<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:
        n = len(nums)
        summ = sum(nums)
        if summ%2 != 0:return False
        target = summ//2 
        dp = [[-1] * (target+1) for _ in range(n)]
        def helper(index,curr_summ):
            if curr_summ == 0:
                return True
            if index >= n or curr_summ == 0:
                return False
            if dp[index][curr_summ] != -1: return dp[index][curr_summ]
            include = helper(index+1,curr_summ-nums[index])
            exclude = helper(index+1,curr_summ)
            dp[index][curr_summ] = include or exclude
            return dp[index][curr_summ]
        return helper(0,target)
         
        
42991