Super Ugly Number.py

'''
Write a program to find the nth super ugly number.

Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k.

Example:

Input: n = 12, primes = [2,7,13,19]
Output: 32 
Explanation: [1,2,4,7,8,13,14,16,19,26,28,32] is the sequence of the first 12 
             super ugly numbers given primes = [2,7,13,19] of size 4.
Note:

1 is a super ugly number for any given primes.
The given numbers in primes are in ascending order.
0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.
The nth super ugly number is guaranteed to fit in a 32-bit signed integer.
'''

class Solution:
    def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
        h = [1]
        res = 1
        visited = set([1])
        for k in range(n):
            res = heapq.heappop(h)
            for p in primes:
                tmp = res * p
                if tmp in visited:
                    continue
                visited.add(tmp)
                heapq.heappush(h, tmp)
        return res