Simplified Fractions

Description

Given an integer n, return a list of all simplified fractions between 0 and 1 (exclusive) such that the denominator is less-than-or-equal-to n. The fractions can be in any order.

 

Example 1:

Input: n = 2
Output: ["1/2"]
Explanation: "1/2" is the only unique fraction with a denominator less-than-or-equal-to 2.

Example 2:

Input: n = 3
Output: ["1/2","1/3","2/3"]

Example 3:

Input: n = 4
Output: ["1/2","1/3","1/4","2/3","3/4"]
Explanation: "2/4" is not a simplified fraction because it can be simplified to "1/2".

Example 4:

Input: n = 1
Output: []

 

Constraints:

• 1 <= n <= 100

Solution(javascript)

/**
 * @param {number} n
 * @return {string[]}
 */
const simplifiedFractions = function (n) {
  const gcd = (x, y) => {
    if (x > y) {
      return gcd(y, x)
    }
    if (x === 0) {
      return y
    }
    if (y === 0) {
      return x
    }
    return gcd(y % x, x)
  }

  const result = []
  for (let i = 1; i < n; i++) {
    for (let j = i + 1; j <= n; j++) {
      if (gcd(i, j) === 1) {
        result.push(`${i}/${j}`)
      }
    }
  }
  return result
}