<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:
        # use dp

        total = sum(nums)
        if total % 2 == 1: return False
        target = total//2

        dp = dict()
        dp[0] = collections.Counter(nums) 
        # saves the number counts in the other partition if one of them is i

        for i in range(target):
            dp_i = dp.get(i, dict())
            copy = dp_i.copy()
            for x, count in dp_i.items():
                if count > 0 and i+x <= target:
                    copy[x] -=1
                    dp[i+x] = copy.copy()
                    copy[x] += 1
                    if i+x == target: return True
        return False
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