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gentourng.c
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/* gentourng.c version 1.4; B D McKay, Jan 20, 2016 */
#define USAGE \
"gentourng [-cd#D#] [-ugsz] [-lq] n [res/mod] [file]"
#define HELPTEXT \
" Generate all tournaments of a specified class.\n\
\n\
n : the number of vertices\n\
res/mod : only generate subset res out of subsets 0..mod-1\n\
\n\
-c : only write strongly-connected tournaments\n\
-d# : a lower bound for the minimum out-degree\n\
-D# : a upper bound for the maximum out-degree\n\
-l : canonically label output graphs\n\
\n\
-u : do not output any graphs, just generate and count them\n\
-g : use graph6 output (lower triangle)\n\
-s : use sparse6 output (lower triangle)\n\
-z : use digraph6 output\n\
-h : write a header (only with -g or -s)\n\
Default output is upper triangle row-by-row in ascii\n\
\n\
-q : suppress auxiliary output\n\
\n\
See program text for much more information.\n"
/* Parameters:
n = the number of vertices (1..min(32,WORDSIZE))
mod, res = a way to restrict the output to a subset.
All the graphs in G(n,mine..maxe) are divided into
disjoint classes C(0,mod),C(1,mod),...,C(mod-1,mod),
of very approximately equal size.
Only the class C(res,mod) is written.
file = a name for the output file (stdout if missing or "-")
All switches can be concatenated or separate. However, the
value of -d must be attached to the "d", and similarly for "x".
-c : only write connected graphs
-d<int> : specify an upper bound for the maximum out-degree.
The value of the upper bound must be adjacent to
the "d". Example: -d6
-l : canonically label output graphs
-u : do not output any graphs, just generate and count them
-z : use digraph6 output
-g : use graph6 output
-s : use sparse6 output
For -g and -s, the lower triangle of the adjacency matrix
is written as if it is an undirected graph. Nauty tools
like labelg do not know this format. To read it you can
read it as an undirected graph then complement the upper
triangle.
-h : for graph6 or sparse6 format, write a header too
-q : suppress auxiliary output (except from -v)
Output formats.
The output format is determined by the mutually exclusive switches
-u, -z, -g and -s. The default is ascii format.
-u suppresses output of graphs completely.
-z uses digraph6 output.
-s and -g specify sparse6 and graph6 format, defined elsewhere.
In this case a header is also written if -h is present.
OUTPROC feature.
By defining the C preprocessor variable OUTPROC at compile time
(for Unix the syntax is -DOUTPROC=procname on the cc command),
gentourng 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 n).
f is a stream open for writing, g is the graph in nauty format,
and n is the number of vertices. Your procedure can be in a
separate file so long as it is linked with gentourng. The global
variables nooutput, and canonise (all type boolean) can be
used to test for the presence of the flags -u and -l,
respectively. If -l is present, the group size and similar
details can be found in the global variable nauty_stats.
PRUNE feature.
By defining the C preprocessor variable PRUNE at compile time, gentourng
can be made to call
int PRUNE(graph *g,int n,int maxn)
for each intermediate (and final) graph, and reject it if
the value returned is nonzero. The arguments are:
g = the graph in nauty format (m=1)
n = the number of vertices in g
maxn = the number of vertices for output
(the value you gave on the command line to gentourng)
gentourng constructs the graph starting with vertex 0, then adding
vertices 1,2,3,... in that order. Each graph in the sequence is
an induced subgraph of all later graphs in the sequence.
A call is made for all orders from 1 to maxn. In testing for
a uniform property (such as a forbidden subgraph or forbidden
induced subgraph) it might save time to notice that a call to
PRUNE for n implies that the call for n-1 already passed.
For very fast tests, it might be worthwhile using PREPRUNE as
well or instead. It has the same meaning but is applied earlier
and more often.
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 PRUNE 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.
CALLING FROM A PROGRAM
It is possible to call gentourng from another program instead of using it
as a stand-alone program. The main requirement is to change the name
of the main program to be other than "main". This is done by defining
the preprocessor variable GENG_MAIN. You might also like to define
OUTPROC to be the name of a procedure to receive the graphs. To call
the program you need to define an argument list argv[] consistent with
the usual one; don't forget that argv[0] is the command name and not
the first argument. The value of argc is the number of strings in
argv[]; that is, one more than the number of arguments. See the
sample program callgeng.c.
Counts:
all strong regular
n tournaments tournaments tournaments
1 1 1 1
2 1 0 1
3 2 1 1
4 4 1 1
5 12 6 1
6 56 35 5
7 456 353 3
8 6880 6008 85
9 191536 178133 15
10 9733056 9355949 13333
11 903753248 884464590 1223
12 154108311168 152310149735 19434757
13 48542114686912 48234782263293 1495297
14 28401423719122304 28304491788158056 276013571133
15 31021002160355166848 30964247546702883729 18400989629
16 63530415842308265100288 63468402142317299907481
17 244912778438520759443245824 244785748571033855024746438 2406183070160597
**************************************************************************
Author: B. D. McKay, Nov 2008.
Copyright B. McKay (2008). All rights reserved.
This software is subject to the conditions and waivers
detailed in the file nauty.h.
**************************************************************************/
#define NAUTY_PGM 3 /* 1 = geng, 2 = genbg, 3 = gentourng */
#ifndef MAXN
#define MAXN 32 /* not more than max(32,WORDSIZE) */
#endif
#if MAXN > 32
#error "Can't have MAXN greater than 32"
#endif
#define ONE_WORD_SETS
#include "gtools.h" /* which includes nauty.h and stdio.h */
typedef unsigned int xword;
static void (*outproc)(FILE*,graph*,int);
static FILE *outfile; /* file for output graphs */
static int connec; /* 1 for -c, 0 for not */
boolean graph6; /* presence of -g */
boolean digraph6; /* presence of -z */
boolean sparse6; /* presence of -s */
boolean nooutput; /* presence of -u */
boolean canonise; /* presence of -l */
boolean quiet; /* presence of -q */
boolean header; /* presence of -h */
statsblk nauty_stats;
static int mindeg,maxdeg,maxn,mod,res;
static boolean regular;
#define PRUNEMULT 20 /* bigger -> more even split at greater cost */
static int min_splitlevel,odometer,splitlevel,multiplicity;
static graph gcan[MAXN];
#if MAXN <= 16
static xword 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 MAXN <= 24
static xword 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 xword 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
{
xword lo,hi; /* work purposes for orbit calculation */
xword xstart[MAXN+1]; /* index into xset[] for each cardinality */
xword *xset; /* array of all x-sets in card order */
xword *xcard; /* cardinalities of all x-sets */
xword *xinv; /* map from x-set to index in xset */
xword *xorb; /* min orbit representative */
} leveldata;
static leveldata data[MAXN]; /* data[n] is data for n -> n+1 */
static nauty_counter nodes[MAXN]; /* nodes at each level */
static nauty_counter nout;
#ifdef INSTRUMENT
static unsigned long rigidnodes[MAXN],fertilenodes[MAXN];
static unsigned long a1calls,a1nauty,a1succs;
static unsigned long a2calls,a2nauty,a2uniq,a2succs;
#endif
#ifdef PLUGIN
#include PLUGIN
#endif
#ifdef OUTPROC
extern void OUTPROC(FILE*,graph*,int);
#endif
#ifdef PRUNE
extern int PRUNE(graph*,int,int);
#endif
#ifdef PREPRUNE
extern int PREPRUNE(graph*,int,int);
#endif
#ifdef SUMMARY
extern void SUMMARY(nauty_counter,double);
#endif
/************************************************************************/
void
write_ascii(FILE *f, graph *g, int n)
/* write tournament g (n vertices) to file f in ascii format */
{
char s[MAXN*(MAXN-1)/2+2];
int i,j;
size_t k;
k = 0;
for (i = 0; i < n-1; ++i)
for (j = i+1; j < n; ++j)
if ((g[i] & bit[j])) s[k++] = '1'; else s[k++] = '0';
s[k++] = '\n';
s[k] = '\0';
if (fwrite(s,1,k,f) != k || ferror(f))
gt_abort(">E write_ascii : error on writing\n");
}
/************************************************************************/
void
writeg6x(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in graph6 format */
{
writeg6(f,g,1,n);
}
/************************************************************************/
void
writes6x(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in sparse6 format */
{
writes6(f,g,1,n);
}
/************************************************************************/
void
writed6x(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in digraph6 format */
{
writed6(f,g,1,n);
}
/***********************************************************************/
static void
nullwrite(FILE *f, graph *g, int n)
/* don't write graph g (n vertices) to file f */
{
}
/***********************************************************************/
static boolean
isstrong(graph *g, int n)
/* test if tournament g is strongly-connected
* This code is strictly for tournaments only.
*/
{
setword seen,expanded,toexpand,allbits;
int i;
allbits = ALLMASK(n);
seen = bit[0] | g[0];
expanded = bit[0];
while (seen != allbits && (toexpand = (seen & ~expanded))) /* not == */
{
i = FIRSTBITNZ(toexpand);
expanded |= bit[i];
seen |= g[i];
}
if (seen != allbits) return FALSE;
seen = (allbits ^ g[0]);
expanded = bit[0];
while (seen != allbits && (toexpand = (seen & ~expanded))) /* not == */
{
i = FIRSTBITNZ(toexpand);
expanded |= bit[i];
seen |= (g[i] ^ allbits);
}
return seen == allbits;
}
/**********************************************************************/
static void
gcomplement(graph *g, graph *gc, int n)
/* Take the complement of g and put it in gc */
{
int i;
setword all;
all = ~(setword)BITMASK(n-1);
for (i = 0; i < n; ++i)
gc[i] = g[i] ^ all ^ bit[i];
}
/**************************************************************************/
static void
makeleveldata(void)
/* make the level data for each level */
{
long h;
int n,dmax,dmin;
long ncj;
leveldata *d;
xword *xcard,*xinv;
xword *xset,xw,tttn,nxsets;
xword cw;
xword i,j;
for (n = 1; n < maxn; ++n)
{
dmax = n/2;
if (maxdeg < dmax) dmax = maxdeg;
dmin = mindeg - maxn + n + 1;
if (dmin < 0) dmin = 0;
ncj = 1;
nxsets = (dmin == 0 ? 1 : 0);
for (j = 1; j <= dmax; ++j)
{
ncj = (ncj * (n-j+1)) / j;
if (j >= dmin) nxsets += ncj;
}
tttn = 1L << n;
d = &data[n];
d->xset = xset = (xword*) calloc(nxsets,sizeof(xword));
d->xcard = xcard = (xword*) calloc(nxsets,sizeof(xword));
d->xinv = xinv = (xword*) calloc(tttn,sizeof(xword));
d->xorb = (xword*) calloc(nxsets,sizeof(xword));
if (xset==NULL || xcard==NULL || xinv==NULL || d->xorb==NULL)
{
fprintf(stderr,
">E gentourng: calloc failed in makeleveldata()\n");
exit(2);
}
j = 0;
for (i = 0;; ++i)
{
if ((h = XPOPCOUNT(i)) <= dmax && h >= dmin)
{
xset[j] = i;
xcard[j] = h;
++j;
}
if (i == (xword)((1L<<n)-1)) break;
}
if (j != nxsets)
{
fprintf(stderr,">E gentourng: j=%u mxsets=%u\n",
j,(unsigned)nxsets);
exit(2);
}
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;
d->xstart[0] = 0;
for (i = 1; i < nxsets; ++i)
if (xcard[i] > xcard[i-1]) d->xstart[xcard[i]] = i;
d->xstart[xcard[nxsets-1]+1] = nxsets;
}
}
/**************************************************************************/
static void
userautomproc(int count, int *p, int *orbits,
int numorbits, int stabvertex, int n)
/* form orbits on powerset of VG
called by nauty; operates on data[n] */
{
xword i,j1,j2,moved,pi,pxi;
xword lo,hi;
xword *xorb,*xinv,*xset,w;
xorb = data[n].xorb;
xset = data[n].xset;
xinv = data[n].xinv;
lo = data[n].lo;
hi = data[n].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,lact;
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;
lact = *active;
split1 = -1;
while (*numcells < n && lact)
{
TAKEBIT(split1,lact);
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;
lact |= bit[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]]) != 0) cnt = POPCOUNT(x);
else cnt = 0;
count[i] = bmin = bmax = cnt;
bucket[cnt] = 1;
while (++i <= cell2)
{
if ((x = workset & g[lab[i]]) != 0)
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)
{
lact |= bit[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 (TRUE)
{
if (lab[i] == n-1) break;
--i;
if (ptn[i] == 0)
{
*code = -1;
return;
}
}
}
}
}
/**************************************************************************/
static void
makecanon(graph *g, graph *gcan, int n)
/* gcan := canonise(g) */
{
int lab[MAXN],ptn[MAXN],orbits[MAXN];
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[200];
options.getcanon = TRUE;
options.digraph = TRUE;
nauty(g,lab,ptn,NULL,orbits,&options,&nauty_stats,
workspace,200,1,n,gcan);
}
/**************************************************************************/
static boolean
accept1(graph *g, int n, xword x, graph *gx, int *deg, boolean *rigid)
/* decide if n in theta(g+x) - version for n+1 < maxn */
{
int i;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int count[MAXN];
graph h[MAXN];
int nx,numcells,code;
int i0,i1,degn;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[200];
#ifdef INSTRUMENT
++a1calls;
#endif
nx = n + 1;
for (i = 0; i < n; ++i) gx[i] = g[i];
gx[n] = 0;
deg[n] = degn = XPOPCOUNT(x);
for (i = 0; i < n; ++i)
{
if ((xbit[i] & x))
gx[n] |= bit[i];
else
{
gx[i] |= bit[n];
++deg[i];
}
}
#ifdef PREPRUNE
if (PREPRUNE(gx,n+1,maxn)) return FALSE;
#endif
i0 = 0;
i1 = n;
for (i = 0; i < nx; ++i)
{
if (deg[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == 0)
{
numcells = 1;
active[0] = bit[0];
}
else
{
numcells = 2;
active[0] = bit[0] | 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
return TRUE;
}
options.getcanon = TRUE;
options.digraph = TRUE;
options.defaultptn = FALSE;
options.userautomproc = userautomproc;
/*
if (!regular || nx != maxn-1) options.userautomproc = userautomproc;
else options.userautomproc = NULL;
*/
active[0] = 0;
#ifdef INSTRUMENT
++a1nauty;
#endif
nauty(gx,lab,ptn,active,orbits,&options,&stats,workspace,200,1,nx,h);
if (orbits[lab[n]] == orbits[n])
{
*rigid = stats.numorbits == nx;
#ifdef INSTRUMENT
++a1succs;
#endif
return TRUE;
}
else
return FALSE;
}
/**************************************************************************/
static boolean
hitinvar(graph *g, int *invar, int n)
/* make hitting invariant
* return FALSE if n-1 not maximal else return TRUE */
{
setword x,y,z;
int inv,i,v,d;
for (v = n-1; v >= 0; --v)
{
inv = 0;
x = y = g[v];
while (y)
{
TAKEBIT(i,y);
z = x & g[i];
d = POPCOUNT(z);
if (d > inv) inv = d;
}
invar[v] = inv;
if (v < n-1 && inv > invar[n-1]) return FALSE;
}
return TRUE;
}
/**************************************************************************/
static boolean
accept2(graph *g, int n, xword x, graph *gx, int *deg, boolean nuniq)
/* decide if n in theta(g+x) -- version for n+1 == maxn */
{
int i;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int degx[MAXN],invar[MAXN];
setword vmax,gv,gxn;
int qn,qv;
int count[MAXN];
int nx,numcells,code;
int degn,i0,i1,j,j0,j1;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[200];
boolean cheapacc;
#ifdef INSTRUMENT
++a2calls;
if (nuniq) ++a2uniq;
#endif
nx = n + 1;
gxn = 0;
for (i = 0; i < n; ++i)
{
if ((xbit[i] & x))
{
gxn |= bit[i];
gx[i] = g[i];
degx[i] = deg[i];
}
else
{
gx[i] = g[i] | bit[n];
degx[i] = deg[i] + 1;
}
}
gx[n] = gxn;
degx[n] = degn = XPOPCOUNT(x);
#ifdef PREPRUNE
if (PREPRUNE(gx,n+1,maxn)) return FALSE;
#endif
if (nuniq)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
i0 = 0;
i1 = n;
for (i = 0; i < nx; ++i)
{
if (degx[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == 0)
{
numcells = 1;
active[0] = bit[0];
if (!hitinvar(gx,invar,nx)) return FALSE;
qn = invar[n];
j0 = 0;
j1 = n;
while (j0 <= j1)
{
j = lab[j0];
qv = invar[j];
if (qv < qn)
++j0;
else
{
lab[j0] = lab[j1];
lab[j1] = j;
--j1;
}
}
if (j0 > 0)
{
if (j0 == n)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
ptn[j1] = 0;
++numcells;
active[0] |= bit[j0];
}
}
else
{
numcells = 2;
ptn[i1] = 0;
active[0] = bit[0] | bit[i1+1];
vmax = 0;
for (i = i1+1; i < nx; ++i) vmax |= bit[lab[i]];
gv = gx[n] & vmax;
qn = POPCOUNT(gv);
j0 = i1+1;
j1 = n;
while (j0 <= j1)
{
j = lab[j0];
gv = gx[j] & vmax;
qv = POPCOUNT(gv);
if (qv > qn)
return FALSE;
else if (qv < qn)
++j0;
else
{
lab[j0] = lab[j1];
lab[j1] = j;
--j1;
}
}
if (j0 > i1+1)
{
if (j0 == n)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
ptn[j1] = 0;
++numcells;
active[0] |= bit[j0];
}
}
refinex(gx,lab,ptn,0,&numcells,count,active,TRUE,&code,1,nx);
if (code < 0) return FALSE;
cheapacc = FALSE;
if (code > 0) cheapacc = TRUE;
if (cheapacc)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
options.getcanon = TRUE;
options.digraph = TRUE;
options.defaultptn = FALSE;