## 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:

1. 1 is typically treated as an ugly number.
2. 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)