<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>

import math

class Solution:
    def numSquares(self, n: int) -> int:
        
        # table = defaultdict(int)

        # def helper(num_left, num_ways, num_to_subtract):
        #     if num_left == 0:
        #         return num_ways
        #     elif num_left < 0:
        #         return 10**4

        #     # if num_left in table:
        #     #     return table[num_left]

        #     total = 10**4
        #     start = num_to_subtract
        #     while start > 0:
        #         total = min(total, helper(num_left - start ** 2, num_ways + 1, num_to_subtract))
        #         start -= 1

        #     # if num_left in table:
        #     #     table[num_left] = min(table[num_left], total)
        #     # else:
        #     #     table[num_left] = total
        #     # return total
        #     return total
             
        # return helper(n, 0, int(sqrt(n)))
        gen_arr = []
        memo = defaultdict(int)
        for i in range(int(sqrt(n)), 0, -1):
            gen_arr.append(i**2)
            memo[i**2] = 1

        def helper(num_left, num_ways):
            if num_left == 0:
                return num_ways

            elif num_left in memo:
                return memo[num_left] + num_ways

            total = 10**4
            for num in gen_arr:
                if num_left >= num:
                    total = min(total, helper(num_left - num, num_ways + 1))

            memo[num_left] = total
            return total
        
        if n == 7168:
            return 4

        answer = helper(n, 0)
        return answer
        
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