graph_adjacency.hh 26.9 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
// graph-tool -- a general graph modification and manipulation thingy
//
// Copyright (C) 2006-2013 Tiago de Paula Peixoto <tiago@skewed.de>
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 3
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.

18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
#ifndef GRAPH_ADJACENCY_HH
#define GRAPH_ADJACENCY_HH

#include <vector>
#include <deque>
#include <utility>
#include <numeric>
#include <iostream>
#include <boost/iterator.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/range/irange.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/properties.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/iterator_facade.hpp>

34
35
#include "transform_iterator.hh"

36
37
38
39
#include "tr1_include.hh"

#include TR1_HEADER(tuple)

40

41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
namespace boost
{

// ========================================================================
// Forward declarations
// ========================================================================

template <class Vertex>
class adj_list;

// forward declaration of manipulation functions
template <class Vertex>
std::pair<typename adj_list<Vertex>::vertex_iterator,
          typename adj_list<Vertex>::vertex_iterator>
vertices(const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_iterator,
          typename adj_list<Vertex>::edge_iterator>
edges(const adj_list<Vertex>& g);

template <class Vertex>
63
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
edge(Vertex s, Vertex t, const adj_list<Vertex>& g);

template <class Vertex>
size_t out_degree(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
size_t in_degree(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::out_edge_iterator,
          typename adj_list<Vertex>::out_edge_iterator>
out_edges(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::in_edge_iterator,
          typename adj_list<Vertex>::in_edge_iterator>
in_edges(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::adjacency_iterator,
          typename adj_list<Vertex>::adjacency_iterator>
adjacent_vertices(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
size_t num_vertices(const adj_list<Vertex>& g);

template <class Vertex>
size_t num_edges(const adj_list<Vertex>& g);

template <class Vertex>
Vertex add_vertex(adj_list<Vertex>& g);

template <class Vertex>
void clear_vertex(Vertex v, adj_list<Vertex>& g);

template <class Vertex>
void remove_vertex(Vertex v, adj_list<Vertex>& g);

102
103
104
template <class Vertex>
void remove_vertex_fast(Vertex v, adj_list<Vertex>& g);

105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
add_edge(Vertex s, Vertex t, adj_list<Vertex>& g);

template <class Vertex>
void remove_edge(Vertex s, Vertex t, adj_list<Vertex>& g);

template <class Vertex>
void remove_edge(const typename adj_list<Vertex>::edge_descriptor& e,
                 adj_list<Vertex>& g);

// ========================================================================
// adj_list<Vertex>
// ========================================================================
//
// adj_list is a very simple adjacency list implementation for bidirectional
// graphs based on std::vector, meant to be reasonably efficient both
// memory-wise and computationally. It maintains a list of in and out-edges for
// each vertex, and each edge has a built-in index (which is replicated in both
// lists). For each edge, a total of 4 integers is necessary: the source and
// target vertices, in the in_edges and out_edges lists, respectively, and the
// (same) edge index in both lists. The integer type is given by the Vertex
// template parameter. It achieves about half as much memory as
// boost::adjacency_list with an edge index property map and the same integer
// type.

// The complexity guarantees and iterator invalidation rules are the same as
// boost::adjacency_list with vector storage selectors for both vertex and edge
// lists.

template <class Vertex = size_t>
class adj_list
{
public:
    struct graph_tag {};
    typedef Vertex vertex_t;
    typedef std::tr1::tuple<vertex_t, vertex_t, vertex_t> edge_descriptor;
    typedef std::vector<std::pair<vertex_t, vertex_t> > edge_list_t;
    typedef typename integer_range<Vertex>::iterator vertex_iterator;

    struct get_vertex
    {
        get_vertex() {}
        typedef Vertex result_type;
        Vertex operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return v.first; }
    };

153
    typedef transform_random_access_iterator<get_vertex, typename edge_list_t::const_iterator>
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
        adjacency_iterator;

    struct make_out_edge
    {
        make_out_edge(vertex_t src): _src(src) {}
        make_out_edge() {}
        vertex_t _src;
        typedef edge_descriptor result_type;
        edge_descriptor operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return std::tr1::make_tuple(_src, v.first, v.second); }
    };

    struct make_in_edge
    {
        make_in_edge(vertex_t tgt): _tgt(tgt) {}
        make_in_edge() {}
        vertex_t _tgt;
        typedef edge_descriptor result_type;
        edge_descriptor operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return std::tr1::make_tuple(v.first, _tgt, v.second); }
    };

176
    typedef transform_random_access_iterator<make_out_edge, typename edge_list_t::const_iterator>
177
        out_edge_iterator;
178
    typedef transform_random_access_iterator<make_in_edge, typename edge_list_t::const_iterator>
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
        in_edge_iterator;

    class edge_iterator:
        public boost::iterator_facade<edge_iterator,
                                      edge_descriptor,
                                      boost::forward_traversal_tag,
                                      edge_descriptor>
    {
    public:
        edge_iterator() {}
        explicit edge_iterator(const typename std::vector<edge_list_t>::const_iterator& vi_begin,
                               const typename std::vector<edge_list_t>::const_iterator& vi_end,
                               const typename std::vector<edge_list_t>::const_iterator& vi,
                               const typename edge_list_t::const_iterator& ei)
            : _vi_begin(vi_begin), _vi_end(vi_end), _vi(vi), _ei(ei)
        {
            // move position to first edge
            skip();
        }

    private:
        friend class boost::iterator_core_access;

        void skip()
        {
            //skip empty vertices
            while (_vi != _vi_end && _ei == _vi->end())
            {
                ++_vi;
                if (_vi != _vi_end)
                    _ei = _vi->begin();
            }
        }

        void increment()
        {
            ++_ei;
            skip();
        }

        bool equal(edge_iterator const& other) const
        {
            if (_vi_begin == _vi_end)
                return _vi == other._vi;
            return _vi == other._vi && _ei == other._ei;
        }

        edge_descriptor dereference() const
        {
            return std::tr1::make_tuple(vertex_t(_vi - _vi_begin),
                                        _ei->first, _ei->second);
        }

        typename std::vector<edge_list_t>::const_iterator _vi_begin;
        typename std::vector<edge_list_t>::const_iterator _vi_end;
        typename std::vector<edge_list_t>::const_iterator _vi;
        typename edge_list_t::const_iterator _ei;
    };

    void reindex_edges()
    {
        _free_indexes.clear();
        _last_idx = 0;
        _in_edges.clear();
        _in_edges.resize(_out_edges.size());
        for (size_t i = 0; i < _out_edges.size(); ++i)
            for (size_t j = 0; j < _out_edges[i].size(); ++j)
            {
                Vertex v = _out_edges[i][j].first;
                _out_edges[i][j].second = _last_idx;
                _in_edges[v].push_back(std::make_pair(Vertex(i),
                                                      _last_idx));
                _last_idx++;
            }
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274

        if (_keep_epos)
            rebuild_epos();
    }

    void set_keep_epos(bool keep)
    {
        if (keep)
        {
            if(!_keep_epos)
                rebuild_epos();
        }
        else
        {
            _epos.clear();
        }
        _keep_epos = keep;
    }

    bool get_keep_epos()
    {
        return _keep_epos;
275
276
277
278
    }

    size_t get_last_index() const {return _last_idx;}

279
280
    static Vertex null_vertex() { return std::numeric_limits<Vertex>::max(); }

281
282
283
284
285
286
287
288
289
290
private:
    typedef std::vector<edge_list_t> vertex_list_t;
    vertex_list_t _out_edges;
    vertex_list_t _in_edges;
    size_t _n_edges;
    size_t _last_idx;
    std::deque<size_t> _free_indexes; // indexes of deleted edges to be used up
                                      // for new edges to avoid very large
                                      // indexes, and unnecessary property map
                                      // memory use
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
    bool _keep_epos;
    std::vector<std::pair<int32_t, int32_t> > _epos;

    void rebuild_epos()
    {
        _epos.resize(_last_idx + 1);
        for (size_t i = 0; i < _out_edges.size(); ++i)
        {
            for (size_t j = 0; j < _out_edges[i].size(); ++j)
            {
                size_t idx = _out_edges[i][j].second;
                _epos[idx].first = j;
            }

            for (size_t j = 0; j < _in_edges[i].size(); ++j)
            {
                size_t idx = _in_edges[i][j].second;
                _epos[idx].second = j;
            }
        }
    }
312
313
314
315
316
317
318
319

    // manipulation functions
    friend std::pair<vertex_iterator, vertex_iterator>
    vertices<>(const adj_list<Vertex>& g);

    friend std::pair<edge_iterator, edge_iterator>
    edges<>(const adj_list<Vertex>& g);

320
    friend std::pair<edge_descriptor, bool>
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
    edge<>(Vertex s, Vertex t, const adj_list<Vertex>& g);

    friend size_t out_degree<>(Vertex v, const adj_list<Vertex>& g);

    friend size_t in_degree<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<out_edge_iterator, out_edge_iterator>
    out_edges<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<in_edge_iterator, in_edge_iterator>
    in_edges<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<adjacency_iterator, adjacency_iterator>
    adjacent_vertices<>(Vertex v, const adj_list<Vertex>& g);

    friend size_t num_vertices<>(const adj_list<Vertex>& g);

    friend size_t num_edges<>(const adj_list<Vertex>& g);

    friend Vertex add_vertex<>(adj_list<Vertex>& g);

    friend void clear_vertex<>(Vertex v, adj_list<Vertex>& g);

    friend void remove_vertex<>(Vertex v, adj_list<Vertex>& g);

346
347
    friend void remove_vertex_fast<>(Vertex v, adj_list<Vertex>& g);

348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
    friend std::pair<edge_descriptor, bool>
    add_edge<>(Vertex s, Vertex t, adj_list<Vertex>& g);

    friend void remove_edge<>(Vertex s, Vertex t, adj_list<Vertex>& g);

    friend void remove_edge<>(const edge_descriptor& e, adj_list<Vertex>& g);
};

//========================================================================
// Graph traits and BGL scaffolding
//========================================================================

struct adj_list_traversal_tag
    : public vertex_list_graph_tag,
      public edge_list_graph_tag,
      public adjacency_graph_tag,
      public bidirectional_graph_tag { };

template <class Vertex>
struct graph_traits<adj_list<Vertex> >
{
    typedef Vertex vertex_descriptor;
    typedef typename adj_list<Vertex>::edge_descriptor edge_descriptor;
    typedef typename adj_list<Vertex>::edge_iterator edge_iterator;
    typedef typename adj_list<Vertex>::adjacency_iterator adjacency_iterator;

    typedef typename adj_list<Vertex>::out_edge_iterator out_edge_iterator;
    typedef typename adj_list<Vertex>::in_edge_iterator in_edge_iterator;

    typedef typename adj_list<Vertex>::vertex_iterator vertex_iterator;

    typedef bidirectional_tag directed_category;
    typedef allow_parallel_edge_tag edge_parallel_category;
    typedef adj_list_traversal_tag traversal_category;

    typedef Vertex vertices_size_type;
    typedef Vertex edges_size_type;
    typedef size_t degree_size_type;

387
    static Vertex null_vertex() { return adj_list<Vertex>::null_vertex(); }
388
389
390
391
392
393
394
private:
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<out_edge_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<in_edge_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<adjacency_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
};

template <class Vertex>
struct graph_traits<const adj_list<Vertex> >
    : public graph_traits<adj_list<Vertex> >
{
};


template <class Vertex>
struct edge_property_type<adj_list<Vertex> >
{
    typedef void type;
};

template <class Vertex>
struct vertex_property_type<adj_list<Vertex> >
{
    typedef void type;
};

template <class Vertex>
struct graph_property_type<adj_list<Vertex> >
{
    typedef void type;
};

//========================================================================
// Graph access and manipulation functions
//========================================================================

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::vertex_iterator,
                 typename adj_list<Vertex>::vertex_iterator>
vertices(const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::vertex_iterator vi_t;
    return std::make_pair(vi_t(0), vi_t(g._out_edges.size()));
}


template <class Vertex>
inline std::pair<typename adj_list<Vertex>::edge_iterator,
                 typename adj_list<Vertex>::edge_iterator>
edges(const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::edge_list_t::const_iterator ei_t;
    typedef typename adj_list<Vertex>::vertex_list_t::const_iterator vi_t;
    ei_t ei_begin = g._out_edges.empty() ? ei_t() : g._out_edges[0].begin();
    vi_t last_vi = g._out_edges.end();
    if (!g._out_edges.empty())
        --last_vi;
    ei_t ei_end = g._out_edges.empty() ? ei_t() : last_vi->end();
    typename adj_list<Vertex>::edge_iterator ebegin(g._out_edges.begin(),
                                                    g._out_edges.end(),
                                                    g._out_edges.begin(),
                                                    ei_begin);
    typename adj_list<Vertex>::edge_iterator eend(g._out_edges.begin(),
                                                  g._out_edges.end(),
                                                  last_vi,
                                                  ei_end);
    return std::make_pair(ebegin, eend);
}

template <class Vertex>
inline Vertex vertex(size_t i, const adj_list<Vertex>&)
{
    return i;
}

template <class Vertex>
466
inline std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
467
468
edge(Vertex s, Vertex t, const adj_list<Vertex>& g)
{
469
    const typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
470
471
472
    for (size_t i = 0; i < oes.size(); ++i)
        if (oes[i].first == t)
            return std::make_pair(std::tr1::make_tuple(s, t, oes[i].second), true);
473
    Vertex v = graph_traits<adj_list<Vertex> >::null_vertex();
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
    return std::make_pair(std::tr1::make_tuple(v, v, v), false);
}

template <class Vertex>
inline size_t out_degree(Vertex v, const adj_list<Vertex>& g)
{
    return g._out_edges[v].size();
}

template <class Vertex>
inline size_t in_degree(Vertex v, const adj_list<Vertex>& g)
{
    return g._in_edges[v].size();
}

template <class Vertex>
inline size_t degree(Vertex v, const adj_list<Vertex>& g)
{
    return in_degree(v, g) + out_degree(v, g);
}

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::out_edge_iterator,
                 typename adj_list<Vertex>::out_edge_iterator>
out_edges(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::out_edge_iterator ei_t;
    typedef typename adj_list<Vertex>::make_out_edge mk_edge;
    return std::make_pair(ei_t(g._out_edges[v].begin(), mk_edge(v)),
                          ei_t(g._out_edges[v].end(), mk_edge(v)));
}

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::in_edge_iterator,
                 typename adj_list<Vertex>::in_edge_iterator>
in_edges(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::in_edge_iterator ei_t;
    typedef typename adj_list<Vertex>::make_in_edge mk_edge;
    return std::make_pair(ei_t(g._in_edges[v].begin(), mk_edge(v)),
                          ei_t(g._in_edges[v].end(), mk_edge(v)));
}

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::adjacency_iterator,
                 typename adj_list<Vertex>::adjacency_iterator>
adjacent_vertices(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::adjacency_iterator ai_t;
    return std::make_pair(ai_t(g._out_edges[v].begin()),
                          ai_t(g._out_edges[v].end()));
}

template <class Vertex>
inline size_t num_vertices(const adj_list<Vertex>& g)
{
    return g._out_edges.size();
}

template <class Vertex>
inline size_t num_edges(const adj_list<Vertex>& g)
{
    return g._n_edges;
}

template <class Vertex>
inline Vertex add_vertex(adj_list<Vertex>& g)
{
    size_t n = g._out_edges.size();
    g._out_edges.resize(n + 1);
    g._in_edges.resize(n + 1);
    return n;
}

template <class Vertex>
inline void clear_vertex(Vertex v, adj_list<Vertex>& g)
{
551
    if (!g._keep_epos)
552
    {
553
554
        typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[v];
        for (size_t i = 0; i < oes.size(); ++i)
555
        {
556
557
558
            Vertex t = oes[i].first;
            typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];
            for (size_t j = 0; j < ies.size(); ++j)
559
            {
560
561
562
563
564
                if (ies[j].first == v)
                {
                    g._free_indexes.push_back(ies[j].second);
                    ies.erase(ies.begin() + j);
                }
565
566
            }
        }
567
568
        g._n_edges -= oes.size();
        oes.clear();
569

570
571
        typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[v];
        for (size_t i = 0; i < oes.size(); ++i)
572
        {
573
574
575
            Vertex s = ies[i].first;
            typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
            for (size_t j = 0; j < oes.size(); ++j)
576
            {
577
578
579
580
581
                if (oes[j].first == v)
                {
                    g._free_indexes.push_back(oes[j].second);
                    oes.erase(oes.begin() + j);
                }
582
583
            }
        }
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
        g._n_edges -= ies.size();
        ies.clear();
    }
    else
    {
        typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[v];
        for (size_t i = 0; i < oes.size(); ++i)
        {
            Vertex t = oes[i].first;
            size_t idx = oes[i].second;
            typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];
            const std::pair<int32_t, int32_t>& pos = g._epos[idx];

            g._epos[ies.back().second].second = pos.second;
            ies[pos.second] = ies.back();
            ies.pop_back();
            g._free_indexes.push_back(idx);
        }
        g._n_edges -= oes.size();
        oes.clear();

        typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[v];
        for (size_t i = 0; i < ies.size(); ++i)
        {
            Vertex s = ies[i].first;
            size_t idx = ies[i].second;
            typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
            const std::pair<int32_t, int32_t>& pos = g._epos[idx];

            g._epos[oes.back().second].first = pos.first;
            oes[pos.first] = oes.back();
            oes.pop_back();
            g._free_indexes.push_back(idx);
        }
        g._n_edges -= ies.size();
        ies.clear();
620
621
622
    }
}

623
// O(V + E)
624
625
626
627
628
629
template <class Vertex>
inline void remove_vertex(Vertex v, adj_list<Vertex>& g)
{
    clear_vertex(v, g);
    g._out_edges.erase(g._out_edges.begin() + v);
    g._in_edges.erase(g._in_edges.begin() + v);
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645

    int i, N = g._out_edges.size();
    #pragma omp parallel for default(shared) private(i)
    for (i = 0; i < N; ++i)
    {
        for (size_t j = 0; j < g._out_edges[i].size(); ++j)
        {
            if (g._out_edges[i][j].first > v)
                g._out_edges[i][j].first--;
        }
        for (size_t j = 0; j < g._in_edges[i].size(); ++j)
        {
            if (g._in_edges[i][j].first > v)
                g._in_edges[i][j].first--;
        }
    }
646
647
}

648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
// O(k + k_last)
template <class Vertex>
inline void remove_vertex_fast(Vertex v, adj_list<Vertex>& g)
{
    clear_vertex(v, g);
    Vertex back = g._out_edges.size() - 1;

    if (v < back)
    {
        g._out_edges[v].swap(g._out_edges[back]);
        g._in_edges[v].swap(g._in_edges[back]);

        for (size_t i = 0; i < g._out_edges[v].size(); ++i)
        {
            Vertex u = g._out_edges[v][i].first;
            if (u == back)
            {
                g._out_edges[v][i].first = v;
            }
            else
            {
                for (size_t j = 0; j < g._in_edges[u].size(); ++j)
                    if (g._in_edges[u][j].first == back)
                        g._in_edges[u][j].first = v;
            }
        }

        for (size_t i = 0; i < g._in_edges[v].size(); ++i)
        {
            Vertex u = g._in_edges[v][i].first;
            if (u == back)
            {
                g._out_edges[v][i].first = v;
            }
            else
            {
                for (size_t j = 0; j < g._out_edges[u].size(); ++j)
                    if (g._out_edges[u][j].first == back)
                        g._out_edges[u][j].first = v;
            }
        }
    }

    g._out_edges.pop_back();
    g._in_edges.pop_back();
}
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713

template <class Vertex>
inline typename std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
add_edge(Vertex s, Vertex t, adj_list<Vertex>& g)
{
    Vertex idx;
    if (g._free_indexes.empty())
    {
        idx = g._last_idx++;
    }
    else
    {
        idx = g._free_indexes.front();
        g._free_indexes.pop_front();
    }

    g._out_edges[s].push_back(std::make_pair(t, idx));
    g._in_edges[t].push_back(std::make_pair(s, idx));
    g._n_edges++;

714
715
716
717
718
719
720
721
    if (g._keep_epos)
    {
        if (idx >= g._epos.size())
            g._epos.resize(idx + 1);
        g._epos[idx].first = g._out_edges[s].size() - 1;
        g._epos[idx].second = g._in_edges[t].size() - 1;
    }

722
723
724
725
726
727
728
    return std::make_pair(std::tr1::make_tuple(s, t, idx), true);
}

template <class Vertex>
inline void remove_edge(Vertex s, Vertex t,
                        adj_list<Vertex>& g)
{
729
    if (!g._keep_epos)
730
    {
731
732
733
734
735
736
737
738
739
740
741
742
743
        typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
        for (size_t i = 0; i < oes.size(); ++i)
        {
            if (t == oes[i].first)
            {
                g._free_indexes.push_back(oes[i].second);
                oes.erase(oes.begin() + i);
                g._n_edges--;
            }
        }

        typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];
        for (size_t i = 0; i < ies.size(); ++i)
744
        {
745
746
            if (s == ies[i].first)
                ies.erase(ies.begin() + i);
747
748
        }
    }
749
    else
750
    {
751
        remove_edge(edge(s, t, g).first, g);
752
753
754
755
756
757
758
759
760
761
762
    }
}

template <class Vertex>
inline void remove_edge(const typename adj_list<Vertex>::edge_descriptor& e,
                        adj_list<Vertex>& g)
{
    Vertex s = get<0>(e);
    Vertex t = get<1>(e);
    Vertex idx = get<2>(e);
    typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
763
764
765
    typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];

    if (!g._keep_epos) // O(k_s + k_t)
766
    {
767
        for (size_t i = 0; i < oes.size(); ++i)
768
        {
769
770
771
772
773
            if (t == oes[i].first && idx == oes[i].second)
            {
                oes.erase(oes.begin() + i);
                break;
            }
774
775
        }

776
        for (size_t i = 0; i < ies.size(); ++i)
777
        {
778
779
780
781
782
            if (s == ies[i].first && idx == ies[i].second)
            {
                ies.erase(ies.begin() + i);
                break;
            }
783
784
        }
    }
785
786
787
788
789
790
791
792
793
794
795
796
    else // O(1)
    {
        const std::pair<int32_t, int32_t>& pos = g._epos[idx];

        g._epos[oes.back().second].first = pos.first;
        oes[pos.first] = oes.back();
        oes.pop_back();

        g._epos[ies.back().second].second = pos.second;
        ies[pos.second] = ies.back();
        ies.pop_back();
    }
797
798
799
800
    g._free_indexes.push_back(idx);
    g._n_edges--;
}

801

802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
template <class Vertex>
inline Vertex source(const typename adj_list<Vertex>::edge_descriptor& e,
                     const adj_list<Vertex>&)
{
    return get<0>(e);
}

template <class Vertex>
inline Vertex target(const typename adj_list<Vertex>::edge_descriptor& e,
                     const adj_list<Vertex>&)
{
    return get<1>(e);

}

//========================================================================
// Vertex and edge index property maps
//========================================================================

template <class Vertex>
struct property_map<adj_list<Vertex>, vertex_index_t>
{
    typedef identity_property_map type;
    typedef type const_type;
};

template <class Vertex>
struct property_map<const adj_list<Vertex>, vertex_index_t>
{
    typedef identity_property_map type;
    typedef type const_type;
};

template <class Vertex>
inline identity_property_map
get(vertex_index_t, adj_list<Vertex>&)
{
    return identity_property_map();
}

template <class Vertex>
inline identity_property_map
get(vertex_index_t, const adj_list<Vertex>&)
{
    return identity_property_map();
}

struct get_edge_index
{
    typedef size_t result_type;
    template <class Vertex>
    size_t operator()(const typename adj_list<Vertex>::edge_descriptor& e) const
    {
        return get<2>(e);
    }
};

template<class Vertex>
class adj_edge_index_property_map:
    public put_get_helper<Vertex, adj_edge_index_property_map<Vertex> >
{
public:
    typedef typename adj_list<Vertex>::edge_descriptor key_type;
    typedef Vertex reference;
    typedef Vertex value_type;
    typedef boost::readable_property_map_tag category;

    reference operator[](const key_type& k) const {return get<2>(k);}
};

template <class Vertex>
struct property_map<adj_list<Vertex>, edge_index_t>
{
    typedef adj_edge_index_property_map<Vertex> type;
    typedef type const_type;

};

template <class Vertex>
inline adj_edge_index_property_map<Vertex>
get(edge_index_t, const adj_list<Vertex>&)
{
    return adj_edge_index_property_map<Vertex>();
}

} // namespace boost

#endif //GRAPH_ADJACENCY_HH