<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:
    def numSquares(self, n: int) -> int:
        MAX_INT = 100001
        squares = list(map(lambda x: x * x, range(int(n ** 0.5) + 1)))[1:]
        adj_list = defaultdict(list)
        for i in range(1, n + 1):
            adj_list[i] = squares[:int(i ** 0.5)].copy()

        dp = [MAX_INT] * (n + 1)
        for s in squares:
            dp[s] = 1

        def traverse(num):
            if dp[num] < MAX_INT:
                return dp[num]
            else:
                for u in adj_list[num]:
                    if dp[num] == MAX_INT:
                        traverse(num - u)
                dp[num] = min([dp[num - u] for u in adj_list[num]]) + 1

        traverse(n)
        return dp[n]

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