ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
110 lines
2.7 KiB
Markdown
110 lines
2.7 KiB
Markdown
---
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id: 59c3ec9f15068017c96eb8a3
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title: Farey sequence
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challengeType: 5
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forumTopicId: 302266
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dashedName: farey-sequence
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---
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# --description--
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The [Farey sequence](<https://en.wikipedia.org/wiki/Farey sequence> "wp: Farey sequence") <code>F<sub>n</sub></code> of order `n` is the sequence of completely reduced fractions between `0` and `1` which, when in lowest terms, have denominators less than or equal to `n`, arranged in order of increasing size.
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The *Farey sequence* is sometimes incorrectly called a *Farey series*.
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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}$.</li>
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</ul>
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The Farey sequences of orders `1` to `5` are:
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<ul>
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<li style='list-style: none;'>${\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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# --instructions--
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Write a function that returns the Farey sequence of order `n`. The function should have one parameter that is `n`. It should return the sequence as an array.
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# --hints--
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`farey` should be a function.
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```js
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assert(typeof farey === 'function');
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```
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`farey(3)` should return an array
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```js
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assert(Array.isArray(farey(3)));
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```
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`farey(3)` should return `["1/3","1/2","2/3"]`
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```js
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assert.deepEqual(farey(3), ['1/3', '1/2', '2/3']);
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```
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`farey(4)` should return `["1/4","1/3","1/2","2/4","2/3","3/4"]`
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```js
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assert.deepEqual(farey(4), ['1/4', '1/3', '1/2', '2/4', '2/3', '3/4']);
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```
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`farey(5)` should return `["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]`
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```js
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assert.deepEqual(farey(5), [
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'1/5',
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'1/4',
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'1/3',
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'2/5',
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'1/2',
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'2/4',
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'3/5',
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'2/3',
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'3/4',
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'4/5'
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]);
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```
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# --seed--
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## --seed-contents--
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```js
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function farey(n) {
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}
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```
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# --solutions--
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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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