# ETOOBUSY ðŸš€ minimal blogging for the impatient

# PWC156 - Weird Number

**TL;DR**

On with TASK #2 from The Weekly Challenge #156. Enjoy!

# The challenge

You are given number,

`$n > 0`

.Write a script to find out if the given number is a

`Weird Number`

.According to Wikipedia, it is defined as:

The sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.

Example 1:`Input: $n = 12 Output: 0 Since the proper divisors of 12 are 1, 2, 3, 4, and 6, which sum to 16; but 2 + 4 + 6 = 12.`

Example 2:`Input: $n = 70 Output: 1 As the proper divisors of 70 are 1, 2, 5, 7, 10, 14, and 35; these sum to 74, but no subset of these sums to 70.`

# The questions

Whatâ€™s in the challenges this week? Is there anything that calls for lazy, brutey force attacks, or is it just me?

# The solution

As anticipated, Iâ€™m very lazy this week. This totally reflects in the
Perl solution, where I summon *three* different modules to get the
job done:

```
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
use FindBin '$Bin';
use lib "$Bin/local/lib/perl5";
use Algorithm::Knapsack;
use ntheory 'divisors';
use List::Util 'sum';
say $_, ' ', is_weird($_) for (@ARGV ? @ARGV : (12, 70));
sub is_weird ($n) {
my @divs = reverse divisors($n);
shift @divs if @divs > 1;
return 0 if $n >= sum @divs;
my $ks = Algorithm::Knapsack->new(capacity => $n, weights => \@divs);
$ks->compute;
for my $solution ($ks->solutions) {
my $sum = sum @divs[$solution->@*];
return 0 if $sum == $n;
}
return 1;
}
```

Need the divisors? There you go, ntheory.

Need to arrange good approximations? There you go, Algorithm::Knapsack.

Need to do sums? There you go, List::Util.

Need some glue? There you go, Perl.

The Raku *translation* shows even more lazyness. While some stuff is
included just like the batteries, like a handy `sum`

method, looking for
proper divisors and using the knapsack algorithm is harder because a
very lazy search did not make anything *stand out*. So I opted for
implementing stuff just to minimize the waste of time for *looking* a
pre-made solution. Iâ€™m ashamed.

Here it is:

```
#!/usr/bin/env raku
use v6;
sub MAIN (*@args) {
my @inputs = @args ?? |@args !! (12, 70);
@inputs.map({
put $_, ' ', is-weird($_);
});
}
sub proper-divisors (Int:D $n) { (1..($n/2)).grep: $n %% * }
sub is-weird (Int:D $n) {
my @divs = proper-divisors($n);
return 0 if @divs.sum <= $n;
loop {
my $sum = @divs.sum;
return 0 if $sum == $n;
return 1 if $sum < $n;
my $ms = @divs.pop;
my $target = $n - $ms;
for (^(2 ** @divs.elems)).reverse -> $k is copy {
my $sum = 0;
my $i = 0;
while $k > 0 {
$sum += @divs[$i] if $k +& 1;
return 0 if $target == $sum;
++$i;
$k +>= 1;
}
}
}
}
```

I guess the implementation if `is-weird`

is closer to what I was
expected to do. I mean, what *I think* I *might have been expected* to
do, i.e. code a solution specific to the problem. Whatever, the Perl
solution is a solution too.

Anyway, here Iâ€™m trying to find out if thereâ€™s an arrangement that sums
up exactly to the input number, *except* that Iâ€™m trying to bail out
early if conditions donâ€™t apply any more. This is obtained by
considering the sums with the highest number(s) first, eliminating them
on the way. When we end up with a residual list whose sum is lower than
the target number, thereâ€™s no way to select a subset that sums exactly
to that and we can safely return early. Not too much of an optimization
but still.

The `proper-divisors`

function finally gave me the occasion to use the
*whatever* variable in a `grep`

. So far I could not manage to get it
right, but as you can see Iâ€™m still trying.

You might have observed that Iâ€™m using the first singular person a lot here, instead of a more inclusive first plural version. This is because I take full responsibility for not thinking too much about the solution to the challenge, and I donâ€™t want to make it appear like itâ€™s somebody elseâ€™s fault too.

Letâ€™s hope the best for people in Ukraine, and the rest of the places that are in a war!

*Comments? Octodon, , GitHub, Reddit, or drop me a line!*