<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 checkEqualPartitionsExists(self, index: int, subset_sum: int, target: int, nums: List[int], cache: Dict) -> bool:
        if subset_sum == target:
            return True
        
        elif index >= len(nums):
            return False
        
        elif (index, subset_sum) in cache:
            return cache[(index, subset_sum)]
        
        case_1 = self.checkEqualPartitionsExists(index + 1, subset_sum, target, nums, cache)
        case_2 = self.checkEqualPartitionsExists(index + 1, subset_sum + nums[index], target, nums, cache)

        cache[(index, subset_sum)] = case_1 or case_2
        return case_1 or case_2

    def canPartition(self, nums: List[int]) -> bool:
        nums_total = sum(nums)
        
        # not possible to divide into 2 subsets if total is odd
        if nums_total % 2 == 1:
            return False

        subset_sum = 0
        cache = dict()
        return self.checkEqualPartitionsExists(0, subset_sum, nums_total // 2, nums, cache)
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