<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:
        total = sum(nums)
        if total % 2 != 0:
            return False

        N = len(nums)
        nums.sort()
        memo = {}
        def dp(i, target):
            if i == N:
                return False
            index = i | target << 10
            if index in memo:
                return memo[index]

            if nums[i] == target:
                memo[index] = True
                return True

            res = dp(i+1, target)
            if not res:
                if nums[i] > target:
                    res = dp(i+1, nums[i] - target)
                else:
                    res = dp(i+1, target - nums[i])
            memo[index] = res
            return res

        return dp(0, total // 2)

108483