-
Notifications
You must be signed in to change notification settings - Fork 9
/
Copy pathgenbg.c
1758 lines (1551 loc) · 47.5 KB
/
genbg.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
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
102
103
104
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
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
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
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
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
346
347
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
387
388
389
390
391
392
393
394
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
466
467
468
469
470
471
472
473
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
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
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
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
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
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
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
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/* genbg.c : version 2.7; B D McKay, 13 June 2023. */
/* TODO: consider colour swaps */
#define USAGE \
"genbg [-c -ugs -vq -lzF] [-Z#] [-D#] [-A] [-d#|-d#:#] [-D#|-D#:#] n1 n2 \n\
[mine[:maxe]] [res/mod] [file]"
#define HELPTEXT \
" Find all bicoloured graphs of a specified class.\n\
\n\
n1 : the number of vertices in the first class\n\
n2 : the number of vertices in the second class\n\
mine:maxe : a range for the number of edges\n\
#:0 means '# or more' except in the case 0:0\n\
res/mod : only generate subset res out of subsets 0..mod-1\n\
file : the name of the output file (default stdout)\n\
-c : only write connected graphs\n\
-z : all the vertices in the second class must have\n\
different neighbourhoods\n\
-F : the vertices in the second class must have at least two\n\
neighbours of degree at least 2\n\
-L : there is no vertex in the first class whose removal leaves\n\
the vertices in the second class unreachable from each other\n\
-Y# : two vertices in the second class must have at least # common nbrs\n\
-Z# : two vertices in the second class must have at most # common nbrs\n\
-A : no vertex in the second class has a neighbourhood which is a\n\
subset of another vertex's neighbourhood in the second class\n\
-D# : specify an upper bound for the maximum degree\n\
Example: -D6. You can also give separate maxima for the\n\
two parts, for example: -D5:6\n\
-d# : specify a lower bound for the minimum degree.\n\
Again, you can specify it separately for the two parts: -d1:2\n\
-g : use graph6 format for output (default)\n\
-s : use sparse6 format for output\n\
-a : use Greechie diagram format for output\n\
-u : do not output any graphs, just generate and count them\n\
-v : display counts by number of edges to stderr\n\
-l : canonically label output graphs (using the 2-part colouring)\n\
\n\
-q : suppress auxiliary output\n\
\n\
See program text for much more information.\n"
/*
Output formats.
If -n is absent, any output graphs are written in graph6 format.
If -n is present, any output graphs are written in nauty format.
For a graph of n vertices, the output consists of n+1 long ints
(even if a setword is shorter than a long int). The first contains
n, and the others contain the adjacency matrix. Long int i of
the adjacency matrix (0 <= i <= n-1) is the set of neighbours of
vertex i, cast from setword to long int.
PRUNE feature.
By defining the C preprocessor variables PRUNE1 and/or PRUNE2 at
compile time, you can filter the output of the program efficiently.
The value of the variable is an int function name with parameter
list (graph *g, int *deg, int n1, int n2, int maxn2)
The function will be called for each intermediate graph generated
by the program, including output graphs. The parameters are:
g = the graph in nauty format
deg = an array giving the degrees of the vertices
n1 = the number of vertices in the first colour class
(same as the n1 parameter on the command line)
n2 = the number of vertices in the second colour class
(this will always be at least 1)
maxn2 = the value of n2 on the command line
If n2=maxn2, the graph has the output size.
If the function returns a non-zero value, neither this graph nor
any of its descendants will be written to the output.
PRUNE1 and PRUNE2 are functionally equivalent, but placed at different
points in the program. Essentially, use PRUNE1 for fast tests that
eliminate many cases and PRUNE2 for slow tests that eliminate few.
If in doubt, try it both ways and choose the fastest.
You can use both PRUNE1 and PRUNE2 if you wish, in which case note
that the PRUNE1 test has already been passed before PRUNE2 is applied.
Vertices 0..n1-1 are always present. The program works by successively
adding one more vertex to the second colour class. Vertex n1+n2-1 is
always the last one that has been added, and (except for n2=1) the
subgraph formed by deleting n1+n2-1 has previously been passed by the
pruning function.
Note that neither PRUNE1 nor PRUNE2 are called with n2=0, even if that
is the output level.
If -c is specified, the connectivity test has NOT been performed yet
at the time the pruning function is called. However the simplicity
test indicated by -z HAS been performed if -z is specified.
OUTPROC feature.
By defining the C preprocessor variable OUTPROC at compile time
(for Unix the syntax is -DOUTPROC=procname on the cc command),
genbg can be made to call a procedure of your manufacture with
each output graph instead of writing anything. Your procedure
needs to have type void and the argument list (FILE *f, graph *g,
int n1, int n2). f is a stream open for writing, g is the graph in
nauty format, and n1,n2 are the numbers of vertices on each side.
Your procedure can be in a separate file so long as it is linked
with genbg. The global variables nooutput, nautyformat and canonise
(all type boolean) can be used to test for the presence of the
flags -u, -n and -l, respectively.
For backward compatibility, it is possible to instead define OUTPROC1 to
be the name of a procedure with argument list (FILE *f, graph *g, int n).
SUMMARY
If the C preprocessor variable SUMMARY is defined at compile time, the
procedure SUMMARY(nauty_counter nout, double cpu) is called just before
the program exits. The purpose is to allow reporting of statistics
collected by PRUNE1/2 or OUTPROC. The values nout and cpu are the output
count and cpu time reported on the >Z line.
Output should be written to stderr.
INSTRUMENT feature.
If the C preprocessor variable INSTRUMENT is defined at compile time,
extra code is inserted to collect statistics during execution, and
more information is written to stderr at termination.
**************************************************************************
Author: B. D. McKay, Oct 1994. [email protected]
Copyright B. McKay (1994-2017). All rights reserved.
This software is subject to the conditions and waivers
detailed in the file COPYRIGHT.
1 May 2003 : fixed PRUNE feature
13 Sep 2003 : added Greechie output, all outprocs have n1,n2
9 Oct 2003 : changed -l to respect partition
11 Apr 2007 : make >A line more atomic
29 Aug 2008 : include PLUGIN insertion
29 Nov 2008 : slight improvement of connectivity testing
27 Jul 2011 : fixed error in PRUNE1 found by Stephen Hartke
8 Jan 2012 : add antichains -A suggested by Andrew Juell
23 Jan 2013 : fix splitlevinc initialization
16 Feb 2014 : add a missing call to PRUNE2
20 Jan 2016 : changed bigint to nauty_counter
14 Nov 2017 : added -Y switch
6 Oct 2019 : declare PRUNE1 and PRUNE2
13 Jun 2023 : simulate -Z1 for trees
**************************************************************************/
/* 1 = geng, 2 = genbg, 3 = genktreeg, 4 = gentreeg, 5 = genktreeg */
#define NAUTY_PGM 2
#undef MAXN
#define MAXN WORDSIZE
#ifndef MAXN1
#define MAXN1 24 /* not more than 30 */
#endif
#define ONE_WORD_SETS
#include "gtools.h" /* which includes nauty.h and stdio.h */
static void (*outproc)(FILE*,graph*,int,int);
#ifdef OUTPROC
extern void OUTPROC(FILE*,graph*,int,int);
#endif
#ifdef SUMMARY
extern void SUMMARY(nauty_counter,double);
#endif
#ifdef PRUNE1
extern int PRUNE1(graph*,int*,int,int,int);
#endif
#ifdef PRUNE2
extern int PRUNE2(graph*,int*,int,int,int);
#endif
static FILE *outfile; /* file for output graphs */
static boolean connec; /* presence of -c */
static boolean verbose; /* presence of -v */
static boolean simple; /* presence of -z */
boolean nautyformat; /* presence of -n */
boolean nooutput; /* presence of -u */
boolean canonise; /* presence of -l */
boolean graph6; /* presence of -g */
boolean sparse6; /* presence of -s */
boolean greout; /* presence of -a */
boolean quiet; /* presence of -q */
boolean footfree; /* presence of -F */
boolean cutfree; /* presence of -L */
boolean antichain; /* presence of -A */
int class1size; /* same as n1 */
int mincommon; /* -1 or value of -Y */
int maxcommon; /* -1 or value of -Z */
static int maxdeg1,maxdeg2,n1,maxn2,mine,maxe,nprune,mod,res,curres;
static int mindeg1,mindeg2;
static graph gcan[MAXN];
static int xval[MAXN]; /* x-bit version of second class, xval[0..] */
#if MAXN1 <= 16
static int xbit[] = {0x0001,0x0002,0x0004,0x0008,
0x0010,0x0020,0x0040,0x0080,
0x0100,0x0200,0x0400,0x0800,
0x1000,0x2000,0x4000,0x8000};
#define XNEXTBIT(x) \
((x)&0xFF ? 7-leftbit[(x)&0xFF] : 15-leftbit[((x)>>8)&0xFF])
#define XPOPCOUNT(x) (bytecount[((x)>>8)&0xFF] + bytecount[(x)&0xFF])
#elif MAXN1 <= 24
static int xbit[] = {0x000001,0x000002,0x000004,0x000008,
0x000010,0x000020,0x000040,0x000080,
0x000100,0x000200,0x000400,0x000800,
0x001000,0x002000,0x004000,0x008000,
0x010000,0x020000,0x040000,0x080000,
0x100000,0x200000,0x400000,0x800000};
#define XNEXTBIT(x) \
((x)&0xFF ? 7-leftbit[(x)&0xFF] : \
(x)&0xFF00 ? 15-leftbit[((x)>>8)&0xFF] : 23-leftbit[((x)>>16)&0xFF])
#define XPOPCOUNT(x) (bytecount[((x)>>8)&0xFF] \
+ bytecount[((x)>>16)&0xFF] + bytecount[(x)&0xFF])
#else
static int xbit[] = {0x00000001,0x00000002,0x00000004,0x00000008,
0x00000010,0x00000020,0x00000040,0x00000080,
0x00000100,0x00000200,0x00000400,0x00000800,
0x00001000,0x00002000,0x00004000,0x00008000,
0x00010000,0x00020000,0x00040000,0x00080000,
0x00100000,0x00200000,0x00400000,0x00800000,
0x01000000,0x02000000,0x04000000,0x08000000,
0x10000000,0x20000000,0x40000000,0x80000000};
#define XNEXTBIT(x) \
((x)&0xFF ? 7-leftbit[(x)&0xFF] : \
(x)&0xFF00 ? 15-leftbit[((x)>>8)&0xFF] : \
(x)&0xFF0000 ? 23-leftbit[((x)>>16)&0xFF] : \
31-leftbit[((x)>>24)&0xFF])
#define XPOPCOUNT(x) (bytecount[((x)>>8)&0xFF] \
+ bytecount[((x)>>16)&0xFF] + \
+ bytecount[((x)>>24)&0xFF] + bytecount[(x)&0xFF])
#endif
typedef struct
{
int ne,dmax; /* values used for xlb,xub calculation */
int xlb,xub; /* saved bounds on extension degree */
int lo,hi; /* work purposes for orbit calculation */
int *xorb; /* min orbit representative */
} leveldata;
#define IFLE1BITS(ww) if (!((ww)&((ww)-1)))
static leveldata data[MAXN]; /* data[n] is data for n -> n+1 */
static nauty_counter ecount[1+MAXN*MAXN/4]; /* counts by number of edges */
static int xstart[MAXN+1]; /* index into xset[] for each cardinality */
static int *xset; /* array of all x-sets in card order */
static int *xcard; /* cardinalities of all x-sets */
static int *xinv; /* map from x-set to index in xset */
#ifdef INSTRUMENT
static long nodes[MAXN],rigidnodes[MAXN],fertilenodes[MAXN];
static long a1calls,a1nauty,a1succs;
static long a2calls,a2nauty,a2uniq,a2succs;
#endif
#ifdef SPLITTEST
static unsigned long splitcases = 0;
#endif
#ifdef PLUGIN
#include PLUGIN
#endif
/************************************************************************/
void
writeny(FILE *f, graph *g, int n1, int n2)
/* write graph g (n1+n2 vertices) to file f in y format */
{
static char ybit[] = {32,16,8,4,2,1};
char s[(MAXN*(MAXN-1)/2 + 5)/6 + 4];
int i,j,k;
char y,*sp;
int n;
n = n1 + n2;
sp = s;
*(sp++) = 0x40 | n;
y = 0x40;
k = -1;
for (j = 1; j < n; ++j)
for (i = 0; i < j; ++i)
{
if (++k == 6)
{
*(sp++) = y;
y = 0x40;
k = 0;
}
if (g[i] & bit[j]) y |= ybit[k];
}
if (n >= 2) *(sp++) = y;
*(sp++) = '\n';
*sp = '\0';
if (fputs(s,f) == EOF || ferror(f))
{
fprintf(stderr,">E writeny : error on writing file\n");
exit(2);
}
}
/************************************************************************/
void
writeg6x(FILE *f, graph *g, int n1, int n2)
/* write graph g (n1+n2 vertices) to file f in graph6 format */
{
writeg6(f,g,1,n1+n2);
}
/************************************************************************/
void
writes6x(FILE *f, graph *g, int n1, int n2)
/* write graph g (n1+n2 vertices) to file f in graph6 format */
{
writes6(f,g,1,n1+n2);
}
/************************************************************************/
void
writegre(FILE *f, graph *g, int n1, int n2)
/* write graph g (n1+n2 vertices) to file f in Greechie diagram format */
{
static char atomname[] = "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\
abcdefghijklmnopqrstuvwxyz!\"#$%&'()*-/:;<=>?@[\\]^_`{|}~";
char grestr[MAXN*MAXN+MAXN+5];
int i,j,k;
setword gi;
k = 0;
for (i = n1; i < n1+n2; ++i)
{
if (i > n1) grestr[k++] = ',';
gi = g[i];
while (gi)
{
TAKEBIT(j,gi);
grestr[k++] = atomname[j];
}
}
grestr[k++] = '.';
grestr[k++] = '\n';
grestr[k] = '\0';
if (fputs(grestr,f) == EOF || ferror(f))
gt_abort(">E genbg : error on writing file\n");
}
/***********************************************************************/
static void
nullwrite(FILE *f, graph *g, int n1, int n2)
/* don't write graph g (n1+n2 vertices) to file f */
{
}
/***********************************************************************/
#ifdef OUTPROC1
static void
write12(FILE *f, graph *g, int n1, int n2)
/* pass to OUTPROC1 */
{
OUTPROC1(f,g,1,n1+n2);
}
#endif
/***********************************************************************/
void
writenauty(FILE *f, graph *g, int n1, int n2)
/* write graph g (n1+n2 vertices) to file f in nauty format */
{
int nn;
nn = n1+n2;
if (fwrite((char *)&nn,sizeof(int),(size_t)1,f) != 1 ||
fwrite((char*)g,sizeof(setword),(size_t)nn,f) != nn)
{
fprintf(stderr,">E writenauty : error on writing file\n");
exit(2);
}
}
/*********************************************************************/
static void
fragments(int *x, int nx, int *frag, int *nfrag)
/* For each v in union(x[0..nx-1]), find the components of the
hypergraph x - v and add them to frag if there are more than one. */
/* This implementation is shocking. Improve it! */
{
int allx,i,j,v;
int vbit,nw,w[MAXN];
boolean done;
allx = 0;
for (i = 0; i < nx; ++i) allx |= x[i];
*nfrag = 0;
while (allx)
{
v = XNEXTBIT(allx);
vbit = xbit[v];
allx &= ~vbit;
for (i = 0; i < nx; ++i) w[i] = x[i] & ~vbit;
nw = nx;
done = FALSE;
while (!done && nw > 1)
{
done = TRUE;
for (i = 0; i < nw-1; ++i)
for (j = i+1; j < nw; )
if ((w[i] & w[j]) != 0)
{
w[i] |= w[j];
w[j] = w[nw-1];
--nw;
done = FALSE;
}
else
++j;
}
if (nw > 1)
for (i = 0; i < nw; ++i)
frag[(*nfrag)++] = w[i];
}
}
/*********************************************************************/
static boolean
isconnected(graph *g, int n)
/* test if g is connected */
{
setword seen,expanded,toexpand,allbits;
int i;
allbits = ALLMASK(n);
expanded = bit[n-1];
seen = expanded | g[n-1];
while (seen != allbits && (toexpand = (seen & ~expanded))) /* not == */
{
i = FIRSTBITNZ(toexpand);
expanded |= bit[i];
seen |= g[i];
}
return seen == allbits;
}
/**************************************************************************/
static boolean
distinvar(graph *g, int *invar, int n1, int n2)
/* make distance invariant/
exit immediately FALSE if n-1 not maximal else exit TRUE
Note: only invar[n1..n1+n2-1] set */
{
int w,n;
setword workset,frontier;
setword sofar;
int inv,d,v;
n = n1 + n2;
for (v = n-1; v >= n1; --v)
{
inv = 0;
sofar = frontier = bit[v];
for (d = 1; frontier != 0; ++d)
{
workset = 0;
inv += POPCOUNT(frontier) ^ (0x57 + d);
while (frontier)
{
w = FIRSTBITNZ(frontier);
frontier &= ~bit[w];
workset |= g[w];
}
frontier = workset & ~sofar;
sofar |= frontier;
}
invar[v] = inv;
if (v < n-1 && inv > invar[n-1]) return FALSE;
}
return TRUE;
}
/**************************************************************************/
static void
makeleveldata(void)
/* make the level data for each level */
{
int i,j,h;
int nn,nxsets,tttn;
long ncj;
leveldata *d;
int xw,cw;
nn = maxdeg2 <= n1 ? maxdeg2 : n1;
ncj = nxsets = 1;
for (j = 1; j <= nn; ++j)
{
ncj = (ncj * (n1 - j + 1)) / j;
nxsets += ncj;
}
tttn = 1 << n1;
xset = (int*) ALLOCS(nxsets,sizeof(int));
xcard = (int*) ALLOCS(nxsets,sizeof(int));
xinv = (int*) ALLOCS(tttn,sizeof(int));
if (xset==NULL || xcard==NULL || xinv==NULL)
{
fprintf(stderr,">E genbg: malloc failed in makeleveldata()\n");
exit(2);
}
j = 0;
for (i = 0; i < tttn; ++i)
if ((h = XPOPCOUNT(i)) <= maxdeg2)
{
xset[j] = i;
xcard[j] = h;
++j;
}
if (j != nxsets)
{
fprintf(stderr,">E genbg: j=%d mxsets=%d\n",j,nxsets);
exit(2);
}
/* The following is not SORT_OF_SORT 1, 2 or 3 */
h = 1;
do
h = 3 * h + 1;
while (h < nxsets);
do
{
for (i = h; i < nxsets; ++i)
{
xw = xset[i];
cw = xcard[i];
for (j = i; xcard[j-h] > cw ||
(xcard[j-h] == cw && xset[j-h] > xw); )
{
xset[j] = xset[j-h];
xcard[j] = xcard[j-h];
if ((j -= h) < h) break;
}
xset[j] = xw;
xcard[j] = cw;
}
h /= 3;
}
while (h > 0);
for (i = 0; i < nxsets; ++i) xinv[xset[i]] = i;
xstart[0] = 0;
for (i = 1; i < nxsets; ++i)
if (xcard[i] > xcard[i-1]) xstart[xcard[i]] = i;
xstart[xcard[nxsets-1]+1] = nxsets;
for (i = 0; i < maxn2; ++i)
{
d = &data[i];
d->xorb = (int*) ALLOCS(nxsets,sizeof(int));
if (d->xorb==NULL)
{
fprintf(stderr,">E genbg: malloc failed in makeleveldata()\n");
exit(2);
}
d->ne = d->dmax = d->xlb = d->xub = -1;
}
}
/**************************************************************************/
static void
userautomproc(int count, int *p, int *orbits, int numorbits,
int stabvertex, int n)
/* Automorphism procedure called by nauty
Form orbits on powerset of VG
Operates on data[n-n1] */
{
int i,j1,j2;
int moved,pxi,pi;
int w,lo,hi;
int *xorb;
xorb = data[n-n1].xorb;
lo = data[n-n1].lo;
hi = data[n-n1].hi;
if (count == 1) /* first automorphism */
for (i = lo; i < hi; ++i) xorb[i] = i;
moved = 0;
for (i = 0; i < n; ++i)
if (p[i] != i) moved |= xbit[i];
for (i = lo; i < hi; ++i)
{
if ((w = xset[i] & moved) == 0) continue;
pxi = xset[i] & ~moved;
while (w)
{
j1 = XNEXTBIT(w);
w &= ~xbit[j1];
pxi |= xbit[p[j1]];
}
pi = xinv[pxi];
j1 = xorb[i];
while (xorb[j1] != j1) j1 = xorb[j1];
j2 = xorb[pi];
while (xorb[j2] != j2) j2 = xorb[j2];
if (j1 < j2) xorb[j2] = xorb[i] = xorb[pi] = j1;
else if (j1 > j2) xorb[j1] = xorb[i] = xorb[pi] = j2;
}
}
/*****************************************************************************
* *
* refinex(g,lab,ptn,level,numcells,count,active,goodret,code,m,n) is a *
* custom version of refine() which can exit quickly if required. *
* *
* Only use at level==0. *
* goodret : whether to do an early return for code 1 *
* code := -1 for n-1 not max, 0 for maybe, 1 for definite *
* *
*****************************************************************************/
static void
refinex(graph *g, int *lab, int *ptn, int level, int *numcells,
int *count, set *active, boolean goodret,
int *code, int m, int n)
{
int i,c1,c2,labc1;
setword x;
int split1,split2,cell1,cell2;
int cnt,bmin,bmax;
set *gptr;
setword workset;
int workperm[MAXN];
int bucket[MAXN+2];
if (n == 1)
{
*code = 1;
return;
}
*code = 0;
split1 = -1;
while (*numcells < n && ((split1 = nextelement(active,1,split1)) >= 0
|| (split1 = nextelement(active,1,-1)) >= 0))
{
DELELEMENT1(active,split1);
for (split2 = split1; ptn[split2] > 0; ++split2)
{}
if (split1 == split2) /* trivial splitting cell */
{
gptr = GRAPHROW(g,lab[split1],1);
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > 0; ++cell2) {}
if (cell1 == cell2) continue;
c1 = cell1;
c2 = cell2;
while (c1 <= c2)
{
labc1 = lab[c1];
if (ISELEMENT1(gptr,labc1))
++c1;
else
{
lab[c1] = lab[c2];
lab[c2] = labc1;
--c2;
}
}
if (c2 >= cell1 && c1 <= cell2)
{
ptn[c2] = 0;
++*numcells;
ADDELEMENT1(active,c1);
}
}
}
else /* nontrivial splitting cell */
{
workset = 0;
for (i = split1; i <= split2; ++i)
workset |= bit[lab[i]];
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > 0; ++cell2) {}
if (cell1 == cell2) continue;
i = cell1;
if ((x = workset & g[lab[i]])) /* not == */
cnt = POPCOUNT(x);
else
cnt = 0;
count[i] = bmin = bmax = cnt;
bucket[cnt] = 1;
while (++i <= cell2)
{
if ((x = workset & g[lab[i]])) /* not == */
cnt = POPCOUNT(x);
else
cnt = 0;
while (bmin > cnt) bucket[--bmin] = 0;
while (bmax < cnt) bucket[++bmax] = 0;
++bucket[cnt];
count[i] = cnt;
}
if (bmin == bmax) continue;
c1 = cell1;
for (i = bmin; i <= bmax; ++i)
if (bucket[i])
{
c2 = c1 + bucket[i];
bucket[i] = c1;
if (c1 != cell1)
{
ADDELEMENT1(active,c1);
++*numcells;
}
if (c2 <= cell2) ptn[c2-1] = 0;
c1 = c2;
}
for (i = cell1; i <= cell2; ++i)
workperm[bucket[count[i]]++] = lab[i];
for (i = cell1; i <= cell2; ++i)
lab[i] = workperm[i];
}
}
if (ptn[n-2] == 0)
{
if (lab[n-1] == n-1)
{
*code = 1;
if (goodret) return;
}
else
{
*code = -1;
return;
}
}
else
{
i = n - 1;
while (1)
{
if (lab[i] == n-1) break;
--i;
if (ptn[i] == 0)
{
*code = -1;
return;
}
}
}
}
}
/**************************************************************************/
static void
makecanon(graph *g, graph *gcan, int n1, int n2)
/* gcan := canonise(g) */
{
int lab[MAXN],ptn[MAXN],orbits[MAXN];
setword active[1];
int i;
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
options.writemarkers = FALSE;
options.writeautoms = FALSE;
options.getcanon = TRUE;
options.defaultptn = FALSE;
for (i = 0; i < n1+n2; ++i)
{
lab[i] = i;
ptn[i] = 1;
}
ptn[n1-1] = ptn[n1+n2-1] = 0;
EMPTYSET(active,1);
ADDELEMENT(active,0);
ADDELEMENT(active,n1);
nauty(g,lab,ptn,active,orbits,&options,&stats,
workspace,50,1,n1+n2,gcan);
}
/**************************************************************************/
static boolean
accept1(graph *g, int n2, int x, graph *gx, int *deg, boolean *rigid)
/* decide if n2 in theta(g+x) -- version for n2+1 < maxn2 */
{
int i,n;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int count[MAXN];
graph h[MAXN];
int xw;
int nx,numcells,code;
int i0,i1,degn;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
#ifdef INSTRUMENT
++a1calls;
#endif
n = n1 + n2;
nx = n + 1;
for (i = 0; i < n; ++i) gx[i] = g[i];
gx[n] = 0;
deg[n] = degn = XPOPCOUNT(x);
xw = x;
while (xw)
{
i = XNEXTBIT(xw);
xw &= ~xbit[i];
gx[i] |= bit[n];
gx[n] |= bit[i];
++deg[i];
}
#ifdef PRUNE1
if (PRUNE1(gx,deg,n1,n2+1,maxn2)) return FALSE;
#endif
for (i = 0; i < n1; ++i)
{
lab[i] = i;
ptn[i] = 1;
}
ptn[n1-1] = 0;
i0 = n1;
i1 = n;
for (i = n1; i < nx; ++i)
{
if (deg[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == n1)
{
numcells = 2;
active[0] = bit[0] | bit[n1];
}
else
{
numcells = 3;
active[0] = bit[0] | bit[n1] | bit[i1+1];
ptn[i1] = 0;
}
refinex(gx,lab,ptn,0,&numcells,count,active,FALSE,&code,1,nx);
if (code < 0) return FALSE;
if (numcells == nx)
{
*rigid = TRUE;
#ifdef INSTRUMENT
++a1succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,deg,n1,n2+1,maxn2)) return FALSE;
#endif
return TRUE;
}
options.writemarkers = FALSE;
options.writeautoms = FALSE;
options.getcanon = TRUE;
options.defaultptn = FALSE;
options.userautomproc = userautomproc;
active[0] = 0;
#ifdef INSTRUMENT
++a1nauty;
#endif
nauty(gx,lab,ptn,active,orbits,&options,&stats,workspace,50,1,nx,h);
if (orbits[lab[n]] == orbits[n])
{
*rigid = stats.numorbits == nx;
#ifdef INSTRUMENT
++a1succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,deg,n1,n2+1,maxn2)) return FALSE;
#endif
return TRUE;
}
else
return FALSE;
}
/**************************************************************************/
static boolean
accept2(graph *g, int n2, int x, graph *gx, int *deg, boolean nuniq)
/* decide if n in theta(g+x) -- version for n+1 == maxn */
{
int i,n;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int degx[MAXN],invar[MAXN];
setword vmax,gv;
int qn,qv;
int count[MAXN];
int xw;
int nx,numcells,code;
int degn,i0,i1,j,j0,j1;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
#ifdef INSTRUMENT
++a2calls;
if (nuniq) ++a2uniq;
#endif
n = n1 + n2;
nx = n + 1;
for (i = 0; i < n; ++i)
{
gx[i] = g[i];
degx[i] = deg[i];
}
gx[n] = 0;
degx[n] = degn = XPOPCOUNT(x);
xw = x;
while (xw)
{
i = XNEXTBIT(xw);
xw &= ~xbit[i];
gx[i] |= bit[n];
gx[n] |= bit[i];
++degx[i];
}
#ifdef PRUNE1
if (PRUNE1(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (nuniq)
{
#ifdef INSTRUMENT
++a2succs;