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

title	id	challengeType	forumTopicId
Farey sequence	59c3ec9f15068017c96eb8a3	5	302266

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.

Tests

tests:
  - text: <code>farey</code> should be a function.
    testString: assert(typeof farey === 'function');
  - text: <code>farey(3)</code> should return an array
    testString: assert(Array.isArray(farey(3)));
  - text: <code>farey(3)</code> should return <code>["1/3","1/2","2/3"]</code>
    testString: assert.deepEqual(farey(3), ["1/3","1/2","2/3"]);
  - text: <code>farey(4)</code> should return <code>["1/4","1/3","1/2","2/4","2/3","3/4"]</code>
    testString: assert.deepEqual(farey(4), ["1/4","1/3","1/2","2/4","2/3","3/4"]);
  - 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>
    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"]);

Challenge Seed

function farey(n) {

}

Solution

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;
}