---
title: Entropy
id: 599d15309e88c813a40baf58
challengeType: 5
---

## Description
<section id='description'>
Task:
<p>Calculate the Shannon entropy  H  of a given input string.</p><p>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 :</p>
<p>$H_2(X) = -\sum_{i=1}^n \frac{count_i}{N} \log_2 \left(\frac{count_i}{N}\right)$</p><p>where $count_i$ is the count of character $n_i$.</p>
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

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

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function entropy (s) {
  // Good luck!
}
```

</div>



</section>

## Solution
<section id='solution'>


```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;
}

```

</section>