# ETOOBUSY ðŸš€ minimal blogging for the impatient

# PWC146 - Curious Fraction Tree

**TL;DR**

On with TASK #2 from The Weekly Challenge #146. Enjoy!

# The challenge

Consider the following

`Curious Fraction Tree`

:You are given a fraction, member of the tree created similar to the above sample.

Write a script to find out the parent and grandparent of the given member.

Example 1:`Input: $member = '3/5'; Output: parent = '3/2' and grandparent = '1/2'`

Example 2:`Input: $member = '4/3'; Output: parent = '1/3' and grandparent = '1/2'`

# The questions

This seems one of those *induction-based* challenges that can probably
give rise to a whole host of wildly different interpretations and
solutions. Iâ€™ll assume my take isâ€¦ the right one (also in lack of
alternatives, right now).

# The solution

From the example image, it seems that the parent of a valid node can be found as follows:

- every fraction has a numerator and a denominator
- if the numerator is smaller than the denominator, the parent shares the same numerator but the denominator is the difference between the denominator and the numerator from the child;
- otherwise, the parentâ€™s numerator is the difference between the two, and the denominator is the same as the child.

Easier coded than told, I suppose. Letâ€™s start with Perl:

```
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
my $member = shift // '4/3';
my $parent = parent_of($member);
my $grandparent = parent_of($parent);
say "parent = '$parent' and grandparent = '$grandparent'";
sub parent_of ($frac) {
my ($num, $den) = split m{/}mxs, $frac;
join '/', $num < $den ? ($num, $den - $num) : ($num - $den, $den);
}
```

Raku now:

```
#!/usr/bin/env raku
use v6;
sub MAIN (Str:D $member = '4/3') {
my $parent = parent-of($member);
my $grandparent = parent-of($parent);
put "parent = '$parent' and grandparent = '$grandparent'";
}
sub parent-of ($frac) {
my ($n, $d) = $frac.split: '/';
($n < $d ?? ($n, $d - $n) !! ($n - $d, $d)).join: '/';
}
```

Itâ€™s basically the same code, just a bit Raku-ized.

Soâ€¦ I hope I did read the challenge right! Anyway, stay safe everybody!