RogerBW's Blog

Perl Weekly Challenge 47: roman calculator and gapful numbers 09 March 2020

I’ve been doing the Perl Weekly Challenges. The latest was about doing Roman arithmetic and generating gapful numbers.

In keeping with my self-imposed rules, I installed the Roman module for Perl5. Then it's just a matter of validating everything and doing the conversions.

use Roman;

my %ol=map {$_ => 1} qw(+ - * /);
my ($a,$op,$b)=@ARGV;

unless (isroman($a)) {
  die "$a is not a valid Roman number\n";
}
unless (exists $ol{$op}) {
  die "$op is not a valid operation\n";
}
unless (isroman($b)) {
  die "$a is not a valid Roman number\n";
}

$a=arabic($a);
$b=arabic($b);
my $c;
if ($op eq '+') {
  $c=$a+$b;
} elsif ($op eq '-') {
  $c=$a-$b;
} elsif ($op eq '*') {
  $c=$a*$b;
} else {
  $c=int($a/$b);
}
if ($c<1 || $c>3999) {
  die "Result $c is out of range\n";
}

print Roman($c),"\n";

For Perl6 I kept the same conversion interface but had to implement the back-end as well, which was rather more interesting. (It will probably miss some invalid Roman numbers, though.) The Roman to Arabic conversion generates a set of matches for each digit place and checks them in descending length order. Probably greedy regexps would do this automatically but I was having a busy day.

The nested flag-checks were needed because last LABEL didn't work as the documentation described it.

sub roman ($in) {
  my @pattern=('','0','00','000','01','1','10','100','1000','02');
  my @phase=(('m','',''),('c','d','m'),('x','l','c'),('i','v','x'));
  if ($in > 3999 or $in < 1) {
    die "$in is out of range\n";
  }
  my @l=comb(/\d/,sprintf('%04d',truncate($in)));
  my $out='';
  for (0..3) -> $phase {
    my $p=@pattern[@l[$phase]];
    for (0..2) -> $ix {
      $p ~~ s:g/$ix/@phase[$phase][$ix]/;
    }
    $out ~= $p;
  }
  return $out;
}

sub Roman ($in) {
 return uc(roman($in));
}

sub arabic ($in) {
  my $im=$in;
  my @pattern=('','0','00','000','01','1','10','100','1000','02');
  my @phase=(('m','?','?'),('c','d','m'),('x','l','c'),('i','v','x'));
  my $mul=1000;
  my $n=0;
  for (0..3) -> $phase {
    my %r;
    for (1..9) -> $pi {
      my $p=@pattern[$pi];
      for (0..2) -> $ix {
        $p ~~ s:g/$ix/@phase[$phase][$ix]/;
      }
      %r{$p.chars}{$p}=$pi;
    }
    my $flag=0;
    for (4,3,2,1) -> $l {
      for (keys %r{$l}) -> $k {
        if ($im ~~ s:i/^$k//) {
          $n += $mul*%r{$l}{$k};
          $flag=1;
          last;
        }
        if ($flag) {
          last;
        }
      }
      if ($flag) {
        last;
      }
    }
    $mul /= 10;
  }
  if ($im) {
    return 0;
  }
  return $n;
}

sub isroman ($in) {
  return (!arabic($in)==0);
}

Part 2 was much simpler: a gapful number is divisible by the concatenation of its first and last digits.

my $count=20;
my $n=100;

while ($count>0) {
  $n =~ /^(.).*(.)/;
  my $d=$1.$2;
  if ($n % $d == 0) {
    print "$n\n";
    $count--;
  }
  $n++;
}

For Perl6 I got a little sneaky with the Match object.

#! /usr/bin/perl6

my $count=20;
my $n=100;

while ($count>0) {
  $n ~~ /^(.).*(.)/;
  my $d=$/.list.join('');
  if ($n % $d == 0) {
    print "$n\n";
    $count--;
  }
  $n++;
}

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