<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 = len(nums)
        total = sum(nums)
        def get_half(arr):
            K = len(arr)
            res = [[] for _ in range(K+1)]
            for i in range(1 << K):
                cnt = 0
                for j in range(K):
                    if i & (1 << j):
                        cnt += arr[j]
                res[i.bit_count()].append(cnt)
            for i in range(K+1):
                res[i].sort()
            return res

        first_part, second_part = get_half(nums[:N//2]), get_half(nums[N//2:])
        res = float(inf)
        for i in range(N//2+1):
            j = N//2 - i
            for x in first_part[i]:
                second = second_part[j]
                left, right = 0, len(second)-1
                target = total//2 - x
                while left < right:
                    mid = left + (right - left) // 2
                    if second[mid] < target:
                        left = mid + 1
                    else:
                        right = mid
                res = min(res, abs(x + second[left] - (total - x - second[left])))
                if left > 0:
                    res = min(res, abs(x + second[left-1] - (total - x - second[left-1])))
        return res


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