@*Intro. Given a nonempty parade on the command line,
this quick-and-dirty program
computes its ``rank,'' as explained in my unpublication
{\sl Parades and poly-Bernoulli bijections}.

The rank might be huge. So I don't actually compute it; I produce
Mathematica code that will do the numerical work.

(Sorry --- I hacked this up in a huge hurry.)

@d maxn 100

@c
#include <stdio.h>
#include <stdlib.h>
int strg[maxn],strb[maxn]; /* the digit strings */
int d; /* the order */
int m,n; /* how many girls and boys? */
int perm[maxn],rgs[maxn],hit[maxn];
main (int argc,char*argv[]) {
  register int i,j,k,prevj,t,p,l;
  @<Process the command line@>;
  @<Print the boilerplate to get Mathematica started@>;
  @<Figure out the permutation and rgs for the girls@>;
  @<Figure out the permutation and rgs for the boys@>;
  printf("extra+((gperm brace[%d,%d]+grgs)%d!+bperm)brace[%d,%d]+brgs\n",
                               m+1,d+1,d,n+1,d+1@q]))@>);
}

@ An incorrect command line aborts the run. But we do explain what was wrong.

@<Process the command line@>=
if (argc<2) {
  fprintf(stderr,"Usage: %s <parade>\n",
                 argv[0]);
  exit(-1);
}
for (k=1;k<maxn;k++) strg[k]=strb[k]=-1;
for (d=0,k=1;argv[k];k++) {
  if (argv[k][0]!='g' && argv[k][0]!='b') {
    fprintf(stderr,"Bad argument `%s'; should start with g or b!\n",
                argv[k]);
    exit(-2);
  }
  for (prevj=j,j=0,i=1;argv[k][i]>='0' && argv[k][i]<='9';i++)
          j=10*j+argv[k][i]-'0';
  if (j==0 || argv[k][i]) {
    fprintf(stderr,"Bad argument `%s'; should be a positive number!\n",
                       argv[k]);
    exit(-3);
  }
  if (j>=maxn) {
    fprintf(stderr,"Recompile me: maxn=%d!\n",
             maxn);
    exit(-6);
  }
  if (argv[k][0]=='g' && j>m) m=j;
  else if (argv[k][0]=='b' && j>n) n=j;
  if ((argv[k][0]=='g' && strg[j]>=0) ||
      (argv[k][0]=='b' && strb[j]>=0)) {
    fprintf(stderr,"You've already mentioned %s!\n",
                  argv[k]);
    exit(-4);
  }
  if (argv[k][0]==argv[k-1][0] && prevj>j) {
    fprintf(stderr,"Out of order: %s>%s!\n",
                          argv[k-1],argv[k]);
    exit(-5);
  }
  if (argv[k][0]=='b' && argv[k-1][0]!='b') d++;
  if (argv[k][0]=='g') strg[j]=d;@+else strb[j]=d;
}
if (argv[k-1][0]=='b') { /* parade ended with a boy: |d| is too large */
  for (j=1;j<=n;j++) if (strb[j]==d) strb[j]=0;
  d--;
}
for (j=1;j<=m;j++) if (strg[j]<0) {
  fprintf(stderr,"girl g%d is missing!\n",
                             j);
  exit(-7);
}
for (j=1;j<=n;j++) if (strb[j]<0) {
  fprintf(stderr,"boy b%d is missing!\n",
                             j);
  exit(-8);
}
fprintf(stderr,
  "OK, that's a valid parade of order %d with %d girls and %d boys!\n",
                     d,m,n);

@ @<Print the boilerplate to get Mathematica started@>=
printf("(* output from %s",
              argv[0]);
for (k=1;argv[k];k++) printf(" %s",
                       argv[k]);
printf(" *)\n");
printf("brace=StirlingS2\n");
printf("prank[inv_]:=Block[{sum=0,n=Length[inv]},\n");
printf(" For[j=1,j<n,j++,sum=(sum+inv[[j]])*(n-j)];sum]\n");
printf("srank[rgs_]:=Block[{sum=0,max=0,n=Length[rgs]},\n");
printf(" For[j=1,j<=n,j++,\n");
printf("  If[rgs[[j]]>max,max++;sum+=(max+1)brace[j,max+1],\n");
printf("   sum+=rgs[[j]]brace[j,max+1]]];\n");
printf(" sum]\n");
printf("extra = Sum[k!^2*brace[%d+1,k+1]*brace[%d+1,k+1],{k,0,%d}]\n",
             m,n,d-1@q}]@>);

@ @<Figure out the permutation and rgs for the girls@>=
for (j=1;j<=d;j++) hit[j]=-1;
for (k=0,j=1;j<=m;j++) {
  if (hit[strg[j]]<0) hit[strg[j]]=++k,perm[k]=strg[j];
  rgs[j]=hit[strg[j]];
}
fprintf(stderr,"girls' rgs is");
for (j=0;j<=m;j++) fprintf(stderr," %d",
                       rgs[j]);
fprintf(stderr,"\nand their permutation is");
for (j=1;j<=d;j++) fprintf(stderr," %d",
                       perm[j]);
fprintf(stderr,"\n");
printf("gperm=prank[{");
for (j=1;j<=d;j++) {
  if (j>1) printf(",");
  for (k=0,i=j+1;i<=d;i++) if (perm[i]<perm[j]) k++;
  printf("%d",
          k);
}
printf("}]\ngrgs=srank[{");
for (j=1;j<=m;j++) {
  if (j>1) printf(",");
  printf("%d",
          rgs[j]);
}
printf("}]\n");

@ @<Figure out the permutation and rgs for the boys@>=
for (j=1;j<=d;j++) hit[j]=-1;
for (k=0,j=1;j<=n;j++) {
  if (hit[strb[j]]<0) hit[strb[j]]=++k,perm[k]=strb[j];
  rgs[j]=hit[strb[j]];
}
fprintf(stderr,"boys' rgs is");
for (j=0;j<=n;j++) fprintf(stderr," %d",
                       rgs[j]);
fprintf(stderr,"\nand their permutation is");
for (j=1;j<=d;j++) fprintf(stderr," %d",
                       perm[j]);
fprintf(stderr,"\n");
printf("bperm=prank[{");
for (j=1;j<=d;j++) {
  if (j>1) printf(",");
  for (k=0,i=j+1;i<=d;i++) if (perm[i]<perm[j]) k++;
  printf("%d",
          k);
}
printf("}]\nbrgs=srank[{");
for (j=1;j<=n;j++) {
  if (j>1) printf(",");
  printf("%d",
          rgs[j]);
}
printf("}]\n");

@*Index.