@i gb_types.w

@*Intro. Given a graph |g| with |m| edges,
make data from which {\mc DLX2} should tell us all ways to label
the vertices, using distinct labels in $\{0,1,\ldots,m\}$,
so that the edges have distinct difference. (Those differences
will be $\{1,\ldots,m\}$.

Selected vertex labels may be prespecified on the command line,
as in {\mc BACK-GRACEFUL}.

@d encode(x) ((x)<10? (x)+'0': (x)<36? (x)-10+'a': (x)<62? (x)-36+'A': (x)+99)
@d maxm 156 /* based on that encoding, but I could go higher in a pinch! */
@d maxn 100

@c
#include <stdio.h>
#include <stdlib.h>
#include "gb_graph.h"
#include "gb_save.h"
int c;
int label; /* a label value read from |argv[k]| */
int prespec[maxn]; /* prespecified labels */
int verttoprespec[maxn]; /* has this vertex been prespecified? */
int prespecptr; /* how many are prespecified? */
main(int argc, char*argv[]) {
  register int i,j,k,m,n,p,x,bad;
  register Arc *a;
  register Graph *g;
  register Vertex *v,*w;
  @<Process the command line, and set |prespec| to the prespecified labelings@>;
  @<Output the item-name line@>;
  for (k=1;k<=m;k++)
    @<Output the options for edge |k|@>;
}

@ @<Process the command line...@>=
if (argc<2) {
  fprintf(stderr,"Usage: %s foo.gb [VERTEX=label...]\n",
               argv[0]);
  exit(-1);
}
g=restore_graph(argv[1]);
if (!g) {
  fprintf(stderr,"I couldn't reconstruct graph %s!\n",argv[1]);
  exit(-2);
}
m=g->m/2,n=g->n;
if (m>maxm) {
  fprintf(stderr,"Sorry, at present I require m<=%d!\n",maxm);
  exit(-3);
}
if (n>maxn) {
  fprintf(stderr,"Sorry, at present I require n<=%d!\n",maxn);
  exit(-4);
}
for (k=2;argv[k];k++) {
  for (i=1;argv[k][i];i++) if (argv[k][i]=='=') break;
  if (!argv[k][i] || sscanf(&argv[k][i+1],"%d",
                             &label)!=1 || label<0 || label>m) {
    fprintf(stderr,"spec `%s' doesn't have the form `VERTEX=label'!\n",
                           argv[k]);
    exit(-3);
  }
  argv[k][i]=0;
  for (j=0;j<n;j++)
    if (strcmp((g->vertices+j)->name,argv[k])==0) break;
  if (j==n) {
    fprintf(stderr,"There's no vertex named `%s'!\n",
                         argv[k]);
    exit(-5);
  }
  if (verttoprespec[j]) {
    fprintf(stderr,"Vertex %s was already specified!\n",
                        (g->vertices+j)->name);
    exit(-6);
  }
  argv[k][i]='=';
  verttoprespec[j]=1;
  prespec[prespecptr++]=(j<<8)+label;
}
fprintf(stderr,
  "OK, I've got a graph with %d vertices, %d edges, %d prespec%s.\n",
                            n,m,prespecptr,prespecptr==1?"":"s");
printf("|");
for (k=0;argv[k];k++) printf(" %s",argv[k]);
printf("\n");

@ There's a primary item $k$ for each edge label, and a primary
item $uv$ for each edge. This enforces a permutation between
edges and labels.

There's a secondary item \.{.$v$} for each vertex; its color will be its label.

There's a secondary item \.{+$k$} for each vertex label; its color will be
the vertex so labeled.

@<Output the item-name line@>=
for (k=1;k<=m;k++) printf("%c ",
                       encode(k));
for (v=g->vertices;v<g->vertices+n;v++)
  for (a=v->arcs;a;a=a->next) if (a->tip>v)
    printf("%s-%s ",
              v->name,a->tip->name);
printf("|");
for (v=g->vertices;v<g->vertices+n;v++)
  printf(" .%s",
              v->name);
for (k=0;k<=m;k++)
  printf(" +%c",
              encode(k));
printf("\n");

@ @d vrt(v) ((int)((v)-g->vertices))

@<Output the options for edge |k|@>=
{
  for (i=0,j=k;j<=m;i++,j++) {
    for (v=g->vertices;v<g->vertices+n;v++)
      for (a=v->arcs;a;a=a->next) if (a->tip>v) {
        for (bad=p=0;p<prespecptr;p++) {
          w=g->vertices+(prespec[p]>>8),x=prespec[p]&0xff;
          if (v==w) {
            if (i!=x) bad|=1;
            if (j!=x) bad|=2;
          }@+else if (a->tip==w) {
            if (j!=x) bad|=1;
            if (i!=x) bad|=2;
          }
          if (i==x) {
            if (v!=w) bad|=1;
            if (a->tip!=w) bad|=2;
          }@+else if (j==x) {
            if (v!=w) bad|=2;
            if (a->tip!=w) bad|=1;
          }
        }
        if ((bad&1)==0)
          printf("%c %s-%s .%s:%c .%s:%c +%c:%c +%c:%c\n",
       encode(k),v->name,a->tip->name,v->name,encode(i),a->tip->name,encode(j),
         encode(i),encode(vrt(v)),encode(j),encode(vrt(a->tip)));
        if ((bad&2)==0)
          printf("%c %s-%s .%s:%c .%s:%c +%c:%c +%c:%c\n",
       encode(k),v->name,a->tip->name,v->name,encode(j),a->tip->name,encode(i),
         encode(j),encode(vrt(v)),encode(i),encode(vrt(a->tip)));
    }
  }
}

@*Index.