note
BrowserUk
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<p>It makes a small -- insignificant -- difference to the outcome.
<p>A quick check -- because quicker than trying to derive a formula -- shows that of the 729,000 3-value combinations, 11,839 contain consecutive numbers:<code>
use Algorithm::Combinatorics qw[ variations_with_repetition ];;
@c = variations_with_repetition( [ 1 .. 90 ], 3 );;
print scalar @c;;
729000
$d = 0; $_->[0]+1 == $_->[1] or $_->[1]+1 == $_->[2] and ++$d for @c; print $d;;
7922
</code>
<p>And there are 8010 combinations of 2 sets of three that must be excluded because the last digit of the first set of 3 is one less that the first digit of the second set:<code>
$d = 0; $_->[0] == $_->[2]+1 and ++$d for @c; print $d;;
8010
</code>
<p>Which means that instead of 531,441,000,000 6-value combinations, there are only (729,000 - 7922 )**2 - 8010 = 519,953,474,074, which means it would still take 40-bits to represent any legal 6-value string; so the math doesn't change: ( 1 - 40/48 ) *100 = 16.67% is best possible for *any* dataset.
<P>Any algorithm that achieves better on any given dataset; will not achieve the same results for all datasets; nor even a high percentage of them.
<P>Ie. To achieve better, you'd need to reduce the size of the domain so that you could compress 36-bits into 48 which would give 25% compression. But that would require throwing away 87% of the possible datasets
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<div>With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'</div>
<div>Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.</div>
<div>"Science is about questioning the status quo. Questioning authority". [http://www.theregister.co.uk/2016/11/02/complexity_in_it/|The enemy of (IT) success is complexity.]</div>
<div>In the absence of evidence, opinion is indistinguishable from prejudice.
<span>[https://www.theregister.co.uk/2017/04/10/mark_shuttleworth_says_some_free_software_contributors_are_deeply_anti_social/|Suck that fhit]</span> </div>
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