<p>Given an integer array <code>nums</code>, return <code>true</code> <em>if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,5,11,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> The array can be partitioned as [1, 5, 5] and [11].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,5]
<strong>Output:</strong> false
<strong>Explanation:</strong> The array cannot be partitioned into equal sum subsets.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
</ul>

class Solution:
    def canPartition(self, nums: List[int]) -> bool:
        def find_target(i: int, remaining: int) -> bool:
            if i == len(nums) or remaining < 0:
                return False
            if remaining == 0:
                return True
            if memo[i][remaining] is not None:
                return bool(memo[i][remaining])

            memo[i + 1][remaining - nums[i]] = find_target(i + 1, remaining - nums[i])
            if memo[i + 1][remaining - nums[i]]:
                return True
            memo[i + 1][remaining] = find_target(i + 1, remaining)
            return bool(memo[i + 1][remaining])

        total_sum = sum(nums)
        if total_sum % 2:
            return False
        target = total_sum // 2

        memo: list[list[bool | None]] = [
            [None for _ in range(target + 1)] for _ in range(len(nums) + 1)
        ]
        return find_target(0, target)

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