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1447. Simplified Fractions

Difficulty Topics

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. 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

simplified-fractions.py
class Solution:
    def simplifiedFractions(self, n: int) -> List[str]:
        res = []
        for i in range(2, n + 1):
            for j in range(1, i):
                if math.gcd(i, j) == 1:
                    res.append(str(j) + '/' + str(i))
        return res