COIN-OR::LEMON - Graph Library

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

Last change on this file since 1270:dceba191c00d was 1270:dceba191c00d, checked in by Alpar Juttner <alpar@…>, 6 years ago

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2013
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_CORE_H
20#define LEMON_CORE_H
21
22#include <vector>
23#include <algorithm>
24
25#include <lemon/config.h>
26#include <lemon/bits/enable_if.h>
27#include <lemon/bits/traits.h>
28#include <lemon/assert.h>
29
30// Disable the following warnings when compiling with MSVC:
31// C4250: 'class1' : inherits 'class2::member' via dominance
32// C4355: 'this' : used in base member initializer list
33// C4503: 'function' : decorated name length exceeded, name was truncated
34// C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)
35// C4996: 'function': was declared deprecated
36#ifdef _MSC_VER
37#pragma warning( disable : 4250 4355 4503 4800 4996 )
38#endif
39
40#ifdef __GNUC__
41#define GCC_VERSION (__GNUC__ * 10000                   \
42                     + __GNUC_MINOR__ * 100             \
43                     + __GNUC_PATCHLEVEL__)
44#endif
45
46#if GCC_VERSION >= 40800
47// Needed by the [DI]GRAPH_TYPEDEFS marcos for gcc 4.8
48#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
49#endif
50
51///\file
52///\brief LEMON core utilities.
53///
54///This header file contains core utilities for LEMON.
55///It is automatically included by all graph types, therefore it usually
56///do not have to be included directly.
57
58namespace lemon {
59
60  /// \brief Dummy type to make it easier to create invalid iterators.
61  ///
62  /// Dummy type to make it easier to create invalid iterators.
63  /// See \ref INVALID for the usage.
64  struct Invalid {
65  public:
66    bool operator==(Invalid) { return true;  }
67    bool operator!=(Invalid) { return false; }
68    bool operator< (Invalid) { return false; }
69  };
70
71  /// \brief Invalid iterators.
72  ///
73  /// \ref Invalid is a global type that converts to each iterator
74  /// in such a way that the value of the target iterator will be invalid.
75#ifdef LEMON_ONLY_TEMPLATES
76  const Invalid INVALID = Invalid();
77#else
78  extern const Invalid INVALID;
79#endif
80
81  /// \addtogroup gutils
82  /// @{
83
84  ///Create convenience typedefs for the digraph types and iterators
85
86  ///This \c \#define creates convenient type definitions for the following
87  ///types of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
88  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
89  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
90  ///
91  ///\note If the graph type is a dependent type, ie. the graph type depend
92  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
93  ///macro.
94#define DIGRAPH_TYPEDEFS(Digraph)                                       \
95  typedef Digraph::Node Node;                                           \
96  typedef Digraph::NodeIt NodeIt;                                       \
97  typedef Digraph::Arc Arc;                                             \
98  typedef Digraph::ArcIt ArcIt;                                         \
99  typedef Digraph::InArcIt InArcIt;                                     \
100  typedef Digraph::OutArcIt OutArcIt;                                   \
101  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
102  typedef Digraph::NodeMap<int> IntNodeMap;                             \
103  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
104  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
105  typedef Digraph::ArcMap<int> IntArcMap;                               \
106  typedef Digraph::ArcMap<double> DoubleArcMap
107
108  ///Create convenience typedefs for the digraph types and iterators
109
110  ///\see DIGRAPH_TYPEDEFS
111  ///
112  ///\note Use this macro, if the graph type is a dependent type,
113  ///ie. the graph type depend on a template parameter.
114#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
115  typedef typename Digraph::Node Node;                                  \
116  typedef typename Digraph::NodeIt NodeIt;                              \
117  typedef typename Digraph::Arc Arc;                                    \
118  typedef typename Digraph::ArcIt ArcIt;                                \
119  typedef typename Digraph::InArcIt InArcIt;                            \
120  typedef typename Digraph::OutArcIt OutArcIt;                          \
121  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
122  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
123  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
124  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
125  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
126  typedef typename Digraph::template ArcMap<double> DoubleArcMap
127
128  ///Create convenience typedefs for the graph types and iterators
129
130  ///This \c \#define creates the same convenient type definitions as defined
131  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
132  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
133  ///\c DoubleEdgeMap.
134  ///
135  ///\note If the graph type is a dependent type, ie. the graph type depend
136  ///on a template parameter, then use \c TEMPLATE_GRAPH_TYPEDEFS()
137  ///macro.
138#define GRAPH_TYPEDEFS(Graph)                                           \
139  DIGRAPH_TYPEDEFS(Graph);                                              \
140  typedef Graph::Edge Edge;                                             \
141  typedef Graph::EdgeIt EdgeIt;                                         \
142  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
143  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
144  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
145  typedef Graph::EdgeMap<double> DoubleEdgeMap
146
147  ///Create convenience typedefs for the graph types and iterators
148
149  ///\see GRAPH_TYPEDEFS
150  ///
151  ///\note Use this macro, if the graph type is a dependent type,
152  ///ie. the graph type depend on a template parameter.
153#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
154  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
155  typedef typename Graph::Edge Edge;                                    \
156  typedef typename Graph::EdgeIt EdgeIt;                                \
157  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
158  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
159  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
160  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
161
162  ///Create convenience typedefs for the bipartite graph types and iterators
163
164  ///This \c \#define creates the same convenient type definitions as
165  ///defined by \ref GRAPH_TYPEDEFS(BpGraph) and ten more, namely it
166  ///creates \c RedNode, \c RedNodeIt, \c BoolRedNodeMap,
167  ///\c IntRedNodeMap, \c DoubleRedNodeMap, \c BlueNode, \c BlueNodeIt,
168  ///\c BoolBlueNodeMap, \c IntBlueNodeMap, \c DoubleBlueNodeMap.
169  ///
170  ///\note If the graph type is a dependent type, ie. the graph type depend
171  ///on a template parameter, then use \c TEMPLATE_BPGRAPH_TYPEDEFS()
172  ///macro.
173#define BPGRAPH_TYPEDEFS(BpGraph)                                       \
174  GRAPH_TYPEDEFS(BpGraph);                                              \
175  typedef BpGraph::RedNode RedNode;                                     \
176  typedef BpGraph::RedNodeIt RedNodeIt;                                 \
177  typedef BpGraph::RedNodeMap<bool> BoolRedNodeMap;                     \
178  typedef BpGraph::RedNodeMap<int> IntRedNodeMap;                       \
179  typedef BpGraph::RedNodeMap<double> DoubleRedNodeMap;                 \
180  typedef BpGraph::BlueNode BlueNode;                                   \
181  typedef BpGraph::BlueNodeIt BlueNodeIt;                               \
182  typedef BpGraph::BlueNodeMap<bool> BoolBlueNodeMap;                   \
183  typedef BpGraph::BlueNodeMap<int> IntBlueNodeMap;                     \
184  typedef BpGraph::BlueNodeMap<double> DoubleBlueNodeMap
185
186  ///Create convenience typedefs for the bipartite graph types and iterators
187
188  ///\see BPGRAPH_TYPEDEFS
189  ///
190  ///\note Use this macro, if the graph type is a dependent type,
191  ///ie. the graph type depend on a template parameter.
192#define TEMPLATE_BPGRAPH_TYPEDEFS(BpGraph)                                  \
193  TEMPLATE_GRAPH_TYPEDEFS(BpGraph);                                         \
194  typedef typename BpGraph::RedNode RedNode;                                \
195  typedef typename BpGraph::RedNodeIt RedNodeIt;                            \
196  typedef typename BpGraph::template RedNodeMap<bool> BoolRedNodeMap;       \
197  typedef typename BpGraph::template RedNodeMap<int> IntRedNodeMap;         \
198  typedef typename BpGraph::template RedNodeMap<double> DoubleRedNodeMap;   \
199  typedef typename BpGraph::BlueNode BlueNode;                              \
200  typedef typename BpGraph::BlueNodeIt BlueNodeIt;                          \
201  typedef typename BpGraph::template BlueNodeMap<bool> BoolBlueNodeMap;     \
202  typedef typename BpGraph::template BlueNodeMap<int> IntBlueNodeMap;       \
203  typedef typename BpGraph::template BlueNodeMap<double> DoubleBlueNodeMap
204
205  /// \brief Function to count the items in a graph.
206  ///
207  /// This function counts the items (nodes, arcs etc.) in a graph.
208  /// The complexity of the function is linear because
209  /// it iterates on all of the items.
210  template <typename Graph, typename Item>
211  inline int countItems(const Graph& g) {
212    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
213    int num = 0;
214    for (ItemIt it(g); it != INVALID; ++it) {
215      ++num;
216    }
217    return num;
218  }
219
220  // Node counting:
221
222  namespace _core_bits {
223
224    template <typename Graph, typename Enable = void>
225    struct CountNodesSelector {
226      static int count(const Graph &g) {
227        return countItems<Graph, typename Graph::Node>(g);
228      }
229    };
230
231    template <typename Graph>
232    struct CountNodesSelector<
233      Graph, typename
234      enable_if<typename Graph::NodeNumTag, void>::type>
235    {
236      static int count(const Graph &g) {
237        return g.nodeNum();
238      }
239    };
240  }
241
242  /// \brief Function to count the nodes in the graph.
243  ///
244  /// This function counts the nodes in the graph.
245  /// The complexity of the function is <em>O</em>(<em>n</em>), but for some
246  /// graph structures it is specialized to run in <em>O</em>(1).
247  ///
248  /// \note If the graph contains a \c nodeNum() member function and a
249  /// \c NodeNumTag tag then this function calls directly the member
250  /// function to query the cardinality of the node set.
251  template <typename Graph>
252  inline int countNodes(const Graph& g) {
253    return _core_bits::CountNodesSelector<Graph>::count(g);
254  }
255
256  namespace _graph_utils_bits {
257
258    template <typename Graph, typename Enable = void>
259    struct CountRedNodesSelector {
260      static int count(const Graph &g) {
261        return countItems<Graph, typename Graph::RedNode>(g);
262      }
263    };
264
265    template <typename Graph>
266    struct CountRedNodesSelector<
267      Graph, typename
268      enable_if<typename Graph::NodeNumTag, void>::type>
269    {
270      static int count(const Graph &g) {
271        return g.redNum();
272      }
273    };
274  }
275
276  /// \brief Function to count the red nodes in the graph.
277  ///
278  /// This function counts the red nodes in the graph.
279  /// The complexity of the function is O(n) but for some
280  /// graph structures it is specialized to run in O(1).
281  ///
282  /// If the graph contains a \e redNum() member function and a
283  /// \e NodeNumTag tag then this function calls directly the member
284  /// function to query the cardinality of the node set.
285  template <typename Graph>
286  inline int countRedNodes(const Graph& g) {
287    return _graph_utils_bits::CountRedNodesSelector<Graph>::count(g);
288  }
289
290  namespace _graph_utils_bits {
291
292    template <typename Graph, typename Enable = void>
293    struct CountBlueNodesSelector {
294      static int count(const Graph &g) {
295        return countItems<Graph, typename Graph::BlueNode>(g);
296      }
297    };
298
299    template <typename Graph>
300    struct CountBlueNodesSelector<
301      Graph, typename
302      enable_if<typename Graph::NodeNumTag, void>::type>
303    {
304      static int count(const Graph &g) {
305        return g.blueNum();
306      }
307    };
308  }
309
310  /// \brief Function to count the blue nodes in the graph.
311  ///
312  /// This function counts the blue nodes in the graph.
313  /// The complexity of the function is O(n) but for some
314  /// graph structures it is specialized to run in O(1).
315  ///
316  /// If the graph contains a \e blueNum() member function and a
317  /// \e NodeNumTag tag then this function calls directly the member
318  /// function to query the cardinality of the node set.
319  template <typename Graph>
320  inline int countBlueNodes(const Graph& g) {
321    return _graph_utils_bits::CountBlueNodesSelector<Graph>::count(g);
322  }
323
324  // Arc counting:
325
326  namespace _core_bits {
327
328    template <typename Graph, typename Enable = void>
329    struct CountArcsSelector {
330      static int count(const Graph &g) {
331        return countItems<Graph, typename Graph::Arc>(g);
332      }
333    };
334
335    template <typename Graph>
336    struct CountArcsSelector<
337      Graph,
338      typename enable_if<typename Graph::ArcNumTag, void>::type>
339    {
340      static int count(const Graph &g) {
341        return g.arcNum();
342      }
343    };
344  }
345
346  /// \brief Function to count the arcs in the graph.
347  ///
348  /// This function counts the arcs in the graph.
349  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
350  /// graph structures it is specialized to run in <em>O</em>(1).
351  ///
352  /// \note If the graph contains a \c arcNum() member function and a
353  /// \c ArcNumTag tag then this function calls directly the member
354  /// function to query the cardinality of the arc set.
355  template <typename Graph>
356  inline int countArcs(const Graph& g) {
357    return _core_bits::CountArcsSelector<Graph>::count(g);
358  }
359
360  // Edge counting:
361
362  namespace _core_bits {
363
364    template <typename Graph, typename Enable = void>
365    struct CountEdgesSelector {
366      static int count(const Graph &g) {
367        return countItems<Graph, typename Graph::Edge>(g);
368      }
369    };
370
371    template <typename Graph>
372    struct CountEdgesSelector<
373      Graph,
374      typename enable_if<typename Graph::EdgeNumTag, void>::type>
375    {
376      static int count(const Graph &g) {
377        return g.edgeNum();
378      }
379    };
380  }
381
382  /// \brief Function to count the edges in the graph.
383  ///
384  /// This function counts the edges in the graph.
385  /// The complexity of the function is <em>O</em>(<em>m</em>), but for some
386  /// graph structures it is specialized to run in <em>O</em>(1).
387  ///
388  /// \note If the graph contains a \c edgeNum() member function and a
389  /// \c EdgeNumTag tag then this function calls directly the member
390  /// function to query the cardinality of the edge set.
391  template <typename Graph>
392  inline int countEdges(const Graph& g) {
393    return _core_bits::CountEdgesSelector<Graph>::count(g);
394
395  }
396
397
398  template <typename Graph, typename DegIt>
399  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
400    int num = 0;
401    for (DegIt it(_g, _n); it != INVALID; ++it) {
402      ++num;
403    }
404    return num;
405  }
406
407  /// \brief Function to count the number of the out-arcs from node \c n.
408  ///
409  /// This function counts the number of the out-arcs from node \c n
410  /// in the graph \c g.
411  template <typename Graph>
412  inline int countOutArcs(const Graph& g,  const typename Graph::Node& n) {
413    return countNodeDegree<Graph, typename Graph::OutArcIt>(g, n);
414  }
415
416  /// \brief Function to count the number of the in-arcs to node \c n.
417  ///
418  /// This function counts the number of the in-arcs to node \c n
419  /// in the graph \c g.
420  template <typename Graph>
421  inline int countInArcs(const Graph& g,  const typename Graph::Node& n) {
422    return countNodeDegree<Graph, typename Graph::InArcIt>(g, n);
423  }
424
425  /// \brief Function to count the number of the inc-edges to node \c n.
426  ///
427  /// This function counts the number of the inc-edges to node \c n
428  /// in the undirected graph \c g.
429  template <typename Graph>
430  inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {
431    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);
432  }
433
434  namespace _core_bits {
435
436    template <typename Digraph, typename Item, typename RefMap>
437    class MapCopyBase {
438    public:
439      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
440
441      virtual ~MapCopyBase() {}
442    };
443
444    template <typename Digraph, typename Item, typename RefMap,
445              typename FromMap, typename ToMap>
446    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
447    public:
448
449      MapCopy(const FromMap& map, ToMap& tmap)
450        : _map(map), _tmap(tmap) {}
451
452      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
453        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
454        for (ItemIt it(digraph); it != INVALID; ++it) {
455          _tmap.set(refMap[it], _map[it]);
456        }
457      }
458
459    private:
460      const FromMap& _map;
461      ToMap& _tmap;
462    };
463
464    template <typename Digraph, typename Item, typename RefMap, typename It>
465    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
466    public:
467
468      ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}
469
470      virtual void copy(const Digraph&, const RefMap& refMap) {
471        _it = refMap[_item];
472      }
473
474    private:
475      Item _item;
476      It& _it;
477    };
478
479    template <typename Digraph, typename Item, typename RefMap, typename Ref>
480    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
481    public:
482
483      RefCopy(Ref& map) : _map(map) {}
484
485      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
486        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
487        for (ItemIt it(digraph); it != INVALID; ++it) {
488          _map.set(it, refMap[it]);
489        }
490      }
491
492    private:
493      Ref& _map;
494    };
495
496    template <typename Digraph, typename Item, typename RefMap,
497              typename CrossRef>
498    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
499    public:
500
501      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
502
503      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
504        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
505        for (ItemIt it(digraph); it != INVALID; ++it) {
506          _cmap.set(refMap[it], it);
507        }
508      }
509
510    private:
511      CrossRef& _cmap;
512    };
513
514    template <typename Digraph, typename Enable = void>
515    struct DigraphCopySelector {
516      template <typename From, typename NodeRefMap, typename ArcRefMap>
517      static void copy(const From& from, Digraph &to,
518                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
519        to.clear();
520        for (typename From::NodeIt it(from); it != INVALID; ++it) {
521          nodeRefMap[it] = to.addNode();
522        }
523        for (typename From::ArcIt it(from); it != INVALID; ++it) {
524          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
525                                    nodeRefMap[from.target(it)]);
526        }
527      }
528    };
529
530    template <typename Digraph>
531    struct DigraphCopySelector<
532      Digraph,
533      typename enable_if<typename Digraph::BuildTag, void>::type>
534    {
535      template <typename From, typename NodeRefMap, typename ArcRefMap>
536      static void copy(const From& from, Digraph &to,
537                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
538        to.build(from, nodeRefMap, arcRefMap);
539      }
540    };
541
542    template <typename Graph, typename Enable = void>
543    struct GraphCopySelector {
544      template <typename From, typename NodeRefMap, typename EdgeRefMap>
545      static void copy(const From& from, Graph &to,
546                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
547        to.clear();
548        for (typename From::NodeIt it(from); it != INVALID; ++it) {
549          nodeRefMap[it] = to.addNode();
550        }
551        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
552          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
553                                      nodeRefMap[from.v(it)]);
554        }
555      }
556    };
557
558    template <typename Graph>
559    struct GraphCopySelector<
560      Graph,
561      typename enable_if<typename Graph::BuildTag, void>::type>
562    {
563      template <typename From, typename NodeRefMap, typename EdgeRefMap>
564      static void copy(const From& from, Graph &to,
565                       NodeRefMap& nodeRefMap,
566                       EdgeRefMap& edgeRefMap) {
567        to.build(from, nodeRefMap, edgeRefMap);
568      }
569    };
570
571    template <typename BpGraph, typename Enable = void>
572    struct BpGraphCopySelector {
573      template <typename From, typename RedNodeRefMap,
574                typename BlueNodeRefMap, typename EdgeRefMap>
575      static void copy(const From& from, BpGraph &to,
576                       RedNodeRefMap& redNodeRefMap,
577                       BlueNodeRefMap& blueNodeRefMap,
578                       EdgeRefMap& edgeRefMap) {
579        to.clear();
580        for (typename From::RedNodeIt it(from); it != INVALID; ++it) {
581          redNodeRefMap[it] = to.addRedNode();
582        }
583        for (typename From::BlueNodeIt it(from); it != INVALID; ++it) {
584          blueNodeRefMap[it] = to.addBlueNode();
585        }
586        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
587          edgeRefMap[it] = to.addEdge(redNodeRefMap[from.redNode(it)],
588                                      blueNodeRefMap[from.blueNode(it)]);
589        }
590      }
591    };
592
593    template <typename BpGraph>
594    struct BpGraphCopySelector<
595      BpGraph,
596      typename enable_if<typename BpGraph::BuildTag, void>::type>
597    {
598      template <typename From, typename RedNodeRefMap,
599                typename BlueNodeRefMap, typename EdgeRefMap>
600      static void copy(const From& from, BpGraph &to,
601                       RedNodeRefMap& redNodeRefMap,
602                       BlueNodeRefMap& blueNodeRefMap,
603                       EdgeRefMap& edgeRefMap) {
604        to.build(from, redNodeRefMap, blueNodeRefMap, edgeRefMap);
605      }
606    };
607
608  }
609
610  /// \brief Check whether a graph is undirected.
611  ///
612  /// This function returns \c true if the given graph is undirected.
613#ifdef DOXYGEN
614  template <typename GR>
615  bool undirected(const GR& g) { return false; }
616#else
617  template <typename GR>
618  typename enable_if<UndirectedTagIndicator<GR>, bool>::type
619  undirected(const GR&) {
620    return true;
621  }
622  template <typename GR>
623  typename disable_if<UndirectedTagIndicator<GR>, bool>::type
624  undirected(const GR&) {
625    return false;
626  }
627#endif
628
629  /// \brief Class to copy a digraph.
630  ///
631  /// Class to copy a digraph to another digraph (duplicate a digraph). The
632  /// simplest way of using it is through the \c digraphCopy() function.
633  ///
634  /// This class not only make a copy of a digraph, but it can create
635  /// references and cross references between the nodes and arcs of
636  /// the two digraphs, and it can copy maps to use with the newly created
637  /// digraph.
638  ///
639  /// To make a copy from a digraph, first an instance of DigraphCopy
640  /// should be created, then the data belongs to the digraph should
641  /// assigned to copy. In the end, the \c run() member should be
642  /// called.
643  ///
644  /// The next code copies a digraph with several data:
645  ///\code
646  ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
647  ///  // Create references for the nodes
648  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
649  ///  cg.nodeRef(nr);
650  ///  // Create cross references (inverse) for the arcs
651  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
652  ///  cg.arcCrossRef(acr);
653  ///  // Copy an arc map
654  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
655  ///  NewGraph::ArcMap<double> namap(new_graph);
656  ///  cg.arcMap(oamap, namap);
657  ///  // Copy a node
658  ///  OrigGraph::Node on;
659  ///  NewGraph::Node nn;
660  ///  cg.node(on, nn);
661  ///  // Execute copying
662  ///  cg.run();
663  ///\endcode
664  template <typename From, typename To>
665  class DigraphCopy {
666  private:
667
668    typedef typename From::Node Node;
669    typedef typename From::NodeIt NodeIt;
670    typedef typename From::Arc Arc;
671    typedef typename From::ArcIt ArcIt;
672
673    typedef typename To::Node TNode;
674    typedef typename To::Arc TArc;
675
676    typedef typename From::template NodeMap<TNode> NodeRefMap;
677    typedef typename From::template ArcMap<TArc> ArcRefMap;
678
679  public:
680
681    /// \brief Constructor of DigraphCopy.
682    ///
683    /// Constructor of DigraphCopy for copying the content of the
684    /// \c from digraph into the \c to digraph.
685    DigraphCopy(const From& from, To& to)
686      : _from(from), _to(to) {}
687
688    /// \brief Destructor of DigraphCopy
689    ///
690    /// Destructor of DigraphCopy.
691    ~DigraphCopy() {
692      for (int i = 0; i < int(_node_maps.size()); ++i) {
693        delete _node_maps[i];
694      }
695      for (int i = 0; i < int(_arc_maps.size()); ++i) {
696        delete _arc_maps[i];
697      }
698
699    }
700
701    /// \brief Copy the node references into the given map.
702    ///
703    /// This function copies the node references into the given map.
704    /// The parameter should be a map, whose key type is the Node type of
705    /// the source digraph, while the value type is the Node type of the
706    /// destination digraph.
707    template <typename NodeRef>
708    DigraphCopy& nodeRef(NodeRef& map) {
709      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
710                           NodeRefMap, NodeRef>(map));
711      return *this;
712    }
713
714    /// \brief Copy the node cross references into the given map.
715    ///
716    /// This function copies the node cross references (reverse references)
717    /// into the given map. The parameter should be a map, whose key type
718    /// is the Node type of the destination digraph, while the value type is
719    /// the Node type of the source digraph.
720    template <typename NodeCrossRef>
721    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
722      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
723                           NodeRefMap, NodeCrossRef>(map));
724      return *this;
725    }
726
727    /// \brief Make a copy of the given node map.
728    ///
729    /// This function makes a copy of the given node map for the newly
730    /// created digraph.
731    /// The key type of the new map \c tmap should be the Node type of the
732    /// destination digraph, and the key type of the original map \c map
733    /// should be the Node type of the source digraph.
734    template <typename FromMap, typename ToMap>
735    DigraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
736      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
737                           NodeRefMap, FromMap, ToMap>(map, tmap));
738      return *this;
739    }
740
741    /// \brief Make a copy of the given node.
742    ///
743    /// This function makes a copy of the given node.
744    DigraphCopy& node(const Node& node, TNode& tnode) {
745      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
746                           NodeRefMap, TNode>(node, tnode));
747      return *this;
748    }
749
750    /// \brief Copy the arc references into the given map.
751    ///
752    /// This function copies the arc references into the given map.
753    /// The parameter should be a map, whose key type is the Arc type of
754    /// the source digraph, while the value type is the Arc type of the
755    /// destination digraph.
756    template <typename ArcRef>
757    DigraphCopy& arcRef(ArcRef& map) {
758      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
759                          ArcRefMap, ArcRef>(map));
760      return *this;
761    }
762
763    /// \brief Copy the arc cross references into the given map.
764    ///
765    /// This function copies the arc cross references (reverse references)
766    /// into the given map. The parameter should be a map, whose key type
767    /// is the Arc type of the destination digraph, while the value type is
768    /// the Arc type of the source digraph.
769    template <typename ArcCrossRef>
770    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
771      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
772                          ArcRefMap, ArcCrossRef>(map));
773      return *this;
774    }
775
776    /// \brief Make a copy of the given arc map.
777    ///
778    /// This function makes a copy of the given arc map for the newly
779    /// created digraph.
780    /// The key type of the new map \c tmap should be the Arc type of the
781    /// destination digraph, and the key type of the original map \c map
782    /// should be the Arc type of the source digraph.
783    template <typename FromMap, typename ToMap>
784    DigraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
785      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
786                          ArcRefMap, FromMap, ToMap>(map, tmap));
787      return *this;
788    }
789
790    /// \brief Make a copy of the given arc.
791    ///
792    /// This function makes a copy of the given arc.
793    DigraphCopy& arc(const Arc& arc, TArc& tarc) {
794      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
795                          ArcRefMap, TArc>(arc, tarc));
796      return *this;
797    }
798
799    /// \brief Execute copying.
800    ///
801    /// This function executes the copying of the digraph along with the
802    /// copying of the assigned data.
803    void run() {
804      NodeRefMap nodeRefMap(_from);
805      ArcRefMap arcRefMap(_from);
806      _core_bits::DigraphCopySelector<To>::
807        copy(_from, _to, nodeRefMap, arcRefMap);
808      for (int i = 0; i < int(_node_maps.size()); ++i) {
809        _node_maps[i]->copy(_from, nodeRefMap);
810      }
811      for (int i = 0; i < int(_arc_maps.size()); ++i) {
812        _arc_maps[i]->copy(_from, arcRefMap);
813      }
814    }
815
816  protected:
817
818    const From& _from;
819    To& _to;
820
821    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
822      _node_maps;
823
824    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
825      _arc_maps;
826
827  };
828
829  /// \brief Copy a digraph to another digraph.
830  ///
831  /// This function copies a digraph to another digraph.
832  /// The complete usage of it is detailed in the DigraphCopy class, but
833  /// a short example shows a basic work:
834  ///\code
835  /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).run();
836  ///\endcode
837  ///
838  /// After the copy the \c nr map will contain the mapping from the
839  /// nodes of the \c from digraph to the nodes of the \c to digraph and
840  /// \c acr will contain the mapping from the arcs of the \c to digraph
841  /// to the arcs of the \c from digraph.
842  ///
843  /// \see DigraphCopy
844  template <typename From, typename To>
845  DigraphCopy<From, To> digraphCopy(const From& from, To& to) {
846    return DigraphCopy<From, To>(from, to);
847  }
848
849  /// \brief Class to copy a graph.
850  ///
851  /// Class to copy a graph to another graph (duplicate a graph). The
852  /// simplest way of using it is through the \c graphCopy() function.
853  ///
854  /// This class not only make a copy of a graph, but it can create
855  /// references and cross references between the nodes, edges and arcs of
856  /// the two graphs, and it can copy maps for using with the newly created
857  /// graph.
858  ///
859  /// To make a copy from a graph, first an instance of GraphCopy
860  /// should be created, then the data belongs to the graph should
861  /// assigned to copy. In the end, the \c run() member should be
862  /// called.
863  ///
864  /// The next code copies a graph with several data:
865  ///\code
866  ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);
867  ///  // Create references for the nodes
868  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
869  ///  cg.nodeRef(nr);
870  ///  // Create cross references (inverse) for the edges
871  ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);
872  ///  cg.edgeCrossRef(ecr);
873  ///  // Copy an edge map
874  ///  OrigGraph::EdgeMap<double> oemap(orig_graph);
875  ///  NewGraph::EdgeMap<double> nemap(new_graph);
876  ///  cg.edgeMap(oemap, nemap);
877  ///  // Copy a node
878  ///  OrigGraph::Node on;
879  ///  NewGraph::Node nn;
880  ///  cg.node(on, nn);
881  ///  // Execute copying
882  ///  cg.run();
883  ///\endcode
884  template <typename From, typename To>
885  class GraphCopy {
886  private:
887
888    typedef typename From::Node Node;
889    typedef typename From::NodeIt NodeIt;
890    typedef typename From::Arc Arc;
891    typedef typename From::ArcIt ArcIt;
892    typedef typename From::Edge Edge;
893    typedef typename From::EdgeIt EdgeIt;
894
895    typedef typename To::Node TNode;
896    typedef typename To::Arc TArc;
897    typedef typename To::Edge TEdge;
898
899    typedef typename From::template NodeMap<TNode> NodeRefMap;
900    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
901
902    struct ArcRefMap {
903      ArcRefMap(const From& from, const To& to,
904                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
905        : _from(from), _to(to),
906          _edge_ref(edge_ref), _node_ref(node_ref) {}
907
908      typedef typename From::Arc Key;
909      typedef typename To::Arc Value;
910
911      Value operator[](const Key& key) const {
912        bool forward = _from.u(key) != _from.v(key) ?
913          _node_ref[_from.source(key)] ==
914          _to.source(_to.direct(_edge_ref[key], true)) :
915          _from.direction(key);
916        return _to.direct(_edge_ref[key], forward);
917      }
918
919      const From& _from;
920      const To& _to;
921      const EdgeRefMap& _edge_ref;
922      const NodeRefMap& _node_ref;
923    };
924
925  public:
926
927    /// \brief Constructor of GraphCopy.
928    ///
929    /// Constructor of GraphCopy for copying the content of the
930    /// \c from graph into the \c to graph.
931    GraphCopy(const From& from, To& to)
932      : _from(from), _to(to) {}
933
934    /// \brief Destructor of GraphCopy
935    ///
936    /// Destructor of GraphCopy.
937    ~GraphCopy() {
938      for (int i = 0; i < int(_node_maps.size()); ++i) {
939        delete _node_maps[i];
940      }
941      for (int i = 0; i < int(_arc_maps.size()); ++i) {
942        delete _arc_maps[i];
943      }
944      for (int i = 0; i < int(_edge_maps.size()); ++i) {
945        delete _edge_maps[i];
946      }
947    }
948
949    /// \brief Copy the node references into the given map.
950    ///
951    /// This function copies the node references into the given map.
952    /// The parameter should be a map, whose key type is the Node type of
953    /// the source graph, while the value type is the Node type of the
954    /// destination graph.
955    template <typename NodeRef>
956    GraphCopy& nodeRef(NodeRef& map) {
957      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
958                           NodeRefMap, NodeRef>(map));
959      return *this;
960    }
961
962    /// \brief Copy the node cross references into the given map.
963    ///
964    /// This function copies the node cross references (reverse references)
965    /// into the given map. The parameter should be a map, whose key type
966    /// is the Node type of the destination graph, while the value type is
967    /// the Node type of the source graph.
968    template <typename NodeCrossRef>
969    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
970      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
971                           NodeRefMap, NodeCrossRef>(map));
972      return *this;
973    }
974
975    /// \brief Make a copy of the given node map.
976    ///
977    /// This function makes a copy of the given node map for the newly
978    /// created graph.
979    /// The key type of the new map \c tmap should be the Node type of the
980    /// destination graph, and the key type of the original map \c map
981    /// should be the Node type of the source graph.
982    template <typename FromMap, typename ToMap>
983    GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
984      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
985                           NodeRefMap, FromMap, ToMap>(map, tmap));
986      return *this;
987    }
988
989    /// \brief Make a copy of the given node.
990    ///
991    /// This function makes a copy of the given node.
992    GraphCopy& node(const Node& node, TNode& tnode) {
993      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
994                           NodeRefMap, TNode>(node, tnode));
995      return *this;
996    }
997
998    /// \brief Copy the arc references into the given map.
999    ///
1000    /// This function copies the arc references into the given map.
1001    /// The parameter should be a map, whose key type is the Arc type of
1002    /// the source graph, while the value type is the Arc type of the
1003    /// destination graph.
1004    template <typename ArcRef>
1005    GraphCopy& arcRef(ArcRef& map) {
1006      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
1007                          ArcRefMap, ArcRef>(map));
1008      return *this;
1009    }
1010
1011    /// \brief Copy the arc cross references into the given map.
1012    ///
1013    /// This function copies the arc cross references (reverse references)
1014    /// into the given map. The parameter should be a map, whose key type
1015    /// is the Arc type of the destination graph, while the value type is
1016    /// the Arc type of the source graph.
1017    template <typename ArcCrossRef>
1018    GraphCopy& arcCrossRef(ArcCrossRef& map) {
1019      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
1020                          ArcRefMap, ArcCrossRef>(map));
1021      return *this;
1022    }
1023
1024    /// \brief Make a copy of the given arc map.
1025    ///
1026    /// This function makes a copy of the given arc map for the newly
1027    /// created graph.
1028    /// The key type of the new map \c tmap should be the Arc type of the
1029    /// destination graph, and the key type of the original map \c map
1030    /// should be the Arc type of the source graph.
1031    template <typename FromMap, typename ToMap>
1032    GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
1033      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
1034                          ArcRefMap, FromMap, ToMap>(map, tmap));
1035      return *this;
1036    }
1037
1038    /// \brief Make a copy of the given arc.
1039    ///
1040    /// This function makes a copy of the given arc.
1041    GraphCopy& arc(const Arc& arc, TArc& tarc) {
1042      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
1043                          ArcRefMap, TArc>(arc, tarc));
1044      return *this;
1045    }
1046
1047    /// \brief Copy the edge references into the given map.
1048    ///
1049    /// This function copies the edge references into the given map.
1050    /// The parameter should be a map, whose key type is the Edge type of
1051    /// the source graph, while the value type is the Edge type of the
1052    /// destination graph.
1053    template <typename EdgeRef>
1054    GraphCopy& edgeRef(EdgeRef& map) {
1055      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
1056                           EdgeRefMap, EdgeRef>(map));
1057      return *this;
1058    }
1059
1060    /// \brief Copy the edge cross references into the given map.
1061    ///
1062    /// This function copies the edge cross references (reverse references)
1063    /// into the given map. The parameter should be a map, whose key type
1064    /// is the Edge type of the destination graph, while the value type is
1065    /// the Edge type of the source graph.
1066    template <typename EdgeCrossRef>
1067    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
1068      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
1069                           Edge, EdgeRefMap, EdgeCrossRef>(map));
1070      return *this;
1071    }
1072
1073    /// \brief Make a copy of the given edge map.
1074    ///
1075    /// This function makes a copy of the given edge map for the newly
1076    /// created graph.
1077    /// The key type of the new map \c tmap should be the Edge type of the
1078    /// destination graph, and the key type of the original map \c map
1079    /// should be the Edge type of the source graph.
1080    template <typename FromMap, typename ToMap>
1081    GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
1082      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
1083                           EdgeRefMap, FromMap, ToMap>(map, tmap));
1084      return *this;
1085    }
1086
1087    /// \brief Make a copy of the given edge.
1088    ///
1089    /// This function makes a copy of the given edge.
1090    GraphCopy& edge(const Edge& edge, TEdge& tedge) {
1091      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
1092                           EdgeRefMap, TEdge>(edge, tedge));
1093      return *this;
1094    }
1095
1096    /// \brief Execute copying.
1097    ///
1098    /// This function executes the copying of the graph along with the
1099    /// copying of the assigned data.
1100    void run() {
1101      NodeRefMap nodeRefMap(_from);
1102      EdgeRefMap edgeRefMap(_from);
1103      ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);
1104      _core_bits::GraphCopySelector<To>::
1105        copy(_from, _to, nodeRefMap, edgeRefMap);
1106      for (int i = 0; i < int(_node_maps.size()); ++i) {
1107        _node_maps[i]->copy(_from, nodeRefMap);
1108      }
1109      for (int i = 0; i < int(_edge_maps.size()); ++i) {
1110        _edge_maps[i]->copy(_from, edgeRefMap);
1111      }
1112      for (int i = 0; i < int(_arc_maps.size()); ++i) {
1113        _arc_maps[i]->copy(_from, arcRefMap);
1114      }
1115    }
1116
1117  private:
1118
1119    const From& _from;
1120    To& _to;
1121
1122    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
1123      _node_maps;
1124
1125    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
1126      _arc_maps;
1127
1128    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
1129      _edge_maps;
1130
1131  };
1132
1133  /// \brief Copy a graph to another graph.
1134  ///
1135  /// This function copies a graph to another graph.
1136  /// The complete usage of it is detailed in the GraphCopy class,
1137  /// but a short example shows a basic work:
1138  ///\code
1139  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
1140  ///\endcode
1141  ///
1142  /// After the copy the \c nr map will contain the mapping from the
1143  /// nodes of the \c from graph to the nodes of the \c to graph and
1144  /// \c ecr will contain the mapping from the edges of the \c to graph
1145  /// to the edges of the \c from graph.
1146  ///
1147  /// \see GraphCopy
1148  template <typename From, typename To>
1149  GraphCopy<From, To>
1150  graphCopy(const From& from, To& to) {
1151    return GraphCopy<From, To>(from, to);
1152  }
1153
1154  /// \brief Class to copy a bipartite graph.
1155  ///
1156  /// Class to copy a bipartite graph to another graph (duplicate a
1157  /// graph). The simplest way of using it is through the
1158  /// \c bpGraphCopy() function.
1159  ///
1160  /// This class not only make a copy of a bipartite graph, but it can
1161  /// create references and cross references between the nodes, edges
1162  /// and arcs of the two graphs, and it can copy maps for using with
1163  /// the newly created graph.
1164  ///
1165  /// To make a copy from a graph, first an instance of BpGraphCopy
1166  /// should be created, then the data belongs to the graph should
1167  /// assigned to copy. In the end, the \c run() member should be
1168  /// called.
1169  ///
1170  /// The next code copies a graph with several data:
1171  ///\code
1172  ///  BpGraphCopy<OrigBpGraph, NewBpGraph> cg(orig_graph, new_graph);
1173  ///  // Create references for the nodes
1174  ///  OrigBpGraph::NodeMap<NewBpGraph::Node> nr(orig_graph);
1175  ///  cg.nodeRef(nr);
1176  ///  // Create cross references (inverse) for the edges
1177  ///  NewBpGraph::EdgeMap<OrigBpGraph::Edge> ecr(new_graph);
1178  ///  cg.edgeCrossRef(ecr);
1179  ///  // Copy a red node map
1180  ///  OrigBpGraph::RedNodeMap<double> ormap(orig_graph);
1181  ///  NewBpGraph::RedNodeMap<double> nrmap(new_graph);
1182  ///  cg.redNodeMap(ormap, nrmap);
1183  ///  // Copy a node
1184  ///  OrigBpGraph::Node on;
1185  ///  NewBpGraph::Node nn;
1186  ///  cg.node(on, nn);
1187  ///  // Execute copying
1188  ///  cg.run();
1189  ///\endcode
1190  template <typename From, typename To>
1191  class BpGraphCopy {
1192  private:
1193
1194    typedef typename From::Node Node;
1195    typedef typename From::RedNode RedNode;
1196    typedef typename From::BlueNode BlueNode;
1197    typedef typename From::NodeIt NodeIt;
1198    typedef typename From::Arc Arc;
1199    typedef typename From::ArcIt ArcIt;
1200    typedef typename From::Edge Edge;
1201    typedef typename From::EdgeIt EdgeIt;
1202
1203    typedef typename To::Node TNode;
1204    typedef typename To::RedNode TRedNode;
1205    typedef typename To::BlueNode TBlueNode;
1206    typedef typename To::Arc TArc;
1207    typedef typename To::Edge TEdge;
1208
1209    typedef typename From::template RedNodeMap<TRedNode> RedNodeRefMap;
1210    typedef typename From::template BlueNodeMap<TBlueNode> BlueNodeRefMap;
1211    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
1212
1213    struct NodeRefMap {
1214      NodeRefMap(const From& from, const RedNodeRefMap& red_node_ref,
1215                 const BlueNodeRefMap& blue_node_ref)
1216        : _from(from), _red_node_ref(red_node_ref),
1217          _blue_node_ref(blue_node_ref) {}
1218
1219      typedef typename From::Node Key;
1220      typedef typename To::Node Value;
1221
1222      Value operator[](const Key& key) const {
1223        if (_from.red(key)) {
1224          return _red_node_ref[_from.asRedNodeUnsafe(key)];
1225        } else {
1226          return _blue_node_ref[_from.asBlueNodeUnsafe(key)];
1227        }
1228      }
1229
1230      const From& _from;
1231      const RedNodeRefMap& _red_node_ref;
1232      const BlueNodeRefMap& _blue_node_ref;
1233    };
1234
1235    struct ArcRefMap {
1236      ArcRefMap(const From& from, const To& to, const EdgeRefMap& edge_ref)
1237        : _from(from), _to(to), _edge_ref(edge_ref) {}
1238
1239      typedef typename From::Arc Key;
1240      typedef typename To::Arc Value;
1241
1242      Value operator[](const Key& key) const {
1243        return _to.direct(_edge_ref[key], _from.direction(key));
1244      }
1245
1246      const From& _from;
1247      const To& _to;
1248      const EdgeRefMap& _edge_ref;
1249    };
1250
1251  public:
1252
1253    /// \brief Constructor of BpGraphCopy.
1254    ///
1255    /// Constructor of BpGraphCopy for copying the content of the
1256    /// \c from graph into the \c to graph.
1257    BpGraphCopy(const From& from, To& to)
1258      : _from(from), _to(to) {}
1259
1260    /// \brief Destructor of BpGraphCopy
1261    ///
1262    /// Destructor of BpGraphCopy.
1263    ~BpGraphCopy() {
1264      for (int i = 0; i < int(_node_maps.size()); ++i) {
1265        delete _node_maps[i];
1266      }
1267      for (int i = 0; i < int(_red_maps.size()); ++i) {
1268        delete _red_maps[i];
1269      }
1270      for (int i = 0; i < int(_blue_maps.size()); ++i) {
1271        delete _blue_maps[i];
1272      }
1273      for (int i = 0; i < int(_arc_maps.size()); ++i) {
1274        delete _arc_maps[i];
1275      }
1276      for (int i = 0; i < int(_edge_maps.size()); ++i) {
1277        delete _edge_maps[i];
1278      }
1279    }
1280
1281    /// \brief Copy the node references into the given map.
1282    ///
1283    /// This function copies the node references into the given map.
1284    /// The parameter should be a map, whose key type is the Node type of
1285    /// the source graph, while the value type is the Node type of the
1286    /// destination graph.
1287    template <typename NodeRef>
1288    BpGraphCopy& nodeRef(NodeRef& map) {
1289      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
1290                           NodeRefMap, NodeRef>(map));
1291      return *this;
1292    }
1293
1294    /// \brief Copy the node cross references into the given map.
1295    ///
1296    /// This function copies the node cross references (reverse references)
1297    /// into the given map. The parameter should be a map, whose key type
1298    /// is the Node type of the destination graph, while the value type is
1299    /// the Node type of the source graph.
1300    template <typename NodeCrossRef>
1301    BpGraphCopy& nodeCrossRef(NodeCrossRef& map) {
1302      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
1303                           NodeRefMap, NodeCrossRef>(map));
1304      return *this;
1305    }
1306
1307    /// \brief Make a copy of the given node map.
1308    ///
1309    /// This function makes a copy of the given node map for the newly
1310    /// created graph.
1311    /// The key type of the new map \c tmap should be the Node type of the
1312    /// destination graph, and the key type of the original map \c map
1313    /// should be the Node type of the source graph.
1314    template <typename FromMap, typename ToMap>
1315    BpGraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {
1316      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
1317                           NodeRefMap, FromMap, ToMap>(map, tmap));
1318      return *this;
1319    }
1320
1321    /// \brief Make a copy of the given node.
1322    ///
1323    /// This function makes a copy of the given node.
1324    BpGraphCopy& node(const Node& node, TNode& tnode) {
1325      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
1326                           NodeRefMap, TNode>(node, tnode));
1327      return *this;
1328    }
1329
1330    /// \brief Copy the red node references into the given map.
1331    ///
1332    /// This function copies the red node references into the given
1333    /// map.  The parameter should be a map, whose key type is the
1334    /// Node type of the source graph with the red item set, while the
1335    /// value type is the Node type of the destination graph.
1336    template <typename RedRef>
1337    BpGraphCopy& redRef(RedRef& map) {
1338      _red_maps.push_back(new _core_bits::RefCopy<From, RedNode,
1339                          RedNodeRefMap, RedRef>(map));
1340      return *this;
1341    }
1342
1343    /// \brief Copy the red node cross references into the given map.
1344    ///
1345    /// This function copies the red node cross references (reverse
1346    /// references) into the given map. The parameter should be a map,
1347    /// whose key type is the Node type of the destination graph with
1348    /// the red item set, while the value type is the Node type of the
1349    /// source graph.
1350    template <typename RedCrossRef>
1351    BpGraphCopy& redCrossRef(RedCrossRef& map) {
1352      _red_maps.push_back(new _core_bits::CrossRefCopy<From, RedNode,
1353                          RedNodeRefMap, RedCrossRef>(map));
1354      return *this;
1355    }
1356
1357    /// \brief Make a copy of the given red node map.
1358    ///
1359    /// This function makes a copy of the given red node map for the newly
1360    /// created graph.
1361    /// The key type of the new map \c tmap should be the Node type of
1362    /// the destination graph with the red items, and the key type of
1363    /// the original map \c map should be the Node type of the source
1364    /// graph.
1365    template <typename FromMap, typename ToMap>
1366    BpGraphCopy& redNodeMap(const FromMap& map, ToMap& tmap) {
1367      _red_maps.push_back(new _core_bits::MapCopy<From, RedNode,
1368                          RedNodeRefMap, FromMap, ToMap>(map, tmap));
1369      return *this;
1370    }
1371
1372    /// \brief Make a copy of the given red node.
1373    ///
1374    /// This function makes a copy of the given red node.
1375    BpGraphCopy& redNode(const RedNode& node, TRedNode& tnode) {
1376      _red_maps.push_back(new _core_bits::ItemCopy<From, RedNode,
1377                          RedNodeRefMap, TRedNode>(node, tnode));
1378      return *this;
1379    }
1380
1381    /// \brief Copy the blue node references into the given map.
1382    ///
1383    /// This function copies the blue node references into the given
1384    /// map.  The parameter should be a map, whose key type is the
1385    /// Node type of the source graph with the blue item set, while the
1386    /// value type is the Node type of the destination graph.
1387    template <typename BlueRef>
1388    BpGraphCopy& blueRef(BlueRef& map) {
1389      _blue_maps.push_back(new _core_bits::RefCopy<From, BlueNode,
1390                           BlueNodeRefMap, BlueRef>(map));
1391      return *this;
1392    }
1393
1394    /// \brief Copy the blue node cross references into the given map.
1395    ///
1396    /// This function copies the blue node cross references (reverse
1397    /// references) into the given map. The parameter should be a map,
1398    /// whose key type is the Node type of the destination graph with
1399    /// the blue item set, while the value type is the Node type of the
1400    /// source graph.
1401    template <typename BlueCrossRef>
1402    BpGraphCopy& blueCrossRef(BlueCrossRef& map) {
1403      _blue_maps.push_back(new _core_bits::CrossRefCopy<From, BlueNode,
1404                           BlueNodeRefMap, BlueCrossRef>(map));
1405      return *this;
1406    }
1407
1408    /// \brief Make a copy of the given blue node map.
1409    ///
1410    /// This function makes a copy of the given blue node map for the newly
1411    /// created graph.
1412    /// The key type of the new map \c tmap should be the Node type of
1413    /// the destination graph with the blue items, and the key type of
1414    /// the original map \c map should be the Node type of the source
1415    /// graph.
1416    template <typename FromMap, typename ToMap>
1417    BpGraphCopy& blueNodeMap(const FromMap& map, ToMap& tmap) {
1418      _blue_maps.push_back(new _core_bits::MapCopy<From, BlueNode,
1419                           BlueNodeRefMap, FromMap, ToMap>(map, tmap));
1420      return *this;
1421    }
1422
1423    /// \brief Make a copy of the given blue node.
1424    ///
1425    /// This function makes a copy of the given blue node.
1426    BpGraphCopy& blueNode(const BlueNode& node, TBlueNode& tnode) {
1427      _blue_maps.push_back(new _core_bits::ItemCopy<From, BlueNode,
1428                           BlueNodeRefMap, TBlueNode>(node, tnode));
1429      return *this;
1430    }
1431
1432    /// \brief Copy the arc references into the given map.
1433    ///
1434    /// This function copies the arc references into the given map.
1435    /// The parameter should be a map, whose key type is the Arc type of
1436    /// the source graph, while the value type is the Arc type of the
1437    /// destination graph.
1438    template <typename ArcRef>
1439    BpGraphCopy& arcRef(ArcRef& map) {
1440      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
1441                          ArcRefMap, ArcRef>(map));
1442      return *this;
1443    }
1444
1445    /// \brief Copy the arc cross references into the given map.
1446    ///
1447    /// This function copies the arc cross references (reverse references)
1448    /// into the given map. The parameter should be a map, whose key type
1449    /// is the Arc type of the destination graph, while the value type is
1450    /// the Arc type of the source graph.
1451    template <typename ArcCrossRef>
1452    BpGraphCopy& arcCrossRef(ArcCrossRef& map) {
1453      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
1454                          ArcRefMap, ArcCrossRef>(map));
1455      return *this;
1456    }
1457
1458    /// \brief Make a copy of the given arc map.
1459    ///
1460    /// This function makes a copy of the given arc map for the newly
1461    /// created graph.
1462    /// The key type of the new map \c tmap should be the Arc type of the
1463    /// destination graph, and the key type of the original map \c map
1464    /// should be the Arc type of the source graph.
1465    template <typename FromMap, typename ToMap>
1466    BpGraphCopy& arcMap(const FromMap& map, ToMap& tmap) {
1467      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
1468                          ArcRefMap, FromMap, ToMap>(map, tmap));
1469      return *this;
1470    }
1471
1472    /// \brief Make a copy of the given arc.
1473    ///
1474    /// This function makes a copy of the given arc.
1475    BpGraphCopy& arc(const Arc& arc, TArc& tarc) {
1476      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
1477                          ArcRefMap, TArc>(arc, tarc));
1478      return *this;
1479    }
1480
1481    /// \brief Copy the edge references into the given map.
1482    ///
1483    /// This function copies the edge references into the given map.
1484    /// The parameter should be a map, whose key type is the Edge type of
1485    /// the source graph, while the value type is the Edge type of the
1486    /// destination graph.
1487    template <typename EdgeRef>
1488    BpGraphCopy& edgeRef(EdgeRef& map) {
1489      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
1490                           EdgeRefMap, EdgeRef>(map));
1491      return *this;
1492    }
1493
1494    /// \brief Copy the edge cross references into the given map.
1495    ///
1496    /// This function copies the edge cross references (reverse references)
1497    /// into the given map. The parameter should be a map, whose key type
1498    /// is the Edge type of the destination graph, while the value type is
1499    /// the Edge type of the source graph.
1500    template <typename EdgeCrossRef>
1501    BpGraphCopy& edgeCrossRef(EdgeCrossRef& map) {
1502      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
1503                           Edge, EdgeRefMap, EdgeCrossRef>(map));
1504      return *this;
1505    }
1506
1507    /// \brief Make a copy of the given edge map.
1508    ///
1509    /// This function makes a copy of the given edge map for the newly
1510    /// created graph.
1511    /// The key type of the new map \c tmap should be the Edge type of the
1512    /// destination graph, and the key type of the original map \c map
1513    /// should be the Edge type of the source graph.
1514    template <typename FromMap, typename ToMap>
1515    BpGraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {
1516      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
1517                           EdgeRefMap, FromMap, ToMap>(map, tmap));
1518      return *this;
1519    }
1520
1521    /// \brief Make a copy of the given edge.
1522    ///
1523    /// This function makes a copy of the given edge.
1524    BpGraphCopy& edge(const Edge& edge, TEdge& tedge) {
1525      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
1526                           EdgeRefMap, TEdge>(edge, tedge));
1527      return *this;
1528    }
1529
1530    /// \brief Execute copying.
1531    ///
1532    /// This function executes the copying of the graph along with the
1533    /// copying of the assigned data.
1534    void run() {
1535      RedNodeRefMap redNodeRefMap(_from);
1536      BlueNodeRefMap blueNodeRefMap(_from);
1537      NodeRefMap nodeRefMap(_from, redNodeRefMap, blueNodeRefMap);
1538      EdgeRefMap edgeRefMap(_from);
1539      ArcRefMap arcRefMap(_from, _to, edgeRefMap);
1540      _core_bits::BpGraphCopySelector<To>::
1541        copy(_from, _to, redNodeRefMap, blueNodeRefMap, edgeRefMap);
1542      for (int i = 0; i < int(_node_maps.size()); ++i) {
1543        _node_maps[i]->copy(_from, nodeRefMap);
1544      }
1545      for (int i = 0; i < int(_red_maps.size()); ++i) {
1546        _red_maps[i]->copy(_from, redNodeRefMap);
1547      }
1548      for (int i = 0; i < int(_blue_maps.size()); ++i) {
1549        _blue_maps[i]->copy(_from, blueNodeRefMap);
1550      }
1551      for (int i = 0; i < int(_edge_maps.size()); ++i) {
1552        _edge_maps[i]->copy(_from, edgeRefMap);
1553      }
1554      for (int i = 0; i < int(_arc_maps.size()); ++i) {
1555        _arc_maps[i]->copy(_from, arcRefMap);
1556      }
1557    }
1558
1559  private:
1560
1561    const From& _from;
1562    To& _to;
1563
1564    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
1565      _node_maps;
1566
1567    std::vector<_core_bits::MapCopyBase<From, RedNode, RedNodeRefMap>* >
1568      _red_maps;
1569
1570    std::vector<_core_bits::MapCopyBase<From, BlueNode, BlueNodeRefMap>* >
1571      _blue_maps;
1572
1573    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
1574      _arc_maps;
1575
1576    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
1577      _edge_maps;
1578
1579  };
1580
1581  /// \brief Copy a graph to another graph.
1582  ///
1583  /// This function copies a graph to another graph.
1584  /// The complete usage of it is detailed in the BpGraphCopy class,
1585  /// but a short example shows a basic work:
1586  ///\code
1587  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();
1588  ///\endcode
1589  ///
1590  /// After the copy the \c nr map will contain the mapping from the
1591  /// nodes of the \c from graph to the nodes of the \c to graph and
1592  /// \c ecr will contain the mapping from the edges of the \c to graph
1593  /// to the edges of the \c from graph.
1594  ///
1595  /// \see BpGraphCopy
1596  template <typename From, typename To>
1597  BpGraphCopy<From, To>
1598  bpGraphCopy(const From& from, To& to) {
1599    return BpGraphCopy<From, To>(from, to);
1600  }
1601
1602  namespace _core_bits {
1603
1604    template <typename Graph, typename Enable = void>
1605    struct FindArcSelector {
1606      typedef typename Graph::Node Node;
1607      typedef typename Graph::Arc Arc;
1608      static Arc find(const Graph &g, Node u, Node v, Arc e) {
1609        if (e == INVALID) {
1610          g.firstOut(e, u);
1611        } else {
1612          g.nextOut(e);
1613        }
1614        while (e != INVALID && g.target(e) != v) {
1615          g.nextOut(e);
1616        }
1617        return e;
1618      }
1619    };
1620
1621    template <typename Graph>
1622    struct FindArcSelector<
1623      Graph,
1624      typename enable_if<typename Graph::FindArcTag, void>::type>
1625    {
1626      typedef typename Graph::Node Node;
1627      typedef typename Graph::Arc Arc;
1628      static Arc find(const Graph &g, Node u, Node v, Arc prev) {
1629        return g.findArc(u, v, prev);
1630      }
1631    };
1632  }
1633
1634  /// \brief Find an arc between two nodes of a digraph.
1635  ///
1636  /// This function finds an arc from node \c u to node \c v in the
1637  /// digraph \c g.
1638  ///
1639  /// If \c prev is \ref INVALID (this is the default value), then
1640  /// it finds the first arc from \c u to \c v. Otherwise it looks for
1641  /// the next arc from \c u to \c v after \c prev.
1642  /// \return The found arc or \ref INVALID if there is no such an arc.
1643  ///
1644  /// Thus you can iterate through each arc from \c u to \c v as it follows.
1645  ///\code
1646  /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {
1647  ///   ...
1648  /// }
1649  ///\endcode
1650  ///
1651  /// \note \ref ConArcIt provides iterator interface for the same
1652  /// functionality.
1653  ///
1654  ///\sa ConArcIt
1655  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1656  template <typename Graph>
1657  inline typename Graph::Arc
1658  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1659          typename Graph::Arc prev = INVALID) {
1660    return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
1661  }
1662
1663  /// \brief Iterator for iterating on parallel arcs connecting the same nodes.
1664  ///
1665  /// Iterator for iterating on parallel arcs connecting the same nodes. It is
1666  /// a higher level interface for the \ref findArc() function. You can
1667  /// use it the following way:
1668  ///\code
1669  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
1670  ///   ...
1671  /// }
1672  ///\endcode
1673  ///
1674  ///\sa findArc()
1675  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp
1676  template <typename GR>
1677  class ConArcIt : public GR::Arc {
1678    typedef typename GR::Arc Parent;
1679
1680  public:
1681
1682    typedef typename GR::Arc Arc;
1683    typedef typename GR::Node Node;
1684
1685    /// \brief Constructor.
1686    ///
1687    /// Construct a new ConArcIt iterating on the arcs that
1688    /// connects nodes \c u and \c v.
1689    ConArcIt(const GR& g, Node u, Node v) : _graph(g) {
1690      Parent::operator=(findArc(_graph, u, v));
1691    }
1692
1693    /// \brief Constructor.
1694    ///
1695    /// Construct a new ConArcIt that continues the iterating from arc \c a.
1696    ConArcIt(const GR& g, Arc a) : Parent(a), _graph(g) {}
1697
1698    /// \brief Increment operator.
1699    ///
1700    /// It increments the iterator and gives back the next arc.
1701    ConArcIt& operator++() {
1702      Parent::operator=(findArc(_graph, _graph.source(*this),
1703                                _graph.target(*this), *this));
1704      return *this;
1705    }
1706  private:
1707    const GR& _graph;
1708  };
1709
1710  namespace _core_bits {
1711
1712    template <typename Graph, typename Enable = void>
1713    struct FindEdgeSelector {
1714      typedef typename Graph::Node Node;
1715      typedef typename Graph::Edge Edge;
1716      static Edge find(const Graph &g, Node u, Node v, Edge e) {
1717        bool b;
1718        if (u != v) {
1719          if (e == INVALID) {
1720            g.firstInc(e, b, u);
1721          } else {
1722            b = g.u(e) == u;
1723            g.nextInc(e, b);
1724          }
1725          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
1726            g.nextInc(e, b);
1727          }
1728        } else {
1729          if (e == INVALID) {
1730            g.firstInc(e, b, u);
1731          } else {
1732            b = true;
1733            g.nextInc(e, b);
1734          }
1735          while (e != INVALID && (!b || g.v(e) != v)) {
1736            g.nextInc(e, b);
1737          }
1738        }
1739        return e;
1740      }
1741    };
1742
1743    template <typename Graph>
1744    struct FindEdgeSelector<
1745      Graph,
1746      typename enable_if<typename Graph::FindEdgeTag, void>::type>
1747    {
1748      typedef typename Graph::Node Node;
1749      typedef typename Graph::Edge Edge;
1750      static Edge find(const Graph &g, Node u, Node v, Edge prev) {
1751        return g.findEdge(u, v, prev);
1752      }
1753    };
1754  }
1755
1756  /// \brief Find an edge between two nodes of a graph.
1757  ///
1758  /// This function finds an edge from node \c u to node \c v in graph \c g.
1759  /// If node \c u and node \c v is equal then each loop edge
1760  /// will be enumerated once.
1761  ///
1762  /// If \c prev is \ref INVALID (this is the default value), then
1763  /// it finds the first edge from \c u to \c v. Otherwise it looks for
1764  /// the next edge from \c u to \c v after \c prev.
1765  /// \return The found edge or \ref INVALID if there is no such an edge.
1766  ///
1767  /// Thus you can iterate through each edge between \c u and \c v
1768  /// as it follows.
1769  ///\code
1770  /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {
1771  ///   ...
1772  /// }
1773  ///\endcode
1774  ///
1775  /// \note \ref ConEdgeIt provides iterator interface for the same
1776  /// functionality.
1777  ///
1778  ///\sa ConEdgeIt
1779  template <typename Graph>
1780  inline typename Graph::Edge
1781  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
1782            typename Graph::Edge p = INVALID) {
1783    return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
1784  }
1785
1786  /// \brief Iterator for iterating on parallel edges connecting the same nodes.
1787  ///
1788  /// Iterator for iterating on parallel edges connecting the same nodes.
1789  /// It is a higher level interface for the findEdge() function. You can
1790  /// use it the following way:
1791  ///\code
1792  /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {
1793  ///   ...
1794  /// }
1795  ///\endcode
1796  ///
1797  ///\sa findEdge()
1798  template <typename GR>
1799  class ConEdgeIt : public GR::Edge {
1800    typedef typename GR::Edge Parent;
1801
1802  public:
1803
1804    typedef typename GR::Edge Edge;
1805    typedef typename GR::Node Node;
1806
1807    /// \brief Constructor.
1808    ///
1809    /// Construct a new ConEdgeIt iterating on the edges that
1810    /// connects nodes \c u and \c v.
1811    ConEdgeIt(const GR& g, Node u, Node v) : _graph(g), _u(u), _v(v) {
1812      Parent::operator=(findEdge(_graph, _u, _v));
1813    }
1814
1815    /// \brief Constructor.
1816    ///
1817    /// Construct a new ConEdgeIt that continues iterating from edge \c e.
1818    ConEdgeIt(const GR& g, Edge e) : Parent(e), _graph(g) {}
1819
1820    /// \brief Increment operator.
1821    ///
1822    /// It increments the iterator and gives back the next edge.
1823    ConEdgeIt& operator++() {
1824      Parent::operator=(findEdge(_graph, _u, _v, *this));
1825      return *this;
1826    }
1827  private:
1828    const GR& _graph;
1829    Node _u, _v;
1830  };
1831
1832
1833  ///Dynamic arc look-up between given endpoints.
1834
1835  ///Using this class, you can find an arc in a digraph from a given
1836  ///source to a given target in amortized time <em>O</em>(log<em>d</em>),
1837  ///where <em>d</em> is the out-degree of the source node.
1838  ///
1839  ///It is possible to find \e all parallel arcs between two nodes with
1840  ///the \c operator() member.
1841  ///
1842  ///This is a dynamic data structure. Consider to use \ref ArcLookUp or
1843  ///\ref AllArcLookUp if your digraph is not changed so frequently.
1844  ///
1845  ///This class uses a self-adjusting binary search tree, the Splay tree
1846  ///of Sleator and Tarjan to guarantee the logarithmic amortized
1847  ///time bound for arc look-ups. This class also guarantees the
1848  ///optimal time bound in a constant factor for any distribution of
1849  ///queries.
1850  ///
1851  ///\tparam GR The type of the underlying digraph.
1852  ///
1853  ///\sa ArcLookUp
1854  ///\sa AllArcLookUp
1855  template <typename GR>
1856  class DynArcLookUp
1857    : protected ItemSetTraits<GR, typename GR::Arc>::ItemNotifier::ObserverBase
1858  {
1859    typedef typename ItemSetTraits<GR, typename GR::Arc>
1860    ::ItemNotifier::ObserverBase Parent;
1861
1862    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1863
1864  public:
1865
1866    /// The Digraph type
1867    typedef GR Digraph;
1868
1869  protected:
1870
1871    class AutoNodeMap : public ItemSetTraits<GR, Node>::template Map<Arc>::Type
1872    {
1873      typedef typename ItemSetTraits<GR, Node>::template Map<Arc>::Type Parent;
1874
1875    public:
1876
1877      AutoNodeMap(const GR& digraph) : Parent(digraph, INVALID) {}
1878
1879      virtual void add(const Node& node) {
1880        Parent::add(node);
1881        Parent::set(node, INVALID);
1882      }
1883
1884      virtual void add(const std::vector<Node>& nodes) {
1885        Parent::add(nodes);
1886        for (int i = 0; i < int(nodes.size()); ++i) {
1887          Parent::set(nodes[i], INVALID);
1888        }
1889      }
1890
1891      virtual void build() {
1892        Parent::build();
1893        Node it;
1894        typename Parent::Notifier* nf = Parent::notifier();
1895        for (nf->first(it); it != INVALID; nf->next(it)) {
1896          Parent::set(it, INVALID);
1897        }
1898      }
1899    };
1900
1901    class ArcLess {
1902      const Digraph &g;
1903    public:
1904      ArcLess(const Digraph &_g) : g(_g) {}
1905      bool operator()(Arc a,Arc b) const
1906      {
1907        return g.target(a)<g.target(b);
1908      }
1909    };
1910
1911  protected:
1912
1913    const Digraph &_g;
1914    AutoNodeMap _head;
1915    typename Digraph::template ArcMap<Arc> _parent;
1916    typename Digraph::template ArcMap<Arc> _left;
1917    typename Digraph::template ArcMap<Arc> _right;
1918
1919  public:
1920
1921    ///Constructor
1922
1923    ///Constructor.
1924    ///
1925    ///It builds up the search database.
1926    DynArcLookUp(const Digraph &g)
1927      : _g(g),_head(g),_parent(g),_left(g),_right(g)
1928    {
1929      Parent::attach(_g.notifier(typename Digraph::Arc()));
1930      refresh();
1931    }
1932
1933  protected:
1934
1935    virtual void add(const Arc& arc) {
1936      insert(arc);
1937    }
1938
1939    virtual void add(const std::vector<Arc>& arcs) {
1940      for (int i = 0; i < int(arcs.size()); ++i) {
1941        insert(arcs[i]);
1942      }
1943    }
1944
1945    virtual void erase(const Arc& arc) {
1946      remove(arc);
1947    }
1948
1949    virtual void erase(const std::vector<Arc>& arcs) {
1950      for (int i = 0; i < int(arcs.size()); ++i) {
1951        remove(arcs[i]);
1952      }
1953    }
1954
1955    virtual void build() {
1956      refresh();
1957    }
1958
1959    virtual void clear() {
1960      for(NodeIt n(_g);n!=INVALID;++n) {
1961        _head[n] = INVALID;
1962      }
1963    }
1964
1965    void insert(Arc arc) {
1966      Node s = _g.source(arc);
1967      Node t = _g.target(arc);
1968      _left[arc] = INVALID;
1969      _right[arc] = INVALID;
1970
1971      Arc e = _head[s];
1972      if (e == INVALID) {
1973        _head[s] = arc;
1974        _parent[arc] = INVALID;
1975        return;
1976      }
1977      while (true) {
1978        if (t < _g.target(e)) {
1979          if (_left[e] == INVALID) {
1980            _left[e] = arc;
1981            _parent[arc] = e;
1982            splay(arc);
1983            return;
1984          } else {
1985            e = _left[e];
1986          }
1987        } else {
1988          if (_right[e] == INVALID) {
1989            _right[e] = arc;
1990            _parent[arc] = e;
1991            splay(arc);
1992            return;
1993          } else {
1994            e = _right[e];
1995          }
1996        }
1997      }
1998    }
1999
2000    void remove(Arc arc) {
2001      if (_left[arc] == INVALID) {
2002        if (_right[arc] != INVALID) {
2003          _parent[_right[arc]] = _parent[arc];
2004        }
2005        if (_parent[arc] != INVALID) {
2006          if (_left[_parent[arc]] == arc) {
2007            _left[_parent[arc]] = _right[arc];
2008          } else {
2009            _right[_parent[arc]] = _right[arc];
2010          }
2011        } else {
2012          _head[_g.source(arc)] = _right[arc];
2013        }
2014      } else if (_right[arc] == INVALID) {
2015        _parent[_left[arc]] = _parent[arc];
2016        if (_parent[arc] != INVALID) {
2017          if (_left[_parent[arc]] == arc) {
2018            _left[_parent[arc]] = _left[arc];
2019          } else {
2020            _right[_parent[arc]] = _left[arc];
2021          }
2022        } else {
2023          _head[_g.source(arc)] = _left[arc];
2024        }
2025      } else {
2026        Arc e = _left[arc];
2027        if (_right[e] != INVALID) {
2028          e = _right[e];
2029          while (_right[e] != INVALID) {
2030            e = _right[e];
2031          }
2032          Arc s = _parent[e];
2033          _right[_parent[e]] = _left[e];
2034          if (_left[e] != INVALID) {
2035            _parent[_left[e]] = _parent[e];
2036          }
2037
2038          _left[e] = _left[arc];
2039          _parent[_left[arc]] = e;
2040          _right[e] = _right[arc];
2041          _parent[_right[arc]] = e;
2042
2043          _parent[e] = _parent[arc];
2044          if (_parent[arc] != INVALID) {
2045            if (_left[_parent[arc]] == arc) {
2046              _left[_parent[arc]] = e;
2047            } else {
2048              _right[_parent[arc]] = e;
2049            }
2050          }
2051          splay(s);
2052        } else {
2053          _right[e] = _right[arc];
2054          _parent[_right[arc]] = e;
2055          _parent[e] = _parent[arc];
2056
2057          if (_parent[arc] != INVALID) {
2058            if (_left[_parent[arc]] == arc) {
2059              _left[_parent[arc]] = e;
2060            } else {
2061              _right[_parent[arc]] = e;
2062            }
2063          } else {
2064            _head[_g.source(arc)] = e;
2065          }
2066        }
2067      }
2068    }
2069
2070    Arc refreshRec(std::vector<Arc> &v,int a,int b)
2071    {
2072      int m=(a+b)/2;
2073      Arc me=v[m];
2074      if (a < m) {
2075        Arc left = refreshRec(v,a,m-1);
2076        _left[me] = left;
2077        _parent[left] = me;
2078      } else {
2079        _left[me] = INVALID;
2080      }
2081      if (m < b) {
2082        Arc right = refreshRec(v,m+1,b);
2083        _right[me] = right;
2084        _parent[right] = me;
2085      } else {
2086        _right[me] = INVALID;
2087      }
2088      return me;
2089    }
2090
2091    void refresh() {
2092      for(NodeIt n(_g);n!=INVALID;++n) {
2093        std::vector<Arc> v;
2094        for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);
2095        if (!v.empty()) {
2096          std::sort(v.begin(),v.end(),ArcLess(_g));
2097          Arc head = refreshRec(v,0,v.size()-1);
2098          _head[n] = head;
2099          _parent[head] = INVALID;
2100        }
2101        else _head[n] = INVALID;
2102      }
2103    }
2104
2105    void zig(Arc v) {
2106      Arc w = _parent[v];
2107      _parent[v] = _parent[w];
2108      _parent[w] = v;
2109      _left[w] = _right[v];
2110      _right[v] = w;
2111      if (_parent[v] != INVALID) {
2112        if (_right[_parent[v]] == w) {
2113          _right[_parent[v]] = v;
2114        } else {
2115          _left[_parent[v]] = v;
2116        }
2117      }
2118      if (_left[w] != INVALID){
2119        _parent[_left[w]] = w;
2120      }
2121    }
2122
2123    void zag(Arc v) {
2124      Arc w = _parent[v];
2125      _parent[v] = _parent[w];
2126      _parent[w] = v;
2127      _right[w] = _left[v];
2128      _left[v] = w;
2129      if (_parent[v] != INVALID){
2130        if (_left[_parent[v]] == w) {
2131          _left[_parent[v]] = v;
2132        } else {
2133          _right[_parent[v]] = v;
2134        }
2135      }
2136      if (_right[w] != INVALID){
2137        _parent[_right[w]] = w;
2138      }
2139    }
2140
2141    void splay(Arc v) {
2142      while (_parent[v] != INVALID) {
2143        if (v == _left[_parent[v]]) {
2144          if (_parent[_parent[v]] == INVALID) {
2145            zig(v);
2146          } else {
2147            if (_parent[v] == _left[_parent[_parent[v]]]) {
2148              zig(_parent[v]);
2149              zig(v);
2150            } else {
2151              zig(v);
2152              zag(v);
2153            }
2154          }
2155        } else {
2156          if (_parent[_parent[v]] == INVALID) {
2157            zag(v);
2158          } else {
2159            if (_parent[v] == _left[_parent[_parent[v]]]) {
2160              zag(v);
2161              zig(v);
2162            } else {
2163              zag(_parent[v]);
2164              zag(v);
2165            }
2166          }
2167        }
2168      }
2169      _head[_g.source(v)] = v;
2170    }
2171
2172
2173  public:
2174
2175    ///Find an arc between two nodes.
2176
2177    ///Find an arc between two nodes.
2178    ///\param s The source node.
2179    ///\param t The target node.
2180    ///\param p The previous arc between \c s and \c t. It it is INVALID or
2181    ///not given, the operator finds the first appropriate arc.
2182    ///\return An arc from \c s to \c t after \c p or
2183    ///\ref INVALID if there is no more.
2184    ///
2185    ///For example, you can count the number of arcs from \c u to \c v in the
2186    ///following way.
2187    ///\code
2188    ///DynArcLookUp<ListDigraph> ae(g);
2189    ///...
2190    ///int n = 0;
2191    ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;
2192    ///\endcode
2193    ///
2194    ///Finding the arcs take at most <em>O</em>(log<em>d</em>)
2195    ///amortized time, specifically, the time complexity of the lookups
2196    ///is equal to the optimal search tree implementation for the
2197    ///current query distribution in a constant factor.
2198    ///
2199    ///\note This is a dynamic data structure, therefore the data
2200    ///structure is updated after each graph alteration. Thus although
2201    ///this data structure is theoretically faster than \ref ArcLookUp
2202    ///and \ref AllArcLookUp, it often provides worse performance than
2203    ///them.
2204    Arc operator()(Node s, Node t, Arc p = INVALID) const  {
2205      if (p == INVALID) {
2206        Arc a = _head[s];
2207        if (a == INVALID) return INVALID;
2208        Arc r = INVALID;
2209        while (true) {
2210          if (_g.target(a) < t) {
2211            if (_right[a] == INVALID) {
2212              const_cast<DynArcLookUp&>(*this).splay(a);
2213              return r;
2214            } else {
2215              a = _right[a];
2216            }
2217          } else {
2218            if (_g.target(a) == t) {
2219              r = a;
2220            }
2221            if (_left[a] == INVALID) {
2222              const_cast<DynArcLookUp&>(*this).splay(a);
2223              return r;
2224            } else {
2225              a = _left[a];
2226            }
2227          }
2228        }
2229      } else {
2230        Arc a = p;
2231        if (_right[a] != INVALID) {
2232          a = _right[a];
2233          while (_left[a] != INVALID) {
2234            a = _left[a];
2235          }
2236          const_cast<DynArcLookUp&>(*this).splay(a);
2237        } else {
2238          while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
2239            a = _parent[a];
2240          }
2241          if (_parent[a] == INVALID) {
2242            return INVALID;
2243          } else {
2244            a = _parent[a];
2245            const_cast<DynArcLookUp&>(*this).splay(a);
2246          }
2247        }
2248        if (_g.target(a) == t) return a;
2249        else return INVALID;
2250      }
2251    }
2252
2253  };
2254
2255  ///Fast arc look-up between given endpoints.
2256
2257  ///Using this class, you can find an arc in a digraph from a given
2258  ///source to a given target in time <em>O</em>(log<em>d</em>),
2259  ///where <em>d</em> is the out-degree of the source node.
2260  ///
2261  ///It is not possible to find \e all parallel arcs between two nodes.
2262  ///Use \ref AllArcLookUp for this purpose.
2263  ///
2264  ///\warning This class is static, so you should call refresh() (or at
2265  ///least refresh(Node)) to refresh this data structure whenever the
2266  ///digraph changes. This is a time consuming (superlinearly proportional
2267  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
2268  ///
2269  ///\tparam GR The type of the underlying digraph.
2270  ///
2271  ///\sa DynArcLookUp
2272  ///\sa AllArcLookUp
2273  template<class GR>
2274  class ArcLookUp
2275  {
2276    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
2277
2278  public:
2279
2280    /// The Digraph type
2281    typedef GR Digraph;
2282
2283  protected:
2284    const Digraph &_g;
2285    typename Digraph::template NodeMap<Arc> _head;
2286    typename Digraph::template ArcMap<Arc> _left;
2287    typename Digraph::template ArcMap<Arc> _right;
2288
2289    class ArcLess {
2290      const Digraph &g;
2291    public:
2292      ArcLess(const Digraph &_g) : g(_g) {}
2293      bool operator()(Arc a,Arc b) const
2294      {
2295        return g.target(a)<g.target(b);
2296      }
2297    };
2298
2299  public:
2300
2301    ///Constructor
2302
2303    ///Constructor.
2304    ///
2305    ///It builds up the search database, which remains valid until the digraph
2306    ///changes.
2307    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
2308
2309  private:
2310    Arc refreshRec(std::vector<Arc> &v,int a,int b)
2311    {
2312      int m=(a+b)/2;
2313      Arc me=v[m];
2314      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;
2315      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;
2316      return me;
2317    }
2318  public:
2319    ///Refresh the search data structure at a node.
2320
2321    ///Build up the search database of node \c n.
2322    ///
2323    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>
2324    ///is the number of the outgoing arcs of \c n.
2325    void refresh(Node n)
2326    {
2327      std::vector<Arc> v;
2328      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
2329      if(v.size()) {
2330        std::sort(v.begin(),v.end(),ArcLess(_g));
2331        _head[n]=refreshRec(v,0,v.size()-1);
2332      }
2333      else _head[n]=INVALID;
2334    }
2335    ///Refresh the full data structure.
2336
2337    ///Build up the full search database. In fact, it simply calls
2338    ///\ref refresh(Node) "refresh(n)" for each node \c n.
2339    ///
2340    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
2341    ///the number of the arcs in the digraph and <em>D</em> is the maximum
2342    ///out-degree of the digraph.
2343    void refresh()
2344    {
2345      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
2346    }
2347
2348    ///Find an arc between two nodes.
2349
2350    ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),
2351    ///where <em>d</em> is the number of outgoing arcs of \c s.
2352    ///\param s The source node.
2353    ///\param t The target node.
2354    ///\return An arc from \c s to \c t if there exists,
2355    ///\ref INVALID otherwise.
2356    ///
2357    ///\warning If you change the digraph, refresh() must be called before using
2358    ///this operator. If you change the outgoing arcs of
2359    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
2360    Arc operator()(Node s, Node t) const
2361    {
2362      Arc e;
2363      for(e=_head[s];
2364          e!=INVALID&&_g.target(e)!=t;
2365          e = t < _g.target(e)?_left[e]:_right[e]) ;
2366      return e;
2367    }
2368
2369  };
2370
2371  ///Fast look-up of all arcs between given endpoints.
2372
2373  ///This class is the same as \ref ArcLookUp, with the addition
2374  ///that it makes it possible to find all parallel arcs between given
2375  ///endpoints.
2376  ///
2377  ///\warning This class is static, so you should call refresh() (or at
2378  ///least refresh(Node)) to refresh this data structure whenever the
2379  ///digraph changes. This is a time consuming (superlinearly proportional
2380  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).
2381  ///
2382  ///\tparam GR The type of the underlying digraph.
2383  ///
2384  ///\sa DynArcLookUp
2385  ///\sa ArcLookUp
2386  template<class GR>
2387  class AllArcLookUp : public ArcLookUp<GR>
2388  {
2389    using ArcLookUp<GR>::_g;
2390    using ArcLookUp<GR>::_right;
2391    using ArcLookUp<GR>::_left;
2392    using ArcLookUp<GR>::_head;
2393
2394    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
2395
2396    typename GR::template ArcMap<Arc> _next;
2397
2398    Arc refreshNext(Arc head,Arc next=INVALID)
2399    {
2400      if(head==INVALID) return next;
2401      else {
2402        next=refreshNext(_right[head],next);
2403        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
2404          ? next : INVALID;
2405        return refreshNext(_left[head],head);
2406      }
2407    }
2408
2409    void refreshNext()
2410    {
2411      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
2412    }
2413
2414  public:
2415
2416    /// The Digraph type
2417    typedef GR Digraph;
2418
2419    ///Constructor
2420
2421    ///Constructor.
2422    ///
2423    ///It builds up the search database, which remains valid until the digraph
2424    ///changes.
2425    AllArcLookUp(const Digraph &g) : ArcLookUp<GR>(g), _next(g) {refreshNext();}
2426
2427    ///Refresh the data structure at a node.
2428
2429    ///Build up the search database of node \c n.
2430    ///
2431    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em> is
2432    ///the number of the outgoing arcs of \c n.
2433    void refresh(Node n)
2434    {
2435      ArcLookUp<GR>::refresh(n);
2436      refreshNext(_head[n]);
2437    }
2438
2439    ///Refresh the full data structure.
2440
2441    ///Build up the full search database. In fact, it simply calls
2442    ///\ref refresh(Node) "refresh(n)" for each node \c n.
2443    ///
2444    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is
2445    ///the number of the arcs in the digraph and <em>D</em> is the maximum
2446    ///out-degree of the digraph.
2447    void refresh()
2448    {
2449      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
2450    }
2451
2452    ///Find an arc between two nodes.
2453
2454    ///Find an arc between two nodes.
2455    ///\param s The source node.
2456    ///\param t The target node.
2457    ///\param prev The previous arc between \c s and \c t. It it is INVALID or
2458    ///not given, the operator finds the first appropriate arc.
2459    ///\return An arc from \c s to \c t after \c prev or
2460    ///\ref INVALID if there is no more.
2461    ///
2462    ///For example, you can count the number of arcs from \c u to \c v in the
2463    ///following way.
2464    ///\code
2465    ///AllArcLookUp<ListDigraph> ae(g);
2466    ///...
2467    ///int n = 0;
2468    ///for(Arc a = ae(u,v); a != INVALID; a=ae(u,v,a)) n++;
2469    ///\endcode
2470    ///
2471    ///Finding the first arc take <em>O</em>(log<em>d</em>) time,
2472    ///where <em>d</em> is the number of outgoing arcs of \c s. Then the
2473    ///consecutive arcs are found in constant time.
2474    ///
2475    ///\warning If you change the digraph, refresh() must be called before using
2476    ///this operator. If you change the outgoing arcs of
2477    ///a single node \c n, then \ref refresh(Node) "refresh(n)" is enough.
2478    ///
2479    Arc operator()(Node s, Node t, Arc prev=INVALID) const
2480    {
2481      if(prev==INVALID)
2482        {
2483          Arc f=INVALID;
2484          Arc e;
2485          for(e=_head[s];
2486              e!=INVALID&&_g.target(e)!=t;
2487              e = t < _g.target(e)?_left[e]:_right[e]) ;
2488          while(e!=INVALID)
2489            if(_g.target(e)==t)
2490              {
2491                f = e;
2492                e = _left[e];
2493              }
2494            else e = _right[e];
2495          return f;
2496        }
2497      else return _next[prev];
2498    }
2499
2500  };
2501
2502  /// @}
2503
2504} //namespace lemon
2505
2506#endif
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