<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;
        int i = 1;
        while (i * i <= n) {
            squares.push_back(i * i);
            ++i;
        }

        queue<tuple<int, int, int>> q;
        q.push(make_tuple(0, n, squares.size() - 1));
        while (true) {
            tuple<int, int, int> front = q.front();
            q.pop();

            if (get<1>(front) == 0) {
                return get<0>(front);
            }

            for (int i = get<2>(front); i >= 0; --i) {
                if (get<1>(front) - squares[i] >= 0)
                    q.push(make_tuple(get<0>(front) + 1, get<1>(front) - squares[i], i));
            }
        }

        return -1;
    }
};
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