<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:
        total_amount = sum(nums)
        if total_amount%2:
            return False
        len_nums = len(nums)
        nums.sort()
        dp = defaultdict()
        def dfs(index, req_sum):
            if (index, req_sum) in dp:
                return dp[(index, req_sum)]
            if req_sum == 0:
                return True
            if index>=len_nums or req_sum<nums[index]:
                return False
            dp[(index, req_sum)] = dfs(index+1, req_sum-nums[index]) or dfs(index+1, req_sum)
            return dp[(index, req_sum)]
        return dfs(0, total_amount//2)
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