Ugly Number II
<p>An <strong>ugly number</strong> is a positive integer whose prime factors are limited to <code>2</code>, <code>3</code>, and <code>5</code>.</p>

<p>Given an integer <code>n</code>, return <em>the</em> <code>n<sup>th</sup></code> <em><strong>ugly number</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 12
<strong>Explanation:</strong> [1, 2, 3, 4, 5, 6, 8, 9, 10, 12] is the sequence of the first 10 ugly numbers.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> 1 has no prime factors, therefore all of its prime factors are limited to 2, 3, and 5.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1690</code></li>
</ul>
Hash Table; Math; Dynamic Programming; Heap (Priority Queue)
class Solution {
public:
    int nthUglyNumber(int n) {
        priority_queue<long, vector<long>, greater<long>> q;
        q.push(1l);
        unordered_set<long> vis{{1l}};
        long ans = 1;
        vector<int> f = {2, 3, 5};
        while (n--) {
            ans = q.top();
            q.pop();
            for (int& v : f) {
                long nxt = ans * v;
                if (!vis.count(nxt)) {
                    vis.insert(nxt);
                    q.push(nxt);
                }
            }
        }
        return (int) ans;
    }
};