<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:
        if sum(nums) % 2 > 0: return False

        target = sum(nums) // 2
        nums.sort()
        n = len(nums)

        memo = {}
        def dp(idx, target):
            # print(f'{idx} {target}')
            if (idx, target) in memo:
                return memo[(idx, target)]

            if target == 0:
                return 0

            if idx == n or target < nums[idx]:
                return -float('inf')

            res = max(1 + dp(idx + 1, target - nums[idx]), dp(idx + 1, target))
            memo[(idx, target)] = res
            return res

        res = dp(0, target)
        memo.clear()
        return res != -float('inf')

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