<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:
    int nthUglyNumber(int n) {
        if (n <= 0) {
            return 0; // Invalid input
        }

        int uglyNumbers[n];
        uglyNumbers[0] = 1;

        int idx2 = 0, idx3 = 0, idx5 = 0; // Pointers for 2, 3, and 5
        int nextMultiple2 = 2, nextMultiple3 = 3, nextMultiple5 = 5;

        for (int i = 1; i < n; ++i) {
            int nextUglyNumber = std::min(nextMultiple2, std::min(nextMultiple3, nextMultiple5));
            uglyNumbers[i] = nextUglyNumber;

            if (nextUglyNumber == nextMultiple2) {
                ++idx2;
                nextMultiple2 = uglyNumbers[idx2] * 2;
            }

            if (nextUglyNumber == nextMultiple3) {
                ++idx3;
                nextMultiple3 = uglyNumbers[idx3] * 3;
            }

            if (nextUglyNumber == nextMultiple5) {
                ++idx5;
                nextMultiple5 = uglyNumbers[idx5] * 5;
            }
        }

        return uglyNumbers[n - 1];
    }
};

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