<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:
        candidates = []
        i = 1
        while i**2 <= n:
            candidates.append(i**2)
            i += 1
        
        #I believe a dfs is our best option, and we begin with larger values first
        failedvals = set()
        successvals = {}

        def Investigate(x):
            if x in failedvals:
                return False, -1
            elif x in successvals:
                return True, successvals[x]

            if x == 0:
                return True, 0
            elif x < 0:
                failedvals.add(x)
                return False, -1

            best = -1
            for c in candidates[::-1]:
                if c <= x:
                    success, num = Investigate(x - c)
                    if success:
                        successvals[x - c] = num
                        if (num <= best or best == -1):
                            best = num
                    else:
                        failedvals.add(x - c)

            if best != -1:
                return True, best + 1
            return True, x

        return Investigate(n)[1]
41975