90 lines
2.8 KiB
Markdown
90 lines
2.8 KiB
Markdown
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---
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title: Entropy
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id: 599d15309e88c813a40baf58
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localeTitle: 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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Tarea:
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<p> Calcule la entropía H de Shannon de una cadena de entrada dada. </p><p> Dada la discreta variable aleatoria $ X $ que es una cadena de $ N $ "símbolos" (caracteres totales) que consta de $ n $ caracteres diferentes (n = 2 para binario), la entropía de X de Shannon en bits / símbolo es: </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> donde $ count_i $ es el conteo del carácter $ 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> es una función.
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testString: 'assert(typeof entropy === "function", "<code>entropy</code> is a function.");'
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- text: <code>entropy("0")</code> debe devolver <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> debe devolver <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> debe devolver <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> debe devolver <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> debe devolver <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> debe devolver <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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