<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>

from functools import lru_cache
class Solution:
    def canPartition(self, nums: List[int]) -> bool:
        target = sum(nums) / 2
        if target % 1 != 0: return False

        # i is the ending index, return true/false
        @lru_cache(10**6)
        def dp(i, target):
            if target <= 0 and i >= 0:
                return False
            elif target == 0 and i < 0:
                return True
            elif i < 0 and target != 0:
                return False
            
            return dp(i - 1, target - nums[i]) or dp(i - 1, target)
        
        return dp(len(nums) - 1, target)
                
        
120390