<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>


const vector<int> limited_prime_factors{ 2,3,5, };
class Solution {
public:


    int nthUglyNumber(int n) {
        set<long long> befores{ 1,};
        long long current_value = 1;
        for (int i = 1; i < n; i++) {
            long long current_min = INT_MAX;
            for (auto it = begin(befores); it != end(befores);) {
                const auto v = *it;
                bool exist = false;
                for (auto&& p: limited_prime_factors) {
                    const auto candidate = p * v;
                    if (current_value < candidate) {
                        current_min = min(current_min, candidate);
                        exist = true;
                    }
                }
                if (exist) {
                    ++it;
                }
                else {
                    it = befores.erase(it);
                }
            }
            current_value = current_min;
            befores.insert(current_min);
        }

        return static_cast<int>(current_value);
    }
};

void test(int n) {
    cout << Solution().nthUglyNumber(n) << endl;
}
25846