313. 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.
'''

import heapq
class Solution:
    def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
        minHeap = []
        x = 1
        for i in range(1,n):
            for p in primes:
                heapq.heappush(minHeap, x*p)
            
            x = heapq.heappop(minHeap)
            while(len(minHeap)>0 and x==minHeap[0]):
                heapq.heappop(minHeap)
                 
        return x