<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) {
        //i know the first ugly number so let dp[n] denote the nth ugly number
        vector<long long>dp(n+1,0);
        unordered_set<long long>s;
        s.insert(1);
        dp[1]=1;
        for(int i=2;i<=n;i++){
            long long a=LLONG_MAX;
            for(int j=1;j<i;j++){
                long long mu1=dp[j]*2;
                long long mu2=dp[j]*3;
                long long mu3=dp[j]*5;
                if(s.find(mu1)==s.end()){
                    a=min(a,mu1);
                }
                else if(s.find(mu2)==s.end()){
                    a=min(a,mu2);
                   
                }
                else if(s.find(mu3)==s.end()){
                    a=min(a,mu3);
                    
                }
            }
            dp[i]=a;
            s.insert(a);
        }
        return dp[n];
    }
};
28696