Ryan J Thompson

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

We’re back with our noses to the mathematical grindstone this week, with two straightforward tasks.

Task 1 › Primordial Numbers

The n^th primordial number is simply the product of the first n primes. P(1) = 2, P(2) = 2×3 = 6, P(3) = 2x3x5 = 30, etc. P(0) is defined to be 1 as a special case. Since I’ve implemented various prime number generators before, I just went with Math::Prime::Util for this one, making use of the prime_iterator function:

my $it = prime_iterator;

say my $pri = 1; # P(0) = 1 by definition
say $pri *= $it->() for 1..$ARGV[0] // 10;

Easy.

Task 2 › Kronecker Products

I haven’t worked with Kronecker products for quite a few years, so when I reviewed the definition, I thought it might be tricky to implement, so I got a fresh caffeinated beverage, but much to my dismay, it was all over before my second sip.

Please do check that link for a more rigorous definition of Kronecker products. As a quick review, I will simply show an example, with ⨂ as the operator for the Kronecker product:

\(A = \begin{bmatrix}2 & 3 \\ 4 & 5 \end{bmatrix} \\
B = \begin{bmatrix}a & b \\ c & d \end{bmatrix} \)

\(A ⨂ B = \begin{bmatrix}
2 & 3 \\
4 & 5
\end{bmatrix} ⨂
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix} =
\begin{bmatrix}
2B & 3B \\ 4B & 5B
\end{bmatrix} =
\begin{bmatrix}
2a & 2b & 3a & 3b \\
2c & 2d & 3c & 3d \\
4a & 4b & 5a & 5b \\
4c & 4d & 5c & 5d
\end{bmatrix}
\)

To make this happen, I opted to loop over the total number of rows in A ⨂ B and use division and modulo arithmetic to determine which sub-row and -column in B we need. I use a triple-nested map to achieve the multiplications and orderings of the final matrix.

sub kronecker {
    my ($A, $B) = @_;

    map {
        my $i = $_;
        [
            map { 
                    my    $aval = $_;
                    map { $aval * $_ } $B->[$i % @$B]->@*;
            } $A->[$i / @$B]->@*
        ]
    } 0..(@$A * @$B)-1;
}

The post-deref (->@*) looked a bit cleaner here, so I went with that, but @{$B->[$i % @$B]} would have worked just as well.

The result is a list of array refs containing the rows of the final product. The problem description didn’t specify, but I opted to also include a pretty-print routine to display the output a little nicer than Data::Dump can:

sub pp_matrix {
    print '[ ' . join(' ', map { sprintf '%3d', $_ } @$_). " ]\n" for @_
}

The output from pp_matrix(kronecker([[1,2],[3,4]], [[5,6],[7,8]])) is nicely formatted:

[   5   6  10  12 ]
[   7   8  14  16 ]
[  15  18  20  24 ]
[  21  24  28  32 ]

We were only asked to implement the solution for a product of two specific 2×2 matrices, but both of the above subs accept arbitrary shaped matrices.

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

This week, both tasks are quite short, so I’ll combine them into a single blog post.

Task 1 › Brilliant Numbers

Brilliant numbers are composite numbers with exactly two prime factors. Additionally, the prime factors must be the same length.

My complete code is as follows:

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

Task #1 this week has us finding circular primes, 3 digits or more. Circular primes are numbers that remain prime through all of their rotations. For example, since all the rotations of 113 (113, 131, and 311) are all primes, 113 is a circular prime. (131 and 311 are circular primes as well, but based on the example given with this task, we are only to give the lowest circular prime in each group.) This would correspond with OEIS A016114.

I just wrote yet another Sieve of Eratosthenes in week 164, so this time I’ll just use Math::Prime::Util. The basic algorithm I came up with is rather naïve, but effective:

for each digit d in [3..∞)
    for each prime n with d digits
        for each unique rotation r
            next digit if circular[r] or ¬prime[r]
        circular[r] ← true
        say "r is circular"

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

Task #2 this week is another one of mine. The idea is to take any number of pathnames on the command line (and we must support at least three), and output a side-by-side diff of the files that are different. This is a skin-deep analysis, so there is no recursion, and no comparison of file sizes, modification times, or contents, although those would be worthy additions if someone wants to take it further.

I will be implementing a fairly basic version, although I have a more complex version I’ve been using for years that I might be persuaded to release if there is interest.

Data Design

I am going to have one main data structure, %dirs, that will be built up as we traverse the directories. It will hold all directory and file information, as well as a maxlen value for each directory, for ease of formatting columns later. Here’s what %dirs might look like, given a very simple set of input directories:

%dirs = (
  dir_a =>  {
      files  => {
                "Arial.ttf"       => 1,
                "Comic_Sans.ttf"  => 1,
              },
      maxlen => 14,
  },
  dir_b => {
      files  => {
                "Arial.ttf"       => 1,
                "Comic_Sans.ttf"  => 1,
                "Courier_New.ttf" => 1,
              },
      maxlen => 15,
  },
)

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

This is another one of my suggested tasks, and another time you’re going to read about a personal story that connects me to a task. For many years, right back to very first days I started hacking filesystems and writing kernel code, I’ve often needed to come up with 16- or 32-bit identifiers for things, usually represented in hexadecimal. And to this day, my repertoire of clever identifiers is more or less limited to 0xdeadbeef and 0xc0dedbad, and a few others. Let’s change that!

The simple version

A very simple solution simply reads the lines, filters out anything that isn’t the right length, or contains characters that can’t be substituted, and prints out the whole works:

use File::Slurper qw< read_lines >;

my $dict = $ARGV[0] // '../../../data/dictionary.txt';

say for map {     y/olist/01157/r    }
       grep { /^[0-9a-folist]{2,8}$/ } read_lines($dict);

That already gives me some great results, like 0xd15abled (“disabled”), and is nice and short. However, we didn’t come here for half measures. This version only returns single words, and doesn’t care how many substitutions it has done, so words like 0x57111e57 (“stillest”‽) are fair game.

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

The tasks this week are ones I devised. Allow me a moment to explain the motivation behind them.

I often have a need to quickly visualize some random bits of data, and while I’ve gotten great mileage out of terminal output, and things like gnuplot or spreadsheet imports, sometimes better and more convenient results are possible by generating the image myself.

There is ImageMagick (see perlmagick for a Perl interface), but its dependencies are heavy, and getting it to run at all on some systems (particularly the embedded systems I work on), can be challenging. And of course, it only works with raster images, which do not scale well.

Fortunately, it’s very easy to generate vector images with pure Perl (or most any language, for that matter). You can even do it easily without any CPAN modules, but remember, even you can use CPAN!

Enter Scalable Vector Graphics (SVG).

Raster images are comprised of a grid of pixels. Vector images use shapes like circles, lines, and curves. Because these are defined mathematically, vector images can be resized, squished, or rotated with no loss in quality.

Quick Introduction to SVG

For this task, I will be using the SVG module by Morgane Oger and recently maintained by our very own Mohammad Anwar. However, SVG files are simply XML documents, so it would not be much harder to generate the XML yourself. Here’s what SVG source looks like:

This post is part of a series on Mohammad Anwar’s excellent Weekly Challenge, where hackers submit solutions in Perl, Raku, or any other language, to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

The first task this week is to list all palindromic primes below 1000. Palindromes are very well known to Weekly Challenge enthusiasts as numbers (or words) that are the same forwards and backwards. Prime numbers should need no introduction.

Prime Sieve

I’m going to jump straight to it. Since the task is simple, I’m not going to use an external library such as Math::Prime::Util, even though that would be quite a bit faster. Instead, I’m going to generate the primes myself, using a Sieve of Eratosthenes. There are faster methods, but you can’t beat Eratosthenes for elegance!