Description
Write a program to check whether a given number is an ugly number.
Ugly numbers are positive numbers whose prime factors only include 2, 3, 5.
Example 1:
Input: 6
Output: true
Explanation: 6 = 2 × 3
Example 2:
Input: 8
Output: true
Explanation: 8 = 2 × 2 × 2
Example 3:
Input: 14
Output: false
Explanation: 14 is not ugly since it includes another prime factor 7.
Note:
1is typically treated as an ugly number.- Input is within the 32-bit signed integer range: [−231, 231 − 1].
Solutions
1. Iterative
# Time: O(n)
# Space: O(1)
class Solution:
def isUgly(self, num: int) -> bool:
if num <= 0:
return False
for p in [2, 3, 5]:
while num % p == 0:
num /= p
return True if num == 1 else False
# 1012/1012 cases passed (32 ms)
# Your runtime beats 46.09 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (12.8 MB)
2. Recurrence
# Time: O(n)
# Space: O(1)
class Solution:
def isUgly(self, num: int) -> bool:
if num <= 0:
return False
if num == 1:
return True
if num % 2 == 0:
return self.isUgly(num / 2)
if num % 3 == 0:
return self.isUgly(num / 3)
if num % 5 == 0:
return self.isUgly(num / 5)
return False
# 1012/1012 cases passed (28 ms)
# Your runtime beats 76.39 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (12.7 MB)