<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:

        tot = sum(nums)
        if tot%2==1:
            return False
        
        self.target = tot//2

        nums.sort()
        
        M= [ [ None for i in range(self.target+1) ] for j in range(len(nums)+1)]

        def check_if_subsetsum_from_i_adds_to_target(i, curr_sum):
            
            if curr_sum>self.target:
                return False

            if M[i][curr_sum] is not None:
                return M[i][curr_sum]
            
            if curr_sum == self.target:
                M[i][curr_sum] = True
                return True

            
            if i==len(nums) and curr_sum != self.target:
                M[i][curr_sum] = False
                return False

            leave_it = check_if_subsetsum_from_i_adds_to_target(i+1, curr_sum)
            take_it = check_if_subsetsum_from_i_adds_to_target(i+1, curr_sum+nums[i])

            M[i][curr_sum] = take_it or leave_it
            return take_it or leave_it

        return check_if_subsetsum_from_i_adds_to_target(0, 0)
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