<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:
        return self.canPartitionImpl(nums, 0, 0, sum(nums), set())
    
    def canPartitionImpl(self, nums, start_index, left_sum, right_sum, memo):
        if (start_index, left_sum) in memo: # right sum is implicit
            return False
        if left_sum == right_sum:
            return True
        if start_index >= len(nums):
            return False
        
        curr_num = nums[start_index]
        add_to_left = self.canPartitionImpl(nums, start_index+1, left_sum + curr_num, right_sum - curr_num, memo)
        if add_to_left:
            return True
        leave_right = self.canPartitionImpl(nums, start_index+1, left_sum, right_sum, memo)
        if leave_right:
            return True
        
        memo.add((start_index, left_sum))
        return False
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