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.

这道题我们主要参考博客：here。代码如下：

class Solution {
public:
    int nthSuperUglyNumber(int n, vector<int>& primes) {
		vector<int> res(1, 1), idx(primes.size(), 0);
		while (res.size() < n) {
			vector<int> tmp;
			int imin = INT_MAX;
			for (int i = 0; i < primes.size(); i++) {
				tmp.push_back(res[idx[i]] * primes[i]);
			}
			for (int i = 0; i < primes.size(); i++) {
				imin = min(imin, tmp[i]);
			}
			for (int i = 0; i < primes.size(); i++) {
				if (imin == tmp[i]) idx[i]++;
			}
			res.push_back(imin);
		}
		return res.back();
    }
};