<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 chain, combinations  
from bisect import *  

powerset = lambda s: chain.from_iterable([  
    (comb, r) for comb in combinations(s, r)  
] for r in range(len(s) + 1))  

class Solution:  
    def minimumDifference(self, nums: List[int]) -> int:  
        adjusted_nums = [num - min(nums) for num in nums]  
        target = sum(adjusted_nums)  
        left_part, right_part = adjusted_nums[::2], adjusted_nums[1::2]  
        total_count, min_diff = len(left_part), 9e9  
        sum_sets = {i: set() for i in range(total_count + 1)}  

        for comb, count in powerset(right_part):  
            sum_sets[count].add(2 * sum(comb))  
        sum_sets = {k: list(sorted(v)) + [9e9] for k, v in sum_sets.items()}  

        for subset, left_count in powerset(left_part):  
            left_sum = 2 * sum(subset)  
            index = bisect_left(sum_sets[total_count - left_count], target - left_sum)  
            min_diff = min(min_diff, abs(sum_sets[total_count - left_count][index] + left_sum - target))  

        return min_diff
2065