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)
/**
 * @param {number} n
 * @return {number}
 */
var nthUglyNumber = function (n) {
    let dp = [1];
    let p2 = 0,
        p3 = 0,
        p5 = 0;
    for (let i = 1; i < n; ++i) {
        const next2 = dp[p2] * 2,
            next3 = dp[p3] * 3,
            next5 = dp[p5] * 5;
        dp[i] = Math.min(next2, Math.min(next3, next5));
        if (dp[i] == next2) ++p2;
        if (dp[i] == next3) ++p3;
        if (dp[i] == next5) ++p5;
        dp.push(dp[i]);
    }
    return dp[n - 1];
};
