<p>Given an integer <code>n</code>, return <em>the least number of perfect square numbers that sum to</em> <code>n</code>.</p>

<p>A <strong>perfect square</strong> is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, <code>1</code>, <code>4</code>, <code>9</code>, and <code>16</code> are perfect squares while <code>3</code> and <code>11</code> are not.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 12
<strong>Output:</strong> 3
<strong>Explanation:</strong> 12 = 4 + 4 + 4.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 13
<strong>Output:</strong> 2
<strong>Explanation:</strong> 13 = 4 + 9.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int numSquares(int n) {
        vector<int> squares;

        for(int i = 1;i*i<=n;i++){
            squares.push_back(i*i);
        }
        
        set<int> q;
        q.insert(n);

        int level = 0;

        while(!q.empty()){
            level++;

            set<int> next_queue;

            for(const int& i : q){
                for(const int& square : squares){
                    if(square == i){
                        return level;
                    } else if(square > i){
                        break;
                    } else{
                        next_queue.insert(i-square);
                    }
                }
            }
            q = next_queue;
        }

        return level;
    }
};
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