Simplified Fractions — LeetCode 1447 Python Solution

The 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

Input

n = 2

Output

["1/2"]

Explanation

"1/2" is the only unique fraction with a denominator less-than-or-equal-to 2.

Python solution

class Solution:
    def simplifiedFractions(self, n: int) -> List[str]:
        return [
            f'{i}/{j}'
            for i in range(1, n)
            for j in range(i + 1, n + 1)
            if gcd(i, j) == 1
        ]

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1447. Simplified Fractions is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Number Theory.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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