22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
106 lines
2.9 KiB
Markdown
106 lines
2.9 KiB
Markdown
---
|
|
id: 5a23c84252665b21eecc8028
|
|
title: Stern-Brocot sequence
|
|
challengeType: 5
|
|
isHidden: false
|
|
forumTopicId: 302324
|
|
---
|
|
|
|
## Description
|
|
|
|
<section id='description'>
|
|
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>.
|
|
<ol>
|
|
<li>The first and second members of the sequence are both 1:</li>
|
|
<ul><li>1, 1</li></ul>
|
|
<li>Start by considering the second member of the sequence</li>
|
|
<li>Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the
|
|
sequence:</li>
|
|
<ul><li>1, 1, 2</li></ul>
|
|
<li>Append the considered member of the sequence to the end of the sequence:</li>
|
|
<ul><li>1, 1, 2, 1</li></ul>
|
|
<li>Consider the next member of the series, (the third member i.e. 2)</li>
|
|
<li>GOTO 3 </li>
|
|
<ul>
|
|
<li></li>
|
|
<li> ─── Expanding another loop we get: ───</li>
|
|
<li></li>
|
|
</ul>
|
|
<li>Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the
|
|
sequence:</li>
|
|
<ul><li>1, 1, 2, 1, 3</li></ul>
|
|
<li>Append the considered member of the sequence to the end of the sequence:</li>
|
|
<ul><li>1, 1, 2, 1, 3, 2</li></ul>
|
|
<li>Consider the next member of the series, (the fourth member i.e. 1)</li>
|
|
</ol>
|
|
</section>
|
|
|
|
## Instructions
|
|
|
|
<section id='instructions'>
|
|
Create a function that returns the $ n^{th} $ member of the sequence using the method outlined above.
|
|
</section>
|
|
|
|
## Tests
|
|
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>sternBrocot</code> should be a function.
|
|
testString: assert(typeof sternBrocot == 'function');
|
|
- text: <code>sternBrocot(2)</code> should return a number.
|
|
testString: assert(typeof sternBrocot(2) == 'number');
|
|
- text: <code>sternBrocot(2)</code> should return <code>3</code>.
|
|
testString: assert.equal(sternBrocot(2), 3);
|
|
- text: <code>sternBrocot(3)</code> should return <code>5</code>.
|
|
testString: assert.equal(sternBrocot(3), 5);
|
|
- text: <code>sternBrocot(5)</code> should return <code>11</code>.
|
|
testString: assert.equal(sternBrocot(5), 11);
|
|
- text: <code>sternBrocot(7)</code> should return <code>19</code>.
|
|
testString: assert.equal(sternBrocot(7), 19);
|
|
- text: <code>sternBrocot(10)</code> should return <code>39</code>.
|
|
testString: assert.equal(sternBrocot(10), 39);
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
|
|
<section id='challengeSeed'>
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function sternBrocot(num) {
|
|
// Good luck!
|
|
}
|
|
```
|
|
|
|
</div>
|
|
</section>
|
|
|
|
## Solution
|
|
|
|
<section id='solution'>
|
|
|
|
```js
|
|
function sternBrocot(num) {
|
|
function f(n) {
|
|
return n < 2
|
|
? n
|
|
: n & 1
|
|
? f(Math.floor(n / 2)) + f(Math.floor(n / 2 + 1))
|
|
: f(Math.floor(n / 2));
|
|
}
|
|
|
|
function gcd(a, b) {
|
|
return a ? (a < b ? gcd(b % a, a) : gcd(a % b, b)) : b;
|
|
}
|
|
var n;
|
|
for (n = 1; f(n) != num; n++);
|
|
return n;
|
|
}
|
|
```
|
|
|
|
</section>
|