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
Related Topics:
Math
// OJ: https://leetcode.com/problems/simplified-fractions/
// Author: github.com/lzl124631x
// Time: O(N^2)
// Space: O(1)
class Solution {
int gcd(int a, int b) {
return b ? gcd(b, a % b) : a;
}
public:
vector<string> simplifiedFractions(int n) {
vector<string> ans;
for (int i = 2; i <= n; ++i) {
for (int j = 1; j < i; ++j) {
if (gcd(i, j) != 1) continue;
ans.push_back(to_string(j) + "/" + to_string(i));
}
}
return ans;
}
};