LeetCode 264. Ugly Number II

'''
Write a program to find the n-th ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5.
'''
class Solution(object):
    def nthUglyNumber(self, n):
        """
        :type n: int
        :rtype: int
        """
        # target = 2**i * 3**j * 5**k
        i = j = k = 0
        l = [1]
        while n > 1:
            n_next = min(2*l[i], 3*l[j], 5*l[k])
            if n_next == 2*l[i]:
                i+=1
            elif n_next == 3*l[j]:
                j+=1
            else:
                k+=1
            if n_next not in l:
                l.append(n_next)
                n-=1
           
        return l[-1]