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Entropy

curriculum/challenges/english/blocks/rosetta-code-challenges/599d15309e88c813a40baf58.md

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--description--

Calculate the Shannon entropy H of a given input string.

Given the discrete 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 $n_i$.

--hints--

entropy should be a function.

js
assert(typeof entropy === 'function');

entropy("0") should return 0

js
assert.equal(entropy('0'), 0);

entropy("01") should return 1

js
assert.equal(entropy('01'), 1);

entropy("0123") should return 2

js
assert.equal(entropy('0123'), 2);

entropy("01234567") should return 3

js
assert.equal(entropy('01234567'), 3);

entropy("0123456789abcdef") should return 4

js
assert.equal(entropy('0123456789abcdef'), 4);

entropy("1223334444") should return 1.8464393446710154

js
assert.equal(entropy('1223334444'), 1.8464393446710154);

--seed--

--seed-contents--

js
function entropy(s) {

}

--solutions--

js
function entropy(s) {
    // Create a dictionary of character frequencies and iterate over it.
  function process(s, evaluator) {
    let h = Object.create(null),
      k;
    s.split('').forEach(c => {
      h[c] && h[c]++ || (h[c] = 1); });
    if (evaluator) for (k in h) evaluator(k, h[k]);
    return h;
  }
    // Measure the entropy of a string in bits per symbol.

  let sum = 0,
    len = s.length;
  process(s, (k, f) => {
    const p = f / len;
    sum -= p * Math.log(p) / Math.log(2);
  });
  return sum;
}