79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
89 lines
2.6 KiB
Markdown
89 lines
2.6 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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