91 lines
2.8 KiB
Markdown
91 lines
2.8 KiB
Markdown
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---
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title: Hofstadter Q sequence
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id: 59637c4d89f6786115efd814
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localeTitle: 59637c4d89f6786115efd814
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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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<p> La <a href="https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Q_sequence" title="wp: Hofstadter_sequence # Hofstadter_Q_sequence">secuencia de Hofstadter Q</a> se define como: </p>
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<p> $ Q (1) = Q (2) = 1, \\ Q (n) = Q \ big (nQ (n-1) \ big) + Q \ big (nQ (n-2)), \ quad n> 2. $ </p>
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<p> Se define como la <a href="http://rosettacode.org/wiki/Fibonacci sequence" title="secuencia Fibonacci">secuencia de Fibonacci</a> , pero mientras que el siguiente término en la secuencia de Fibonacci es la suma de los dos términos anteriores, en la secuencia Q los dos términos anteriores le dicen a qué distancia retroceder en la secuencia Q para encontrar los dos números Para sumar hacer el siguiente término de la secuencia. </p>
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Tarea:
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Implementar la ecuación de secuencia Q de Hofstadter en JavaScript
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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>hofstadterQ</code> es una función.
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testString: 'assert(typeof hofstadterQ === "function", "<code>hofstadterQ</code> is a function.");'
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- text: <code>hofstadterQ()</code> debe devolver un <code>integer</code>
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testString: 'assert(Number.isInteger(hofstadterQ(1000)), "<code>hofstadterQ()</code> should return <code>integer</code>");'
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- text: <code>hofstadterQ(1000)</code> debe devolver <code>502</code>
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testString: 'assert.equal(hofstadterQ(testCase[0]), res[0], "<code>hofstadterQ(1000)</code> should return <code>502</code>");'
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- text: <code>hofstadterQ(1500)</code> debe devolver <code>755</code>
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testString: 'assert.equal(hofstadterQ(testCase[1]), res[1], "<code>hofstadterQ(1500)</code> should return <code>755</code>");'
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- text: <code>hofstadterQ(2000)</code> debe devolver <code>1005</code>
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testString: 'assert.equal(hofstadterQ(testCase[2]), res[2], "<code>hofstadterQ(2000)</code> should return <code>1005</code>");'
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- text: <code>hofstadterQ(2500)</code> debe devolver <code>1261</code>
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testString: 'assert.equal(hofstadterQ(testCase[3]), res[3], "<code>hofstadterQ(2500)</code> should return <code>1261</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 hofstadterQ (n) {
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// Good luck!
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return n;
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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console.info('after the test');
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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 hofstadterQ (n) {
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const memo = [1, 1, 1];
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const Q = function (i) {
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let result = memo[i];
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if (typeof result !== 'number') {
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result = Q(i - Q(i - 1)) + Q(i - Q(i - 2));
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memo[i] = result;
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}
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return result;
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};
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return Q(n);
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}
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```
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</section>
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