Solution.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.


"""


import heapq

class Solution:
    def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
        pq = [1]
        ret = set()
        candidates = set((1,))
        while len(ret) < n:
            curr = heapq.heappop(pq)
            ret.add(curr)
            for p in primes:
                elem = p * curr
                if elem in candidates:
                    continue
                heapq.heappush(pq, elem)
                candidates.add(elem)
        return sorted(ret)[-1]