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