<p>You are given an integer array <code>nums</code> of <code>2 * n</code> integers. You need to partition <code>nums</code> into <strong>two</strong> arrays of length <code>n</code> to <strong>minimize the absolute difference</strong> of the <strong>sums</strong> of the arrays. To partition <code>nums</code>, put each element of <code>nums</code> into <strong>one</strong> of the two arrays.</p>

<p>Return <em>the <strong>minimum</strong> possible absolute difference</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="example-1" src="https://assets.leetcode.com/uploads/2021/10/02/ex1.png" style="width: 240px; height: 106px;" />
<pre>
<strong>Input:</strong> nums = [3,9,7,3]
<strong>Output:</strong> 2
<strong>Explanation:</strong> One optimal partition is: [3,9] and [7,3].
The absolute difference between the sums of the arrays is abs((3 + 9) - (7 + 3)) = 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [-36,36]
<strong>Output:</strong> 72
<strong>Explanation:</strong> One optimal partition is: [-36] and [36].
The absolute difference between the sums of the arrays is abs((-36) - (36)) = 72.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="example-3" src="https://assets.leetcode.com/uploads/2021/10/02/ex3.png" style="width: 316px; height: 106px;" />
<pre>
<strong>Input:</strong> nums = [2,-1,0,4,-2,-9]
<strong>Output:</strong> 0
<strong>Explanation:</strong> One optimal partition is: [2,4,-9] and [-1,0,-2].
The absolute difference between the sums of the arrays is abs((2 + 4 + -9) - (-1 + 0 + -2)) = 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 15</code></li>
	<li><code>nums.length == 2 * n</code></li>
	<li><code>-10<sup>7</sup> &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
</ul>

class Solution:
    def findSums(self, nums: List[int], res: List[Set[int]]):
        n = len(nums)
        res[0] = {0}
        for num in nums:
            for k in range(n,0,-1):
                for prev_sum in res[k-1]:
                    res[k].add(prev_sum+num)

    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums)//2
        ln,rn = nums[0:n],nums[n:len(nums)] #arbitrary halves
        lsum,rsum = sum(ln),sum(rn)
        total_sum = lsum+rsum
        target = total_sum//2
        lCombSums,rCombSums= [set() for _ in range(n+1)],[set() for _ in range(n+1)]
        self.findSums(ln,lCombSums)
        self.findSums(rn,rCombSums)
        min_dif = math.inf
        for k in range(n):
            lSums, rSums= lCombSums[k],rCombSums[n-k]
            rSumsSorted = sorted(rSums)
            for l in lSums:
                pos = bisect_left(rSumsSorted,target-l)
                if pos < len(rSums):
                    cur_sum = l+rSumsSorted[pos]
                    cur_dif = abs(total_sum-2*cur_sum)
                    min_dif = min(min_dif,cur_dif)
                if pos > 0:
                    cur_sum = l+rSumsSorted[pos-1]
                    cur_dif = abs(total_sum-2*cur_sum)
                    min_dif = min(min_dif,cur_dif)
        return min_dif



        

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