89 lines
2.7 KiB
Markdown
89 lines
2.7 KiB
Markdown
---
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title: Entropy
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id: 599d15309e88c813a40baf58
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challengeType: 5
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---
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## Description
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<section id='description'>
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Task:
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<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>
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<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>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- 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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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function entropy (s) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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