<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:

        @cache
        def dfs(i: int, curr: int) -> bool:
            if curr == target:
                return True

            # generate 
            for j in range(i, n):
                # remove duplicates
                if j > i and nums[j] == nums[j-1]:
                    continue

                # mutate state
                if dfs(j+1, curr + nums[j]):
                    return True
            
            return False

        s = sum(nums)

        if s % 2 == 1:
            return False

        n = len(nums)
        target = s//2 
        nums.sort() 
        return dfs(0, 0) 

#  1, 5, 11, 5 | 22

#  1 
#   6
#    17
#  5
#    6

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