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Overkill III: Permutations of Overkill (Perl6)

Long-time readers remember my previous code with the Magic Box. In short, given the numbers [ 3, 4, 5, 6, 7, 8, 9, 10, 11 ] , arrange them in a 3x3 square such that every row, column and diagonal adds up to 21.

My first pass, on a very old computer, had the C version taking a second and a half, the Perl5 version taking a minute and a half, and the Perl6 version taking an hour and a half. But I no longer use that computer, and am now using a much newer one, so I took the opportunity to try again.

I have Nvidia cards in my box, so I could eventually write Overkill IV about that, but I don't have the knowledge or time right now. I did install rakudobrew and the newest version of Perl6, but otherwise, everything was unchanged.

C dropped to 0.6 seconds. Perl5 now takes 16 seconds. Perl6 now takes 10 minutes. So, the newer computer brought substantial speed gains for each, but the most dramatic is with Perl6, which tells us that the Perl6 developers have not only worked on correctness and completeness, but speed. Good for them! Good for us!

But wait! There's more!

@loltimo saw the post and suggested that I use permutations.

"What are permutations?", you ask? That's what basically happens in recursive_magic_box(), where all the possible variations are created. Given A, B and C, there are six possible orderings: ABC ACB BAC BCA CAB CBA. If I was given all possible orderings of an array, rather than (mis)handling it on my own and having to check that I got it right, would that make things faster?

As it turns out, yes. 47 seconds, rather than 10 minutes. More than 10x faster. But still, not as fast as Perl5. I now want to implement permutations for Perl5 and see if it makes that one faster.

And, it makes me feel much better about Perl6.

Code Samples Below