Entropy

Entropy
You are encouraged to solve this task according to the task description, using any language you may know.

Calculate the entropy (shannon entropy) of a given input sequence. Use "1223334444" as an example sequence. The result should be around 1.84644 bits.

Burlesque

<lang burlesque> blsq ) "1223334444"F:u[vv^^{1\/?/2\/LG}m[?*++ 1.8464393446710157 </lang>

Haskell

<lang haskell> import Data.List

main = print $ entropy "1223334444"

entropy s =

sum . map lg' . fq' . map (fromIntegral.length) . group . sort $ s
 where lg' c = (c * ) . logBase 2 $ 1.0 / c
       fq' c = map (\x -> x / (sum c)) c 

</lang>

Perl 6

<lang Perl 6>sub entropy(@a) {

   my %count; %count{$_}++ for @a;
   my @p = %count.values »/» @a.elems;
   -log(2) R/ [+] map { $_ * log $_ }, @p;

}

say entropy "1223334444".comb;</lang>