Description
An ugly number is a positive integer whose prime factors are limited to 2
, 3
, and 5
.
Given an integer n
, return the nth
ugly number.
Example 1:
Input: n = 10 Output: 12 Explanation: [1, 2, 3, 4, 5, 6, 8, 9, 10, 12] is the sequence of the first 10 ugly numbers.
Example 2:
Input: n = 1 Output: 1 Explanation: 1 has no prime factors, therefore all of its prime factors are limited to 2, 3, and 5.
Constraints:
1 <= n <= 1690
Solution
Python3
class Solution:
def nthUglyNumber(self, n: int) -> int:
t2 = t3 = t5 = 0
dp = [1] * n
for i in range(1, n):
dp[i] = min(dp[t2] * 2, dp[t3] * 3, dp[t5] * 5)
if dp[i] == dp[t2] * 2: t2 += 1
if dp[i] == dp[t3] * 3: t3 += 1
if dp[i] == dp[t5] * 5: t5 += 1
return dp[-1]