<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>

class Solution {
public:
    template <class T> using minHeap = priority_queue<T, vector<T>, greater<T>>;
    int nthUglyNumber(int n) {
        minHeap<int> pq;
        unordered_set<int> count;
        long long cur_max = 0;
        long long tmp_max = 0;

        pq.push(1);

        for (int i = 0; i < n;) {
            long long cur = pq.top();
            pq.pop();

            if (cur > cur_max) {
                cur_max = cur;
                if (count.count(cur * 2) == 0 && (tmp_max > cur * 2 || pq.size() < n - i)) {
                    tmp_max = max(tmp_max, cur * 2);
                    count.insert(cur * 2);
                    pq.push(cur * 2);
                }
                
                if (count.count(cur * 3) == 0 && (tmp_max > cur * 3 || pq.size() < n - i)) {
                    tmp_max = max(tmp_max, cur * 3);
                    count.insert(cur * 3);
                    pq.push(cur * 3);
                }

                if (count.count(cur * 5) == 0 && (tmp_max > cur * 5 || pq.size() < n - i)) {
                    tmp_max = max(tmp_max, cur * 5);
                    count.insert(cur * 5);
                    pq.push(cur * 5);
                }

                ++i;
            }
        }

        return cur_max;
    }
};
27271