<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 = sum(nums)
        nums.sort()
        if total_sum % 2 == 1: return False

        target_sum = total_sum // 2

        memo = dict()
        arr_memo = dict()

        def f(target, arr):
            key = str(target) + str(arr)
            if key in memo: return memo[key]

            if sum(arr) < target:
                return False

            if not arr: return False
            if len(arr) == 1: return arr[0] == target

            if len(arr) - 1 not in arr_memo:
                arr_memo[len(arr) - 1] = arr[1:]
            next_arr = arr_memo[len(arr) - 1]
            out = f(target - arr[0], next_arr) or f(target, next_arr)
            memo[key] = out
            return out

        for i in range(len(nums)):
            curr = nums[i]
            if f(target_sum, nums[i:]):
                return True

        return False
        
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