<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::set<int> sq;
        int lim = sqrt(n);
        for(int i = 1; i <= lim; ++i)
            sq.insert(i*i);

        int result = 0;
        std::unordered_set<int> qu;
        qu.insert(n);
        while( !qu.empty()){
            ++result;
            std::unordered_set<int> new_qu;
            for(int remainder : qu){
                for(int square : sq){
                    if(remainder == square) return result;
                    else if( remainder < square) break;
                    else new_qu.insert(remainder - square);
                }
            }
            qu = std::move(new_qu);
        }
        return result;
    }
};
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