<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:
        summ  = sum(nums)
        # print("sum",summ)
        # print("summ //2",summ //2)
        if summ%2 == 1 or len(nums)==1:
            return False

        t = int(summ/2)
        self.th = {}
        return self.tsum(t, 0, len(nums), nums)

    
    def tsum(self, t, i, n, arr):
        if i>=n or t<0:
            return False
        
        if t==0:
            return True
        
        ky = str(t) + ":" + str(i)
        if ky in self.th:
            return self.th[ky]
        
        inc  =  self.tsum(t-arr[i], i+1, n, arr)
        self.th[ky] = inc
        if inc:
            return inc
        ex  =  self.tsum(t, i+1, n, arr)
        self.th[ky] = ex
        return ex
        
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