Disarium Numbers: brute force won't cut it


A brute force attack to the Disarium Numbers challenge did not work for me.

My routine for The Weekly Challenge is to attack the first one in Raku then Perl order and the second one the other way around.

My approach is also to use brute force whenever possible, even though I feel that there might be more to it. There’s an interesting internal tension between the more scientific part that would like to know more, and the more engineering part that just wants to get the job done with as few resources as possible (I mean, my resources).

So this time I went for the usual way and wrote a very basic brute-force solution in Raku:

#!/usr/bin/env raku
use v6;
sub MAIN (Int:D $n where * > 0 = 19) {
   my $candidate = 0;
   my $i = 0;
   while $i < $n {
      if is-disarium($candidate) {
         "\%0{$n.chars()}d. %d".sprintf(++$i, $candidate).put;

sub is-disarium (Int:D $n where $n >= 0) {
   $n == $n.comb.kv.map(-> $x, $y { $y ** ($x + 1) }).sum;

Curiously, it took me ages to get the map right, first because I initially used pairs instead of kv, which put me incredibly close to the event horizon of a black hole from where I would have never escaped (except, possibly, as Hawking radiation), and second because I was insisting on round parentheses around $x, $y, which are not needed when using ->. Ouch.

This program gets the first 18 Disarium Numbers pretty quickly, but it takes ages for the 19th. Which is needed to complete the challenge.

So yes, the code above will find the requested solution… eventually. Yet it takes too much to accept it, even by engineering standards.

I’ll leave with a final note about the need for exactly 19 members of the Disarium Numbers 20-members family. I mean, that’s being mean in two senses:

  • the 19th member is considerably greater than the first 18, which means that brute-force approaches will suffer (at least in languages that have margins for optimization);
  • the 20th member feels excluded. I mean, it’s the last one and there’s no other after, why leave it outside in the cold? Or, well, in the heat, if you’re in Roma these times?

See you next time!

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