COIN-OR::LEMON - Graph Library

source: lemon/lemon/core.h @ 515:7992dcb0d0e6

Last change on this file since 515:7992dcb0d0e6 was 449:b0f74ca2e3ac, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Bug fix in ConEdgeIt? (#195)

File size: 58.5 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) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_CORE_H
20#define LEMON_CORE_H
21
22#include <vector>
23#include <algorithm>
24
25#include <lemon/bits/enable_if.h>
26#include <lemon/bits/traits.h>
27#include <lemon/assert.h>
28
29///\file
30///\brief LEMON core utilities.
31///
32///This header file contains core utilities for LEMON.
33///It is automatically included by all graph types, therefore it usually
34///do not have to be included directly.
35
36namespace lemon {
37
38  /// \brief Dummy type to make it easier to create invalid iterators.
39  ///
40  /// Dummy type to make it easier to create invalid iterators.
41  /// See \ref INVALID for the usage.
42  struct Invalid {
43  public:
44    bool operator==(Invalid) { return true;  }
45    bool operator!=(Invalid) { return false; }
46    bool operator< (Invalid) { return false; }
47  };
48
49  /// \brief Invalid iterators.
50  ///
51  /// \ref Invalid is a global type that converts to each iterator
52  /// in such a way that the value of the target iterator will be invalid.
53#ifdef LEMON_ONLY_TEMPLATES
54  const Invalid INVALID = Invalid();
55#else
56  extern const Invalid INVALID;
57#endif
58
59  /// \addtogroup gutils
60  /// @{
61
62  ///Create convenience typedefs for the digraph types and iterators
63
64  ///This \c \#define creates convenient type definitions for the following
65  ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
66  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
67  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
68  ///
69  ///\note If the graph type is a dependent type, ie. the graph type depend
70  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
71  ///macro.
72#define DIGRAPH_TYPEDEFS(Digraph)                                       \
73  typedef Digraph::Node Node;                                           \
74  typedef Digraph::NodeIt NodeIt;                                       \
75  typedef Digraph::Arc Arc;                                             \
76  typedef Digraph::ArcIt ArcIt;                                         \
77  typedef Digraph::InArcIt InArcIt;                                     \
78  typedef Digraph::OutArcIt OutArcIt;                                   \
79  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
80  typedef Digraph::NodeMap<int> IntNodeMap;                             \
81  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
82  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
83  typedef Digraph::ArcMap<int> IntArcMap;                               \
84  typedef Digraph::ArcMap<double> DoubleArcMap
85
86  ///Create convenience typedefs for the digraph types and iterators
87
88  ///\see DIGRAPH_TYPEDEFS
89  ///
90  ///\note Use this macro, if the graph type is a dependent type,
91  ///ie. the graph type depend on a template parameter.
92#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
93  typedef typename Digraph::Node Node;                                  \
94  typedef typename Digraph::NodeIt NodeIt;                              \
95  typedef typename Digraph::Arc Arc;                                    \
96  typedef typename Digraph::ArcIt ArcIt;                                \
97  typedef typename Digraph::InArcIt InArcIt;                            \
98  typedef typename Digraph::OutArcIt OutArcIt;                          \
99  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
100  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
101  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
102  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
103  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
104  typedef typename Digraph::template ArcMap<double> DoubleArcMap
105
106  ///Create convenience typedefs for the graph types and iterators
107
108  ///This \c \#define creates the same convenient type definitions as defined
109  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
110  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
111  ///\c DoubleEdgeMap.
112  ///
113  ///\note If the graph type is a dependent type, ie. the graph type depend
114  ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
115  ///macro.
116#define GRAPH_TYPEDEFS(Graph)                                           \
117  DIGRAPH_TYPEDEFS(Graph);                                              \
118  typedef Graph::Edge Edge;                                             \
119  typedef Graph::EdgeIt EdgeIt;                                         \
120  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
121  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
122  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
123  typedef Graph::EdgeMap<double> DoubleEdgeMap
124
125  ///Create convenience typedefs for the graph types and iterators
126
127  ///\see GRAPH_TYPEDEFS
128  ///
129  ///\note Use this macro, if the graph type is a dependent type,
130  ///ie. the graph type depend on a template parameter.
131#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
132  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
133  typedef typename Graph::Edge Edge;                                    \
134  typedef typename Graph::EdgeIt EdgeIt;                                \
135  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
136  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
137  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
138  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
139
140  /// \brief Function to count the items in a graph.
141  ///
142  /// This function counts the items (nodes, arcs etc.) in a graph.
143  /// The complexity of the function is linear because
144  /// it iterates on all of the items.
145  template <typename Graph, typename Item>
146  inline int countItems(const Graph& g) {
147    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
148    int num = 0;
149    for (ItemIt it(g); it != INVALID; ++it) {
150      ++num;
151    }
152    return num;
153  }
154
155  // Node counting:
156
157  namespace _core_bits {
158
159    template <typename Graph, typename Enable = void>
160    struct CountNodesSelector {
161      static int count(const Graph &g) {
162        return countItems<Graph, typename Graph::Node>(g);
163      }
164    };
165
166    template <typename Graph>
167    struct CountNodesSelector<
168      Graph, typename
169      enable_if<typename Graph::NodeNumTag, void>::type>
170    {
171      static int count(const Graph &g) {
172        return g.nodeNum();
173      }
174    };
175  }
176
177  /// \brief Function to count the nodes in the graph.
178  ///
179  /// This function counts the nodes in the graph.
180  /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
181  /// graph structures it is specialized to run in <em>O</em>(1).
182  ///
183  /// \note If the graph contains a \c nodeNum() member function and a
184  /// \c NodeNumTag tag then this function calls directly the member
185  /// function to query the cardinality of the node set.
186  template <typename Graph>
187  inline int countNodes(const Graph& g) {
188    return _core_bits::CountNodesSelector<Graph>::count(g);
189  }
190
191  // Arc counting:
192
193  namespace _core_bits {
194
195    template <typename Graph, typename Enable = void>
196    struct CountArcsSelector {
197      static int count(const Graph &g) {
198        return countItems<Graph, typename Graph::Arc>(g);
199      }
200    };
201
202    template <typename Graph>
203    struct CountArcsSelector<
204      Graph,
205      typename enable_if<typename Graph::ArcNumTag, void>::type>
206    {
207      static int count(const Graph &g) {
208        return g.arcNum();
209      }
210    };
211  }
212
213  /// \brief Function to count the arcs in the graph.
214  ///
215  /// This function counts the arcs in the graph.
216  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
217  /// graph structures it is specialized to run in <em>O</em>(1).
218  ///
219  /// \note If the graph contains a \c arcNum() member function and a
220  /// \c ArcNumTag tag then this function calls directly the member
221  /// function to query the cardinality of the arc set.
222  template <typename Graph>
223  inline int countArcs(const Graph& g) {
224    return _core_bits::CountArcsSelector<Graph>::count(g);
225  }
226
227  // Edge counting:
228
229  namespace _core_bits {
230
231    template <typename Graph, typename Enable = void>
232    struct CountEdgesSelector {
233      static int count(const Graph &g) {
234        return countItems<Graph, typename Graph::Edge>(g);
235      }
236    };
237
238    template <typename Graph>
239    struct CountEdgesSelector<
240      Graph,
241      typename enable_if<typename Graph::EdgeNumTag, void>::type>
242    {
243      static int count(const Graph &g) {
244        return g.edgeNum();
245      }
246    };
247  }
248
249  /// \brief Function to count the edges in the graph.
250  ///
251  /// This function counts the edges in the graph.
252  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
253  /// graph structures it is specialized to run in <em>O</em>(1).
254  ///
255  /// \note If the graph contains a \c edgeNum() member function and a
256  /// \c EdgeNumTag tag then this function calls directly the member
257  /// function to query the cardinality of the edge set.
258  template <typename Graph>
259  inline int countEdges(const Graph& g) {
260    return _core_bits::CountEdgesSelector<Graph>::count(g);
261
262  }
263
264
265  template <typename Graph, typename DegIt>
266  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
267    int num = 0;
268    for (DegIt it(_g, _n); it != INVALID; ++it) {
269      ++num;
270    }
271    return num;
272  }
273
274  /// \brief Function to count the number of the out-arcs from node \c n.
275  ///
276  /// This function counts the number of the out-arcs from node \c n
277  /// in the graph \c g.
278  template <typename Graph>
279  inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
280    return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
281  }
282
283  /// \brief Function to count the number of the in-arcs to node \c n.
284  ///
285  /// This function counts the number of the in-arcs to node \c n
286  /// in the graph \c g.
287  template <typename Graph>
288  inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
289    return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
290  }
291
292  /// \brief Function to count the number of the inc-edges to node \c n.
293  ///
294  /// This function counts the number of the inc-edges to node \c n
295  /// in the undirected graph \c g.
296  template <typename Graph>
297  inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
298    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
299  }
300
301  namespace _core_bits {
302
303    template <typename Digraph, typename Item, typename RefMap>
304    class MapCopyBase {
305    public:
306      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
307
308      virtual ~MapCopyBase() {}
309    };
310
311    template <typename Digraph, typename Item, typename RefMap,
312              typename FromMap, typename ToMap>
313    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
314    public:
315
316      MapCopy(const FromMap& map, ToMap& tmap)
317        : _map(map), _tmap(tmap) {}
318
319      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
320        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
321        for (ItemIt it(digraph); it != INVALID; ++it) {
322          _tmap.set(refMap[it], _map[it]);
323        }
324      }
325
326    private:
327      const FromMap& _map;
328      ToMap& _tmap;
329    };
330
331    template <typename Digraph, typename Item, typename RefMap, typename It>
332    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
333    public:
334
335      ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
336
337      virtual void copy(const Digraph&, const RefMap& refMap) {
338        _it = refMap[_item];
339      }
340
341    private:
342      Item _item;
343      It& _it;
344    };
345
346    template <typename Digraph, typename Item, typename RefMap, typename Ref>
347    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
348    public:
349
350      RefCopy(Ref& map) : _map(map) {}
351
352      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
353        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
354        for (ItemIt it(digraph); it != INVALID; ++it) {
355          _map.set(it, refMap[it]);
356        }
357      }
358
359    private:
360      Ref& _map;
361    };
362
363    template <typename Digraph, typename Item, typename RefMap,
364              typename CrossRef>
365    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
366    public:
367
368      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
369
370      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
371        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
372        for (ItemIt it(digraph); it != INVALID; ++it) {
373          _cmap.set(refMap[it], it);
374        }
375      }
376
377    private:
378      CrossRef& _cmap;
379    };
380
381    template <typename Digraph, typename Enable = void>
382    struct DigraphCopySelector {
383      template <typename From, typename NodeRefMap, typename ArcRefMap>
384      static void copy(const From& from, Digraph &to,
385                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
386        for (typename From::NodeIt it(from); it != INVALID; ++it) {
387          nodeRefMap[it] = to.addNode();
388        }
389        for (typename From::ArcIt it(from); it != INVALID; ++it) {
390          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
391                                    nodeRefMap[from.target(it)]);
392        }
393      }
394    };
395
396    template <typename Digraph>
397    struct DigraphCopySelector<
398      Digraph,
399      typename enable_if<typename Digraph::BuildTag, void>::type>
400    {
401      template <typename From, typename NodeRefMap, typename ArcRefMap>
402      static void copy(const From& from, Digraph &to,
403                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
404        to.build(from, nodeRefMap, arcRefMap);
405      }
406    };
407
408    template <typename Graph, typename Enable = void>
409    struct GraphCopySelector {
410      template <typename From, typename NodeRefMap, typename EdgeRefMap>
411      static void copy(const From& from, Graph &to,
412                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
413        for (typename From::NodeIt it(from); it != INVALID; ++it) {
414          nodeRefMap[it] = to.addNode();
415        }
416        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
417          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
418                                      nodeRefMap[from.v(it)]);
419        }
420      }
421    };
422
423    template <typename Graph>
424    struct GraphCopySelector<
425      Graph,
426      typename enable_if<typename Graph::BuildTag, void>::type>
427    {
428      template <typename From, typename NodeRefMap, typename EdgeRefMap>
429      static void copy(const From& from, Graph &to,
430                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
431        to.build(from, nodeRefMap, edgeRefMap);
432      }
433    };
434
435  }
436
437  /// \brief Class to copy a digraph.
438  ///
439  /// Class to copy a digraph to another digraph (duplicate a digraph). The
440  /// simplest way of using it is through the \c digraphCopy() function.
441  ///
442  /// This class not only make a copy of a digraph, but it can create
443  /// references and cross references between the nodes and arcs of
444  /// the two digraphs, and it can copy maps to use with the newly created
445  /// digraph.
446  ///
447  /// To make a copy from a digraph, first an instance of DigraphCopy
448  /// should be created, then the data belongs to the digraph should
449  /// assigned to copy. In the end, the \c run() member should be
450  /// called.
451  ///
452  /// The next code copies a digraph with several data:
453  ///\code
454  ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
455  ///  // Create references for the nodes
456  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
457  ///  cg.nodeRef(nr);
458  ///  // Create cross references (inverse) for the arcs
459  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
460  ///  cg.arcCrossRef(acr);
461  ///  // Copy an arc map
462  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
463  ///  NewGraph::ArcMap<double> namap(new_graph);
464  ///  cg.arcMap(oamap, namap);
465  ///  // Copy a node
466  ///  OrigGraph::Node on;
467  ///  NewGraph::Node nn;
468  ///  cg.node(on, nn);
469  ///  // Execute copying
470  ///  cg.run();
471  ///\endcode
472  template <typename From, typename To>
473  class DigraphCopy {
474  private:
475
476    typedef typename From::Node Node;
477    typedef typename From::NodeIt NodeIt;
478    typedef typename From::Arc Arc;
479    typedef typename From::ArcIt ArcIt;
480
481    typedef typename To::Node TNode;
482    typedef typename To::Arc TArc;
483
484    typedef typename From::template NodeMap<TNode> NodeRefMap;
485    typedef typename From::template ArcMap<TArc> ArcRefMap;
486
487  public:
488
489    /// \brief Constructor of DigraphCopy.
490    ///
491    /// Constructor of DigraphCopy for copying the content of the
492    /// \c from digraph into the \c to digraph.
493    DigraphCopy(const From& from, To& to)
494      : _from(from), _to(to) {}
495
496    /// \brief Destructor of DigraphCopy
497    ///
498    /// Destructor of DigraphCopy.
499    ~DigraphCopy() {
500      for (int i = 0; i < int(_node_maps.size()); ++i) {
501        delete _node_maps[i];
502      }
503      for (int i = 0; i < int(_arc_maps.size()); ++i) {
504        delete _arc_maps[i];
505      }
506
507    }
508
509    /// \brief Copy the node references into the given map.
510    ///
511    /// This function copies the node references into the given map.
512    /// The parameter should be a map, whose key type is the Node type of
513    /// the source digraph, while the value type is the Node type of the
514    /// destination digraph.
515    template <typename NodeRef>
516    DigraphCopy& nodeRef(NodeRef& map) {
517      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
518                           NodeRefMap, NodeRef>(map));
519      return *this;
520    }
521
522    /// \brief Copy the node cross references into the given map.
523    ///
524    /// This function copies the node cross references (reverse references)
525    /// into the given map. The parameter should be a map, whose key type
526    /// is the Node type of the destination digraph, while the value type is
527    /// the Node type of the source digraph.
528    template <typename NodeCrossRef>
529    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
530      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
531                           NodeRefMap, NodeCrossRef>(map));
532      return *this;
533    }
534
535    /// \brief Make a copy of the given node map.
536    ///
537    /// This function makes a copy of the given node map for the newly
538    /// created digraph.
539    /// The key type of the new map \c tmap should be the Node type of the
540    /// destination digraph, and the key type of the original map \c map
541    /// should be the Node type of the source digraph.
542    template <typename FromMap, typename ToMap>
543    DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
544      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
545                           NodeRefMap, FromMap, ToMap>(map, tmap));
546      return *this;
547    }
548
549    /// \brief Make a copy of the given node.
550    ///
551    /// This function makes a copy of the given node.
552    DigraphCopy& node(const Node& node, TNode& tnode) {
553      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
554                           NodeRefMap, TNode>(node, tnode));
555      return *this;
556    }
557
558    /// \brief Copy the arc references into the given map.
559    ///
560    /// This function copies the arc references into the given map.
561    /// The parameter should be a map, whose key type is the Arc type of
562    /// the source digraph, while the value type is the Arc type of the
563    /// destination digraph.
564    template <typename ArcRef>
565    DigraphCopy& arcRef(ArcRef& map) {
566      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
567                          ArcRefMap, ArcRef>(map));
568      return *this;
569    }
570
571    /// \brief Copy the arc cross references into the given map.
572    ///
573    /// This function copies the arc cross references (reverse references)
574    /// into the given map. The parameter should be a map, whose key type
575    /// is the Arc type of the destination digraph, while the value type is
576    /// the Arc type of the source digraph.
577    template <typename ArcCrossRef>
578    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
579      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
580                          ArcRefMap, ArcCrossRef>(map));
581      return *this;
582    }
583
584    /// \brief Make a copy of the given arc map.
585    ///
586    /// This function makes a copy of the given arc map for the newly
587    /// created digraph.
588    /// The key type of the new map \c tmap should be the Arc type of the
589    /// destination digraph, and the key type of the original map \c map
590    /// should be the Arc type of the source digraph.
591    template <typename FromMap, typename ToMap>
592    DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
593      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
594                          ArcRefMap, FromMap, ToMap>(map, tmap));
595      return *this;
596    }
597
598    /// \brief Make a copy of the given arc.
599    ///
600    /// This function makes a copy of the given arc.
601    DigraphCopy& arc(const Arc& arc, TArc& tarc) {
602      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
603                          ArcRefMap, TArc>(arc, tarc));
604      return *this;
605    }
606
607    /// \brief Execute copying.
608    ///
609    /// This function executes the copying of the digraph along with the
610    /// copying of the assigned data.
611    void run() {
612      NodeRefMap nodeRefMap(_from);
613      ArcRefMap arcRefMap(_from);
614      _core_bits::DigraphCopySelector<To>::
615        copy(_from, _to, nodeRefMap, arcRefMap);
616      for (int i = 0; i < int(_node_maps.size()); ++i) {
617        _node_maps[i]->copy(_from, nodeRefMap);
618      }
619      for (int i = 0; i < int(_arc_maps.size()); ++i) {
620        _arc_maps[i]->copy(_from, arcRefMap);
621      }
622    }
623
624  protected:
625
626    const From& _from;
627    To& _to;
628
629    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
630      _node_maps;
631
632    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
633      _arc_maps;
634
635  };
636
637  /// \brief Copy a digraph to another digraph.
638  ///
639  /// This function copies a digraph to another digraph.
640  /// The complete usage of it is detailed in the DigraphCopy class, but
641  /// a short example shows a basic work:
642  ///\code
643  /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
644  ///\endcode
645  ///
646  /// After the copy the \c nr map will contain the mapping from the
647  /// nodes of the \c from digraph to the nodes of the \c to digraph and
648  /// \c acr will contain the mapping from the arcs of the \c to digraph
649  /// to the arcs of the \c from digraph.
650  ///
651  /// \see DigraphCopy
652  template <typename From, typename To>
653  DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
654    return DigraphCopy<From, To>(from, to);
655  }
656
657  /// \brief Class to copy a graph.
658  ///
659  /// Class to copy a graph to another graph (duplicate a graph). The
660  /// simplest way of using it is through the \c graphCopy() function.
661  ///
662  /// This class not only make a copy of a graph, but it can create
663  /// references and cross references between the nodes, edges and arcs of
664  /// the two graphs, and it can copy maps for using with the newly created
665  /// graph.
666  ///
667  /// To make a copy from a graph, first an instance of GraphCopy
668  /// should be created, then the data belongs to the graph should
669  /// assigned to copy. In the end, the \c run() member should be
670  /// called.
671  ///
672  /// The next code copies a graph with several data:
673  ///\code
674  ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
675  ///  // Create references for the nodes
676  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
677  ///  cg.nodeRef(nr);
678  ///  // Create cross references (inverse) for the edges
679  ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
680  ///  cg.edgeCrossRef(ecr);
681  ///  // Copy an edge map
682  ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
683  ///  NewGraph::EdgeMap<double> nemap(new_graph);
684  ///  cg.edgeMap(oemap, nemap);
685  ///  // Copy a node
686  ///  OrigGraph::Node on;
687  ///  NewGraph::Node nn;
688  ///  cg.node(on, nn);
689  ///  // Execute copying
690  ///  cg.run();
691  ///\endcode
692  template <typename From, typename To>
693  class GraphCopy {
694  private:
695
696    typedef typename From::Node Node;
697    typedef typename From::NodeIt NodeIt;
698    typedef typename From::Arc Arc;
699    typedef typename From::ArcIt ArcIt;
700    typedef typename From::Edge Edge;
701    typedef typename From::EdgeIt EdgeIt;
702
703    typedef typename To::Node TNode;
704    typedef typename To::Arc TArc;
705    typedef typename To::Edge TEdge;
706
707    typedef typename From::template NodeMap<TNode> NodeRefMap;
708    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
709
710    struct ArcRefMap {
711      ArcRefMap(const From& from, const To& to,
712                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
713        : _from(from), _to(to),
714          _edge_ref(edge_ref), _node_ref(node_ref) {}
715
716      typedef typename From::Arc Key;
717      typedef typename To::Arc Value;
718
719      Value operator[](const Key& key) const {
720        bool forward = _from.u(key) != _from.v(key) ?
721          _node_ref[_from.source(key)] ==
722          _to.source(_to.direct(_edge_ref[key], true)) :
723          _from.direction(key);
724        return _to.direct(_edge_ref[key], forward);
725      }
726
727      const From& _from;
728      const To& _to;
729      const EdgeRefMap& _edge_ref;
730      const NodeRefMap& _node_ref;
731    };
732
733  public:
734
735    /// \brief Constructor of GraphCopy.
736    ///
737    /// Constructor of GraphCopy for copying the content of the
738    /// \c from graph into the \c to graph.
739    GraphCopy(const From& from, To& to)
740      : _from(from), _to(to) {}
741
742    /// \brief Destructor of GraphCopy
743    ///
744    /// Destructor of GraphCopy.
745    ~GraphCopy() {
746      for (int i = 0; i < int(_node_maps.size()); ++i) {
747        delete _node_maps[i];
748      }
749      for (int i = 0; i < int(_arc_maps.size()); ++i) {
750        delete _arc_maps[i];
751      }
752      for (int i = 0; i < int(_edge_maps.size()); ++i) {
753        delete _edge_maps[i];
754      }
755    }
756
757    /// \brief Copy the node references into the given map.
758    ///
759    /// This function copies the node references into the given map.
760    /// The parameter should be a map, whose key type is the Node type of
761    /// the source graph, while the value type is the Node type of the
762    /// destination graph.
763    template <typename NodeRef>
764    GraphCopy& nodeRef(NodeRef& map) {
765      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
766                           NodeRefMap, NodeRef>(map));
767      return *this;
768    }
769
770    /// \brief Copy the node cross references into the given map.
771    ///
772    /// This function copies the node cross references (reverse references)
773    /// into the given map. The parameter should be a map, whose key type
774    /// is the Node type of the destination graph, while the value type is
775    /// the Node type of the source graph.
776    template <typename NodeCrossRef>
777    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
778      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
779                           NodeRefMap, NodeCrossRef>(map));
780      return *this;
781    }
782
783    /// \brief Make a copy of the given node map.
784    ///
785    /// This function makes a copy of the given node map for the newly
786    /// created graph.
787    /// The key type of the new map \c tmap should be the Node type of the
788    /// destination graph, and the key type of the original map \c map
789    /// should be the Node type of the source graph.
790    template <typename FromMap, typename ToMap>
791    GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
792      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
793                           NodeRefMap, FromMap, ToMap>(map, tmap));
794      return *this;
795    }
796
797    /// \brief Make a copy of the given node.
798    ///
799    /// This function makes a copy of the given node.
800    GraphCopy& node(const Node& node, TNode& tnode) {
801      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
802                           NodeRefMap, TNode>(node, tnode));
803      return *this;
804    }
805
806    /// \brief Copy the arc references into the given map.
807    ///
808    /// This function copies the arc references into the given map.
809    /// The parameter should be a map, whose key type is the Arc type of
810    /// the source graph, while the value type is the Arc type of the
811    /// destination graph.
812    template <typename ArcRef>
813    GraphCopy& arcRef(ArcRef& map) {
814      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
815                          ArcRefMap, ArcRef>(map));
816      return *this;
817    }
818
819    /// \brief Copy the arc cross references into the given map.
820    ///
821    /// This function copies the arc cross references (reverse references)
822    /// into the given map. The parameter should be a map, whose key type
823    /// is the Arc type of the destination graph, while the value type is
824    /// the Arc type of the source graph.
825    template <typename ArcCrossRef>
826    GraphCopy& arcCrossRef(ArcCrossRef& map) {
827      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
828                          ArcRefMap, ArcCrossRef>(map));
829      return *this;
830    }
831
832    /// \brief Make a copy of the given arc map.
833    ///
834    /// This function makes a copy of the given arc map for the newly
835    /// created graph.
836    /// The key type of the new map \c tmap should be the Arc type of the
837    /// destination graph, and the key type of the original map \c map
838    /// should be the Arc type of the source graph.
839    template <typename FromMap, typename ToMap>
840    GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
841      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
842                          ArcRefMap, FromMap, ToMap>(map, tmap));
843      return *this;
844    }
845
846    /// \brief Make a copy of the given arc.
847    ///
848    /// This function makes a copy of the given arc.
849    GraphCopy& arc(const Arc& arc, TArc& tarc) {
850      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
851                          ArcRefMap, TArc>(arc, tarc));
852      return *this;
853    }
854
855    /// \brief Copy the edge references into the given map.
856    ///
857    /// This function copies the edge references into the given map.
858    /// The parameter should be a map, whose key type is the Edge type of
859    /// the source graph, while the value type is the Edge type of the
860    /// destination graph.
861    template <typename EdgeRef>
862    GraphCopy& edgeRef(EdgeRef& map) {
863      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
864                           EdgeRefMap, EdgeRef>(map));
865      return *this;
866    }
867
868    /// \brief Copy the edge cross references into the given map.
869    ///
870    /// This function copies the edge cross references (reverse references)
871    /// into the given map. The parameter should be a map, whose key type
872    /// is the Edge type of the destination graph, while the value type is
873    /// the Edge type of the source graph.
874    template <typename EdgeCrossRef>
875    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
876      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
877                           Edge, EdgeRefMap, EdgeCrossRef>(map));
878      return *this;
879    }
880
881    /// \brief Make a copy of the given edge map.
882    ///
883    /// This function makes a copy of the given edge map for the newly
884    /// created graph.
885    /// The key type of the new map \c tmap should be the Edge type of the
886    /// destination graph, and the key type of the original map \c map
887    /// should be the Edge type of the source graph.
888    template <typename FromMap, typename ToMap>
889    GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
890      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
891                           EdgeRefMap, FromMap, ToMap>(map, tmap));
892      return *this;
893    }
894
895    /// \brief Make a copy of the given edge.
896    ///
897    /// This function makes a copy of the given edge.
898    GraphCopy& edge(const Edge& edge, TEdge& tedge) {
899      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
900                           EdgeRefMap, TEdge>(edge, tedge));
901      return *this;
902    }
903
904    /// \brief Execute copying.
905    ///
906    /// This function executes the copying of the graph along with the
907    /// copying of the assigned data.
908    void run() {
909      NodeRefMap nodeRefMap(_from);
910      EdgeRefMap edgeRefMap(_from);
911      ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
912      _core_bits::GraphCopySelector<To>::
913        copy(_from, _to, nodeRefMap, edgeRefMap);
914      for (int i = 0; i < int(_node_maps.size()); ++i) {
915        _node_maps[i]->copy(_from, nodeRefMap);
916      }
917      for (int i = 0; i < int(_edge_maps.size()); ++i) {
918        _edge_maps[i]->copy(_from, edgeRefMap);
919      }
920      for (int i = 0; i < int(_arc_maps.size()); ++i) {
921        _arc_maps[i]->copy(_from, arcRefMap);
922      }
923    }
924
925  private:
926
927    const From& _from;
928    To& _to;
929
930    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
931      _node_maps;
932
933    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
934      _arc_maps;
935
936    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
937      _edge_maps;
938
939  };
940
941  /// \brief Copy a graph to another graph.
942  ///
943  /// This function copies a graph to another graph.
944  /// The complete usage of it is detailed in the GraphCopy class,
945  /// but a short example shows a basic work:
946  ///\code
947  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
948  ///\endcode
949  ///
950  /// After the copy the \c nr map will contain the mapping from the
951  /// nodes of the \c from graph to the nodes of the \c to graph and
952  /// \c ecr will contain the mapping from the edges of the \c to graph
953  /// to the edges of the \c from graph.
954  ///
955  /// \see GraphCopy
956  template <typename From, typename To>
957  GraphCopy<From, To>
958  graphCopy(const From& from, To& to) {
959    return GraphCopy<From, To>(from, to);
960  }
961
962  namespace _core_bits {
963
964    template <typename Graph, typename Enable = void>
965    struct FindArcSelector {
966      typedef typename Graph::Node Node;
967      typedef typename Graph::Arc Arc;
968      static Arc find(const Graph &g, Node u, Node v, Arc e) {
969        if (e == INVALID) {
970          g.firstOut(e, u);
971        } else {
972          g.nextOut(e);
973        }
974        while (e != INVALID && g.target(e) != v) {
975          g.nextOut(e);
976        }
977        return e;
978      }
979    };
980
981    template <typename Graph>
982    struct FindArcSelector<
983      Graph,
984      typename enable_if<typename Graph::FindArcTag, void>::type>
985    {
986      typedef typename Graph::Node Node;
987      typedef typename Graph::Arc Arc;
988      static Arc find(const Graph &g, Node u, Node v, Arc prev) {
989        return g.findArc(u, v, prev);
990      }
991    };
992  }
993
994  /// \brief Find an arc between two nodes of a digraph.
995  ///
996  /// This function finds an arc from node \c u to node \c v in the
997  /// digraph \c g.
998  ///
999  /// If \c prev is \ref INVALID (this is the default value), then
1000  /// it finds the first arc from \c u to \c v. Otherwise it looks for
1001  /// the next arc from \c u to \c v after \c prev.
1002  /// \return The found arc or \ref INVALID if there is no such an arc.
1003  ///
1004  /// Thus you can iterate through each arc from \c u to \c v as it follows.
1005  ///\code
1006  /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
1007  ///   ...
1008  /// }
1009  ///\endcode
1010  ///
1011  /// \note \ref ConArcIt provides iterator interface for the same
1012  /// functionality.
1013  ///
1014  ///\sa ConArcIt
1015  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1016  template <typename Graph>
1017  inline typename Graph::Arc
1018  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1019          typename Graph::Arc prev = INVALID) {
1020    return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
1021  }
1022
1023  /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
1024  ///
1025  /// Iterator for iterating on parallel arcs connecting the same nodes. It is
1026  /// a higher level interface for the \ref findArc() function. You can
1027  /// use it the following way:
1028  ///\code
1029  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
1030  ///   ...
1031  /// }
1032  ///\endcode
1033  ///
1034  ///\sa findArc()
1035  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1036  template <typename _Graph>
1037  class ConArcIt : public _Graph::Arc {
1038  public:
1039
1040    typedef _Graph Graph;
1041    typedef typename Graph::Arc Parent;
1042
1043    typedef typename Graph::Arc Arc;
1044    typedef typename Graph::Node Node;
1045
1046    /// \brief Constructor.
1047    ///
1048    /// Construct a new ConArcIt iterating on the arcs that
1049    /// connects nodes \c u and \c v.
1050    ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
1051      Parent::operator=(findArc(_graph, u, v));
1052    }
1053
1054    /// \brief Constructor.
1055    ///
1056    /// Construct a new ConArcIt that continues the iterating from arc \c a.
1057    ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
1058
1059    /// \brief Increment operator.
1060    ///
1061    /// It increments the iterator and gives back the next arc.
1062    ConArcIt& operator++() {
1063      Parent::operator=(findArc(_graph, _graph.source(*this),
1064                                _graph.target(*this), *this));
1065      return *this;
1066    }
1067  private:
1068    const Graph& _graph;
1069  };
1070
1071  namespace _core_bits {
1072
1073    template <typename Graph, typename Enable = void>
1074    struct FindEdgeSelector {
1075      typedef typename Graph::Node Node;
1076      typedef typename Graph::Edge Edge;
1077      static Edge find(const Graph &g, Node u, Node v, Edge e) {
1078        bool b;
1079        if (u != v) {
1080          if (e == INVALID) {
1081            g.firstInc(e, b, u);
1082          } else {
1083            b = g.u(e) == u;
1084            g.nextInc(e, b);
1085          }
1086          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
1087            g.nextInc(e, b);
1088          }
1089        } else {
1090          if (e == INVALID) {
1091            g.firstInc(e, b, u);
1092          } else {
1093            b = true;
1094            g.nextInc(e, b);
1095          }
1096          while (e != INVALID && (!b || g.v(e) != v)) {
1097            g.nextInc(e, b);
1098          }
1099        }
1100        return e;
1101      }
1102    };
1103
1104    template <typename Graph>
1105    struct FindEdgeSelector<
1106      Graph,
1107      typename enable_if<typename Graph::FindEdgeTag, void>::type>
1108    {
1109      typedef typename Graph::Node Node;
1110      typedef typename Graph::Edge Edge;
1111      static Edge find(const Graph &g, Node u, Node v, Edge prev) {
1112        return g.findEdge(u, v, prev);
1113      }
1114    };
1115  }
1116
1117  /// \brief Find an edge between two nodes of a graph.
1118  ///
1119  /// This function finds an edge from node \c u to node \c v in graph \c g.
1120  /// If node \c u and node \c v is equal then each loop edge
1121  /// will be enumerated once.
1122  ///
1123  /// If \c prev is \ref INVALID (this is the default value), then
1124  /// it finds the first edge from \c u to \c v. Otherwise it looks for
1125  /// the next edge from \c u to \c v after \c prev.
1126  /// \return The found edge or \ref INVALID if there is no such an edge.
1127  ///
1128  /// Thus you can iterate through each edge between \c u and \c v
1129  /// as it follows.
1130  ///\code
1131  /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
1132  ///   ...
1133  /// }
1134  ///\endcode
1135  ///
1136  /// \note \ref ConEdgeIt provides iterator interface for the same
1137  /// functionality.
1138  ///
1139  ///\sa ConEdgeIt
1140  template <typename Graph>
1141  inline typename Graph::Edge
1142  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1143            typename Graph::Edge p = INVALID) {
1144    return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
1145  }
1146
1147  /// \brief Iterator for iterating on parallel edges connecting the same nodes.
1148  ///
1149  /// Iterator for iterating on parallel edges connecting the same nodes.
1150  /// It is a higher level interface for the findEdge() function. You can
1151  /// use it the following way:
1152  ///\code
1153  /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
1154  ///   ...
1155  /// }
1156  ///\endcode
1157  ///
1158  ///\sa findEdge()
1159  template <typename _Graph>
1160  class ConEdgeIt : public _Graph::Edge {
1161  public:
1162
1163    typedef _Graph Graph;
1164    typedef typename Graph::Edge Parent;
1165
1166    typedef typename Graph::Edge Edge;
1167    typedef typename Graph::Node Node;
1168
1169    /// \brief Constructor.
1170    ///
1171    /// Construct a new ConEdgeIt iterating on the edges that
1172    /// connects nodes \c u and \c v.
1173    ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
1174      Parent::operator=(findEdge(_graph, _u, _v));
1175    }
1176
1177    /// \brief Constructor.
1178    ///
1179    /// Construct a new ConEdgeIt that continues iterating from edge \c e.
1180    ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
1181
1182    /// \brief Increment operator.
1183    ///
1184    /// It increments the iterator and gives back the next edge.
1185    ConEdgeIt& operator++() {
1186      Parent::operator=(findEdge(_graph, _u, _v, *this));
1187      return *this;
1188    }
1189  private:
1190    const Graph& _graph;
1191    Node _u, _v;
1192  };
1193
1194
1195  ///Dynamic arc look-up between given endpoints.
1196
1197  ///Using this class, you can find an arc in a digraph from a given
1198  ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
1199  ///where <em>d</em> is the out-degree of the source node.
1200  ///
1201  ///It is possible to find \e all parallel arcs between two nodes with
1202  ///the \c operator() member.
1203  ///
1204  ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
1205  ///\ref AllArcLookUp if your digraph is not changed so frequently.
1206  ///
1207  ///This class uses a self-adjusting binary search tree, the Splay tree
1208  ///of Sleator and Tarjan to guarantee the logarithmic amortized
1209  ///time bound for arc look-ups. This class also guarantees the
1210  ///optimal time bound in a constant factor for any distribution of
1211  ///queries.
1212  ///
1213  ///\tparam G The type of the underlying digraph.
1214  ///
1215  ///\sa ArcLookUp
1216  ///\sa AllArcLookUp
1217  template<class G>
1218  class DynArcLookUp
1219    : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
1220  {
1221  public:
1222    typedef typename ItemSetTraits<G, typename G::Arc>
1223    ::ItemNotifier::ObserverBase Parent;
1224
1225    TEMPLATE_DIGRAPH_TYPEDEFS(G);
1226    typedef G Digraph;
1227
1228  protected:
1229
1230    class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {
1231    public:
1232
1233      typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;
1234
1235      AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
1236
1237      virtual void add(const Node& node) {
1238        Parent::add(node);
1239        Parent::set(node, INVALID);
1240      }
1241
1242      virtual void add(const std::vector<Node>& nodes) {
1243        Parent::add(nodes);
1244        for (int i = 0; i < int(nodes.size()); ++i) {
1245          Parent::set(nodes[i], INVALID);
1246        }
1247      }
1248
1249      virtual void build() {
1250        Parent::build();
1251        Node it;
1252        typename Parent::Notifier* nf = Parent::notifier();
1253        for (nf->first(it); it != INVALID; nf->next(it)) {
1254          Parent::set(it, INVALID);
1255        }
1256      }
1257    };
1258
1259    const Digraph &_g;
1260    AutoNodeMap _head;
1261    typename Digraph::template ArcMap<Arc> _parent;
1262    typename Digraph::template ArcMap<Arc> _left;
1263    typename Digraph::template ArcMap<Arc> _right;
1264
1265    class ArcLess {
1266      const Digraph &g;
1267    public:
1268      ArcLess(const Digraph &_g) : g(_g) {}
1269      bool operator()(Arc a,Arc b) const
1270      {
1271        return g.target(a)<g.target(b);
1272      }
1273    };
1274
1275  public:
1276
1277    ///Constructor
1278
1279    ///Constructor.
1280    ///
1281    ///It builds up the search database.
1282    DynArcLookUp(const Digraph &g)
1283      : _g(g),_head(g),_parent(g),_left(g),_right(g)
1284    {
1285      Parent::attach(_g.notifier(typename Digraph::Arc()));
1286      refresh();
1287    }
1288
1289  protected:
1290
1291    virtual void add(const Arc& arc) {
1292      insert(arc);
1293    }
1294
1295    virtual void add(const std::vector<Arc>& arcs) {
1296      for (int i = 0; i < int(arcs.size()); ++i) {
1297        insert(arcs[i]);
1298      }
1299    }
1300
1301    virtual void erase(const Arc& arc) {
1302      remove(arc);
1303    }
1304
1305    virtual void erase(const std::vector<Arc>& arcs) {
1306      for (int i = 0; i < int(arcs.size()); ++i) {
1307        remove(arcs[i]);
1308      }
1309    }
1310
1311    virtual void build() {
1312      refresh();
1313    }
1314
1315    virtual void clear() {
1316      for(NodeIt n(_g);n!=INVALID;++n) {
1317        _head.set(n, INVALID);
1318      }
1319    }
1320
1321    void insert(Arc arc) {
1322      Node s = _g.source(arc);
1323      Node t = _g.target(arc);
1324      _left.set(arc, INVALID);
1325      _right.set(arc, INVALID);
1326
1327      Arc e = _head[s];
1328      if (e == INVALID) {
1329        _head.set(s, arc);
1330        _parent.set(arc, INVALID);
1331        return;
1332      }
1333      while (true) {
1334        if (t < _g.target(e)) {
1335          if (_left[e] == INVALID) {
1336            _left.set(e, arc);
1337            _parent.set(arc, e);
1338            splay(arc);
1339            return;
1340          } else {
1341            e = _left[e];
1342          }
1343        } else {
1344          if (_right[e] == INVALID) {
1345            _right.set(e, arc);
1346            _parent.set(arc, e);
1347            splay(arc);
1348            return;
1349          } else {
1350            e = _right[e];
1351          }
1352        }
1353      }
1354    }
1355
1356    void remove(Arc arc) {
1357      if (_left[arc] == INVALID) {
1358        if (_right[arc] != INVALID) {
1359          _parent.set(_right[arc], _parent[arc]);
1360        }
1361        if (_parent[arc] != INVALID) {
1362          if (_left[_parent[arc]] == arc) {
1363            _left.set(_parent[arc], _right[arc]);
1364          } else {
1365            _right.set(_parent[arc], _right[arc]);
1366          }
1367        } else {
1368          _head.set(_g.source(arc), _right[arc]);
1369        }
1370      } else if (_right[arc] == INVALID) {
1371        _parent.set(_left[arc], _parent[arc]);
1372        if (_parent[arc] != INVALID) {
1373          if (_left[_parent[arc]] == arc) {
1374            _left.set(_parent[arc], _left[arc]);
1375          } else {
1376            _right.set(_parent[arc], _left[arc]);
1377          }
1378        } else {
1379          _head.set(_g.source(arc), _left[arc]);
1380        }
1381      } else {
1382        Arc e = _left[arc];
1383        if (_right[e] != INVALID) {
1384          e = _right[e];
1385          while (_right[e] != INVALID) {
1386            e = _right[e];
1387          }
1388          Arc s = _parent[e];
1389          _right.set(_parent[e], _left[e]);
1390          if (_left[e] != INVALID) {
1391            _parent.set(_left[e], _parent[e]);
1392          }
1393
1394          _left.set(e, _left[arc]);
1395          _parent.set(_left[arc], e);
1396          _right.set(e, _right[arc]);
1397          _parent.set(_right[arc], e);
1398
1399          _parent.set(e, _parent[arc]);
1400          if (_parent[arc] != INVALID) {
1401            if (_left[_parent[arc]] == arc) {
1402              _left.set(_parent[arc], e);
1403            } else {
1404              _right.set(_parent[arc], e);
1405            }
1406          }
1407          splay(s);
1408        } else {
1409          _right.set(e, _right[arc]);
1410          _parent.set(_right[arc], e);
1411          _parent.set(e, _parent[arc]);
1412
1413          if (_parent[arc] != INVALID) {
1414            if (_left[_parent[arc]] == arc) {
1415              _left.set(_parent[arc], e);
1416            } else {
1417              _right.set(_parent[arc], e);
1418            }
1419          } else {
1420            _head.set(_g.source(arc), e);
1421          }
1422        }
1423      }
1424    }
1425
1426    Arc refreshRec(std::vector<Arc> &v,int a,int b)
1427    {
1428      int m=(a+b)/2;
1429      Arc me=v[m];
1430      if (a < m) {
1431        Arc left = refreshRec(v,a,m-1);
1432        _left.set(me, left);
1433        _parent.set(left, me);
1434      } else {
1435        _left.set(me, INVALID);
1436      }
1437      if (m < b) {
1438        Arc right = refreshRec(v,m+1,b);
1439        _right.set(me, right);
1440        _parent.set(right, me);
1441      } else {
1442        _right.set(me, INVALID);
1443      }
1444      return me;
1445    }
1446
1447    void refresh() {
1448      for(NodeIt n(_g);n!=INVALID;++n) {
1449        std::vector<Arc> v;
1450        for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
1451        if (!v.empty()) {
1452          std::sort(v.begin(),v.end(),ArcLess(_g));
1453          Arc head = refreshRec(v,0,v.size()-1);
1454          _head.set(n, head);
1455          _parent.set(head, INVALID);
1456        }
1457        else _head.set(n, INVALID);
1458      }
1459    }
1460
1461    void zig(Arc v) {
1462      Arc w = _parent[v];
1463      _parent.set(v, _parent[w]);
1464      _parent.set(w, v);
1465      _left.set(w, _right[v]);
1466      _right.set(v, w);
1467      if (_parent[v] != INVALID) {
1468        if (_right[_parent[v]] == w) {
1469          _right.set(_parent[v], v);
1470        } else {
1471          _left.set(_parent[v], v);
1472        }
1473      }
1474      if (_left[w] != INVALID){
1475        _parent.set(_left[w], w);
1476      }
1477    }
1478
1479    void zag(Arc v) {
1480      Arc w = _parent[v];
1481      _parent.set(v, _parent[w]);
1482      _parent.set(w, v);
1483      _right.set(w, _left[v]);
1484      _left.set(v, w);
1485      if (_parent[v] != INVALID){
1486        if (_left[_parent[v]] == w) {
1487          _left.set(_parent[v], v);
1488        } else {
1489          _right.set(_parent[v], v);
1490        }
1491      }
1492      if (_right[w] != INVALID){
1493        _parent.set(_right[w], w);
1494      }
1495    }
1496
1497    void splay(Arc v) {
1498      while (_parent[v] != INVALID) {
1499        if (v == _left[_parent[v]]) {
1500          if (_parent[_parent[v]] == INVALID) {
1501            zig(v);
1502          } else {
1503            if (_parent[v] == _left[_parent[_parent[v]]]) {
1504              zig(_parent[v]);
1505              zig(v);
1506            } else {
1507              zig(v);
1508              zag(v);
1509            }
1510          }
1511        } else {
1512          if (_parent[_parent[v]] == INVALID) {
1513            zag(v);
1514          } else {
1515            if (_parent[v] == _left[_parent[_parent[v]]]) {
1516              zag(v);
1517              zig(v);
1518            } else {
1519              zag(_parent[v]);
1520              zag(v);
1521            }
1522          }
1523        }
1524      }
1525      _head[_g.source(v)] = v;
1526    }
1527
1528
1529  public:
1530
1531    ///Find an arc between two nodes.
1532
1533    ///Find an arc between two nodes.
1534    ///\param s The source node.
1535    ///\param t The target node.
1536    ///\param p The previous arc between \c s and \c t. It it is INVALID or
1537    ///not given, the operator finds the first appropriate arc.
1538    ///\return An arc from \c s to \c t after \c p or
1539    ///\ref INVALID if there is no more.
1540    ///
1541    ///For example, you can count the number of arcs from \c u to \c v in the
1542    ///following way.
1543    ///\code
1544    ///DynArcLookUp<ListDigraph> ae(g);
1545    ///...
1546    ///int n = 0;
1547    ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
1548    ///\endcode
1549    ///
1550    ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
1551    ///amortized time, specifically, the time complexity of the lookups
1552    ///is equal to the optimal search tree implementation for the
1553    ///current query distribution in a constant factor.
1554    ///
1555    ///\note This is a dynamic data structure, therefore the data
1556    ///structure is updated after each graph alteration. Thus although
1557    ///this data structure is theoretically faster than \ref ArcLookUp
1558    ///and \ref AllArcLookUp, it often provides worse performance than
1559    ///them.
1560    Arc operator()(Node s, Node t, Arc p = INVALID) const  {
1561      if (p == INVALID) {
1562        Arc a = _head[s];
1563        if (a == INVALID) return INVALID;
1564        Arc r = INVALID;
1565        while (true) {
1566          if (_g.target(a) < t) {
1567            if (_right[a] == INVALID) {
1568              const_cast<DynArcLookUp&>(*this).splay(a);
1569              return r;
1570            } else {
1571              a = _right[a];
1572            }
1573          } else {
1574            if (_g.target(a) == t) {
1575              r = a;
1576            }
1577            if (_left[a] == INVALID) {
1578              const_cast<DynArcLookUp&>(*this).splay(a);
1579              return r;
1580            } else {
1581              a = _left[a];
1582            }
1583          }
1584        }
1585      } else {
1586        Arc a = p;
1587        if (_right[a] != INVALID) {
1588          a = _right[a];
1589          while (_left[a] != INVALID) {
1590            a = _left[a];
1591          }
1592          const_cast<DynArcLookUp&>(*this).splay(a);
1593        } else {
1594          while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
1595            a = _parent[a];
1596          }
1597          if (_parent[a] == INVALID) {
1598            return INVALID;
1599          } else {
1600            a = _parent[a];
1601            const_cast<DynArcLookUp&>(*this).splay(a);
1602          }
1603        }
1604        if (_g.target(a) == t) return a;
1605        else return INVALID;
1606      }
1607    }
1608
1609  };
1610
1611  ///Fast arc look-up between given endpoints.
1612
1613  ///Using this class, you can find an arc in a digraph from a given
1614  ///source to a given target in time <em>O</em>(log<em>d</em>),
1615  ///where <em>d</em> is the out-degree of the source node.
1616  ///
1617  ///It is not possible to find \e all parallel arcs between two nodes.
1618  ///Use \ref AllArcLookUp for this purpose.
1619  ///
1620  ///\warning This class is static, so you should call refresh() (or at
1621  ///least refresh(Node)) to refresh this data structure whenever the
1622  ///digraph changes. This is a time consuming (superlinearly proportional
1623  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
1624  ///
1625  ///\tparam G The type of the underlying digraph.
1626  ///
1627  ///\sa DynArcLookUp
1628  ///\sa AllArcLookUp
1629  template<class G>
1630  class ArcLookUp
1631  {
1632  public:
1633    TEMPLATE_DIGRAPH_TYPEDEFS(G);
1634    typedef G Digraph;
1635
1636  protected:
1637    const Digraph &_g;
1638    typename Digraph::template NodeMap<Arc> _head;
1639    typename Digraph::template ArcMap<Arc> _left;
1640    typename Digraph::template ArcMap<Arc> _right;
1641
1642    class ArcLess {
1643      const Digraph &g;
1644    public:
1645      ArcLess(const Digraph &_g) : g(_g) {}
1646      bool operator()(Arc a,Arc b) const
1647      {
1648        return g.target(a)<g.target(b);
1649      }
1650    };
1651
1652  public:
1653
1654    ///Constructor
1655
1656    ///Constructor.
1657    ///
1658    ///It builds up the search database, which remains valid until the digraph
1659    ///changes.
1660    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
1661
1662  private:
1663    Arc refreshRec(std::vector<Arc> &v,int a,int b)
1664    {
1665      int m=(a+b)/2;
1666      Arc me=v[m];
1667      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
1668      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
1669      return me;
1670    }
1671  public:
1672    ///Refresh the search data structure at a node.
1673
1674    ///Build up the search database of node \c n.
1675    ///
1676    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
1677    ///is the number of the outgoing arcs of \c n.
1678    void refresh(Node n)
1679    {
1680      std::vector<Arc> v;
1681      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
1682      if(v.size()) {
1683        std::sort(v.begin(),v.end(),ArcLess(_g));
1684        _head[n]=refreshRec(v,0,v.size()-1);
1685      }
1686      else _head[n]=INVALID;
1687    }
1688    ///Refresh the full data structure.
1689
1690    ///Build up the full search database. In fact, it simply calls
1691    ///\ref refresh(Node) "refresh(n)" for each node \c n.
1692    ///
1693    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
1694    ///the number of the arcs in the digraph and <em>D</em> is the maximum
1695    ///out-degree of the digraph.
1696    void refresh()
1697    {
1698      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
1699    }
1700
1701    ///Find an arc between two nodes.
1702
1703    ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
1704    ///where <em>d</em> is the number of outgoing arcs of \c s.
1705    ///\param s The source node.
1706    ///\param t The target node.
1707    ///\return An arc from \c s to \c t if there exists,
1708    ///\ref INVALID otherwise.
1709    ///
1710    ///\warning If you change the digraph, refresh() must be called before using
1711    ///this operator. If you change the outgoing arcs of
1712    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
1713    Arc operator()(Node s, Node t) const
1714    {
1715      Arc e;
1716      for(e=_head[s];
1717          e!=INVALID&&_g.target(e)!=t;
1718          e = t < _g.target(e)?_left[e]:_right[e]) ;
1719      return e;
1720    }
1721
1722  };
1723
1724  ///Fast look-up of all arcs between given endpoints.
1725
1726  ///This class is the same as \ref ArcLookUp, with the addition
1727  ///that it makes it possible to find all parallel arcs between given
1728  ///endpoints.
1729  ///
1730  ///\warning This class is static, so you should call refresh() (or at
1731  ///least refresh(Node)) to refresh this data structure whenever the
1732  ///digraph changes. This is a time consuming (superlinearly proportional
1733  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
1734  ///
1735  ///\tparam G The type of the underlying digraph.
1736  ///
1737  ///\sa DynArcLookUp
1738  ///\sa ArcLookUp
1739  template<class G>
1740  class AllArcLookUp : public ArcLookUp<G>
1741  {
1742    using ArcLookUp<G>::_g;
1743    using ArcLookUp<G>::_right;
1744    using ArcLookUp<G>::_left;
1745    using ArcLookUp<G>::_head;
1746
1747    TEMPLATE_DIGRAPH_TYPEDEFS(G);
1748    typedef G Digraph;
1749
1750    typename Digraph::template ArcMap<Arc> _next;
1751
1752    Arc refreshNext(Arc head,Arc next=INVALID)
1753    {
1754      if(head==INVALID) return next;
1755      else {
1756        next=refreshNext(_right[head],next);
1757        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
1758          ? next : INVALID;
1759        return refreshNext(_left[head],head);
1760      }
1761    }
1762
1763    void refreshNext()
1764    {
1765      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
1766    }
1767
1768  public:
1769    ///Constructor
1770
1771    ///Constructor.
1772    ///
1773    ///It builds up the search database, which remains valid until the digraph
1774    ///changes.
1775    AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
1776
1777    ///Refresh the data structure at a node.
1778
1779    ///Build up the search database of node \c n.
1780    ///
1781    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
1782    ///the number of the outgoing arcs of \c n.
1783    void refresh(Node n)
1784    {
1785      ArcLookUp<G>::refresh(n);
1786      refreshNext(_head[n]);
1787    }
1788
1789    ///Refresh the full data structure.
1790
1791    ///Build up the full search database. In fact, it simply calls
1792    ///\ref refresh(Node) "refresh(n)" for each node \c n.
1793    ///
1794    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
1795    ///the number of the arcs in the digraph and <em>D</em> is the maximum
1796    ///out-degree of the digraph.
1797    void refresh()
1798    {
1799      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
1800    }
1801
1802    ///Find an arc between two nodes.
1803
1804    ///Find an arc between two nodes.
1805    ///\param s The source node.
1806    ///\param t The target node.
1807    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
1808    ///not given, the operator finds the first appropriate arc.
1809    ///\return An arc from \c s to \c t after \c prev or
1810    ///\ref INVALID if there is no more.
1811    ///
1812    ///For example, you can count the number of arcs from \c u to \c v in the
1813    ///following way.
1814    ///\code
1815    ///AllArcLookUp<ListDigraph> ae(g);
1816    ///...
1817    ///int n = 0;
1818    ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
1819    ///\endcode
1820    ///
1821    ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
1822    ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
1823    ///consecutive arcs are found in constant time.
1824    ///
1825    ///\warning If you change the digraph, refresh() must be called before using
1826    ///this operator. If you change the outgoing arcs of
1827    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
1828    ///
1829#ifdef DOXYGEN
1830    Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
1831#else
1832    using ArcLookUp<G>::operator() ;
1833    Arc operator()(Node s, Node t, Arc prev) const
1834    {
1835      return prev==INVALID?(*this)(s,t):_next[prev];
1836    }
1837#endif
1838
1839  };
1840
1841  /// @}
1842
1843} //namespace lemon
1844
1845#endif
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