97 lines
1.8 KiB
Markdown
97 lines
1.8 KiB
Markdown
---
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id: 599d15309e88c813a40baf58
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title: Entropy
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challengeType: 5
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forumTopicId: 302254
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dashedName: entropy
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---
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# --description--
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Calculate the Shannon entropy H of a given input string.
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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:
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$H_2(X) = -\\sum\_{i=1}^n \\frac{count_i}{N} \\log_2 \\left(\\frac{count_i}{N}\\right)$
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where $count_i$ is the count of character $n_i$.
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# --hints--
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`entropy` should be a function.
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```js
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assert(typeof entropy === 'function');
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```
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`entropy("0")` should return `0`
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```js
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assert.equal(entropy('0'), 0);
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```
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`entropy("01")` should return `1`
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```js
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assert.equal(entropy('01'), 1);
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```
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`entropy("0123")` should return `2`
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```js
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assert.equal(entropy('0123'), 2);
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```
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`entropy("01234567")` should return `3`
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```js
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assert.equal(entropy('01234567'), 3);
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```
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`entropy("0123456789abcdef")` should return `4`
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```js
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assert.equal(entropy('0123456789abcdef'), 4);
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```
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`entropy("1223334444")` should return `1.8464393446710154`
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```js
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assert.equal(entropy('1223334444'), 1.8464393446710154);
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```
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# --seed--
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## --seed-contents--
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```js
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function entropy(s) {
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}
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```
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# --solutions--
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```js
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function entropy(s) {
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// Create a dictionary of character frequencies and iterate over it.
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function process(s, evaluator) {
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let h = Object.create(null),
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k;
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s.split('').forEach(c => {
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h[c] && h[c]++ || (h[c] = 1); });
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if (evaluator) for (k in h) evaluator(k, h[k]);
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return h;
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}
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// Measure the entropy of a string in bits per symbol.
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let sum = 0,
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len = s.length;
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process(s, (k, f) => {
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const p = f / len;
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sum -= p * Math.log(p) / Math.log(2);
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});
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return sum;
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}
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```
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