313. Super Ugly

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本文介绍了一种算法，用于找到序列中的第N个超丑数。超丑数是指其所有质因数都在给定质数列表中的正整数。文章详细解释了算法的工作原理，并提供了一个具体的Java实现示例。

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. For example, [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) 1 is a super ugly number for any given primes.
(2) The given numbers in primes are in ascending order.
(3) 0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.
(4) The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

Credits:
Special thanks to @dietpepsi for adding this problem and creating all test cases.

public class Solution {

    public int nthSuperUglyNumber(int n, int[] primes) {
        
        int[] superUglyNumbers = new int[n];
        superUglyNumbers[0] = 1;
        int[] idxPrimes = new int[primes.length];
        for (int i = 0; i < idxPrimes.length; i++) {
            idxPrimes[i] = 0;
        }
        
        int counter = 1;
        while (counter < n) {
            
            int min = Integer.MAX_VALUE;
            for (int i = 0; i < primes.length; i++) {
                int temp = superUglyNumbers[idxPrimes[i]] * primes[i];
                min = min < temp ? min : temp;
            }

            for (int i = 0; i < primes.length; i++) {
                if (min == superUglyNumbers[idxPrimes[i]] * primes[i]) {
                    idxPrimes[i]++;
                }
            }
            
            superUglyNumbers[counter] = min;
            counter++;
        }
        
        return superUglyNumbers[n - 1];
    }
}