95 lines
3.0 KiB
Markdown
95 lines
3.0 KiB
Markdown
---
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title: Farey sequence
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id: 59c3ec9f15068017c96eb8a3
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challengeType: 5
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forumTopicId: 302266
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---
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## Description
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<section id='description'>
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The <a href="https://en.wikipedia.org/wiki/Farey sequence" title="wp: Farey sequence" target="_blank">Farey sequence</a> <code>F<sub>n</sub></code> of order <code>n</code> is the sequence of completely reduced fractions between <code>0</code> and <code>1</code> which, when in lowest terms, have denominators less than or equal to <code>n</code>, arranged in order of increasing size.
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The <i>Farey sequence</i> is sometimes incorrectly called a <i>Farey series</i>.
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Each Farey sequence:
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<ul>
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<li>starts with the value 0, denoted by the fraction $ \frac{0}{1} $</li>
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<li>ends with the value 1, denoted by the fraction $ \frac{1}{1}$.</li>
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</ul>
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The Farey sequences of orders <code>1</code> to <code>5</code> are:
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<ul>
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<li style="list-style: none;">${\bf\it{F}}_1 = \frac{0}{1}, \frac{1}{1}$</li>
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<li style="list-style: none;">${\bf\it{F}}_2 = \frac{0}{1}, \frac{1}{2}, \frac{1}{1}$</li>
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<li style="list-style: none;">${\bf\it{F}}_3 = \frac{0}{1}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{1}{1}$</li>
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<li style="list-style: none;">${\bf\it{F}}_4 = \frac{0}{1}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{1}{1}$</li>
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<li style="list-style: none;">${\bf\it{F}}_5 = \frac{0}{1}, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{1}{1}$</li>
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</ul>
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</section>
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## Instructions
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<section id='instructions'>
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Write a function that returns the Farey sequence of order <code>n</code>. The function should have one parameter that is <code>n</code>. It should return the sequence as an array.
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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>farey</code> is a function.
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testString: assert(typeof farey === 'function');
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- text: <code>farey(3)</code> should return an array
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testString: assert(Array.isArray(farey(3)));
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- text: <code>farey(3)</code> should return <code>["1/3","1/2","2/3"]</code>
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testString: assert.deepEqual(farey(3), ["1/3","1/2","2/3"]);
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- text: <code>farey(4)</code> should return <code>["1/4","1/3","1/2","2/4","2/3","3/4"]</code>
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testString: assert.deepEqual(farey(4), ["1/4","1/3","1/2","2/4","2/3","3/4"]);
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- text: <code>farey(5)</code> should return <code>["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]</code>
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testString: assert.deepEqual(farey(5), ["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]);
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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 farey(n) {
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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 farey(n){
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let farSeq=[];
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for(let den = 1; den <= n; den++){
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for(let num = 1; num < den; num++){
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farSeq.push({
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str:num+"/"+den,
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val:num/den});
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}
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}
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farSeq.sort(function(a,b){
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return a.val-b.val;
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});
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farSeq=farSeq.map(function(a){
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return a.str;
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});
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return farSeq;
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}
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```
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</section>
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