1447. Simplified Fractions

Problem

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. You can return the answer 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".

  Constraints:

• 1 <= n <= 100

Solution (Java)

class Solution {
    public List<String> simplifiedFractions(int n) {
        List<String> result = new ArrayList<>();
        if (n == 1) {
            return result;
        }
        StringBuilder str = new StringBuilder();
        for (int denom = 2; denom <= n; denom++) {
            for (int num = 1; num < denom; num++) {
                if (checkGCD(num, denom) == 1) {
                    result.add(str.append(num).append("/").append(denom).toString());
                }
                str.setLength(0);
            }
        }
        return result;
    }

    private int checkGCD(int a, int b) {
        if (a < b) {
            return checkGCD(b, a);
        }
        if (a == b || a % b == 0 || b == 1) {
            return b;
        }
        return checkGCD(a % b, b);
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).