# 0313. Super Ugly Number

<https://leetcode.com/problems/super-ugly-number>

## Description

A **super ugly number** is a positive integer whose prime factors are in the array `primes`.

Given an integer `n` and an array of integers `primes`, return *the* `nth` ***super ugly number***.

The `nth` **super ugly number** is **guaranteed** to fit in a **32-bit** signed integer.

**Example 1:**

```
**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].
```

**Example 2:**

```
**Input:** n = 1, primes = [2,3,5]
**Output:** 1
**Explanation:** 1 has no prime factors, therefore all of its prime factors are in the array primes = [2,3,5].
```

**Constraints:**

* `1 <= n <= 106`
* `1 <= primes.length <= 100`
* `2 <= primes[i] <= 1000`
* `primes[i]` is **guaranteed** to be a prime number.
* All the values of `primes` are **unique** and sorted in **ascending order**.

## ac

<https://leetcode.com/problems/super-ugly-number/discuss/277313/My-view-of-this-question-hope-it-can-help-you-understand!!!>

```java
class Solution {
    public int nthSuperUglyNumber(int n, int[] primes) {
        PriorityQueue<int[]> queue=new PriorityQueue<>((a,b)->(a[0]-b[0]));
        for (int i=0;i<primes.length;i++)
            queue.offer(new int[]{primes[i], primes[i], 0});

        int[] nums=new int[n+1];
        nums[0]=1;

        int i=1;
        while (i<n){
            int[] entry=queue.poll();
            int num=entry[0], prime=entry[1], index=entry[2];
            // remove duplicate
            if (num!=nums[i-1]){
                nums[i]=num;
                i++;
            }
            queue.offer(new int[]{prime*nums[index+1], prime, index+1});
        }
        return nums[n-1];
    }
}
```


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