COIN-OR::LEMON - Graph Library

source: lemon-main/lemon/core.h @ 1184:3c00344f49c9

Last change on this file since 1184:3c00344f49c9 was 1135:c199e9976d93, checked in by Alpar Juttner <alpar@…>, 5 years ago

Resolve VS and MinGW warnings (#595)

File size: 82.6 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2013
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_CORE_H
20#define LEMON_CORE_H
21
22///\file
23///\brief LEMON core utilities.
24///
25///This header file contains core utilities for LEMON.
26///It is automatically included by all graph types, therefore it usually
27///do not have to be included directly.
28
29// Disable the following warnings when compiling with MSVC:
30// C4250: 'class1' : inherits 'class2::member' via dominance
31// C4267: conversion from 'size_t' to 'type', possible loss of data
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 4267 4355 4503 4800 4996 )
38#endif
39
40#if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 8)
41// Needed by the [DI]GRAPH_TYPEDEFS marcos for gcc 4.8
42#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
43#endif
44
45#include <vector>
46#include <algorithm>
47
48#include <lemon/config.h>
49#include <lemon/bits/enable_if.h>
50#include <lemon/bits/traits.h>
51#include <lemon/assert.h>
52
53
54
55namespace lemon {
56
57  /// \brief Dummy type to make it easier to create invalid iterators.
58  ///
59  /// Dummy type to make it easier to create invalid iterators.
60  /// See \ref INVALID for the usage.
61  struct Invalid {
62  public:
63    bool operator==(Invalid) { return true;  }
64    bool operator!=(Invalid) { return false; }
65    bool operator< (Invalid) { return false; }
66  };
67
68  /// \brief Invalid iterators.
69  ///
70  /// \ref Invalid is a global type that converts to each iterator
71  /// in such a way that the value of the target iterator will be invalid.
72#ifdef LEMON_ONLY_TEMPLATES
73  const Invalid INVALID = Invalid();
74#else
75  extern const Invalid INVALID;
76#endif
77
78  /// \addtogroup gutils
79  /// @{
80
81  ///Create convenience typedefs for the digraph types and iterators
82
83  ///This \c \#define creates convenient type definitions for the following
84  ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
85  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
86  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
87  ///
88  ///\note If the graph type is a dependent type, ie. the graph type depend
89  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
90  ///macro.
91#define DIGRAPH_TYPEDEFS(Digraph)                                       \
92  typedef Digraph::Node Node;                                           \
93  typedef Digraph::NodeIt NodeIt;                                       \
94  typedef Digraph::Arc Arc;                                             \
95  typedef Digraph::ArcIt ArcIt;                                         \
96  typedef Digraph::InArcIt InArcIt;                                     \
97  typedef Digraph::OutArcIt OutArcIt;                                   \
98  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
99  typedef Digraph::NodeMap<int> IntNodeMap;                             \
100  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
101  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
102  typedef Digraph::ArcMap<int> IntArcMap;                               \
103  typedef Digraph::ArcMap<double> DoubleArcMap
104
105  ///Create convenience typedefs for the digraph types and iterators
106
107  ///\see DIGRAPH_TYPEDEFS
108  ///
109  ///\note Use this macro, if the graph type is a dependent type,
110  ///ie. the graph type depend on a template parameter.
111#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
112  typedef typename Digraph::Node Node;                                  \
113  typedef typename Digraph::NodeIt NodeIt;                              \
114  typedef typename Digraph::Arc Arc;                                    \
115  typedef typename Digraph::ArcIt ArcIt;                                \
116  typedef typename Digraph::InArcIt InArcIt;                            \
117  typedef typename Digraph::OutArcIt OutArcIt;                          \
118  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
119  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
120  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
121  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
122  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
123  typedef typename Digraph::template ArcMap<double> DoubleArcMap
124
125  ///Create convenience typedefs for the graph types and iterators
126
127  ///This \c \#define creates the same convenient type definitions as defined
128  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
129  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
130  ///\c DoubleEdgeMap.
131  ///
132  ///\note If the graph type is a dependent type, ie. the graph type depend
133  ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
134  ///macro.
135#define GRAPH_TYPEDEFS(Graph)                                           \
136  DIGRAPH_TYPEDEFS(Graph);                                              \
137  typedef Graph::Edge Edge;                                             \
138  typedef Graph::EdgeIt EdgeIt;                                         \
139  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
140  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
141  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
142  typedef Graph::EdgeMap<double> DoubleEdgeMap
143
144  ///Create convenience typedefs for the graph types and iterators
145
146  ///\see GRAPH_TYPEDEFS
147  ///
148  ///\note Use this macro, if the graph type is a dependent type,
149  ///ie. the graph type depend on a template parameter.
150#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
151  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
152  typedef typename Graph::Edge Edge;                                    \
153  typedef typename Graph::EdgeIt EdgeIt;                                \
154  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
155  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
156  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
157  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
158
159  ///Create convenience typedefs for the bipartite graph types and iterators
160
161  ///This \c \#define creates the same convenient type definitions as
162  ///defined by \ref GRAPH_TYPEDEFS(BpGraph) and ten more, namely it
163  ///creates \c RedNode, \c RedNodeIt, \c BoolRedNodeMap,
164  ///\c IntRedNodeMap, \c DoubleRedNodeMap, \c BlueNode, \c BlueNodeIt,
165  ///\c BoolBlueNodeMap, \c IntBlueNodeMap, \c DoubleBlueNodeMap.
166  ///
167  ///\note If the graph type is a dependent type, ie. the graph type depend
168  ///on a template parameter, then use \c TEMPLATE_BPGRAPH_TYPEDEFS()
169  ///macro.
170#define BPGRAPH_TYPEDEFS(BpGraph)                                       \
171  GRAPH_TYPEDEFS(BpGraph);                                              \
172  typedef BpGraph::RedNode RedNode;                                     \
173  typedef BpGraph::RedNodeIt RedNodeIt;                                 \
174  typedef BpGraph::RedNodeMap<bool> BoolRedNodeMap;                     \
175  typedef BpGraph::RedNodeMap<int> IntRedNodeMap;                       \
176  typedef BpGraph::RedNodeMap<double> DoubleRedNodeMap;                 \
177  typedef BpGraph::BlueNode BlueNode;                                   \
178  typedef BpGraph::BlueNodeIt BlueNodeIt;                               \
179  typedef BpGraph::BlueNodeMap<bool> BoolBlueNodeMap;                   \
180  typedef BpGraph::BlueNodeMap<int> IntBlueNodeMap;                     \
181  typedef BpGraph::BlueNodeMap<double> DoubleBlueNodeMap
182
183  ///Create convenience typedefs for the bipartite graph types and iterators
184
185  ///\see BPGRAPH_TYPEDEFS
186  ///
187  ///\note Use this macro, if the graph type is a dependent type,
188  ///ie. the graph type depend on a template parameter.
189#define TEMPLATE_BPGRAPH_TYPEDEFS(BpGraph)                                  \
190  TEMPLATE_GRAPH_TYPEDEFS(BpGraph);                                         \
191  typedef typename BpGraph::RedNode RedNode;                                \
192  typedef typename BpGraph::RedNodeIt RedNodeIt;                            \
193  typedef typename BpGraph::template RedNodeMap<bool> BoolRedNodeMap;       \
194  typedef typename BpGraph::template RedNodeMap<int> IntRedNodeMap;         \
195  typedef typename BpGraph::template RedNodeMap<double> DoubleRedNodeMap;   \
196  typedef typename BpGraph::BlueNode BlueNode;                              \
197  typedef typename BpGraph::BlueNodeIt BlueNodeIt;                          \
198  typedef typename BpGraph::template BlueNodeMap<bool> BoolBlueNodeMap;     \
199  typedef typename BpGraph::template BlueNodeMap<int> IntBlueNodeMap;       \
200  typedef typename BpGraph::template BlueNodeMap<double> DoubleBlueNodeMap
201
202  /// \brief Function to count the items in a graph.
203  ///
204  /// This function counts the items (nodes, arcs etc.) in a graph.
205  /// The complexity of the function is linear because
206  /// it iterates on all of the items.
207  template <typename Graph, typename Item>
208  inline int countItems(const Graph& g) {
209    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
210    int num = 0;
211    for (ItemIt it(g); it != INVALID; ++it) {
212      ++num;
213    }
214    return num;
215  }
216
217  // Node counting:
218
219  namespace _core_bits {
220
221    template <typename Graph, typename Enable = void>
222    struct CountNodesSelector {
223      static int count(const Graph &g) {
224        return countItems<Graph, typename Graph::Node>(g);
225      }
226    };
227
228    template <typename Graph>
229    struct CountNodesSelector<
230      Graph, typename
231      enable_if<typename Graph::NodeNumTag, void>::type>
232    {
233      static int count(const Graph &g) {
234        return g.nodeNum();
235      }
236    };
237  }
238
239  /// \brief Function to count the nodes in the graph.
240  ///
241  /// This function counts the nodes in the graph.
242  /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
243  /// graph structures it is specialized to run in <em>O</em>(1).
244  ///
245  /// \note If the graph contains a \c nodeNum() member function and a
246  /// \c NodeNumTag tag then this function calls directly the member
247  /// function to query the cardinality of the node set.
248  template <typename Graph>
249  inline int countNodes(const Graph& g) {
250    return _core_bits::CountNodesSelector<Graph>::count(g);
251  }
252
253  namespace _graph_utils_bits {
254
255    template <typename Graph, typename Enable = void>
256    struct CountRedNodesSelector {
257      static int count(const Graph &g) {
258        return countItems<Graph, typename Graph::RedNode>(g);
259      }
260    };
261
262    template <typename Graph>
263    struct CountRedNodesSelector<
264      Graph, typename
265      enable_if<typename Graph::NodeNumTag, void>::type>
266    {
267      static int count(const Graph &g) {
268        return g.redNum();
269      }
270    };
271  }
272
273  /// \brief Function to count the red nodes in the graph.
274  ///
275  /// This function counts the red nodes in the graph.
276  /// The complexity of the function is O(n) but for some
277  /// graph structures it is specialized to run in O(1).
278  ///
279  /// If the graph contains a \e redNum() member function and a
280  /// \e NodeNumTag tag then this function calls directly the member
281  /// function to query the cardinality of the node set.
282  template <typename Graph>
283  inline int countRedNodes(const Graph& g) {
284    return _graph_utils_bits::CountRedNodesSelector<Graph>::count(g);
285  }
286
287  namespace _graph_utils_bits {
288
289    template <typename Graph, typename Enable = void>
290    struct CountBlueNodesSelector {
291      static int count(const Graph &g) {
292        return countItems<Graph, typename Graph::BlueNode>(g);
293      }
294    };
295
296    template <typename Graph>
297    struct CountBlueNodesSelector<
298      Graph, typename
299      enable_if<typename Graph::NodeNumTag, void>::type>
300    {
301      static int count(const Graph &g) {
302        return g.blueNum();
303      }
304    };
305  }
306
307  /// \brief Function to count the blue nodes in the graph.
308  ///
309  /// This function counts the blue nodes in the graph.
310  /// The complexity of the function is O(n) but for some
311  /// graph structures it is specialized to run in O(1).
312  ///
313  /// If the graph contains a \e blueNum() member function and a
314  /// \e NodeNumTag tag then this function calls directly the member
315  /// function to query the cardinality of the node set.
316  template <typename Graph>
317  inline int countBlueNodes(const Graph& g) {
318    return _graph_utils_bits::CountBlueNodesSelector<Graph>::count(g);
319  }
320
321  // Arc counting:
322
323  namespace _core_bits {
324
325    template <typename Graph, typename Enable = void>
326    struct CountArcsSelector {
327      static int count(const Graph &g) {
328        return countItems<Graph, typename Graph::Arc>(g);
329      }
330    };
331
332    template <typename Graph>
333    struct CountArcsSelector<
334      Graph,
335      typename enable_if<typename Graph::ArcNumTag, void>::type>
336    {
337      static int count(const Graph &g) {
338        return g.arcNum();
339      }
340    };
341  }
342
343  /// \brief Function to count the arcs in the graph.
344  ///
345  /// This function counts the arcs in the graph.
346  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
347  /// graph structures it is specialized to run in <em>O</em>(1).
348  ///
349  /// \note If the graph contains a \c arcNum() member function and a
350  /// \c ArcNumTag tag then this function calls directly the member
351  /// function to query the cardinality of the arc set.
352  template <typename Graph>
353  inline int countArcs(const Graph& g) {
354    return _core_bits::CountArcsSelector<Graph>::count(g);
355  }
356
357  // Edge counting:
358
359  namespace _core_bits {
360
361    template <typename Graph, typename Enable = void>
362    struct CountEdgesSelector {
363      static int count(const Graph &g) {
364        return countItems<Graph, typename Graph::Edge>(g);
365      }
366    };
367
368    template <typename Graph>
369    struct CountEdgesSelector<
370      Graph,
371      typename enable_if<typename Graph::EdgeNumTag, void>::type>
372    {
373      static int count(const Graph &g) {
374        return g.edgeNum();
375      }
376    };
377  }
378
379  /// \brief Function to count the edges in the graph.
380  ///
381  /// This function counts the edges in the graph.
382  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
383  /// graph structures it is specialized to run in <em>O</em>(1).
384  ///
385  /// \note If the graph contains a \c edgeNum() member function and a
386  /// \c EdgeNumTag tag then this function calls directly the member
387  /// function to query the cardinality of the edge set.
388  template <typename Graph>
389  inline int countEdges(const Graph& g) {
390    return _core_bits::CountEdgesSelector<Graph>::count(g);
391
392  }
393
394
395  template <typename Graph, typename DegIt>
396  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
397    int num = 0;
398    for (DegIt it(_g, _n); it != INVALID; ++it) {
399      ++num;
400    }
401    return num;
402  }
403
404  /// \brief Function to count the number of the out-arcs from node \c n.
405  ///
406  /// This function counts the number of the out-arcs from node \c n
407  /// in the graph \c g.
408  template <typename Graph>
409  inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
410    return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
411  }
412
413  /// \brief Function to count the number of the in-arcs to node \c n.
414  ///
415  /// This function counts the number of the in-arcs to node \c n
416  /// in the graph \c g.
417  template <typename Graph>
418  inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
419    return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
420  }
421
422  /// \brief Function to count the number of the inc-edges to node \c n.
423  ///
424  /// This function counts the number of the inc-edges to node \c n
425  /// in the undirected graph \c g.
426  template <typename Graph>
427  inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
428    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
429  }
430
431  namespace _core_bits {
432
433    template <typename Digraph, typename Item, typename RefMap>
434    class MapCopyBase {
435    public:
436      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
437
438      virtual ~MapCopyBase() {}
439    };
440
441    template <typename Digraph, typename Item, typename RefMap,
442              typename FromMap, typename ToMap>
443    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
444    public:
445
446      MapCopy(const FromMap& map, ToMap& tmap)
447        : _map(map), _tmap(tmap) {}
448
449      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
450        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
451        for (ItemIt it(digraph); it != INVALID; ++it) {
452          _tmap.set(refMap[it], _map[it]);
453        }
454      }
455
456    private:
457      const FromMap& _map;
458      ToMap& _tmap;
459    };
460
461    template <typename Digraph, typename Item, typename RefMap, typename It>
462    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
463    public:
464
465      ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
466
467      virtual void copy(const Digraph&, const RefMap& refMap) {
468        _it = refMap[_item];
469      }
470
471    private:
472      Item _item;
473      It& _it;
474    };
475
476    template <typename Digraph, typename Item, typename RefMap, typename Ref>
477    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
478    public:
479
480      RefCopy(Ref& map) : _map(map) {}
481
482      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
483        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
484        for (ItemIt it(digraph); it != INVALID; ++it) {
485          _map.set(it, refMap[it]);
486        }
487      }
488
489    private:
490      Ref& _map;
491    };
492
493    template <typename Digraph, typename Item, typename RefMap,
494              typename CrossRef>
495    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
496    public:
497
498      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
499
500      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
501        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
502        for (ItemIt it(digraph); it != INVALID; ++it) {
503          _cmap.set(refMap[it], it);
504        }
505      }
506
507    private:
508      CrossRef& _cmap;
509    };
510
511    template <typename Digraph, typename Enable = void>
512    struct DigraphCopySelector {
513      template <typename From, typename NodeRefMap, typename ArcRefMap>
514      static void copy(const From& from, Digraph &to,
515                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
516        to.clear();
517        for (typename From::NodeIt it(from); it != INVALID; ++it) {
518          nodeRefMap[it] = to.addNode();
519        }
520        for (typename From::ArcIt it(from); it != INVALID; ++it) {
521          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
522                                    nodeRefMap[from.target(it)]);
523        }
524      }
525    };
526
527    template <typename Digraph>
528    struct DigraphCopySelector<
529      Digraph,
530      typename enable_if<typename Digraph::BuildTag, void>::type>
531    {
532      template <typename From, typename NodeRefMap, typename ArcRefMap>
533      static void copy(const From& from, Digraph &to,
534                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
535        to.build(from, nodeRefMap, arcRefMap);
536      }
537    };
538
539    template <typename Graph, typename Enable = void>
540    struct GraphCopySelector {
541      template <typename From, typename NodeRefMap, typename EdgeRefMap>
542      static void copy(const From& from, Graph &to,
543                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
544        to.clear();
545        for (typename From::NodeIt it(from); it != INVALID; ++it) {
546          nodeRefMap[it] = to.addNode();
547        }
548        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
549          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
550                                      nodeRefMap[from.v(it)]);
551        }
552      }
553    };
554
555    template <typename Graph>
556    struct GraphCopySelector<
557      Graph,
558      typename enable_if<typename Graph::BuildTag, void>::type>
559    {
560      template <typename From, typename NodeRefMap, typename EdgeRefMap>
561      static void copy(const From& from, Graph &to,
562                       NodeRefMap& nodeRefMap,
563                       EdgeRefMap& edgeRefMap) {
564        to.build(from, nodeRefMap, edgeRefMap);
565      }
566    };
567
568    template <typename BpGraph, typename Enable = void>
569    struct BpGraphCopySelector {
570      template <typename From, typename RedNodeRefMap,
571                typename BlueNodeRefMap, typename EdgeRefMap>
572      static void copy(const From& from, BpGraph &to,
573                       RedNodeRefMap& redNodeRefMap,
574                       BlueNodeRefMap& blueNodeRefMap,
575                       EdgeRefMap& edgeRefMap) {
576        to.clear();
577        for (typename From::RedNodeIt it(from); it != INVALID; ++it) {
578          redNodeRefMap[it] = to.addRedNode();
579        }
580        for (typename From::BlueNodeIt it(from); it != INVALID; ++it) {
581          blueNodeRefMap[it] = to.addBlueNode();
582        }
583        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
584          edgeRefMap[it] = to.addEdge(redNodeRefMap[from.redNode(it)],
585                                      blueNodeRefMap[from.blueNode(it)]);
586        }
587      }
588    };
589
590    template <typename BpGraph>
591    struct BpGraphCopySelector<
592      BpGraph,
593      typename enable_if<typename BpGraph::BuildTag, void>::type>
594    {
595      template <typename From, typename RedNodeRefMap,
596                typename BlueNodeRefMap, typename EdgeRefMap>
597      static void copy(const From& from, BpGraph &to,
598                       RedNodeRefMap& redNodeRefMap,
599                       BlueNodeRefMap& blueNodeRefMap,
600                       EdgeRefMap& edgeRefMap) {
601        to.build(from, redNodeRefMap, blueNodeRefMap, edgeRefMap);
602      }
603    };
604
605  }
606
607  /// \brief Check whether a graph is undirected.
608  ///
609  /// This function returns \c true if the given graph is undirected.
610#ifdef DOXYGEN
611  template <typename GR>
612  bool undirected(const GR& g) { return false; }
613#else
614  template <typename GR>
615  typename enable_if<UndirectedTagIndicator<GR>, bool>::type
616  undirected(const GR&) {
617    return true;
618  }
619  template <typename GR>
620  typename disable_if<UndirectedTagIndicator<GR>, bool>::type
621  undirected(const GR&) {
622    return false;
623  }
624#endif
625
626  /// \brief Class to copy a digraph.
627  ///
628  /// Class to copy a digraph to another digraph (duplicate a digraph). The
629  /// simplest way of using it is through the \c digraphCopy() function.
630  ///
631  /// This class not only make a copy of a digraph, but it can create
632  /// references and cross references between the nodes and arcs of
633  /// the two digraphs, and it can copy maps to use with the newly created
634  /// digraph.
635  ///
636  /// To make a copy from a digraph, first an instance of DigraphCopy
637  /// should be created, then the data belongs to the digraph should
638  /// assigned to copy. In the end, the \c run() member should be
639  /// called.
640  ///
641  /// The next code copies a digraph with several data:
642  ///\code
643  ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
644  ///  // Create references for the nodes
645  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
646  ///  cg.nodeRef(nr);
647  ///  // Create cross references (inverse) for the arcs
648  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
649  ///  cg.arcCrossRef(acr);
650  ///  // Copy an arc map
651  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
652  ///  NewGraph::ArcMap<double> namap(new_graph);
653  ///  cg.arcMap(oamap, namap);
654  ///  // Copy a node
655  ///  OrigGraph::Node on;
656  ///  NewGraph::Node nn;
657  ///  cg.node(on, nn);
658  ///  // Execute copying
659  ///  cg.run();
660  ///\endcode
661  template <typename From, typename To>
662  class DigraphCopy {
663  private:
664
665    typedef typename From::Node Node;
666    typedef typename From::NodeIt NodeIt;
667    typedef typename From::Arc Arc;
668    typedef typename From::ArcIt ArcIt;
669
670    typedef typename To::Node TNode;
671    typedef typename To::Arc TArc;
672
673    typedef typename From::template NodeMap<TNode> NodeRefMap;
674    typedef typename From::template ArcMap<TArc> ArcRefMap;
675
676  public:
677
678    /// \brief Constructor of DigraphCopy.
679    ///
680    /// Constructor of DigraphCopy for copying the content of the
681    /// \c from digraph into the \c to digraph.
682    DigraphCopy(const From& from, To& to)
683      : _from(from), _to(to) {}
684
685    /// \brief Destructor of DigraphCopy
686    ///
687    /// Destructor of DigraphCopy.
688    ~DigraphCopy() {
689      for (int i = 0; i < int(_node_maps.size()); ++i) {
690        delete _node_maps[i];
691      }
692      for (int i = 0; i < int(_arc_maps.size()); ++i) {
693        delete _arc_maps[i];
694      }
695
696    }
697
698    /// \brief Copy the node references into the given map.
699    ///
700    /// This function copies the node references into the given map.
701    /// The parameter should be a map, whose key type is the Node type of
702    /// the source digraph, while the value type is the Node type of the
703    /// destination digraph.
704    template <typename NodeRef>
705    DigraphCopy& nodeRef(NodeRef& map) {
706      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
707                           NodeRefMap, NodeRef>(map));
708      return *this;
709    }
710
711    /// \brief Copy the node cross references into the given map.
712    ///
713    /// This function copies the node cross references (reverse references)
714    /// into the given map. The parameter should be a map, whose key type
715    /// is the Node type of the destination digraph, while the value type is
716    /// the Node type of the source digraph.
717    template <typename NodeCrossRef>
718    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
719      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
720                           NodeRefMap, NodeCrossRef>(map));
721      return *this;
722    }
723
724    /// \brief Make a copy of the given node map.
725    ///
726    /// This function makes a copy of the given node map for the newly
727    /// created digraph.
728    /// The key type of the new map \c tmap should be the Node type of the
729    /// destination digraph, and the key type of the original map \c map
730    /// should be the Node type of the source digraph.
731    template <typename FromMap, typename ToMap>
732    DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
733      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
734                           NodeRefMap, FromMap, ToMap>(map, tmap));
735      return *this;
736    }
737
738    /// \brief Make a copy of the given node.
739    ///
740    /// This function makes a copy of the given node.
741    DigraphCopy& node(const Node& node, TNode& tnode) {
742      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
743                           NodeRefMap, TNode>(node, tnode));
744      return *this;
745    }
746
747    /// \brief Copy the arc references into the given map.
748    ///
749    /// This function copies the arc references into the given map.
750    /// The parameter should be a map, whose key type is the Arc type of
751    /// the source digraph, while the value type is the Arc type of the
752    /// destination digraph.
753    template <typename ArcRef>
754    DigraphCopy& arcRef(ArcRef& map) {
755      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
756                          ArcRefMap, ArcRef>(map));
757      return *this;
758    }
759
760    /// \brief Copy the arc cross references into the given map.
761    ///
762    /// This function copies the arc cross references (reverse references)
763    /// into the given map. The parameter should be a map, whose key type
764    /// is the Arc type of the destination digraph, while the value type is
765    /// the Arc type of the source digraph.
766    template <typename ArcCrossRef>
767    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
768      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
769                          ArcRefMap, ArcCrossRef>(map));
770      return *this;
771    }
772
773    /// \brief Make a copy of the given arc map.
774    ///
775    /// This function makes a copy of the given arc map for the newly
776    /// created digraph.
777    /// The key type of the new map \c tmap should be the Arc type of the
778    /// destination digraph, and the key type of the original map \c map
779    /// should be the Arc type of the source digraph.
780    template <typename FromMap, typename ToMap>
781    DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
782      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
783                          ArcRefMap, FromMap, ToMap>(map, tmap));
784      return *this;
785    }
786
787    /// \brief Make a copy of the given arc.
788    ///
789    /// This function makes a copy of the given arc.
790    DigraphCopy& arc(const Arc& arc, TArc& tarc) {
791      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
792                          ArcRefMap, TArc>(arc, tarc));
793      return *this;
794    }
795
796    /// \brief Execute copying.
797    ///
798    /// This function executes the copying of the digraph along with the
799    /// copying of the assigned data.
800    void run() {
801      NodeRefMap nodeRefMap(_from);
802      ArcRefMap arcRefMap(_from);
803      _core_bits::DigraphCopySelector<To>::
804        copy(_from, _to, nodeRefMap, arcRefMap);
805      for (int i = 0; i < int(_node_maps.size()); ++i) {
806        _node_maps[i]->copy(_from, nodeRefMap);
807      }
808      for (int i = 0; i < int(_arc_maps.size()); ++i) {
809        _arc_maps[i]->copy(_from, arcRefMap);
810      }
811    }
812
813  protected:
814
815    const From& _from;
816    To& _to;
817
818    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
819      _node_maps;
820
821    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
822      _arc_maps;
823
824  };
825
826  /// \brief Copy a digraph to another digraph.
827  ///
828  /// This function copies a digraph to another digraph.
829  /// The complete usage of it is detailed in the DigraphCopy class, but
830  /// a short example shows a basic work:
831  ///\code
832  /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
833  ///\endcode
834  ///
835  /// After the copy the \c nr map will contain the mapping from the
836  /// nodes of the \c from digraph to the nodes of the \c to digraph and
837  /// \c acr will contain the mapping from the arcs of the \c to digraph
838  /// to the arcs of the \c from digraph.
839  ///
840  /// \see DigraphCopy
841  template <typename From, typename To>
842  DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
843    return DigraphCopy<From, To>(from, to);
844  }
845
846  /// \brief Class to copy a graph.
847  ///
848  /// Class to copy a graph to another graph (duplicate a graph). The
849  /// simplest way of using it is through the \c graphCopy() function.
850  ///
851  /// This class not only make a copy of a graph, but it can create
852  /// references and cross references between the nodes, edges and arcs of
853  /// the two graphs, and it can copy maps for using with the newly created
854  /// graph.
855  ///
856  /// To make a copy from a graph, first an instance of GraphCopy
857  /// should be created, then the data belongs to the graph should
858  /// assigned to copy. In the end, the \c run() member should be
859  /// called.
860  ///
861  /// The next code copies a graph with several data:
862  ///\code
863  ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
864  ///  // Create references for the nodes
865  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
866  ///  cg.nodeRef(nr);
867  ///  // Create cross references (inverse) for the edges
868  ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
869  ///  cg.edgeCrossRef(ecr);
870  ///  // Copy an edge map
871  ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
872  ///  NewGraph::EdgeMap<double> nemap(new_graph);
873  ///  cg.edgeMap(oemap, nemap);
874  ///  // Copy a node
875  ///  OrigGraph::Node on;
876  ///  NewGraph::Node nn;
877  ///  cg.node(on, nn);
878  ///  // Execute copying
879  ///  cg.run();
880  ///\endcode
881  template <typename From, typename To>
882  class GraphCopy {
883  private:
884
885    typedef typename From::Node Node;
886    typedef typename From::NodeIt NodeIt;
887    typedef typename From::Arc Arc;
888    typedef typename From::ArcIt ArcIt;
889    typedef typename From::Edge Edge;
890    typedef typename From::EdgeIt EdgeIt;
891
892    typedef typename To::Node TNode;
893    typedef typename To::Arc TArc;
894    typedef typename To::Edge TEdge;
895
896    typedef typename From::template NodeMap<TNode> NodeRefMap;
897    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
898
899    struct ArcRefMap {
900      ArcRefMap(const From& from, const To& to,
901                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
902        : _from(from), _to(to),
903          _edge_ref(edge_ref), _node_ref(node_ref) {}
904
905      typedef typename From::Arc Key;
906      typedef typename To::Arc Value;
907
908      Value operator[](const Key& key) const {
909        bool forward = _from.u(key) != _from.v(key) ?
910          _node_ref[_from.source(key)] ==
911          _to.source(_to.direct(_edge_ref[key], true)) :
912          _from.direction(key);
913        return _to.direct(_edge_ref[key], forward);
914      }
915
916      const From& _from;
917      const To& _to;
918      const EdgeRefMap& _edge_ref;
919      const NodeRefMap& _node_ref;
920    };
921
922  public:
923
924    /// \brief Constructor of GraphCopy.
925    ///
926    /// Constructor of GraphCopy for copying the content of the
927    /// \c from graph into the \c to graph.
928    GraphCopy(const From& from, To& to)
929      : _from(from), _to(to) {}
930
931    /// \brief Destructor of GraphCopy
932    ///
933    /// Destructor of GraphCopy.
934    ~GraphCopy() {
935      for (int i = 0; i < int(_node_maps.size()); ++i) {
936        delete _node_maps[i];
937      }
938      for (int i = 0; i < int(_arc_maps.size()); ++i) {
939        delete _arc_maps[i];
940      }
941      for (int i = 0; i < int(_edge_maps.size()); ++i) {
942        delete _edge_maps[i];
943      }
944    }
945
946    /// \brief Copy the node references into the given map.
947    ///
948    /// This function copies the node references into the given map.
949    /// The parameter should be a map, whose key type is the Node type of
950    /// the source graph, while the value type is the Node type of the
951    /// destination graph.
952    template <typename NodeRef>
953    GraphCopy& nodeRef(NodeRef& map) {
954      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
955                           NodeRefMap, NodeRef>(map));
956      return *this;
957    }
958
959    /// \brief Copy the node cross references into the given map.
960    ///
961    /// This function copies the node cross references (reverse references)
962    /// into the given map. The parameter should be a map, whose key type
963    /// is the Node type of the destination graph, while the value type is
964    /// the Node type of the source graph.
965    template <typename NodeCrossRef>
966    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
967      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
968                           NodeRefMap, NodeCrossRef>(map));
969      return *this;
970    }
971
972    /// \brief Make a copy of the given node map.
973    ///
974    /// This function makes a copy of the given node map for the newly
975    /// created graph.
976    /// The key type of the new map \c tmap should be the Node type of the
977    /// destination graph, and the key type of the original map \c map
978    /// should be the Node type of the source graph.
979    template <typename FromMap, typename ToMap>
980    GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
981      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
982                           NodeRefMap, FromMap, ToMap>(map, tmap));
983      return *this;
984    }
985
986    /// \brief Make a copy of the given node.
987    ///
988    /// This function makes a copy of the given node.
989    GraphCopy& node(const Node& node, TNode& tnode) {
990      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
991                           NodeRefMap, TNode>(node, tnode));
992      return *this;
993    }
994
995    /// \brief Copy the arc references into the given map.
996    ///
997    /// This function copies the arc references into the given map.
998    /// The parameter should be a map, whose key type is the Arc type of
999    /// the source graph, while the value type is the Arc type of the
1000    /// destination graph.
1001    template <typename ArcRef>
1002    GraphCopy& arcRef(ArcRef& map) {
1003      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
1004                          ArcRefMap, ArcRef>(map));
1005      return *this;
1006    }
1007
1008    /// \brief Copy the arc cross references into the given map.
1009    ///
1010    /// This function copies the arc cross references (reverse references)
1011    /// into the given map. The parameter should be a map, whose key type
1012    /// is the Arc type of the destination graph, while the value type is
1013    /// the Arc type of the source graph.
1014    template <typename ArcCrossRef>
1015    GraphCopy& arcCrossRef(ArcCrossRef& map) {
1016      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
1017                          ArcRefMap, ArcCrossRef>(map));
1018      return *this;
1019    }
1020
1021    /// \brief Make a copy of the given arc map.
1022    ///
1023    /// This function makes a copy of the given arc map for the newly
1024    /// created graph.
1025    /// The key type of the new map \c tmap should be the Arc type of the
1026    /// destination graph, and the key type of the original map \c map
1027    /// should be the Arc type of the source graph.
1028    template <typename FromMap, typename ToMap>
1029    GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
1030      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
1031                          ArcRefMap, FromMap, ToMap>(map, tmap));
1032      return *this;
1033    }
1034
1035    /// \brief Make a copy of the given arc.
1036    ///
1037    /// This function makes a copy of the given arc.
1038    GraphCopy& arc(const Arc& arc, TArc& tarc) {
1039      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
1040                          ArcRefMap, TArc>(arc, tarc));
1041      return *this;
1042    }
1043
1044    /// \brief Copy the edge references into the given map.
1045    ///
1046    /// This function copies the edge references into the given map.
1047    /// The parameter should be a map, whose key type is the Edge type of
1048    /// the source graph, while the value type is the Edge type of the
1049    /// destination graph.
1050    template <typename EdgeRef>
1051    GraphCopy& edgeRef(EdgeRef& map) {
1052      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
1053                           EdgeRefMap, EdgeRef>(map));
1054      return *this;
1055    }
1056
1057    /// \brief Copy the edge cross references into the given map.
1058    ///
1059    /// This function copies the edge cross references (reverse references)
1060    /// into the given map. The parameter should be a map, whose key type
1061    /// is the Edge type of the destination graph, while the value type is
1062    /// the Edge type of the source graph.
1063    template <typename EdgeCrossRef>
1064    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
1065      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
1066                           Edge, EdgeRefMap, EdgeCrossRef>(map));
1067      return *this;
1068    }
1069
1070    /// \brief Make a copy of the given edge map.
1071    ///
1072    /// This function makes a copy of the given edge map for the newly
1073    /// created graph.
1074    /// The key type of the new map \c tmap should be the Edge type of the
1075    /// destination graph, and the key type of the original map \c map
1076    /// should be the Edge type of the source graph.
1077    template <typename FromMap, typename ToMap>
1078    GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
1079      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
1080                           EdgeRefMap, FromMap, ToMap>(map, tmap));
1081      return *this;
1082    }
1083
1084    /// \brief Make a copy of the given edge.
1085    ///
1086    /// This function makes a copy of the given edge.
1087    GraphCopy& edge(const Edge& edge, TEdge& tedge) {
1088      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
1089                           EdgeRefMap, TEdge>(edge, tedge));
1090      return *this;
1091    }
1092
1093    /// \brief Execute copying.
1094    ///
1095    /// This function executes the copying of the graph along with the
1096    /// copying of the assigned data.
1097    void run() {
1098      NodeRefMap nodeRefMap(_from);
1099      EdgeRefMap edgeRefMap(_from);
1100      ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
1101      _core_bits::GraphCopySelector<To>::
1102        copy(_from, _to, nodeRefMap, edgeRefMap);
1103      for (int i = 0; i < int(_node_maps.size()); ++i) {
1104        _node_maps[i]->copy(_from, nodeRefMap);
1105      }
1106      for (int i = 0; i < int(_edge_maps.size()); ++i) {
1107        _edge_maps[i]->copy(_from, edgeRefMap);
1108      }
1109      for (int i = 0; i < int(_arc_maps.size()); ++i) {
1110        _arc_maps[i]->copy(_from, arcRefMap);
1111      }
1112    }
1113
1114  private:
1115
1116    const From& _from;
1117    To& _to;
1118
1119    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
1120      _node_maps;
1121
1122    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
1123      _arc_maps;
1124
1125    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
1126      _edge_maps;
1127
1128  };
1129
1130  /// \brief Copy a graph to another graph.
1131  ///
1132  /// This function copies a graph to another graph.
1133  /// The complete usage of it is detailed in the GraphCopy class,
1134  /// but a short example shows a basic work:
1135  ///\code
1136  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
1137  ///\endcode
1138  ///
1139  /// After the copy the \c nr map will contain the mapping from the
1140  /// nodes of the \c from graph to the nodes of the \c to graph and
1141  /// \c ecr will contain the mapping from the edges of the \c to graph
1142  /// to the edges of the \c from graph.
1143  ///
1144  /// \see GraphCopy
1145  template <typename From, typename To>
1146  GraphCopy<From, To>
1147  graphCopy(const From& from, To& to) {
1148    return GraphCopy<From, To>(from, to);
1149  }
1150
1151  /// \brief Class to copy a bipartite graph.
1152  ///
1153  /// Class to copy a bipartite graph to another graph (duplicate a
1154  /// graph). The simplest way of using it is through the
1155  /// \c bpGraphCopy() function.
1156  ///
1157  /// This class not only make a copy of a bipartite graph, but it can
1158  /// create references and cross references between the nodes, edges
1159  /// and arcs of the two graphs, and it can copy maps for using with
1160  /// the newly created graph.
1161  ///
1162  /// To make a copy from a graph, first an instance of BpGraphCopy
1163  /// should be created, then the data belongs to the graph should
1164  /// assigned to copy. In the end, the \c run() member should be
1165  /// called.
1166  ///
1167  /// The next code copies a graph with several data:
1168  ///\code
1169  ///  BpGraphCopy<OrigBpGraph, NewBpGraph> cg(orig_graph, new_graph);
1170  ///  // Create references for the nodes
1171  ///  OrigBpGraph::NodeMap<NewBpGraph::Node> nr(orig_graph);
1172  ///  cg.nodeRef(nr);
1173  ///  // Create cross references (inverse) for the edges
1174  ///  NewBpGraph::EdgeMap<OrigBpGraph::Edge> ecr(new_graph);
1175  ///  cg.edgeCrossRef(ecr);
1176  ///  // Copy a red node map
1177  ///  OrigBpGraph::RedNodeMap<double> ormap(orig_graph);
1178  ///  NewBpGraph::RedNodeMap<double> nrmap(new_graph);
1179  ///  cg.redNodeMap(ormap, nrmap);
1180  ///  // Copy a node
1181  ///  OrigBpGraph::Node on;
1182  ///  NewBpGraph::Node nn;
1183  ///  cg.node(on, nn);
1184  ///  // Execute copying
1185  ///  cg.run();
1186  ///\endcode
1187  template <typename From, typename To>
1188  class BpGraphCopy {
1189  private:
1190
1191    typedef typename From::Node Node;
1192    typedef typename From::RedNode RedNode;
1193    typedef typename From::BlueNode BlueNode;
1194    typedef typename From::NodeIt NodeIt;
1195    typedef typename From::Arc Arc;
1196    typedef typename From::ArcIt ArcIt;
1197    typedef typename From::Edge Edge;
1198    typedef typename From::EdgeIt EdgeIt;
1199
1200    typedef typename To::Node TNode;
1201    typedef typename To::RedNode TRedNode;
1202    typedef typename To::BlueNode TBlueNode;
1203    typedef typename To::Arc TArc;
1204    typedef typename To::Edge TEdge;
1205
1206    typedef typename From::template RedNodeMap<TRedNode> RedNodeRefMap;
1207    typedef typename From::template BlueNodeMap<TBlueNode> BlueNodeRefMap;
1208    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
1209
1210    struct NodeRefMap {
1211      NodeRefMap(const From& from, const RedNodeRefMap& red_node_ref,
1212                 const BlueNodeRefMap& blue_node_ref)
1213        : _from(from), _red_node_ref(red_node_ref),
1214          _blue_node_ref(blue_node_ref) {}
1215
1216      typedef typename From::Node Key;
1217      typedef typename To::Node Value;
1218
1219      Value operator[](const Key& key) const {
1220        if (_from.red(key)) {
1221          return _red_node_ref[_from.asRedNodeUnsafe(key)];
1222        } else {
1223          return _blue_node_ref[_from.asBlueNodeUnsafe(key)];
1224        }
1225      }
1226
1227      const From& _from;
1228      const RedNodeRefMap& _red_node_ref;
1229      const BlueNodeRefMap& _blue_node_ref;
1230    };
1231
1232    struct ArcRefMap {
1233      ArcRefMap(const From& from, const To& to, const EdgeRefMap& edge_ref)
1234        : _from(from), _to(to), _edge_ref(edge_ref) {}
1235
1236      typedef typename From::Arc Key;
1237      typedef typename To::Arc Value;
1238
1239      Value operator[](const Key& key) const {
1240        return _to.direct(_edge_ref[key], _from.direction(key));
1241      }
1242
1243      const From& _from;
1244      const To& _to;
1245      const EdgeRefMap& _edge_ref;
1246    };
1247
1248  public:
1249
1250    /// \brief Constructor of BpGraphCopy.
1251    ///
1252    /// Constructor of BpGraphCopy for copying the content of the
1253    /// \c from graph into the \c to graph.
1254    BpGraphCopy(const From& from, To& to)
1255      : _from(from), _to(to) {}
1256
1257    /// \brief Destructor of BpGraphCopy
1258    ///
1259    /// Destructor of BpGraphCopy.
1260    ~BpGraphCopy() {
1261      for (int i = 0; i < int(_node_maps.size()); ++i) {
1262        delete _node_maps[i];
1263      }
1264      for (int i = 0; i < int(_red_maps.size()); ++i) {
1265        delete _red_maps[i];
1266      }
1267      for (int i = 0; i < int(_blue_maps.size()); ++i) {
1268        delete _blue_maps[i];
1269      }
1270      for (int i = 0; i < int(_arc_maps.size()); ++i) {
1271        delete _arc_maps[i];
1272      }
1273      for (int i = 0; i < int(_edge_maps.size()); ++i) {
1274        delete _edge_maps[i];
1275      }
1276    }
1277
1278    /// \brief Copy the node references into the given map.
1279    ///
1280    /// This function copies the node references into the given map.
1281    /// The parameter should be a map, whose key type is the Node type of
1282    /// the source graph, while the value type is the Node type of the
1283    /// destination graph.
1284    template <typename NodeRef>
1285    BpGraphCopy& nodeRef(NodeRef& map) {
1286      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
1287                           NodeRefMap, NodeRef>(map));
1288      return *this;
1289    }
1290
1291    /// \brief Copy the node cross references into the given map.
1292    ///
1293    /// This function copies the node cross references (reverse references)
1294    /// into the given map. The parameter should be a map, whose key type
1295    /// is the Node type of the destination graph, while the value type is
1296    /// the Node type of the source graph.
1297    template <typename NodeCrossRef>
1298    BpGraphCopy& nodeCrossRef(NodeCrossRef& map) {
1299      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
1300                           NodeRefMap, NodeCrossRef>(map));
1301      return *this;
1302    }
1303
1304    /// \brief Make a copy of the given node map.
1305    ///
1306    /// This function makes a copy of the given node map for the newly
1307    /// created graph.
1308    /// The key type of the new map \c tmap should be the Node type of the
1309    /// destination graph, and the key type of the original map \c map
1310    /// should be the Node type of the source graph.
1311    template <typename FromMap, typename ToMap>
1312    BpGraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
1313      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
1314                           NodeRefMap, FromMap, ToMap>(map, tmap));
1315      return *this;
1316    }
1317
1318    /// \brief Make a copy of the given node.
1319    ///
1320    /// This function makes a copy of the given node.
1321    BpGraphCopy& node(const Node& node, TNode& tnode) {
1322      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
1323                           NodeRefMap, TNode>(node, tnode));
1324      return *this;
1325    }
1326
1327    /// \brief Copy the red node references into the given map.
1328    ///
1329    /// This function copies the red node references into the given
1330    /// map.  The parameter should be a map, whose key type is the
1331    /// Node type of the source graph with the red item set, while the
1332    /// value type is the Node type of the destination graph.
1333    template <typename RedRef>
1334    BpGraphCopy& redRef(RedRef& map) {
1335      _red_maps.push_back(new _core_bits::RefCopy<From, RedNode,
1336                          RedNodeRefMap, RedRef>(map));
1337      return *this;
1338    }
1339
1340    /// \brief Copy the red node cross references into the given map.
1341    ///
1342    /// This function copies the red node cross references (reverse
1343    /// references) into the given map. The parameter should be a map,
1344    /// whose key type is the Node type of the destination graph with
1345    /// the red item set, while the value type is the Node type of the
1346    /// source graph.
1347    template <typename RedCrossRef>
1348    BpGraphCopy& redCrossRef(RedCrossRef& map) {
1349      _red_maps.push_back(new _core_bits::CrossRefCopy<From, RedNode,
1350                          RedNodeRefMap, RedCrossRef>(map));
1351      return *this;
1352    }
1353
1354    /// \brief Make a copy of the given red node map.
1355    ///
1356    /// This function makes a copy of the given red node map for the newly
1357    /// created graph.
1358    /// The key type of the new map \c tmap should be the Node type of
1359    /// the destination graph with the red items, and the key type of
1360    /// the original map \c map should be the Node type of the source
1361    /// graph.
1362    template <typename FromMap, typename ToMap>
1363    BpGraphCopy& redNodeMap(const FromMap& map, ToMap& tmap) {
1364      _red_maps.push_back(new _core_bits::MapCopy<From, RedNode,
1365                          RedNodeRefMap, FromMap, ToMap>(map, tmap));
1366      return *this;
1367    }
1368
1369    /// \brief Make a copy of the given red node.
1370    ///
1371    /// This function makes a copy of the given red node.
1372    BpGraphCopy& redNode(const RedNode& node, TRedNode& tnode) {
1373      _red_maps.push_back(new _core_bits::ItemCopy<From, RedNode,
1374                          RedNodeRefMap, TRedNode>(node, tnode));
1375      return *this;
1376    }
1377
1378    /// \brief Copy the blue node references into the given map.
1379    ///
1380    /// This function copies the blue node references into the given
1381    /// map.  The parameter should be a map, whose key type is the
1382    /// Node type of the source graph with the blue item set, while the
1383    /// value type is the Node type of the destination graph.
1384    template <typename BlueRef>
1385    BpGraphCopy& blueRef(BlueRef& map) {
1386      _blue_maps.push_back(new _core_bits::RefCopy<From, BlueNode,
1387                           BlueNodeRefMap, BlueRef>(map));
1388      return *this;
1389    }
1390
1391    /// \brief Copy the blue node cross references into the given map.
1392    ///
1393    /// This function copies the blue node cross references (reverse
1394    /// references) into the given map. The parameter should be a map,
1395    /// whose key type is the Node type of the destination graph with
1396    /// the blue item set, while the value type is the Node type of the
1397    /// source graph.
1398    template <typename BlueCrossRef>
1399    BpGraphCopy& blueCrossRef(BlueCrossRef& map) {
1400      _blue_maps.push_back(new _core_bits::CrossRefCopy<From, BlueNode,
1401                           BlueNodeRefMap, BlueCrossRef>(map));
1402      return *this;
1403    }
1404
1405    /// \brief Make a copy of the given blue node map.
1406    ///
1407    /// This function makes a copy of the given blue node map for the newly
1408    /// created graph.
1409    /// The key type of the new map \c tmap should be the Node type of
1410    /// the destination graph with the blue items, and the key type of
1411    /// the original map \c map should be the Node type of the source
1412    /// graph.
1413    template <typename FromMap, typename ToMap>
1414    BpGraphCopy& blueNodeMap(const FromMap& map, ToMap& tmap) {
1415      _blue_maps.push_back(new _core_bits::MapCopy<From, BlueNode,
1416                           BlueNodeRefMap, FromMap, ToMap>(map, tmap));
1417      return *this;
1418    }
1419
1420    /// \brief Make a copy of the given blue node.
1421    ///
1422    /// This function makes a copy of the given blue node.
1423    BpGraphCopy& blueNode(const BlueNode& node, TBlueNode& tnode) {
1424      _blue_maps.push_back(new _core_bits::ItemCopy<From, BlueNode,
1425                           BlueNodeRefMap, TBlueNode>(node, tnode));
1426      return *this;
1427    }
1428
1429    /// \brief Copy the arc references into the given map.
1430    ///
1431    /// This function copies the arc references into the given map.
1432    /// The parameter should be a map, whose key type is the Arc type of
1433    /// the source graph, while the value type is the Arc type of the
1434    /// destination graph.
1435    template <typename ArcRef>
1436    BpGraphCopy& arcRef(ArcRef& map) {
1437      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
1438                          ArcRefMap, ArcRef>(map));
1439      return *this;
1440    }
1441
1442    /// \brief Copy the arc cross references into the given map.
1443    ///
1444    /// This function copies the arc cross references (reverse references)
1445    /// into the given map. The parameter should be a map, whose key type
1446    /// is the Arc type of the destination graph, while the value type is
1447    /// the Arc type of the source graph.
1448    template <typename ArcCrossRef>
1449    BpGraphCopy& arcCrossRef(ArcCrossRef& map) {
1450      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
1451                          ArcRefMap, ArcCrossRef>(map));
1452      return *this;
1453    }
1454
1455    /// \brief Make a copy of the given arc map.
1456    ///
1457    /// This function makes a copy of the given arc map for the newly
1458    /// created graph.
1459    /// The key type of the new map \c tmap should be the Arc type of the
1460    /// destination graph, and the key type of the original map \c map
1461    /// should be the Arc type of the source graph.
1462    template <typename FromMap, typename ToMap>
1463    BpGraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
1464      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
1465                          ArcRefMap, FromMap, ToMap>(map, tmap));
1466      return *this;
1467    }
1468
1469    /// \brief Make a copy of the given arc.
1470    ///
1471    /// This function makes a copy of the given arc.
1472    BpGraphCopy& arc(const Arc& arc, TArc& tarc) {
1473      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
1474                          ArcRefMap, TArc>(arc, tarc));
1475      return *this;
1476    }
1477
1478    /// \brief Copy the edge references into the given map.
1479    ///
1480    /// This function copies the edge references into the given map.
1481    /// The parameter should be a map, whose key type is the Edge type of
1482    /// the source graph, while the value type is the Edge type of the
1483    /// destination graph.
1484    template <typename EdgeRef>
1485    BpGraphCopy& edgeRef(EdgeRef& map) {
1486      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
1487                           EdgeRefMap, EdgeRef>(map));
1488      return *this;
1489    }
1490
1491    /// \brief Copy the edge cross references into the given map.
1492    ///
1493    /// This function copies the edge cross references (reverse references)
1494    /// into the given map. The parameter should be a map, whose key type
1495    /// is the Edge type of the destination graph, while the value type is
1496    /// the Edge type of the source graph.
1497    template <typename EdgeCrossRef>
1498    BpGraphCopy& edgeCrossRef(EdgeCrossRef& map) {
1499      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
1500                           Edge, EdgeRefMap, EdgeCrossRef>(map));
1501      return *this;
1502    }
1503
1504    /// \brief Make a copy of the given edge map.
1505    ///
1506    /// This function makes a copy of the given edge map for the newly
1507    /// created graph.
1508    /// The key type of the new map \c tmap should be the Edge type of the
1509    /// destination graph, and the key type of the original map \c map
1510    /// should be the Edge type of the source graph.
1511    template <typename FromMap, typename ToMap>
1512    BpGraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
1513      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
1514                           EdgeRefMap, FromMap, ToMap>(map, tmap));
1515      return *this;
1516    }
1517
1518    /// \brief Make a copy of the given edge.
1519    ///
1520    /// This function makes a copy of the given edge.
1521    BpGraphCopy& edge(const Edge& edge, TEdge& tedge) {
1522      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
1523                           EdgeRefMap, TEdge>(edge, tedge));
1524      return *this;
1525    }
1526
1527    /// \brief Execute copying.
1528    ///
1529    /// This function executes the copying of the graph along with the
1530    /// copying of the assigned data.
1531    void run() {
1532      RedNodeRefMap redNodeRefMap(_from);
1533      BlueNodeRefMap blueNodeRefMap(_from);
1534      NodeRefMap nodeRefMap(_from, redNodeRefMap, blueNodeRefMap);
1535      EdgeRefMap edgeRefMap(_from);
1536      ArcRefMap arcRefMap(_from, _to, edgeRefMap);
1537      _core_bits::BpGraphCopySelector<To>::
1538        copy(_from, _to, redNodeRefMap, blueNodeRefMap, edgeRefMap);
1539      for (int i = 0; i < int(_node_maps.size()); ++i) {
1540        _node_maps[i]->copy(_from, nodeRefMap);
1541      }
1542      for (int i = 0; i < int(_red_maps.size()); ++i) {
1543        _red_maps[i]->copy(_from, redNodeRefMap);
1544      }
1545      for (int i = 0; i < int(_blue_maps.size()); ++i) {
1546        _blue_maps[i]->copy(_from, blueNodeRefMap);
1547      }
1548      for (int i = 0; i < int(_edge_maps.size()); ++i) {
1549        _edge_maps[i]->copy(_from, edgeRefMap);
1550      }
1551      for (int i = 0; i < int(_arc_maps.size()); ++i) {
1552        _arc_maps[i]->copy(_from, arcRefMap);
1553      }
1554    }
1555
1556  private:
1557
1558    const From& _from;
1559    To& _to;
1560
1561    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
1562      _node_maps;
1563
1564    std::vector<_core_bits::MapCopyBase<From, RedNode, RedNodeRefMap>* >
1565      _red_maps;
1566
1567    std::vector<_core_bits::MapCopyBase<From, BlueNode, BlueNodeRefMap>* >
1568      _blue_maps;
1569
1570    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
1571      _arc_maps;
1572
1573    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
1574      _edge_maps;
1575
1576  };
1577
1578  /// \brief Copy a graph to another graph.
1579  ///
1580  /// This function copies a graph to another graph.
1581  /// The complete usage of it is detailed in the BpGraphCopy class,
1582  /// but a short example shows a basic work:
1583  ///\code
1584  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
1585  ///\endcode
1586  ///
1587  /// After the copy the \c nr map will contain the mapping from the
1588  /// nodes of the \c from graph to the nodes of the \c to graph and
1589  /// \c ecr will contain the mapping from the edges of the \c to graph
1590  /// to the edges of the \c from graph.
1591  ///
1592  /// \see BpGraphCopy
1593  template <typename From, typename To>
1594  BpGraphCopy<From, To>
1595  bpGraphCopy(const From& from, To& to) {
1596    return BpGraphCopy<From, To>(from, to);
1597  }
1598
1599  namespace _core_bits {
1600
1601    template <typename Graph, typename Enable = void>
1602    struct FindArcSelector {
1603      typedef typename Graph::Node Node;
1604      typedef typename Graph::Arc Arc;
1605      static Arc find(const Graph &g, Node u, Node v, Arc e) {
1606        if (e == INVALID) {
1607          g.firstOut(e, u);
1608        } else {
1609          g.nextOut(e);
1610        }
1611        while (e != INVALID && g.target(e) != v) {
1612          g.nextOut(e);
1613        }
1614        return e;
1615      }
1616    };
1617
1618    template <typename Graph>
1619    struct FindArcSelector<
1620      Graph,
1621      typename enable_if<typename Graph::FindArcTag, void>::type>
1622    {
1623      typedef typename Graph::Node Node;
1624      typedef typename Graph::Arc Arc;
1625      static Arc find(const Graph &g, Node u, Node v, Arc prev) {
1626        return g.findArc(u, v, prev);
1627      }
1628    };
1629  }
1630
1631  /// \brief Find an arc between two nodes of a digraph.
1632  ///
1633  /// This function finds an arc from node \c u to node \c v in the
1634  /// digraph \c g.
1635  ///
1636  /// If \c prev is \ref INVALID (this is the default value), then
1637  /// it finds the first arc from \c u to \c v. Otherwise it looks for
1638  /// the next arc from \c u to \c v after \c prev.
1639  /// \return The found arc or \ref INVALID if there is no such an arc.
1640  ///
1641  /// Thus you can iterate through each arc from \c u to \c v as it follows.
1642  ///\code
1643  /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
1644  ///   ...
1645  /// }
1646  ///\endcode
1647  ///
1648  /// \note \ref ConArcIt provides iterator interface for the same
1649  /// functionality.
1650  ///
1651  ///\sa ConArcIt
1652  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1653  template <typename Graph>
1654  inline typename Graph::Arc
1655  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1656          typename Graph::Arc prev = INVALID) {
1657    return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
1658  }
1659
1660  /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
1661  ///
1662  /// Iterator for iterating on parallel arcs connecting the same nodes. It is
1663  /// a higher level interface for the \ref findArc() function. You can
1664  /// use it the following way:
1665  ///\code
1666  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
1667  ///   ...
1668  /// }
1669  ///\endcode
1670  ///
1671  ///\sa findArc()
1672  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1673  template <typename GR>
1674  class ConArcIt : public GR::Arc {
1675    typedef typename GR::Arc Parent;
1676
1677  public:
1678
1679    typedef typename GR::Arc Arc;
1680    typedef typename GR::Node Node;
1681
1682    /// \brief Constructor.
1683    ///
1684    /// Construct a new ConArcIt iterating on the arcs that
1685    /// connects nodes \c u and \c v.
1686    ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
1687      Parent::operator=(findArc(_graph, u, v));
1688    }
1689
1690    /// \brief Constructor.
1691    ///
1692    /// Construct a new ConArcIt that continues the iterating from arc \c a.
1693    ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
1694
1695    /// \brief Increment operator.
1696    ///
1697    /// It increments the iterator and gives back the next arc.
1698    ConArcIt& operator++() {
1699      Parent::operator=(findArc(_graph, _graph.source(*this),
1700                                _graph.target(*this), *this));
1701      return *this;
1702    }
1703  private:
1704    const GR& _graph;
1705  };
1706
1707  namespace _core_bits {
1708
1709    template <typename Graph, typename Enable = void>
1710    struct FindEdgeSelector {
1711      typedef typename Graph::Node Node;
1712      typedef typename Graph::Edge Edge;
1713      static Edge find(const Graph &g, Node u, Node v, Edge e) {
1714        bool b;
1715        if (u != v) {
1716          if (e == INVALID) {
1717            g.firstInc(e, b, u);
1718          } else {
1719            b = g.u(e) == u;
1720            g.nextInc(e, b);
1721          }
1722          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
1723            g.nextInc(e, b);
1724          }
1725        } else {
1726          if (e == INVALID) {
1727            g.firstInc(e, b, u);
1728          } else {
1729            b = true;
1730            g.nextInc(e, b);
1731          }
1732          while (e != INVALID && (!b || g.v(e) != v)) {
1733            g.nextInc(e, b);
1734          }
1735        }
1736        return e;
1737      }
1738    };
1739
1740    template <typename Graph>
1741    struct FindEdgeSelector<
1742      Graph,
1743      typename enable_if<typename Graph::FindEdgeTag, void>::type>
1744    {
1745      typedef typename Graph::Node Node;
1746      typedef typename Graph::Edge Edge;
1747      static Edge find(const Graph &g, Node u, Node v, Edge prev) {
1748        return g.findEdge(u, v, prev);
1749      }
1750    };
1751  }
1752
1753  /// \brief Find an edge between two nodes of a graph.
1754  ///
1755  /// This function finds an edge from node \c u to node \c v in graph \c g.
1756  /// If node \c u and node \c v is equal then each loop edge
1757  /// will be enumerated once.
1758  ///
1759  /// If \c prev is \ref INVALID (this is the default value), then
1760  /// it finds the first edge from \c u to \c v. Otherwise it looks for
1761  /// the next edge from \c u to \c v after \c prev.
1762  /// \return The found edge or \ref INVALID if there is no such an edge.
1763  ///
1764  /// Thus you can iterate through each edge between \c u and \c v
1765  /// as it follows.
1766  ///\code
1767  /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
1768  ///   ...
1769  /// }
1770  ///\endcode
1771  ///
1772  /// \note \ref ConEdgeIt provides iterator interface for the same
1773  /// functionality.
1774  ///
1775  ///\sa ConEdgeIt
1776  template <typename Graph>
1777  inline typename Graph::Edge
1778  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1779            typename Graph::Edge p = INVALID) {
1780    return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
1781  }
1782
1783  /// \brief Iterator for iterating on parallel edges connecting the same nodes.
1784  ///
1785  /// Iterator for iterating on parallel edges connecting the same nodes.
1786  /// It is a higher level interface for the findEdge() function. You can
1787  /// use it the following way:
1788  ///\code
1789  /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
1790  ///   ...
1791  /// }
1792  ///\endcode
1793  ///
1794  ///\sa findEdge()
1795  template <typename GR>
1796  class ConEdgeIt : public GR::Edge {
1797    typedef typename GR::Edge Parent;
1798
1799  public:
1800
1801    typedef typename GR::Edge Edge;
1802    typedef typename GR::Node Node;
1803
1804    /// \brief Constructor.
1805    ///
1806    /// Construct a new ConEdgeIt iterating on the edges that
1807    /// connects nodes \c u and \c v.
1808    ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
1809      Parent::operator=(findEdge(_graph, _u, _v));
1810    }
1811
1812    /// \brief Constructor.
1813    ///
1814    /// Construct a new ConEdgeIt that continues iterating from edge \c e.
1815    ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
1816
1817    /// \brief Increment operator.
1818    ///
1819    /// It increments the iterator and gives back the next edge.
1820    ConEdgeIt& operator++() {
1821      Parent::operator=(findEdge(_graph, _u, _v, *this));
1822      return *this;
1823    }
1824  private:
1825    const GR& _graph;
1826    Node _u, _v;
1827  };
1828
1829
1830  ///Dynamic arc look-up between given endpoints.
1831
1832  ///Using this class, you can find an arc in a digraph from a given
1833  ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
1834  ///where <em>d</em> is the out-degree of the source node.
1835  ///
1836  ///It is possible to find \e all parallel arcs between two nodes with
1837  ///the \c operator() member.
1838  ///
1839  ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
1840  ///\ref AllArcLookUp if your digraph is not changed so frequently.
1841  ///
1842  ///This class uses a self-adjusting binary search tree, the Splay tree
1843  ///of Sleator and Tarjan to guarantee the logarithmic amortized
1844  ///time bound for arc look-ups. This class also guarantees the
1845  ///optimal time bound in a constant factor for any distribution of
1846  ///queries.
1847  ///
1848  ///\tparam GR The type of the underlying digraph.
1849  ///
1850  ///\sa ArcLookUp
1851  ///\sa AllArcLookUp
1852  template <typename GR>
1853  class DynArcLookUp
1854    : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
1855  {
1856    typedef typename ItemSetTraits<GR, typename GR::Arc>
1857    ::ItemNotifier::ObserverBase Parent;
1858
1859    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1860
1861  public:
1862
1863    /// The Digraph type
1864    typedef GR Digraph;
1865
1866  protected:
1867
1868    class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type
1869    {
1870      typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
1871
1872    public:
1873
1874      AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
1875
1876      virtual void add(const Node& node) {
1877        Parent::add(node);
1878        Parent::set(node, INVALID);
1879      }
1880
1881      virtual void add(const std::vector<Node>& nodes) {
1882        Parent::add(nodes);
1883        for (int i = 0; i < int(nodes.size()); ++i) {
1884          Parent::set(nodes[i], INVALID);
1885        }
1886      }
1887
1888      virtual void build() {
1889        Parent::build();
1890        Node it;
1891        typename Parent::Notifier* nf = Parent::notifier();
1892        for (nf->first(it); it != INVALID; nf->next(it)) {
1893          Parent::set(it, INVALID);
1894        }
1895      }
1896    };
1897
1898    class ArcLess {
1899      const Digraph &g;
1900    public:
1901      ArcLess(const Digraph &_g) : g(_g) {}
1902      bool operator()(Arc a,Arc b) const
1903      {
1904        return g.target(a)<g.target(b);
1905      }
1906    };
1907
1908  protected:
1909
1910    const Digraph &_g;
1911    AutoNodeMap _head;
1912    typename Digraph::template ArcMap<Arc> _parent;
1913    typename Digraph::template ArcMap<Arc> _left;
1914    typename Digraph::template ArcMap<Arc> _right;
1915
1916  public:
1917
1918    ///Constructor
1919
1920    ///Constructor.
1921    ///
1922    ///It builds up the search database.
1923    DynArcLookUp(const Digraph &g)
1924      : _g(g),_head(g),_parent(g),_left(g),_right(g)
1925    {
1926      Parent::attach(_g.notifier(typename Digraph::Arc()));
1927      refresh();
1928    }
1929
1930  protected:
1931
1932    virtual void add(const Arc& arc) {
1933      insert(arc);
1934    }
1935
1936    virtual void add(const std::vector<Arc>& arcs) {
1937      for (int i = 0; i < int(arcs.size()); ++i) {
1938        insert(arcs[i]);
1939      }
1940    }
1941
1942    virtual void erase(const Arc& arc) {
1943      remove(arc);
1944    }
1945
1946    virtual void erase(const std::vector<Arc>& arcs) {
1947      for (int i = 0; i < int(arcs.size()); ++i) {
1948        remove(arcs[i]);
1949      }
1950    }
1951
1952    virtual void build() {
1953      refresh();
1954    }
1955
1956    virtual void clear() {
1957      for(NodeIt n(_g);n!=INVALID;++n) {
1958        _head[n] = INVALID;
1959      }
1960    }
1961
1962    void insert(Arc arc) {
1963      Node s = _g.source(arc);
1964      Node t = _g.target(arc);
1965      _left[arc] = INVALID;
1966      _right[arc] = INVALID;
1967
1968      Arc e = _head[s];
1969      if (e == INVALID) {
1970        _head[s] = arc;
1971        _parent[arc] = INVALID;
1972        return;
1973      }
1974      while (true) {
1975        if (t < _g.target(e)) {
1976          if (_left[e] == INVALID) {
1977            _left[e] = arc;
1978            _parent[arc] = e;
1979            splay(arc);
1980            return;
1981          } else {
1982            e = _left[e];
1983          }
1984        } else {
1985          if (_right[e] == INVALID) {
1986            _right[e] = arc;
1987            _parent[arc] = e;
1988            splay(arc);
1989            return;
1990          } else {
1991            e = _right[e];
1992          }
1993        }
1994      }
1995    }
1996
1997    void remove(Arc arc) {
1998      if (_left[arc] == INVALID) {
1999        if (_right[arc] != INVALID) {
2000          _parent[_right[arc]] = _parent[arc];
2001        }
2002        if (_parent[arc] != INVALID) {
2003          if (_left[_parent[arc]] == arc) {
2004            _left[_parent[arc]] = _right[arc];
2005          } else {
2006            _right[_parent[arc]] = _right[arc];
2007          }
2008        } else {
2009          _head[_g.source(arc)] = _right[arc];
2010        }
2011      } else if (_right[arc] == INVALID) {
2012        _parent[_left[arc]] = _parent[arc];
2013        if (_parent[arc] != INVALID) {
2014          if (_left[_parent[arc]] == arc) {
2015            _left[_parent[arc]] = _left[arc];
2016          } else {
2017            _right[_parent[arc]] = _left[arc];
2018          }
2019        } else {
2020          _head[_g.source(arc)] = _left[arc];
2021        }
2022      } else {
2023        Arc e = _left[arc];
2024        if (_right[e] != INVALID) {
2025          e = _right[e];
2026          while (_right[e] != INVALID) {
2027            e = _right[e];
2028          }
2029          Arc s = _parent[e];
2030          _right[_parent[e]] = _left[e];
2031          if (_left[e] != INVALID) {
2032            _parent[_left[e]] = _parent[e];
2033          }
2034
2035          _left[e] = _left[arc];
2036          _parent[_left[arc]] = e;
2037          _right[e] = _right[arc];
2038          _parent[_right[arc]] = e;
2039
2040          _parent[e] = _parent[arc];
2041          if (_parent[arc] != INVALID) {
2042            if (_left[_parent[arc]] == arc) {
2043              _left[_parent[arc]] = e;
2044            } else {
2045              _right[_parent[arc]] = e;
2046            }
2047          }
2048          splay(s);
2049        } else {
2050          _right[e] = _right[arc];
2051          _parent[_right[arc]] = e;
2052          _parent[e] = _parent[arc];
2053
2054          if (_parent[arc] != INVALID) {
2055            if (_left[_parent[arc]] == arc) {
2056              _left[_parent[arc]] = e;
2057            } else {
2058              _right[_parent[arc]] = e;
2059            }
2060          } else {
2061            _head[_g.source(arc)] = e;
2062          }
2063        }
2064      }
2065    }
2066
2067    Arc refreshRec(std::vector<Arc> &v,int a,int b)
2068    {
2069      int m=(a+b)/2;
2070      Arc me=v[m];
2071      if (a < m) {
2072        Arc left = refreshRec(v,a,m-1);
2073        _left[me] = left;
2074        _parent[left] = me;
2075      } else {
2076        _left[me] = INVALID;
2077      }
2078      if (m < b) {
2079        Arc right = refreshRec(v,m+1,b);
2080        _right[me] = right;
2081        _parent[right] = me;
2082      } else {
2083        _right[me] = INVALID;
2084      }
2085      return me;
2086    }
2087
2088    void refresh() {
2089      for(NodeIt n(_g);n!=INVALID;++n) {
2090        std::vector<Arc> v;
2091        for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
2092        if (!v.empty()) {
2093          std::sort(v.begin(),v.end(),ArcLess(_g));
2094          Arc head = refreshRec(v,0,v.size()-1);
2095          _head[n] = head;
2096          _parent[head] = INVALID;
2097        }
2098        else _head[n] = INVALID;
2099      }
2100    }
2101
2102    void zig(Arc v) {
2103      Arc w = _parent[v];
2104      _parent[v] = _parent[w];
2105      _parent[w] = v;
2106      _left[w] = _right[v];
2107      _right[v] = w;
2108      if (_parent[v] != INVALID) {
2109        if (_right[_parent[v]] == w) {
2110          _right[_parent[v]] = v;
2111        } else {
2112          _left[_parent[v]] = v;
2113        }
2114      }
2115      if (_left[w] != INVALID){
2116        _parent[_left[w]] = w;
2117      }
2118    }
2119
2120    void zag(Arc v) {
2121      Arc w = _parent[v];
2122      _parent[v] = _parent[w];
2123      _parent[w] = v;
2124      _right[w] = _left[v];
2125      _left[v] = w;
2126      if (_parent[v] != INVALID){
2127        if (_left[_parent[v]] == w) {
2128          _left[_parent[v]] = v;
2129        } else {
2130          _right[_parent[v]] = v;
2131        }
2132      }
2133      if (_right[w] != INVALID){
2134        _parent[_right[w]] = w;
2135      }
2136    }
2137
2138    void splay(Arc v) {
2139      while (_parent[v] != INVALID) {
2140        if (v == _left[_parent[v]]) {
2141          if (_parent[_parent[v]] == INVALID) {
2142            zig(v);
2143          } else {
2144            if (_parent[v] == _left[_parent[_parent[v]]]) {
2145              zig(_parent[v]);
2146              zig(v);
2147            } else {
2148              zig(v);
2149              zag(v);
2150            }
2151          }
2152        } else {
2153          if (_parent[_parent[v]] == INVALID) {
2154            zag(v);
2155          } else {
2156            if (_parent[v] == _left[_parent[_parent[v]]]) {
2157              zag(v);
2158              zig(v);
2159            } else {
2160              zag(_parent[v]);
2161              zag(v);
2162            }
2163          }
2164        }
2165      }
2166      _head[_g.source(v)] = v;
2167    }
2168
2169
2170  public:
2171
2172    ///Find an arc between two nodes.
2173
2174    ///Find an arc between two nodes.
2175    ///\param s The source node.
2176    ///\param t The target node.
2177    ///\param p The previous arc between \c s and \c t. It it is INVALID or
2178    ///not given, the operator finds the first appropriate arc.
2179    ///\return An arc from \c s to \c t after \c p or
2180    ///\ref INVALID if there is no more.
2181    ///
2182    ///For example, you can count the number of arcs from \c u to \c v in the
2183    ///following way.
2184    ///\code
2185    ///DynArcLookUp<ListDigraph> ae(g);
2186    ///...
2187    ///int n = 0;
2188    ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
2189    ///\endcode
2190    ///
2191    ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
2192    ///amortized time, specifically, the time complexity of the lookups
2193    ///is equal to the optimal search tree implementation for the
2194    ///current query distribution in a constant factor.
2195    ///
2196    ///\note This is a dynamic data structure, therefore the data
2197    ///structure is updated after each graph alteration. Thus although
2198    ///this data structure is theoretically faster than \ref ArcLookUp
2199    ///and \ref AllArcLookUp, it often provides worse performance than
2200    ///them.
2201    Arc operator()(Node s, Node t, Arc p = INVALID) const  {
2202      if (p == INVALID) {
2203        Arc a = _head[s];
2204        if (a == INVALID) return INVALID;
2205        Arc r = INVALID;
2206        while (true) {
2207          if (_g.target(a) < t) {
2208            if (_right[a] == INVALID) {
2209              const_cast<DynArcLookUp&>(*this).splay(a);
2210              return r;
2211            } else {
2212              a = _right[a];
2213            }
2214          } else {
2215            if (_g.target(a) == t) {
2216              r = a;
2217            }
2218            if (_left[a] == INVALID) {
2219              const_cast<DynArcLookUp&>(*this).splay(a);
2220              return r;
2221            } else {
2222              a = _left[a];
2223            }
2224          }
2225        }
2226      } else {
2227        Arc a = p;
2228        if (_right[a] != INVALID) {
2229          a = _right[a];
2230          while (_left[a] != INVALID) {
2231            a = _left[a];
2232          }
2233          const_cast<DynArcLookUp&>(*this).splay(a);
2234        } else {
2235          while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
2236            a = _parent[a];
2237          }
2238          if (_parent[a] == INVALID) {
2239            return INVALID;
2240          } else {
2241            a = _parent[a];
2242            const_cast<DynArcLookUp&>(*this).splay(a);
2243          }
2244        }
2245        if (_g.target(a) == t) return a;
2246        else return INVALID;
2247      }
2248    }
2249
2250  };
2251
2252  ///Fast arc look-up between given endpoints.
2253
2254  ///Using this class, you can find an arc in a digraph from a given
2255  ///source to a given target in time <em>O</em>(log<em>d</em>),
2256  ///where <em>d</em> is the out-degree of the source node.
2257  ///
2258  ///It is not possible to find \e all parallel arcs between two nodes.
2259  ///Use \ref AllArcLookUp for this purpose.
2260  ///
2261  ///\warning This class is static, so you should call refresh() (or at
2262  ///least refresh(Node)) to refresh this data structure whenever the
2263  ///digraph changes. This is a time consuming (superlinearly proportional
2264  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
2265  ///
2266  ///\tparam GR The type of the underlying digraph.
2267  ///
2268  ///\sa DynArcLookUp
2269  ///\sa AllArcLookUp
2270  template<class GR>
2271  class ArcLookUp
2272  {
2273    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
2274
2275  public:
2276
2277    /// The Digraph type
2278    typedef GR Digraph;
2279
2280  protected:
2281    const Digraph &_g;
2282    typename Digraph::template NodeMap<Arc> _head;
2283    typename Digraph::template ArcMap<Arc> _left;
2284    typename Digraph::template ArcMap<Arc> _right;
2285
2286    class ArcLess {
2287      const Digraph &g;
2288    public:
2289      ArcLess(const Digraph &_g) : g(_g) {}
2290      bool operator()(Arc a,Arc b) const
2291      {
2292        return g.target(a)<g.target(b);
2293      }
2294    };
2295
2296  public:
2297
2298    ///Constructor
2299
2300    ///Constructor.
2301    ///
2302    ///It builds up the search database, which remains valid until the digraph
2303    ///changes.
2304    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
2305
2306  private:
2307    Arc refreshRec(std::vector<Arc> &v,int a,int b)
2308    {
2309      int m=(a+b)/2;
2310      Arc me=v[m];
2311      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
2312      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
2313      return me;
2314    }
2315  public:
2316    ///Refresh the search data structure at a node.
2317
2318    ///Build up the search database of node \c n.
2319    ///
2320    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
2321    ///is the number of the outgoing arcs of \c n.
2322    void refresh(Node n)
2323    {
2324      std::vector<Arc> v;
2325      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
2326      if(v.size()) {
2327        std::sort(v.begin(),v.end(),ArcLess(_g));
2328        _head[n]=refreshRec(v,0,v.size()-1);
2329      }
2330      else _head[n]=INVALID;
2331    }
2332    ///Refresh the full data structure.
2333
2334    ///Build up the full search database. In fact, it simply calls
2335    ///\ref refresh(Node) "refresh(n)" for each node \c n.
2336    ///
2337    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
2338    ///the number of the arcs in the digraph and <em>D</em> is the maximum
2339    ///out-degree of the digraph.
2340    void refresh()
2341    {
2342      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
2343    }
2344
2345    ///Find an arc between two nodes.
2346
2347    ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
2348    ///where <em>d</em> is the number of outgoing arcs of \c s.
2349    ///\param s The source node.
2350    ///\param t The target node.
2351    ///\return An arc from \c s to \c t if there exists,
2352    ///\ref INVALID otherwise.
2353    ///
2354    ///\warning If you change the digraph, refresh() must be called before using
2355    ///this operator. If you change the outgoing arcs of
2356    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
2357    Arc operator()(Node s, Node t) const
2358    {
2359      Arc e;
2360      for(e=_head[s];
2361          e!=INVALID&&_g.target(e)!=t;
2362          e = t < _g.target(e)?_left[e]:_right[e]) ;
2363      return e;
2364    }
2365
2366  };
2367
2368  ///Fast look-up of all arcs between given endpoints.
2369
2370  ///This class is the same as \ref ArcLookUp, with the addition
2371  ///that it makes it possible to find all parallel arcs between given
2372  ///endpoints.
2373  ///
2374  ///\warning This class is static, so you should call refresh() (or at
2375  ///least refresh(Node)) to refresh this data structure whenever the
2376  ///digraph changes. This is a time consuming (superlinearly proportional
2377  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
2378  ///
2379  ///\tparam GR The type of the underlying digraph.
2380  ///
2381  ///\sa DynArcLookUp
2382  ///\sa ArcLookUp
2383  template<class GR>
2384  class AllArcLookUp : public ArcLookUp<GR>
2385  {
2386    using ArcLookUp<GR>::_g;
2387    using ArcLookUp<GR>::_right;
2388    using ArcLookUp<GR>::_left;
2389    using ArcLookUp<GR>::_head;
2390
2391    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
2392
2393    typename GR::template ArcMap<Arc> _next;
2394
2395    Arc refreshNext(Arc head,Arc next=INVALID)
2396    {
2397      if(head==INVALID) return next;
2398      else {
2399        next=refreshNext(_right[head],next);
2400        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
2401          ? next : INVALID;
2402        return refreshNext(_left[head],head);
2403      }
2404    }
2405
2406    void refreshNext()
2407    {
2408      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
2409    }
2410
2411  public:
2412
2413    /// The Digraph type
2414    typedef GR Digraph;
2415
2416    ///Constructor
2417
2418    ///Constructor.
2419    ///
2420    ///It builds up the search database, which remains valid until the digraph
2421    ///changes.
2422    AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
2423
2424    ///Refresh the data structure at a node.
2425
2426    ///Build up the search database of node \c n.
2427    ///
2428    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
2429    ///the number of the outgoing arcs of \c n.
2430    void refresh(Node n)
2431    {
2432      ArcLookUp<GR>::refresh(n);
2433      refreshNext(_head[n]);
2434    }
2435
2436    ///Refresh the full data structure.
2437
2438    ///Build up the full search database. In fact, it simply calls
2439    ///\ref refresh(Node) "refresh(n)" for each node \c n.
2440    ///
2441    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
2442    ///the number of the arcs in the digraph and <em>D</em> is the maximum
2443    ///out-degree of the digraph.
2444    void refresh()
2445    {
2446      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
2447    }
2448
2449    ///Find an arc between two nodes.
2450
2451    ///Find an arc between two nodes.
2452    ///\param s The source node.
2453    ///\param t The target node.
2454    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
2455    ///not given, the operator finds the first appropriate arc.
2456    ///\return An arc from \c s to \c t after \c prev or
2457    ///\ref INVALID if there is no more.
2458    ///
2459    ///For example, you can count the number of arcs from \c u to \c v in the
2460    ///following way.
2461    ///\code
2462    ///AllArcLookUp<ListDigraph> ae(g);
2463    ///...
2464    ///int n = 0;
2465    ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
2466    ///\endcode
2467    ///
2468    ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
2469    ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
2470    ///consecutive arcs are found in constant time.
2471    ///
2472    ///\warning If you change the digraph, refresh() must be called before using
2473    ///this operator. If you change the outgoing arcs of
2474    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
2475    ///
2476    Arc operator()(Node s, Node t, Arc prev=INVALID) const
2477    {
2478      if(prev==INVALID)
2479        {
2480          Arc f=INVALID;
2481          Arc e;
2482          for(e=_head[s];
2483              e!=INVALID&&_g.target(e)!=t;
2484              e = t < _g.target(e)?_left[e]:_right[e]) ;
2485          while(e!=INVALID)
2486            if(_g.target(e)==t)
2487              {
2488                f = e;
2489                e = _left[e];
2490              }
2491            else e = _right[e];
2492          return f;
2493        }
2494      else return _next[prev];
2495    }
2496
2497  };
2498
2499  /// @}
2500
2501} //namespace lemon
2502
2503#endif
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