Entropy

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Calculate the Shannon entropy H of a given input string.

Given the discreet random variable $X$ that is a string of $N$ "symbols" (total characters) consisting of $n$ different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is:

$H_2(X) = -\sum_{i=1}^n \frac{count_i}{N} \log_2 \left(\frac{count_i}{N}\right)$

where $count_i$ is the count of character $n_i$.