freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/rosetta-code/farey-sequence.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
59c3ec9f15068017c96eb8a3	Farey sequence	5	302266	farey-sequence

--description--

The Farey sequence Fn 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.

The Farey sequence is sometimes incorrectly called a Farey series.

Each Farey sequence:

• starts with the value 0, denoted by the fraction $ \frac{0}{1} $
• ends with the value 1, denoted by the fraction $ \frac{1}{1}$.

The Farey sequences of orders 1 to 5 are:

• ${\bf\it{F}}_1 = \frac{0}{1}, \frac{1}{1}$
• ${\bf\it{F}}_2 = \frac{0}{1}, \frac{1}{2}, \frac{1}{1}$
• ${\bf\it{F}}_3 = \frac{0}{1}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{1}{1}$
• ${\bf\it{F}}_4 = \frac{0}{1}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{1}{1}$
• ${\bf\it{F}}_5 = \frac{0}{1}, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{1}{1}$

--instructions--

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.

--hints--

farey should be a function.

assert(typeof farey === 'function');

farey(3) should return an array

assert(Array.isArray(farey(3)));

farey(3) should return ["1/3","1/2","2/3"]

assert.deepEqual(farey(3), ['1/3', '1/2', '2/3']);

farey(4) should return ["1/4","1/3","1/2","2/4","2/3","3/4"]

assert.deepEqual(farey(4), ['1/4', '1/3', '1/2', '2/4', '2/3', '3/4']);

farey(5) should return ["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]

assert.deepEqual(farey(5), [
  '1/5',
  '1/4',
  '1/3',
  '2/5',
  '1/2',
  '2/4',
  '3/5',
  '2/3',
  '3/4',
  '4/5'
]);

--seed--

--seed-contents--

function farey(n) {

}

--solutions--

function farey(n){
    let farSeq=[];
    for(let den = 1; den <= n; den++){
        for(let num = 1; num < den; num++){
            farSeq.push({
                str:num+"/"+den,
                val:num/den});
        }
    }
    farSeq.sort(function(a,b){
        return a.val-b.val;
    });
    farSeq=farSeq.map(function(a){
        return a.str;
    });
    return farSeq;
}