/* gentree version 1.2; Brendan McKay Aug 2017 */
/* This program is a wrapper for the program FreeTrees.c written
 * by Gang Li & Frank Ruskey.  See below for their original
 * comments. */

#define USAGE \
 "gentreeg [-D#] [-Z#:#] [-ulps] [-q] n [res/mod] [file]"

#define HELPTEXT \
" Generate (unrooted) trees.\n\
\n\
      n    : the number of vertices\n\
   res/mod : only generate subset res out of subsets 0..mod-1\n\
\n\
     -D#   : an upper bound for the maximum degree\n\
     -Z#:# : bounds for the diameter\n\
\n\
     -s    : use sparse6 output (default)\n\
     -p    : write a parent array\n\
     -l    : write a level array \n\
     -u    : do not output any graphs, just generate and count them\n\
\n\
     -q    : suppress auxiliary output\n\
\n\
  See program text for much more information.\n"

/* Comments on original program by original authors */
/*==============================================================*/
/* program: freetree.c                                          */
/* purpose: generating all free trees                           */
/* input  : n -- number of nodes                                */
/*          m -- max degree                                     */
/*          lb,ub -- lower and upper bound on diameter          */
/*          res/mod -- splitting into parts                     */
/* output : listing of free trees in relex order                */ 
/* date   : September 1995, updated Sept 2000                   */
/* programmers: Gang Li & Frank Ruskey                          */
/* algorithm: From the paper: G. Li and F. Ruskey,  "The        */
/*    Advantages of Forward Thinking in Generating Rooted and   */
/*    Free Trees",  10th Annual ACM-SIAM Symposium on Discrete  */
/*    Algorithms (SODA), (1999) S939-940.  See the web page at  */
/*    http://www.theory.csc.UVic.CA/~fruskey/                   */
/*      Publications/RootedFreeTree.html                        */
/* more info: See                                               */
/*    http://www.theory.csc.UVic.CA/~cos/inf/FreeTrees.html     */
/*==============================================================*/

#define MAXN  128  /* max size of the tree.
	              Check MAXOUTLEN if more than 1000 */
#include "gtools.h"

/*****************************************************************

OUTPROC feature.

   By defining the C preprocessor variable OUTPROC at compile time
   (for Unix the syntax is  -DOUTPROC=procname  on the cc command),
   gentreeg can be made to call
       void OUTPROC(FILE *f, int *par, int n)
   instead of the usual output routines.

   par[1..n] is the parent array of the tree.
   The edges in 1..n labelling are {j,par[j]} for j=2..n.
   WARNING: The vertices are 1..n, not 0..n-1, and also par[]
   uses elements 1..n, not 0..n-1.

   Your procedure can be in a separate file so long as it is linked
   with gentreeg. 

PRUNE feature.

   By defining the C preprocessor variable PRUNE at compile time,
   gentreeg can be made to call
        int PRUNE(int *par, int n)
   for each tree.  The meaning of par[] is above and n is the number
   of vertices.  If a non-zero value is returned, the tree is rejected:
   it is not included in the count, and output routines including
   OUTPROC are not called.

SUMMARY

   If the C preprocessor variable SUMMARY is defined at compile
   time, the procedure/macro 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 as reported on the
   >Z line. Output should be written to stderr.

CALLING FROM A PROGRAM

   It is possible to call gentreeg 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 GENTREEG_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.
*/

static int
 par[MAXN+1],                 /* parent position of i  */
 maxchild,                    /* max number of children */
 chi[MAXN+1],                 /* number of children of a node */
 nextp[MAXN+1],               /* next good pos to add nodes */
 rChi[MAXN+1],                /* the right most child of node i */
 ub;                          /* upper bound on something */

static nauty_counter nout;                 /* number of trees */
static FILE *outfile;

static int splitlevel,splitcount,mod,res;   /* -s res/mod */

static int nv;  /* number of vertices */
static int mindiam; 
static int maxdeg; 
static int maxdiam;

/* MAXOUTLEN must be at least the longest output line length */
#define MAXOUTLEN (10 + 4*MAXN)
static char outstring[MAXOUTLEN];

void (*outproc)(FILE *f, int vpar[], int n);
#ifdef OUTPROC
extern void OUTPROC(FILE *f, int vpar[], int n);
#endif
#ifdef PRUNE
extern int PRUNE(int vpar[], int n);
#endif

void WritePar(FILE *f, int vpar[], int n)
/* Write parent array */
{
   int i,j;
   char *pout,*p,one[8];
   size_t len;

   pout = outstring;

   for (i=1;i<=nv;++i) {
       j = vpar[i];
       if (j == 0) *(pout++) = '0';
       else {
	  for (p = one; j > 0; j /= 10)
	      *(p++) = '0' + j%10;
	  while (--p >= one) *(pout++) = *p;
       }
       if (i < nv) *(pout++) = ' ';
       else       *(pout++) = '\n';
   }
   len = pout - outstring;

   if (fwrite(outstring,sizeof(char),len,f) != len)
        gt_abort(">E gentreeg: fwrite() failed\n");
}

static void
WriteLev(FILE *f, int vpar[], int n)
/* Write levels array */
{
   int i,j;
   char *pout,*p,one[8];
   size_t len;
   int lev[MAXN+1];

   lev[1]=0;
   for ( i=2; i<=nv; ++i ) lev[i] = lev[vpar[i]]+1;

   pout = outstring;

   for (i=1;i<=nv;++i) {
       j = lev[i];
       if (j == 0) *(pout++) = '0';
       else {
	  for (p = one; j > 0; j /= 10)
	      *(p++) = '0' + j%10;
	  while (--p >= one) *(pout++) = *p;
       }
       if (i < nv) *(pout++) = ' ';
       else       *(pout++) = '\n';
   }
   len = pout - outstring;

   if (fwrite(outstring,sizeof(char),len,f) != len)
        gt_abort(">E gentreeg: fwrite() failed\n");
}

static void
DontWrite(FILE *f, int vpar[], int n)
/* Null print routine */
{
}

static void
WriteS6(FILE *f, int vpar[], int n)
/* Write in sparse6 format */
{
    char *pout;
    int nb,i,j,lastj,x,k,r,rr,topbit;
    size_t len;

    pout = outstring;
    *pout++ = ':';
    encodegraphsize(n,&pout);

    for (i = n-1, nb = 0; i != 0 ; i >>= 1, ++nb) {}
    topbit = 1 << (nb-1);
    k = 6;
    x = 0;

    lastj = 0;
    for (j = 1; j < n; ++j)
    {
        i = vpar[j+1] - 1;
        if (j == lastj)
        {
            x <<= 1;
            if (--k == 0)
            {
                *pout++ = 63 + x;
                k = 6;
                x = 0;
            }
        }
        else
        {
            x = (x << 1) | 1;
            if (--k == 0)
            {
                *pout++ = 63 + x;
                k = 6;
                x = 0;
            }
            if (j > lastj+1)
            {
                for (r = 0, rr = j; r < nb; ++r, rr <<= 1)
                {
                    if (rr & topbit) x = (x << 1) | 1;
                    else             x <<= 1;
                    if (--k == 0)
                    {
                        *pout++ = 63 + x;
                        k = 6;
                        x = 0;
                    }
                }
                x <<= 1;
                if (--k == 0)
                {
                    *pout++ = 63 + x;
                    k = 6;
                    x = 0;
                }
            }
            lastj = j;
        }
        for (r = 0, rr = i; r < nb; ++r, rr <<= 1)
        {
            if (rr & topbit) x = (x << 1) | 1;
            else             x <<= 1;
            if (--k == 0)
            {
                *pout++ = 63 + x;
                k = 6;
                x = 0;
            }
        }
    }

    if (k != 6) *pout++ = 63 + ((x << k) | ((1 << k) - 1));

    *pout++ = '\n';
    len = pout - outstring;

    if (fwrite(outstring,sizeof(char),len,f) != len)
        gt_abort(">E gentreeg: fwrite() failed\n");
}

static void
WriteIt(int level)
{
   int i;

   if (level < splitlevel && res != 0) return;

#ifdef PRUNE
   if (PRUNE(par,nv)) return;
#endif

   ++nout;
   (*outproc)(outfile,par,nv);
}

static boolean
good( int p, int h, int t ) {
  if (p==2 && mindiam<=2 && t==0) return TRUE;
  if (t == 1) {
     if (2*h>=mindiam+1 && 2*h <= maxdiam+1) {
        if ((p-1)*2 >= nv) return TRUE;  
        else if (p - h-1 == 1) {
          if (par[p]> 2) return TRUE;
        } else
          if ((p - h-1 >=2) && ((par[h+2]>2) || (par[h+3]>2))) return TRUE;
     }
  } else 
  if (nv-p >= h && 2*h>=mindiam) { 
     if (maxdiam==nv-1 && nv%2==0) return 2*h<=maxdiam+1; 
     else return 2*h <= maxdiam;
  }
  return FALSE;
} /* good */   


static void
Gen( int level, int p, int s, int cL, int h, int l, int n, int f, int g )
/* The main generation procedure. */
{
  int hh,flag,entry,temp;

  if (level == splitlevel)
  {
      if (splitcount-- != 0) return;
      splitcount = mod - 1;
  }

  if (p > n) 
     if (f == 0) {
        if (good(p-1,h,0)) Gen(level+1, p, 2, p-2,h,n,nv,1,0); 
        if (good(p-1,h,1)) Gen(level+1, p, 2, p-3,h,n,nv,1,1);
     } else { WriteIt(level);}
  else {
     if (cL == 0) {
        if ( p< ub+2 ) par[p] = p-1;
        else {
           Gen(level+1, p, p-1, 1, h, l, n, f, g );
           return; 
        }
     } else  
        if (par[p-cL] < s) par[p]=par[p-cL];       
        else {
           par[p] = cL + par[p-cL];
           if (g==1) 
	   {
               if (((l-1)*2 < n) && (p-cL<=l) && (
                   ((p-cL+1<l) &&  (par[p-cL+1]==2)  
                   && (p-cL+2<=l) && (par[p-cL+2]==2))     /*case 1*/
                   || ((p-cL+1==l) && (par[p-cL+1]==2))    /*case 2*/
                   || (p-cL+1>l))) {                       /*case 3*/
                  s= par[p]; cL= p-s;
                  par[p] = par[par[p]];
               } else 
                  if (par[p-cL]==2) par[p]=1;  
           }
        }
        if (s!=0 || p<=ub+1) {
           chi[par[p]] = chi[par[p]] + 1;
           temp = rChi[par[p]]; rChi[par[p]] = p;
           if (chi[par[p]] <= ((par[p]==1)?maxchild:maxchild-1)) {
              if (chi[par[p]] < (par[p]==1?maxchild:maxchild-1)) nextp[p] = par[p];
              else nextp[p] = nextp[par[p]];
              Gen(level+1, p+1, s, cL,h,l,n,f,g ); 
           }
           chi[par[p]] = chi[par[p]] - 1;
           rChi[par[p]] = temp;
        }
        if (s==0 && 2*(p-2)<mindiam) return;

        nextp[p] = nextp[par[p]];
        entry = nextp[p];
        flag= 0; hh=1;
        while ((((f==0) && (entry>=2)) ||
	       ((f==1) && (entry>=1))) && (flag==0)) {
           if (s==0) h = p-2;
           if (p<=l+h-g) hh = 0; 
           if ((f==0) || (hh==1)) {
              /*s = par[p]; par[p] = par[s];*/
              par[p] = entry;

              chi[entry] = chi[entry] + 1;
	      temp = rChi[par[p]];  rChi[par[p]] = p;
	      if (chi[entry] >= (entry==1?maxchild:maxchild-1)) nextp[p] = nextp[entry];
              if (f == 0) Gen(level+1,p+1,temp,p-temp,h,0,nv-h+1,f,g);
              else if (hh == 1) Gen(level+1,p+1,temp,p-temp,h,l,n,f,g);
	      chi[entry] = chi[entry] - 1;
	      rChi[par[p]] = temp;
	      entry = nextp[entry];
	      nextp[p] = entry;
           } else flag= 1;
        }
        if (f == 0) {
           if (good(p-1,h,0)) Gen(level+1,p,2,p-2,h,p-1,nv,1,0);
           if (good(p-1,h,1)) Gen(level+1,p,2,p-3,h,p-1,nv,1,1);
        }
  }
} /* Gen */

/**************************************************************************/
/**************************************************************************/

#ifdef GENTREEG_MAIN
int
GENTREEG_MAIN(int argc, char *argv[])
#else
int
main(int argc, char *argv[])
#endif
{
        char *arg;
        boolean badargs,uswitch,sswitch,pswitch,lswitch,Zswitch;
        boolean qswitch,Dswitch,gotmr,gotf;
        long Z1,Z2;
	char *outfilename,sw;
        int i,j,argnum;
	int splitlevinc;
        double t1,t2;
	char msg[201];

	HELP; PUTVERSION;

        badargs = FALSE;
	uswitch = sswitch = pswitch = lswitch = Zswitch = FALSE;
        qswitch = Dswitch = gotmr = gotf = FALSE;
	outfilename = NULL;

	splitlevinc = 0;
	
        argnum = 0;
        for (j = 1; !badargs && j < argc; ++j)
        {
            arg = argv[j];
            if (arg[0] == '-' && arg[1] != '\0')
            {
		++arg;
		while (*arg != '\0')
		{
		    sw = *arg++;
		         SWBOOLEAN('u',uswitch)
		    else SWBOOLEAN('s',sswitch)
		    else SWBOOLEAN('p',pswitch)
		    else SWBOOLEAN('l',lswitch)
		    else SWRANGE('Z',":-",Zswitch,Z1,Z2,"gentreeg -Z")
		    else SWBOOLEAN('q',qswitch)
		    else SWINT('D',Dswitch,maxdeg,"gentreeg -D")
#ifdef PLUGIN_SWITCHES
PLUGIN_SWITCHES
#endif
                    else badargs = TRUE;
		}
            }
            else if (arg[0] == '-' && arg[1] == '\0')
		gotf = TRUE;
	    else
            {
                if (argnum == 0)
                {
                    if (sscanf(arg,"%d",&nv) != 1) badargs = TRUE;
		    ++argnum;
		}
		else if (gotf)
		    badargs = TRUE;
		else
		{
		    if (!gotmr)
		    {
			if (sscanf(arg,"%d/%d",&res,&mod) == 2)
                        { 
                            gotmr = TRUE; 
                            continue; 
                        }
		    }
		    if (!gotf)
		    {
			outfilename = arg;
			gotf = TRUE;
			continue;
		    }
                }
            }
        }

        if (argnum == 0)
            badargs = TRUE;
        else if (nv < 1 || nv > MAXN)
        {
            fprintf(stderr,">E gentreeg: n must be in the range 1..%d\n",MAXN);
	    exit(1);
        }

        if (!gotmr)
        {
            mod = 1;
            res = 0;
        }

        if (!Dswitch || maxdeg >= nv) maxdeg = nv - 1;
        if (!Zswitch || Z2 >= nv) Z2 = nv - 1;
        if (!Zswitch || Z1 <= 1) Z1 = (nv == 1 ? 0 : nv == 2 ? 1 : 2);
	mindiam = Z1;
        maxdiam = Z2;

	if (!badargs &&
	     (maxdiam < mindiam || maxdiam < (nv == 1 ? 0 : nv == 2 ? 1 : 2)))
            gt_abort(">E gentreeg: impossible diameter bounds\n");
	if (!badargs && maxdeg < (nv == 1 ? 0 : nv == 2 ? 1 : 2))
            gt_abort(">E gentreeg: impossible degree bound\n");

        if (!badargs && (res < 0 || res >= mod))
            gt_abort(">E gentreeg: must have 0 <= res < mod\n");

        if (badargs)
        {
            fprintf(stderr,">E Usage: %s\n",USAGE);
	    GETHELP;
            exit(1);
        }

	if ((lswitch!=0) + (pswitch!=0) + (sswitch!=0) + (uswitch!=0) > 1)
	    gt_abort(">E gentreeg: -uslp are incompatible\n");

#ifdef OUTPROC
        outproc = OUTPROC;
#else
        if      (uswitch)  outproc = DontWrite;
        else if (lswitch)  outproc = WriteLev;
        else if (pswitch)  outproc = WritePar;
	else               outproc = WriteS6;
#endif

#ifdef PLUGIN_INIT
PLUGIN_INIT
#endif

	if (qswitch)
	    outfile = stdout;
	else if (!gotf || outfilename == NULL)
	{
            outfilename = "stdout";
            outfile = stdout;
        }
        else if ((outfile = fopen(outfilename,"w")) == NULL)
        {
            fprintf(stderr,
                  ">E gentree: can't open %s for writing\n",outfilename);
            gt_abort(NULL);
        }

	if (!qswitch)
	{
	    msg[0] = '\0';
	    if (strlen(argv[0]) > 75)
		fprintf(stderr,">A %s",argv[0]);
	    else
		CATMSG1(">A %s",argv[0]);
	   
	    CATMSG2(" Z=%d:%d",mindiam,maxdiam);
	    CATMSG2(" D=%d n=%d",maxdeg,nv);
	    if (mod > 1) CATMSG2(" class=%d/%d",res,mod);
	    CATMSG0("\n");
	    fputs(msg,stderr);
	    fflush(stderr);
	}

        t1 = CPUTIME;

        nout = 0;

        if (nv == 1)
        {
            if (res == 0)
            {
                ++nout;
		par[1] = 0;
                WriteIt(0);
            }
        }
        else if (nv == 2)
        {
            if (res == 0)
            {
                ++nout;
		par[1] = 0;
		par[2] = 1;
                WriteIt(0);
            }
        }
        else
        {
            if (mod > 1 && nv > 3)
            {
                splitlevel = nv/2;
                splitcount = res;
            }
            else
            {
                splitlevel = -1;
                mod = 1;
            }
            if ( maxdeg > 0 ) maxchild = maxdeg; 
            else maxchild = -1;

            ub = (maxdiam+1)/2;
            for(i=1;i<=nv;i++) chi[i]=0;

            par[1] = 0; par[2] = 1;
            nextp[1]=0; nextp[2]=1;chi[1]=1;
            Gen( 0, 3, 0, 0, ub, 0, nv-ub+1, 0, 0 ); 
	}

        t2 = CPUTIME;

#ifdef SUMMARY
	SUMMARY(nout,t2-t1);
#endif

	if (!qswitch)
	{
            fprintf(stderr,">Z " COUNTER_FMT 
	            " trees generated in %3.2f sec\n",nout,t2-t1);
	}

#ifdef GENTREEG_MAIN
	return 0;
#else
        exit(0);
#endif
}