### PWC 164 › Happy Numbers

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 comes to us from Robert DiCicco, and Robert demands happiness! Or at least numbers that are happy. Either way, I could use some right about now.

We are to find the first 8 Happy Numbers in base 10. To test whether a number is Happy:

replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1.

Those numbers for which this process end in 1 are happy numbers, while those numbers that do not end in 1 are unhappy numbers.

Weekly Challenge #164

## If You’re Happy and You Know It return 1

Using the algorithm exactly as described above, the Perl code is straightforward:

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### PWC 163 › A tail of two sums

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’s challenges are very quick, so I’m putting them in one blog post. The title is a bit of a play on words, given the tail recursion in part 2.

Full solutions are available at GitHub.

## Task 1 › Bitwise Sum

For the first task, we’re asked to first bitwise AND (&) each unique pair of numbers, and then compute the sum of those operations. So, given an input of (a, b, c), we would compute:

a & b + a & c + b & c

To formalize this a bit, in preparation for writing the code, consider a pair (ni, nj) where i and j are the indices in the input array. Unique pairs could be interpreted to mean ji. However, the provided example clearly implies that self pairs are to be avoided, so we’ll include pairs where j > i. So for an array of length k (n1 … nk), this looks like:

$${ \displaystyle \sum \limits_{i=1}^{k} } \sum_{j=i+1}^{k} n_i\ \&\ n_j$$

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### PWC 162 › Wheatstone–Playfair Cipher

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.)

Challenge #2 this week asks us to implement a version of the Playfair Cipher, which is a simple symmetric key cipher, invented in 1854 by Charles Wheatstone, that was used with pencil and paper. It ended up being called the Playfair Cipher because⁠—as I understand it⁠—the ironically named Lord Playfair promoted its use and basked in the glory.

This cipher was used by the Brits up to and including the First World War, to encrypt messages sent via telegraph. Without the key, messages can be decrypted eventually (and it’s easier, the longer the ciphertext, as it is vulnerable to frequency analysis), but the British knew that by the time the enemy decoded the message, the information would no longer be relevant.

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### PWC 162 › ISBN-13

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‘s first task is simple: validate ISBN-13 codes.

ISBNs have been around for a long time and come in many different flavours. ISBN-13 is a thirteen-digit code consisting of twelve digits plus a check digit. The checksum calculation is simple. Given the digits x1, x2, …, x12, and the check digit, x13:

(10 – (x1 + 3x2 + x3 + 3x4 + … + x11 + 3x12 + x13)) ≡ 0 (mod 10)

To make calculation a little easier, we can move the check digit (x13) out of the sum and compare it at the end. For example, given the code 978-0-306-40615-7, we can calculate:

10 – (9 + 3×7 + 8 + 3×0 + 3 + 3×0 + 6 + 3×4 + 0 + 3×6 + 1 + 3×5) % 10) = 7

Using List::Util‘s pairmap function, we can simplify the calculation significantly:

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### PWC 161 › Pangrams

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.)

For this week’s second challenge, the task is to generate a pangram.

A pangram is simply a collection of words that contain every letter in the alphabet (English, in this case). A classic pangram example is:

the quick brown fox jumped over the lazy dog

Wikipedia

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### PWC 161 › Abecedarian Words

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.)

I know, it’s been a long time!

This week, I’m back. I submitted the challenges for this week, so I thought it’s only fair that I give them a go myself. Unfortunately, I realized too late that this Abecedarian Words is essentially the same as Week 111’s “Ordered Letters” submitted by the venerable E. Choroba. I thought we hadn’t done it. Nuts. I’m sorry.

### Challenge Description

An abecedarian word is a word whose letters are arranged in alphabetical order. For example, “knotty” is an abecedarian word, but “knots” is not. Output or return a list of all abecedarian words in the dictionary, sorted in decreasing order of length.

From: PWC Challenge #161
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### PWC 110 › Phone Number Validation

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.)

Personal note: I’ve had to take a break from participating in the PWC, but I’m back for this week, at least. Hopefully I’ll be able to contribute more again.

The first task this week is a sort of simple phone number validation, based on provided templates. Numbers must match the following, where n is any decimal digit:

+nn  nnnnnnnnnn
(nn) nnnnnnnnnn
nnnn nnnnnnnnnn


Based on the provided sample output, it seems clear that leading and trailing whitespace are ignored. Internal whitespace is also compressed, as the first provided template has two spaces after +nn, yet the phone number +44 1148820341 is supposed to match.

Let’s try two different methods of matching, with Perl and Raku.

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### PWC 110 › Transpose CSV File

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 second task this week is simple: given a (simplified) comma-separated-value (CSV) file, transpose its rows and columns. For example:

$$\begin{bmatrix} A & B & C & D \\ 1 & 2 & 3 & 4 \\ w & x & y & z \end{bmatrix}^T \Rightarrow \begin{bmatrix} A & 1 & w \\ B & 2 & x \\ C & 3 & y \\ D & 4 & z \end{bmatrix}$$

The challenge task does not actually refer to the input as CSV, so I’m using that term loosely, with simplified parsing to match the input specification. If more compliant parsing is needed, one could use the usual Text::CSV module in Perl, or ports in Raku.

There are a couple of ways to transpose files, which I’ll explore in Raku and Perl.

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### PWC 056 › Path Sum

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 a simple tree traversal:

You are given a binary tree and a sum, write a script to find if the tree has a path such that adding up all the values along the path equals the given sum. Only complete paths (from root to leaf node) may be considered for a sum.

For both my Perl and Raku versions, I’m going super-lean with the implementation, using only array references. The “node,” which recursively defines an entire (sub)tree, looks like this:

• Element 0: Node’s value
• Elements 1..N: References to child nodes

Thus, the (Raku) syntax my @tree = [10, [18, [5], [2]], [8, [16, [18]], [9]]] describes a tree that looks like this:

              10
/    \
18     8
/ \    / \
5   2  16  9
/
18


If we look for a path sum of 30, there is precisely one path with that sum: 10 18 2.

It’s worth noting that, although the task is limited to binary trees, my implementation will handle m-ary trees. Forcing it to handle only binary trees would actually be slightly more difficult, and a lot less useful.

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### PWC 056 › Diff-K

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 is to implement the Diff-K algorithm, as explained by Mohammad:

You are given an array @N of positive integers (sorted) and another non negative integer k. Write a script to find if there exists 2 indices i and j such that A[i] – A[j] = k and i != j.

This one is pretty easy. We can boil down the solution into two operations for each element ($_) of @N: • First, filter @N for elements where$k+$_ exists in @N. • For the remaining elements, return an array containing the indexes of$k+$_ and$_.

To make this easier and more efficient, we’ll create an %idx_of hash to store the index of each element in @N. This can be created in linear time, and gives us O(1) lookups for both operations, above.

I really like how easy it is to create a reverse hash like this in Raku:

my %idx_of = @N.antipairs;

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