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:
class Solution:
def gcd(self, a, b):
while b:
a, b = b, a % b
return a
def simplifiedFractions(self, n: int) -> List[str]:
op = set()
for j in range(1, n + 1):
for i in range(1, j):
mul = self.gcd(i, j)
op.add("{}/{}".format(i // mul, j // mul))
return op
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