<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 minimumDifference(self, nums: List[int]) -> int:
        n, n2, res = len(nums) // 2, len(nums) // 4, inf
        def dfs(i: int, end: int, k: int, s: int, sums: List[List[int]]):
            if i == end or k >= n2:
                sums[k].append(s)
                return sums
            return (dfs(i + 1, end, k, s, sums), dfs(i + 1, end, k + 1, s + nums[i], sums))[0]
        sum1, sum2 = sum(nums[:n]), sum(nums[n:])
        s1 = dfs(0, n, 0, 0, [[] for _ in range(n2 + 1)])
        s2 = dfs(n, n * 2, 0, 0, [[] for _ in range(n2 + 1)])
        for k in range(n2 + 1):
            s2[k].sort()
            for s1k in s1[k]:
                comp, diff = (sum1 + sum2) // 2 - (sum1 - s1k), sum1 - sum2 - s1k * 2
                j = bisect.bisect_left(s2[k], comp)
                if j < len(s2[k]):
                    res = min(res, abs(diff + s2[k][j] * 2))
                if j > 0:
                    res = min(res, abs(diff + s2[k][j - 1] * 2))
        return res

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