<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:
    struct P {
        long long val;
        int k2;
        int k3;
        int k5;
    };

    struct PCompare {
        bool operator()(const P& y, const P& x) const { return x.val < y.val; }
    };

    int nthUglyNumber(int n) {
        std::priority_queue<P, std::vector<P>, PCompare> q;
        q.push({ 1, 0, 0, 0 });

        int prv_val{ 0 };

        for (;;) {
            P cur_p{ q.top() };
            q.pop();

            if (prv_val == cur_p.val) { continue; }

            prv_val = cur_p.val;

            if (--n == 0) { break; }

            q.push(P{ cur_p.val * 2, cur_p.k2 + 1, cur_p.k3, cur_p.k5 });
            q.push(P{ cur_p.val * 3, cur_p.k2, cur_p.k3 + 1, cur_p.k5 });
            q.push(P{ cur_p.val * 5, cur_p.k2, cur_p.k3, cur_p.k5 + 1 });
        }

        return prv_val;
    }
};

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