[leetcode] 1447. 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

分析

题目的意思是：给定一个数n，求出其简化的分数形式，其中分母小于等于n。思路也很简单，双循环，其中一个循环为分母，另一个循环为分子，由于需要简化形式，所以需要求一下公约数，然后把分子分母除以公约数变成字符串就行了。最后去重一下就行了。

代码

class Solution:
    def common_factor(self,m,n):
        if(n==0):
            return m
        return self.common_factor(n,m%n)
    def simplifiedFractions(self, n: int) -> List[str]:
        res=[]
        for i in range(1,n+1):
            for j in range(1,i):
                fac=self.common_factor(i,j)
                res.append(str(j//fac)+'/'+str(i//fac))
        return list(set(res)) 

参考文献

梳理使用Python实现求两数最大公约数（四种方法）