<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:
        target = sum(nums) / 2
        if int(target) != target:
            return False
        
        seen = set()
        
        def dp(_sum, index):
            if (_sum, index) in seen:
                return False
            if _sum == target:
                return True
            if index >= len(nums):
                return False
            if dp(_sum + nums[index], index + 1):
                return True
            else:
                seen.add((_sum + nums[index], index + 1))
            if dp(_sum, index + 1):
                return True
            else:
                seen.add((_sum, index + 1))
            
            return False
            
    
        return dp(0, 0)
459754