<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) {
        // map<int, bool> uglyMap; 
        // int count = 0;
        // int i = 1;
        // while ( count < n ) {
        //     if ( i == 1 ) {
        //         uglyMap[i] = true;
        //     } else if ( i%2 == 0 ) {
        //         uglyMap[i] = uglyMap[i/2];
        //     } else if ( i%3 == 0 ) {
        //         uglyMap[i] = uglyMap[i/3];
        //     } else if ( i%5 == 0 ) {
        //         uglyMap[i] = uglyMap[i/5];
        //     } else {
        //         uglyMap[i] = false;
        //     }
        //     if ( uglyMap[i] )
        //         count++;
        //     i++;
        // }
        // return (i-1);
        vector<int> uglyArray;
        vector<int> twoArray;
        vector<int> threeArray;
        vector<int> fiveArray;
        uglyArray.push_back(1);
        twoArray.push_back(1);
        threeArray.push_back(1);
        fiveArray.push_back(1);
        int uglyIdx = 0;
        int twoIdx = 0;
        int threeIdx = 0;
        int fiveIdx = 0;
        if (n == 1){
            return 1;
        }
        for ( int i = 1; i < n; i++ ) {
            int val = 0;
            int twoVal = twoArray[twoIdx] * 2;
            int threeVal = threeArray[threeIdx] * 3;
            int fiveVal = fiveArray[fiveIdx] * 5;
            if ( twoVal <= threeVal && twoVal <= fiveVal ) {
                val = twoVal;
            } else if ( threeVal <= twoVal && threeVal <= fiveVal ) {
                val = threeVal;
            } else {
                val = fiveVal;
            }
            cout << "val : " << val << endl;
            uglyArray.push_back(val);
            twoArray.push_back(val);
            threeArray.push_back(val);
            fiveArray.push_back(val);
            while ( twoVal == val ) {
                twoIdx++;
                twoVal = twoArray[twoIdx] * 2;
            }
            while ( threeVal == val ) {
                threeIdx++;
                threeVal = threeArray[threeIdx] * 3;
            }
            while ( fiveVal == val ) {
                fiveIdx++;
                fiveVal = fiveArray[fiveIdx] * 5;
            }
        }
        return uglyArray[n-1];      
    }
};
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