@*Intro. This program makes {\mc DLX3} data for an interesting problem
posed by Ian Cullis in 2022: Fill a $10\times10$ array with 1s, 2s, 3s, 4s
so that there are exactly $k$ occurrences of $k$ in each row and each column.
Also the 2s should form nontouching dominoes, the 3s should form nontouching
trominoes, and the 4s should form nontouching ell-tetrominoes, where
``nontouching'' means not having edges in common.

This program is to be used with the UNIX command line
$$\.{cat ian.dat {\char124} polyomino-dlx {\char124} ian-dlx}$$
so that |stdin| contains appropriate data about the possible
configurations of individual polynominoes and their boundaries.

@d bufsize 1024

@c
#include <stdio.h>
#include <stdlib.h>
char buf[bufsize];
main() {
  register int i,j,k;
  @<Print the item-name line@>;
  @<Print the options for individual cells@>;
  @<Print the options for vetting polyominoes@>;
}

@ There are primary items $R_{ik}$ and $C_{jk}$ for $0\le i,j<10$ and
$1\le k\le 4$, indicating the number of $k$s in row or column~$k$.
There also are primary items $\#_{ij}$, meaning that cell $ij$ has
been ``vetted'' as a polyomino that matches its number.

There are secondary items $ijk$, which are essentially Boolean variables
that state whether or not cell~$ij$ contains~$k$.

I've also added primary items $ij$, with four options apiece. These aren't
necessary, but they speed up the search.

@<Print the item-name line@>=
for (i=0;i<10;i++) for (j=0;j<10;j++)
  printf("%d%d ",
             i,j);
for (i=0;i<10;i++) for (k=1;k<=4;k++)
  printf("%d|R%d%d %d|C%d%d ",
             k,i,k,k,i,k);
for (i=0;i<10;i++) for (j=0;j<10;j++)
  printf("#%d%d ",
               i,j);
printf("|");
for (i=0;i<10;i++) for (j=0;j<10;j++) for (k=1;k<=4;k++)
  printf(" %d%d%d",
             i,j,k);
printf("\n");

@ @<Print the options for individual cells@>=
for (i=0;i<10;i++) for (j=0;j<10;j++) {
  printf("%d%d R%d1 C%d1 %d%d1:1 %d%d2:0 %d%d3:0 %d%d4:0\n",
             i,j,i,j,i,j,i,j,i,j,i,j);
  printf("%d%d R%d2 C%d2 %d%d1:0 %d%d2:1 %d%d3:0 %d%d4:0\n",
             i,j,i,j,i,j,i,j,i,j,i,j);
  printf("%d%d R%d3 C%d3 %d%d1:0 %d%d2:0 %d%d3:1 %d%d4:0\n",
             i,j,i,j,i,j,i,j,i,j,i,j);
  printf("%d%d R%d4 C%d4 %d%d1:0 %d%d2:0 %d%d3:0 %d%d4:1\n",
             i,j,i,j,i,j,i,j,i,j,i,j);
}

@ @d less_one(k) (buf[k]=='a'? 9: buf[k]-'1')

@<Print the options for vetting polyominoes@>=
while (1) {
  if (!fgets(buf,bufsize,stdin)) break;
  switch (buf[0]) {
case '|': case ' ': continue;
case 'o': i=less_one(2),j=less_one(3);
  printf("#%d%d %d%d1:1",
             i,j,i,j);
  break;
case 'd': for (k=1;buf[k]==' ';k+=3) {
    i=less_one(k+1),j=less_one(k+2);
    if (buf[k+3]=='b') {
      k++;
      if (i>=0 && i<10 && j>=0 && j<10) printf("%d%d2:0 ",
               i,j);
    }@+else {
      printf("#%d%d %d%d2:1 ",
                   i,j,i,j);
    }
  }
  break;
case 'v': case 't': for (k=1;buf[k]==' ';k+=3) {
    i=less_one(k+1),j=less_one(k+2);
    if (buf[k+3]=='b') {
      k++;
      if (i>=0 && i<10 && j>=0 && j<10) printf("%d%d3:0 ",
               i,j);
    }@+else {
      printf("#%d%d %d%d3:1 ",
                   i,j,i,j);
    }
  }
  break;
case 'l': for (k=1;buf[k]==' ';k+=3) {
    i=less_one(k+1),j=less_one(k+2);
    if (buf[k+3]=='b') {
      k++;
      if (i>=0 && i<10 && j>=0 && j<10) printf("%d%d4:0 ",
               i,j);
    }@+else {
      printf("#%d%d %d%d4:1 ",
                   i,j,i,j);
    }
  }
  break;
default: fprintf(stderr,"Bad input line! %s",
                         buf);
  }
  printf("\n");
}

@*Index.