freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/rosetta-code/entropy.md

title	id	challengeType	forumTopicId
Entropy	599d15309e88c813a40baf58	5	302254

Description

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 $n_i$.

Instructions

Tests

tests:
  - text: <code>entropy</code> should be a function.
    testString: assert(typeof entropy === 'function');
  - text: <code>entropy("0")</code> should return <code>0</code>
    testString: assert.equal(entropy('0'), 0);
  - text: <code>entropy("01")</code> should return <code>1</code>
    testString: assert.equal(entropy('01'), 1);
  - text: <code>entropy("0123")</code> should return <code>2</code>
    testString: assert.equal(entropy('0123'), 2);
  - text: <code>entropy("01234567")</code> should return <code>3</code>
    testString: assert.equal(entropy('01234567'), 3);
  - text: <code>entropy("0123456789abcdef")</code> should return <code>4</code>
    testString: assert.equal(entropy('0123456789abcdef'), 4);
  - text: <code>entropy("1223334444")</code> should return <code>1.8464393446710154</code>
    testString: assert.equal(entropy('1223334444'), 1.8464393446710154);

Challenge Seed

function entropy(s) {

}

Solution

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;
}