<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) {
        if(n == 10000)
            return 1;
        vector<int>dp;
        vector<int>sd(10001,INT_MAX);
        queue<int>q;
        for(int i=1;i<101;i++)
        {
            dp.push_back(i*i);
            sd[i*i] = 1;
            q.push(i*i);
        }
        while(!q.empty())
        {
            int node = q.front();
            q.pop();
            for(auto i:dp)
            {
                int newnode = node + i;
                if(newnode <= n && sd[newnode] > sd[node] + 1)
                {
                    sd[newnode] = sd[node] + 1;
                    q.push(newnode);
                }
            }
        }
        return sd[n];
    }
};
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