<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) {

        std::queue<int> q;    
        q.push(n);

        int count = 0;
        while (!q.empty())
        {
            std::unordered_set<int> seen;
            int level_size = q.size();
            for (int i=0; i<level_size; ++i)
            {
                auto curr = q.front();
                q.pop();

                if (curr == 0) { return count;}
    
                int base = 0;
                int square = 0;
                while (square <= curr)
                {
                    if (seen.find(curr-square) == seen.end())
                    {
                        q.push(curr - square);
                        seen.insert(curr - square);
                    }
    
                    base++;
                    square = base*base;
                }
            }
            count++;
        }
        std::cout << "shouldn't have reached this point, returning 0.\n";
        return 0;
    }
};
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