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86 lines
2.5 KiB
Markdown
86 lines
2.5 KiB
Markdown
---
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title: Entropy
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id: 599d15309e88c813a40baf58
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challengeType: 5
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forumTopicId: 302254
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localeTitle: Энтропия
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---
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## Description
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<section id='description'>
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Задача: <p> Вычислите энтропию Шеннона H данной входной строки. </p><p> Учитывая выборочную случайную переменную $ X $, которая представляет собой строку из $ N $ "символов" (всего символов), состоящую из $ n $ различных символов (n = 2 для двоичных), энтропия Шеннона X в битах / символе: </p><p> $ H_2 (X) = - \ sum_ {i = 1} ^ n \ frac {count_i} {N} \ log_2 \ left (\ frac {count_i} {N} \ right) $ </p><p> где $ count_i $ - количество символов $ 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');
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- text: <code>entropy("0")</code> should return <code>0</code>
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testString: assert.equal(entropy('0'), 0);
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- text: <code>entropy("01")</code> should return <code>1</code>
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testString: assert.equal(entropy('01'), 1);
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- text: <code>entropy("0123")</code> should return <code>2</code>
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testString: assert.equal(entropy('0123'), 2);
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- text: <code>entropy("01234567")</code> should return <code>3</code>
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testString: assert.equal(entropy('01234567'), 3);
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- text: <code>entropy("0123456789abcdef")</code> should return <code>4</code>
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testString: assert.equal(entropy('0123456789abcdef'), 4);
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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);
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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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