _from(from), _to(to) {}
765
766    /// \brief Destructor of GraphCopy
767    ///
768    /// Destructor of GraphCopy.
769    ~GraphCopy() {
770      for (int i = 0; i < int(_node_maps.size()); ++i) {
771        delete _node_maps[i];
772      }
773      for (int i = 0; i < int(_arc_maps.size()); ++i) {
774        delete _arc_maps[i];
775      }
776      for (int i = 0; i < int(_edge_maps.size()); ++i) {
777        delete _edge_maps[i];
778      }
779    }
780
781    /// \brief Copy the node references into the given map.
782    ///
783    /// This function copies the node references into the given map.
784    /// The parameter should be a map, whose key type is the Node type of
785    /// the source graph, while the value type is the Node type of the
786    /// destination graph.
787    template <typename NodeRef>
788    GraphCopy& nodeRef(NodeRef& map) {
789      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
790                           NodeRefMap, NodeRef>(map));
791      return *this;
792    }
793
794    /// \brief Copy the node cross references into the given map.
795    ///
796    /// This function copies the node cross references (reverse references)
797    /// into the given map. The parameter should be a map, whose key type
798    /// is the Node type of the destination graph, while the value type is
799    /// the Node type of the source graph.
800    template <typename NodeCrossRef>
801    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
802      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
803                           NodeRefMap, NodeCrossRef>(map));
804      return *this;
805    }
806
807    /// \brief Make a copy of the given node map.
808    ///
809    /// This function makes a copy of the given node map for the newly
810    /// created graph.
811    /// The key type of the new map \c tmap should be the Node type of the
812    /// destination graph, and the key type of the original map \c map
813    /// should be the Node type of the source graph.
814    template <typename FromMap, typename ToMap>
815    GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
816      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
817                           NodeRefMap, FromMap, ToMap>(map, tmap));
818      return *this;
819    }
820
821    /// \brief Make a copy of the given node.
822    ///
823    /// This function makes a copy of the given node.
824    GraphCopy& node(const Node& node, TNode& tnode) {
825      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
826                           NodeRefMap, TNode>(node, tnode));
827      return *this;
828    }
829
830    /// \brief Copy the arc references into the given map.
831    ///
832    /// This function copies the arc references into the given map.
833    /// The parameter should be a map, whose key type is the Arc type of
834    /// the source graph, while the value type is the Arc type of the
835    /// destination graph.
836    template <typename ArcRef>
837    GraphCopy& arcRef(ArcRef& map) {
838      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
839                          ArcRefMap, ArcRef>(map));
840      return *this;
841    }
842
843    /// \brief Copy the arc cross references into the given map.
844    ///
845    /// This function copies the arc cross references (reverse references)
846    /// into the given map. The parameter should be a map, whose key type
847    /// is the Arc type of the destination graph, while the value type is
848    /// the Arc type of the source graph.
849    template <typename ArcCrossRef>
850    GraphCopy& arcCrossRef(ArcCrossRef& map) {
851      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
852                          ArcRefMap, ArcCrossRef>(map));
853      return *this;
854    }
855
856    /// \brief Make a copy of the given arc map.
857    ///
858    /// This function makes a copy of the given arc map for the newly
859    /// created graph.
860    /// The key type of the new map \c tmap should be the Arc type of the
861    /// destination graph, and the key type of the original map \c map
862    /// should be the Arc type of the source graph.
863    template <typename FromMap, typename ToMap>
864    GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
865      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
866                          ArcRefMap, FromMap, ToMap>(map, tmap));
867      return *this;
868    }
869
870    /// \brief Make a copy of the given arc.
871    ///
872    /// This function makes a copy of the given arc.
873    GraphCopy& arc(const Arc& arc, TArc& tarc) {
874      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
875                          ArcRefMap, TArc>(arc, tarc));
876      return *this;
877    }
878
879    /// \brief Copy the edge references into the given map.
880    ///
881    /// This function copies the edge references into the given map.
882    /// The parameter should be a map, whose key type is the Edge type of
883    /// the source graph, while the value type is the Edge type of the
884    /// destination graph.
885    template <typename EdgeRef>
886    GraphCopy& edgeRef(EdgeRef& map) {
887      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
888                           EdgeRefMap, EdgeRef>(map));
889      return *this;
890    }
891
892    /// \brief Copy the edge cross references into the given map.
893    ///
894    /// This function copies the edge cross references (reverse references)
895    /// into the given map. The parameter should be a map, whose key type
896    /// is the Edge type of the destination graph, while the value type is
897    /// the Edge type of the source graph.
898    template <typename EdgeCrossRef>
899    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
900      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
901                           Edge, EdgeRefMap, EdgeCrossRef>(map));
902      return *this;
903    }
904
905    /// \brief Make a copy of the given edge map.
906    ///
907    /// This function makes a copy of the given edge map for the newly
908    /// created graph.
909    /// The key type of the new map \c tmap should be the Edge type of the
910    /// destination graph, and the key type of the original map \c map
911    /// should be the Edge type of the source graph.
912    template <typename FromMap, typename ToMap>
913    GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
914      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
915                           EdgeRefMap, FromMap, ToMap>(map, tmap));
916      return *this;
917    }
918
919    /// \brief Make a copy of the given edge.
920    ///
921    /// This function makes a copy of the given edge.
922    GraphCopy& edge(const Edge& edge, TEdge& tedge) {
923      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
924                           EdgeRefMap, TEdge>(edge, tedge));
925      return *this;
926    }
927
928    /// \brief Execute copying.
929    ///
930    /// This function executes the copying of the graph along with the
931    /// copying of the assigned data.
932    void run() {
933      NodeRefMap nodeRefMap(_from);
934      EdgeRefMap edgeRefMap(_from);
935      ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
936      _core_bits::GraphCopySelector<To>::
937        copy(_from, _to, nodeRefMap, edgeRefMap);
938      for (int i = 0; i < int(_node_maps.size()); ++i) {
939        _node_maps[i]->copy(_from, nodeRefMap);
940      }
941      for (int i = 0; i < int(_edge_maps.size()); ++i) {
942        _edge_maps[i]->copy(_from, edgeRefMap);
943      }
944      for (int i = 0; i < int(_arc_maps.size()); ++i) {
945        _arc_maps[i]->copy(_from, arcRefMap);
946      }
947    }
948
949  private:
950
951    const From& _from;
952    To& _to;
953
954    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
955      _node_maps;
956
957    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
958      _arc_maps;
959
960    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
961      _edge_maps;
962
963  };
964
965  /// \brief Copy a graph to another graph.
966  ///
967  /// This function copies a graph to another graph.
968  /// The complete usage of it is detailed in the GraphCopy class,
969  /// but a short example shows a basic work:
970  ///\code
971  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
972  ///\endcode
973  ///
974  /// After the copy the \c nr map will contain the mapping from the
975  /// nodes of the \c from graph to the nodes of the \c to graph and
976  /// \c ecr will contain the mapping from the edges of the \c to graph
977  /// to the edges of the \c from graph.
978  ///
979  /// \see GraphCopy
980  template <typename From, typename To>
981  GraphCopy<From, To>
982  graphCopy(const From& from, To& to) {
983    return GraphCopy<From, To>(from, to);
984  }
985
986  namespace _core_bits {
987
988    template <typename Graph, typename Enable = void>
989    struct FindArcSelector {
990      typedef typename Graph::Node Node;
991      typedef typename Graph::Arc Arc;
992      static Arc find(const Graph &g, Node u, Node v, Arc e) {
993        if (e == INVALID) {
994          g.firstOut(e, u);
995        } else {
996          g.nextOut(e);
997        }
998        while (e != INVALID && g.target(e) != v) {
999          g.nextOut(e);
1000        }
1001        return e;
1002      }
1003    };
1004
1005    template <typename Graph>
1006    struct FindArcSelector<
1007      Graph,
1008      typename enable_if<typename Graph::FindArcTag, void>::type>
1009    {
1010      typedef typename Graph::Node Node;
1011      typedef typename Graph::Arc Arc;
1012      static Arc find(const Graph &g, Node u, Node v, Arc prev) {
1013        return g.findArc(u, v, prev);
1014      }
1015    };
1016  }
1017
1018  /// \brief Find an arc between two nodes of a digraph.
1019  ///
1020  /// This function finds an arc from node \c u to node \c v in the
1021  /// digraph \c g.
1022  ///
1023  /// If \c prev is \ref INVALID (this is the default value), then
1024  /// it finds the first arc from \c u to \c v. Otherwise it looks for
1025  /// the next arc from \c u to \c v after \c prev.
1026  /// \return The found arc or \ref INVALID if there is no such an arc.
1027  ///
1028  /// Thus you can iterate through each arc from \c u to \c v as it follows.
1029  ///\code
1030  /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
1031  ///   ...
1032  /// }
1033  ///\endcode
1034  ///
1035  /// \note \ref ConArcIt provides iterator interface for the same
1036  /// functionality.
1037  ///
1038  ///\sa ConArcIt
1039  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1040  template <typename Graph>
1041  inline typename Graph::Arc
1042  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1043          typename Graph::Arc prev = INVALID) {
1044    return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
1045  }
1046
1047  /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
1048  ///
1049  /// Iterator for iterating on parallel arcs connecting the same nodes. It is
1050  /// a higher level interface for the \ref findArc() function. You can
1051  /// use it the following way:
1052  ///\code
1053  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
1054  ///   ...
1055  /// }
1056  ///\endcode
1057  ///
1058  ///\sa findArc()
1059  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1060  template <typename GR>
1061  class ConArcIt : public GR::Arc {
1062    typedef typename GR::Arc Parent;
1063
1064  public:
1065
1066    typedef typename GR::Arc Arc;
1067    typedef typename GR::Node Node;
1068
1069    /// \brief Constructor.
1070    ///
1071    /// Construct a new ConArcIt iterating on the arcs that
1072    /// connects nodes \c u and \c v.
1073    ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
1074      Parent::operator=(findArc(_graph, u, v));
1075    }
1076
1077    /// \brief Constructor.
1078    ///
1079    /// Construct a new ConArcIt that continues the iterating from arc \c a.
1080    ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
1081
1082    /// \brief Increment operator.
1083    ///
1084    /// It increments the iterator and gives back the next arc.
1085    ConArcIt& operator++() {
1086      Parent::operator=(findArc(_graph, _graph.source(*this),
1087                                _graph.target(*this), *this));
1088      return *this;
1089    }
1090  private:
1091    const GR& _graph;
1092  };
1093
1094  namespace _core_bits {
1095
1096    template <typename Graph, typename Enable = void>
1097    struct FindEdgeSelector {
1098      typedef typename Graph::Node Node;
1099      typedef typename Graph::Edge Edge;
1100      static Edge find(const Graph &g, Node u, Node v, Edge e) {
1101        bool b;
1102        if (u != v) {
1103          if (e == INVALID) {
1104            g.firstInc(e, b, u);
1105          } else {
1106            b = g.u(e) == u;
1107            g.nextInc(e, b);
1108          }
1109          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
1110            g.nextInc(e, b);
1111          }
1112        } else {
1113          if (e == INVALID) {
1114            g.firstInc(e, b, u);
1115          } else {
1116            b = true;
1117            g.nextInc(e, b);
1118          }
1119          while (e != INVALID && (!b || g.v(e) != v)) {
1120            g.nextInc(e, b);
1121          }
1122        }
1123        return e;
1124      }
1125    };
1126
1127    template <typename Graph>
1128    struct FindEdgeSelector<
1129      Graph,
1130      typename enable_if<typename Graph::FindEdgeTag, void>::type>
1131    {
1132      typedef typename Graph::Node Node;
1133      typedef typename Graph::Edge Edge;
1134      static Edge find(const Graph &g, Node u, Node v, Edge prev) {
1135        return g.findEdge(u, v, prev);
1136      }
1137    };
1138  }
1139
1140  /// \brief Find an edge between two nodes of a graph.
1141  ///
1142  /// This function finds an edge from node \c u to node \c v in graph \c g.
1143  /// If node \c u and node \c v is equal then each loop edge
1144  /// will be enumerated once.
1145  ///
1146  /// If \c prev is \ref INVALID (this is the default value), then
1147  /// it finds the first edge from \c u to \c v. Otherwise it looks for
1148  /// the next edge from \c u to \c v after \c prev.
1149  /// \return The found edge or \ref INVALID if there is no such an edge.
1150  ///
1151  /// Thus you can iterate through each edge between \c u and \c v
1152  /// as it follows.
1153  ///\code
1154  /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
1155  ///   ...
1156  /// }
1157  ///\endcode
1158  ///
1159  /// \note \ref ConEdgeIt provides iterator interface for the same
1160  /// functionality.
1161  ///
1162  ///\sa ConEdgeIt
1163  template <typename Graph>
1164  inline typename Graph::Edge
1165  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1166            typename Graph::Edge p = INVALID) {
1167    return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
1168  }
1169
1170  /// \brief Iterator for iterating on parallel edges connecting the same nodes.
1171  ///
1172  /// Iterator for iterating on parallel edges connecting the same nodes.
1173  /// It is a higher level interface for the findEdge() function. You can
1174  /// use it the following way:
1175  ///\code
1176  /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
1177  ///   ...
1178  /// }
1179  ///\endcode
1180  ///
1181  ///\sa findEdge()
1182  template <typename GR>
1183  class ConEdgeIt : public GR::Edge {
1184    typedef typename GR::Edge Parent;
1185
1186  public:
1187
1188    typedef typename GR::Edge Edge;
1189    typedef typename GR::Node Node;
1190
1191    /// \brief Constructor.
1192    ///
1193    /// Construct a new ConEdgeIt iterating on the edges that
1194    /// connects nodes \c u and \c v.
1195    ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
1196      Parent::operator=(findEdge(_graph, _u, _v));
1197    }
1198
1199    /// \brief Constructor.
1200    ///
1201    /// Construct a new ConEdgeIt that continues iterating from edge \c e.
1202    ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
1203
1204    /// \brief Increment operator.
1205    ///
1206    /// It increments the iterator and gives back the next edge.
1207    ConEdgeIt& operator++() {
1208      Parent::operator=(findEdge(_graph, _u, _v, *this));
1209      return *this;
1210    }
1211  private:
1212    const GR& _graph;
1213    Node _u, _v;
1214  };
1215
1216
1217  ///Dynamic arc look-up between given endpoints.
1218
1219  ///Using this class, you can find an arc in a digraph from a given
1220  ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
1221  ///where <em>d</em> is the out-degree of the source node.
1222  ///
1223  ///It is possible to find \e all parallel arcs between two nodes with
1224  ///the \c operator() member.
1225  ///
1226  ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
1227  ///\ref AllArcLookUp if your digraph is not changed so frequently.
1228  ///
1229  ///This class uses a self-adjusting binary search tree, the Splay tree
1230  ///of Sleator and Tarjan to guarantee the logarithmic amortized
1231  ///time bound for arc look-ups. This class also guarantees the
1232  ///optimal time bound in a constant factor for any distribution of
1233  ///queries.
1234  ///
1235  ///\tparam GR The type of the underlying digraph.
1236  ///
1237  ///\sa ArcLookUp
1238  ///\sa AllArcLookUp
1239  template <typename GR>
1240  class DynArcLookUp
1241    : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
1242  {
1243    typedef typename ItemSetTraits<GR, typename GR::Arc>
1244    ::ItemNotifier::ObserverBase Parent;
1245
1246    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1247
1248  public:
1249
1250    /// The Digraph type
1251    typedef GR Digraph;
1252
1253  protected:
1254
1255    class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type
1256    {
1257      typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
1258
1259    public:
1260
1261      AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
1262
1263      virtual void add(const Node& node) {
1264        Parent::add(node);
1265        Parent::set(node, INVALID);
1266      }
1267
1268      virtual void add(const std::vector<Node>& nodes) {
1269        Parent::add(nodes);
1270        for (int i = 0; i < int(nodes.size()); ++i) {
1271          Parent::set(nodes[i], INVALID);
1272        }
1273      }
1274
1275      virtual void build() {
1276        Parent::build();
1277        Node it;
1278        typename Parent::Notifier* nf = Parent::notifier();
1279        for (nf->first(it); it != INVALID; nf->next(it)) {
1280          Parent::set(it, INVALID);
1281        }
1282      }
1283    };
1284
1285    class ArcLess {
1286      const Digraph &g;
1287    public:
1288      ArcLess(const Digraph &_g) : g(_g) {}
1289      bool operator()(Arc a,Arc b) const
1290      {
1291        return g.target(a)<g.target(b);
1292      }
1293    };
1294
1295  protected:
1296
1297    const Digraph &_g;
1298    AutoNodeMap _head;
1299    typename Digraph::template ArcMap<Arc> _parent;
1300    typename Digraph::template ArcMap<Arc> _left;
1301    typename Digraph::template ArcMap<Arc> _right;
1302
1303  public:
1304
1305    ///Constructor
1306
1307    ///Constructor.
1308    ///
1309    ///It builds up the search database.
1310    DynArcLookUp(const Digraph &g)
1311      : _g(g),_head(g),_parent(g),_left(g),_right(g)
1312    {
1313      Parent::attach(_g.notifier(typename Digraph::Arc()));
1314      refresh();
1315    }
1316
1317  protected:
1318
1319    virtual void add(const Arc& arc) {
1320      insert(arc);
1321    }
1322
1323    virtual void add(const std::vector<Arc>& arcs) {
1324      for (int i = 0; i < int(arcs.size()); ++i) {
1325        insert(arcs[i]);
1326      }
1327    }
1328
1329    virtual void erase(const Arc& arc) {
1330      remove(arc);
1331    }
1332
1333    virtual void erase(const std::vector<Arc>& arcs) {
1334      for (int i = 0; i < int(arcs.size()); ++i) {
1335        remove(arcs[i]);
1336      }
1337    }
1338
1339    virtual void build() {
1340      refresh();
1341    }
1342
1343    virtual void clear() {
1344      for(NodeIt n(_g);n!=INVALID;++n) {
1345        _head[n] = INVALID;
1346      }
1347    }
1348
1349    void insert(Arc arc) {
1350      Node s = _g.source(arc);
1351      Node t = _g.target(arc);
1352      _left[arc] = INVALID;
1353      _right[arc] = INVALID;
1354
1355      Arc e = _head[s];
1356      if (e == INVALID) {
1357        _head[s] = arc;
1358        _parent[arc] = INVALID;
1359        return;
1360      }
1361      while (true) {
1362        if (t < _g.target(e)) {
1363          if (_left[e] == INVALID) {
1364            _left[e] = arc;
1365            _parent[arc] = e;
1366            splay(arc);
1367            return;
1368          } else {
1369            e = _left[e];
1370          }
1371        } else {
1372          if (_right[e] == INVALID) {
1373            _right[e] = arc;
1374            _parent[arc] = e;
1375            splay(arc);
1376            return;
1377          } else {
1378            e = _right[e];
1379          }
1380        }
1381      }
1382    }
1383
1384    void remove(Arc arc) {
1385      if (_left[arc] == INVALID) {
1386        if (_right[arc] != INVALID) {
1387          _parent[_right[arc]] = _parent[arc];
1388        }
1389        if (_parent[arc] != INVALID) {
1390          if (_left[_parent[arc]] == arc) {
1391            _left[_parent[arc]] = _right[arc];
1392          } else {
1393            _right[_parent[arc]] = _right[arc];
1394          }
1395        } else {
1396          _head[_g.source(arc)] = _right[arc];
1397        }
1398      } else if (_right[arc] == INVALID) {
1399        _parent[_left[arc]] = _parent[arc];
1400        if (_parent[arc] != INVALID) {
1401          if (_left[_parent[arc]] == arc) {
1402            _left[_parent[arc]] = _left[arc];
1403          } else {
1404            _right[_parent[arc]] = _left[arc];
1405          }
1406        } else {
1407          _head[_g.source(arc)] = _left[arc];
1408        }
1409      } else {
1410        Arc e = _left[arc];
1411        if (_right[e] != INVALID) {
1412          e = _right[e];
1413          while (_right[e] != INVALID) {
1414            e = _right[e];
1415          }
1416          Arc s = _parent[e];
1417          _right[_parent[e]] = _left[e];
1418          if (_left[e] != INVALID) {
1419            _parent[_left[e]] = _parent[e];
1420          }
1421
1422          _left[e] = _left[arc];
1423          _parent[_left[arc]] = e;
1424          _right[e] = _right[arc];
1425          _parent[_right[arc]] = e;
1426
1427          _parent[e] = _parent[arc];
1428          if (_parent[arc] != INVALID) {
1429            if (_left[_parent[arc]] == arc) {
1430              _left[_parent[arc]] = e;
1431            } else {
1432              _right[_parent[arc]] = e;
1433            }
1434          }
1435          splay(s);
1436        } else {
1437          _right[e] = _right[arc];
1438          _parent[_right[arc]] = e;
1439          _parent[e] = _parent[arc];
1440
1441          if (_parent[arc] != INVALID) {
1442            if (_left[_parent[arc]] == arc) {
1443              _left[_parent[arc]] = e;
1444            } else {
1445              _right[_parent[arc]] = e;
1446            }
1447          } else {
1448            _head[_g.source(arc)] = e;
1449          }
1450        }
1451      }
1452    }
1453
1454    Arc refreshRec(std::vector<Arc> &v,int a,int b)
1455    {
1456      int m=(a+b)/2;
1457      Arc me=v[m];
1458      if (a < m) {
1459        Arc left = refreshRec(v,a,m-1);
1460        _left[me] = left;
1461        _parent[left] = me;
1462      } else {
1463        _left[me] = INVALID;
1464      }
1465      if (m < b) {
1466        Arc right = refreshRec(v,m+1,b);
1467        _right[me] = right;
1468        _parent[right] = me;
1469      } else {
1470        _right[me] = INVALID;
1471      }
1472      return me;
1473    }
1474
1475    void refresh() {
1476      for(NodeIt n(_g);n!=INVALID;++n) {
1477        std::vector<Arc> v;
1478        for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
1479        if (!v.empty()) {
1480          std::sort(v.begin(),v.end(),ArcLess(_g));
1481          Arc head = refreshRec(v,0,v.size()-1);
1482          _head[n] = head;
1483          _parent[head] = INVALID;
1484        }
1485        else _head[n] = INVALID;
1486      }
1487    }
1488
1489    void zig(Arc v) {
1490      Arc w = _parent[v];
1491      _parent[v] = _parent[w];
1492      _parent[w] = v;
1493      _left[w] = _right[v];
1494      _right[v] = w;
1495      if (_parent[v] != INVALID) {
1496        if (_right[_parent[v]] == w) {
1497          _right[_parent[v]] = v;
1498        } else {
1499          _left[_parent[v]] = v;
1500        }
1501      }
1502      if (_left[w] != INVALID){
1503        _parent[_left[w]] = w;
1504      }
1505    }
1506
1507    void zag(Arc v) {
1508      Arc w = _parent[v];
1509      _parent[v] = _parent[w];
1510      _parent[w] = v;
1511      _right[w] = _left[v];
1512      _left[v] = w;
1513      if (_parent[v] != INVALID){
1514        if (_left[_parent[v]] == w) {
1515          _left[_parent[v]] = v;
1516        } else {
1517          _right[_parent[v]] = v;
1518        }
1519      }
1520      if (_right[w] != INVALID){
1521        _parent[_right[w]] = w;
1522      }
1523    }
1524
1525    void splay(Arc v) {
1526      while (_parent[v] != INVALID) {
1527        if (v == _left[_parent[v]]) {
1528          if (_parent[_parent[v]] == INVALID) {
1529            zig(v);
1530          } else {
1531            if (_parent[v] == _left[_parent[_parent[v]]]) {
1532              zig(_parent[v]);
1533              zig(v);
1534            } else {
1535              zig(v);
1536              zag(v);
1537            }
1538          }
1539        } else {
1540          if (_parent[_parent[v]] == INVALID) {
1541            zag(v);
1542          } else {
1543            if (_parent[v] == _left[_parent[_parent[v]]]) {
1544              zag(v);
1545              zig(v);
1546            } else {
1547              zag(_parent[v]);
1548              zag(v);
1549            }
1550          }
1551        }
1552      }
1553      _head[_g.source(v)] = v;
1554    }
1555
1556
1557  public:
1558
1559    ///Find an arc between two nodes.
1560
1561    ///Find an arc between two nodes.
1562    ///\param s The source node.
1563    ///\param t The target node.
1564    ///\param p The previous arc between \c s and \c t. It it is INVALID or
1565    ///not given, the operator finds the first appropriate arc.
1566    ///\return An arc from \c s to \c t after \c p or
1567    ///\ref INVALID if there is no more.
1568    ///
1569    ///For example, you can count the number of arcs from \c u to \c v in the
1570    ///following way.
1571    ///\code
1572    ///DynArcLookUp<ListDigraph> ae(g);
1573    ///...
1574    ///int n = 0;
1575    ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
1576    ///\endcode
1577    ///
1578    ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
1579    ///amortized time, specifically, the time complexity of the lookups
1580    ///is equal to the optimal search tree implementation for the
1581    ///current query distribution in a constant factor.
1582    ///
1583    ///\note This is a dynamic data structure, therefore the data
1584    ///structure is updated after each graph alteration. Thus although
1585    ///this data structure is theoretically faster than \ref ArcLookUp
1586    ///and \ref AllArcLookUp, it often provides worse performance than
1587    ///them.
1588    Arc operator()(Node s, Node t, Arc p = INVALID) const  {
1589      if (p == INVALID) {
1590        Arc a = _head[s];
1591        if (a == INVALID) return INVALID;
1592        Arc r = INVALID;
1593        while (true) {
1594          if (_g.target(a) < t) {
1595            if (_right[a] == INVALID) {
1596              const_cast<DynArcLookUp&>(*this).splay(a);
1597              return r;
1598            } else {
1599              a = _right[a];
1600            }
1601          } else {
1602            if (_g.target(a) == t) {
1603              r = a;
1604            }
1605            if (_left[a] == INVALID) {
1606              const_cast<DynArcLookUp&>(*this).splay(a);
1607              return r;
1608            } else {
1609              a = _left[a];
1610            }
1611          }
1612        }
1613      } else {
1614        Arc a = p;
1615        if (_right[a] != INVALID) {
1616          a = _right[a];
1617          while (_left[a] != INVALID) {
1618            a = _left[a];
1619          }
1620          const_cast<DynArcLookUp&>(*this).splay(a);
1621        } else {
1622          while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
1623            a = _parent[a];
1624          }
1625          if (_parent[a] == INVALID) {
1626            return INVALID;
1627          } else {
1628            a = _parent[a];
1629            const_cast<DynArcLookUp&>(*this).splay(a);
1630          }
1631        }
1632        if (_g.target(a) == t) return a;
1633        else return INVALID;
1634      }
1635    }
1636
1637  };
1638
1639  ///Fast arc look-up between given endpoints.
1640
1641  ///Using this class, you can find an arc in a digraph from a given
1642  ///source to a given target in time <em>O</em>(log<em>d</em>),
1643  ///where <em>d</em> is the out-degree of the source node.
1644  ///
1645  ///It is not possible to find \e all parallel arcs between two nodes.
1646  ///Use \ref AllArcLookUp for this purpose.
1647  ///
1648  ///\warning This class is static, so you should call refresh() (or at
1649  ///least refresh(Node)) to refresh this data structure whenever the
1650  ///digraph changes. This is a time consuming (superlinearly proportional
1651  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
1652  ///
1653  ///\tparam GR The type of the underlying digraph.
1654  ///
1655  ///\sa DynArcLookUp
1656  ///\sa AllArcLookUp
1657  template<class GR>
1658  class ArcLookUp
1659  {
1660    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1661
1662  public:
1663
1664    /// The Digraph type
1665    typedef GR Digraph;
1666
1667  protected:
1668    const Digraph &_g;
1669    typename Digraph::template NodeMap<Arc> _head;
1670    typename Digraph::template ArcMap<Arc> _left;
1671    typename Digraph::template ArcMap<Arc> _right;
1672
1673    class ArcLess {
1674      const Digraph &g;
1675    public:
1676      ArcLess(const Digraph &_g) : g(_g) {}
1677      bool operator()(Arc a,Arc b) const
1678      {
1679        return g.target(a)<g.target(b);
1680      }
1681    };
1682
1683  public:
1684
1685    ///Constructor
1686
1687    ///Constructor.
1688    ///
1689    ///It builds up the search database, which remains valid until the digraph
1690    ///changes.
1691    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
1692
1693  private:
1694    Arc refreshRec(std::vector<Arc> &v,int a,int b)
1695    {
1696      int m=(a+b)/2;
1697      Arc me=v[m];
1698      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
1699      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
1700      return me;
1701    }
1702  public:
1703    ///Refresh the search data structure at a node.
1704
1705    ///Build up the search database of node \c n.
1706    ///
1707    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
1708    ///is the number of the outgoing arcs of \c n.
1709    void refresh(Node n)
1710    {
1711      std::vector<Arc> v;
1712      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
1713      if(v.size()) {
1714        std::sort(v.begin(),v.end(),ArcLess(_g));
1715        _head[n]=refreshRec(v,0,v.size()-1);
1716      }
1717      else _head[n]=INVALID;
1718    }
1719    ///Refresh the full data structure.
1720
1721    ///Build up the full search database. In fact, it simply calls
1722    ///\ref refresh(Node) "refresh(n)" for each node \c n.
1723    ///
1724    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
1725    ///the number of the arcs in the digraph and <em>D</em> is the maximum
1726    ///out-degree of the digraph.
1727    void refresh()
1728    {
1729      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
1730    }
1731
1732    ///Find an arc between two nodes.
1733
1734    ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
1735    ///where <em>d</em> is the number of outgoing arcs of \c s.
1736    ///\param s The source node.
1737    ///\param t The target node.
1738    ///\return An arc from \c s to \c t if there exists,
1739    ///\ref INVALID otherwise.
1740    ///
1741    ///\warning If you change the digraph, refresh() must be called before using
1742    ///this operator. If you change the outgoing arcs of
1743    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
1744    Arc operator()(Node s, Node t) const
1745    {
1746      Arc e;
1747      for(e=_head[s];
1748          e!=INVALID&&_g.target(e)!=t;
1749          e = t < _g.target(e)?_left[e]:_right[e]) ;
1750      return e;
1751    }
1752
1753  };
1754
1755  ///Fast look-up of all arcs between given endpoints.
1756
1757  ///This class is the same as \ref ArcLookUp, with the addition
1758  ///that it makes it possible to find all parallel arcs between given
1759  ///endpoints.
1760  ///
1761  ///\warning This class is static, so you should call refresh() (or at
1762  ///least refresh(Node)) to refresh this data structure whenever the
1763  ///digraph changes. This is a time consuming (superlinearly proportional
1764  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
1765  ///
1766  ///\tparam GR The type of the underlying digraph.
1767  ///
1768  ///\sa DynArcLookUp
1769  ///\sa ArcLookUp
1770  template<class GR>
1771  class AllArcLookUp : public ArcLookUp<GR>
1772  {
1773    using ArcLookUp<GR>::_g;
1774    using ArcLookUp<GR>::_right;
1775    using ArcLookUp<GR>::_left;
1776    using ArcLookUp<GR>::_head;
1777
1778    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1779
1780    typename GR::template ArcMap<Arc> _next;
1781
1782    Arc refreshNext(Arc head,Arc next=INVALID)
1783    {
1784      if(head==INVALID) return next;
1785      else {
1786        next=refreshNext(_right[head],next);
1787        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
1788          ? next : INVALID;
1789        return refreshNext(_left[head],head);
1790      }
1791    }
1792
1793    void refreshNext()
1794    {
1795      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
1796    }
1797
1798  public:
1799
1800    /// The Digraph type
1801    typedef GR Digraph;
1802
1803    ///Constructor
1804
1805    ///Constructor.
1806    ///
1807    ///It builds up the search database, which remains valid until the digraph
1808    ///changes.
1809    AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
1810
1811    ///Refresh the data structure at a node.
1812
1813    ///Build up the search database of node \c n.
1814    ///
1815    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
1816    ///the number of the outgoing arcs of \c n.
1817    void refresh(Node n)
1818    {
1819      ArcLookUp<GR>::refresh(n);
1820      refreshNext(_head[n]);
1821    }
1822
1823    ///Refresh the full data structure.
1824
1825    ///Build up the full search database. In fact, it simply calls
1826    ///\ref refresh(Node) "refresh(n)" for each node \c n.
1827    ///
1828    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
1829    ///the number of the arcs in the digraph and <em>D</em> is the maximum
1830    ///out-degree of the digraph.
1831    void refresh()
1832    {
1833      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
1834    }
1835
1836    ///Find an arc between two nodes.
1837
1838    ///Find an arc between two nodes.
1839    ///\param s The source node.
1840    ///\param t The target node.
1841    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
1842    ///not given, the operator finds the first appropriate arc.
1843    ///\return An arc from \c s to \c t after \c prev or
1844    ///\ref INVALID if there is no more.
1845    ///
1846    ///For example, you can count the number of arcs from \c u to \c v in the
1847    ///following way.
1848    ///\code
1849    ///AllArcLookUp<ListDigraph> ae(g);
1850    ///...
1851    ///int n = 0;
1852    ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
1853    ///\endcode
1854    ///
1855    ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
1856    ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
1857    ///consecutive arcs are found in constant time.
1858    ///
1859    ///\warning If you change the digraph, refresh() must be called before using
1860    ///this operator. If you change the outgoing arcs of
1861    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
1862    ///
1863    Arc operator()(Node s, Node t, Arc prev=INVALID) const
1864    {
1865      if(prev==INVALID)
1866        {
1867          Arc f=INVALID;
1868          Arc e;
1869          for(e=_head[s];
1870              e!=INVALID&&_g.target(e)!=t;
1871              e = t < _g.target(e)?_left[e]:_right[e]) ;
1872          while(e!=INVALID)
1873            if(_g.target(e)==t)
1874              {
1875                f = e;
1876                e = _left[e];
1877              }
1878            else e = _right[e];
1879          return f;
1880        }
1881      else return _next[prev];
1882    }
1883
1884  };
1885
1886  /// @}
1887
1888} //namespace lemon
1889
1890#endif
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