<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>

from itertools import combinations
from bisect import bisect_left

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums) // 2
        total_sum = sum(nums)
        half_sum = total_sum // 2

        def get_sums(arr):
            result = defaultdict(set)
            for k in range(1, len(arr) + 1):
                for comb in combinations(arr, k):
                    result[k].add(sum(comb))
            return result

        left_sums = get_sums(nums[:n])
        right_sums = get_sums(nums[n:])

        min_diff = abs(total_sum - 2 * sum(nums[:n]))

        for k in range(1, n + 1):
            left_list = sorted(left_sums[k])
            right_list = sorted(right_sums[n - k])

            for left_sum in left_list:
                pos = bisect_left(right_list, half_sum - left_sum)
                if pos < len(right_list):
                    right_sum = right_list[pos]
                    left_total = left_sum + right_sum
                    right_total = total_sum - left_total
                    min_diff = min(min_diff, abs(left_total - right_total))
                if pos > 0:
                    right_sum = right_list[pos - 1]
                    left_total = left_sum + right_sum
                    right_total = total_sum - left_total
                    min_diff = min(min_diff, abs(left_total - right_total))

        return min_diff

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