96 lines
3.3 KiB
Markdown
96 lines
3.3 KiB
Markdown
---
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id: 5a23c84252665b21eecc8028
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title: Stern-Brocot sequence
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challengeType: 5
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forumTopicId: 302324
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---
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## Description
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<section id='description'>
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For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the <a href="https://rosettacode.org/wiki/Fibonacci sequence" target="_blank">Fibonacci sequence</a>.
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<ol>
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<li>The first and second members of the sequence are both 1:</li>
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<ul><li>1, 1</li></ul>
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<li>Start by considering the second member of the sequence</li>
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<li>Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the
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sequence:</li>
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<ul><li>1, 1, 2</li></ul>
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<li>Append the considered member of the sequence to the end of the sequence:</li>
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<ul><li>1, 1, 2, 1</li></ul>
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<li>Consider the next member of the series, (the third member i.e. 2)</li>
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<li>GOTO 3 </li>
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<ul>
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<li></li>
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<li> ─── Expanding another loop we get: ───</li>
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<li></li>
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</ul>
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<li>Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the
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sequence:</li>
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<ul><li>1, 1, 2, 1, 3</li></ul>
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<li>Append the considered member of the sequence to the end of the sequence:</li>
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<ul><li>1, 1, 2, 1, 3, 2</li></ul>
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<li>Consider the next member of the series, (the fourth member i.e. 1)</li>
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</ol>
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</section>
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## Instructions
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<section id='instructions'>
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Create a function that returns the $ n^{th} $ member of the sequence using the method outlined above.
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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>sternBrocot</code> should be a function.
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testString: assert(typeof sternBrocot == 'function', '<code>sternBrocot</code> should be a function.');
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- text: <code>sternBrocot(2)</code> should return a number.
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testString: assert(typeof sternBrocot(2) == 'number', '<code>sternBrocot(2)</code> should return a number.');
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- text: <code>sternBrocot(2)</code> should return <code>3</code>.
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testString: assert.equal(sternBrocot(2), 3, '<code>sternBrocot(2)</code> should return <code>3</code>.');
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- text: <code>sternBrocot(3)</code> should return <code>5</code>.
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testString: assert.equal(sternBrocot(3), 5, '<code>sternBrocot(3)</code> should return <code>5</code>.');
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- text: <code>sternBrocot(5)</code> should return <code>11</code>.
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testString: assert.equal(sternBrocot(5), 11, '<code>sternBrocot(5)</code> should return <code>11</code>.');
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- text: <code>sternBrocot(7)</code> should return <code>19</code>.
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testString: assert.equal(sternBrocot(7), 19, '<code>sternBrocot(7)</code> should return <code>19</code>.');
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- text: <code>sternBrocot(10)</code> should return <code>39</code>.
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testString: assert.equal(sternBrocot(10), 39, '<code>sternBrocot(10)</code> should return <code>39</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 sternBrocot(num) {
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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 sternBrocot(num) {
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function f(n) {
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return n < 2 ? n : (n & 1) ? f(Math.floor(n / 2)) + f(Math.floor(n / 2 + 1)) : f(Math.floor(n / 2));
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}
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function gcd(a, b) {
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return a ? a < b ? gcd(b % a, a) : gcd(a % b, b) : b;
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}
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var n;
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for (n = 1; f(n) != num; n++);
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return n;
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}
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```
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</section>
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