<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<std::pair<int, int>> q;
        q.push({n, 0});
        vector<bool> visited(n + 1, false);

        while (!q.empty()) {
            auto [num, dist] = q.front();
            q.pop();

            if (num == 0)
                return dist;

            for (int i = 1;; i++) {
                int value = num - i * i;
                if (value < 0)
                    break;

                if (!visited[value]) {
                    q.push({value, dist + 1});
                    visited[value] = true;
                }
            }
        }
        return n;
    }
};
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