<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
import bisect

class Solution:
    def minimumDifference(self, nums):
        n = len(nums) // 2
        total_sum = sum(nums)
        first_half = nums[:n]
        second_half = nums[n:]
        
        # Generate all possible subset sums for each half
        sums_first_half = [[] for _ in range(n+1)]  # sums_first_half[k] stores sums of subsets of size k
        sums_second_half = [[] for _ in range(n+1)]
        
        # Generate subsets for first half
        for k in range(n+1):
            for comb in combinations(first_half, k):
                sums_first_half[k].append(sum(comb))
        
        # Generate subsets for second half
        for k in range(n+1):
            for comb in combinations(second_half, k):
                sums_second_half[k].append(sum(comb))
        
        # Sort the sums in second half for each subset size
        for k in range(n+1):
            sums_second_half[k].sort()
        
        min_diff = float('inf')
        
        # For each possible k, combine sums from both halves
        for k in range(n+1):
            sums1 = sums_first_half[k]
            sums2 = sums_second_half[n - k]
            sums2_list = sums2
            for s1 in sums1:
                target = (total_sum / 2) - s1
                idx = bisect.bisect_left(sums2_list, target)
                
                # Check sums2_list[idx]
                if idx < len(sums2_list):
                    s2 = sums2_list[idx]
                    total_selected_sum = s1 + s2
                    diff = abs(2 * total_selected_sum - total_sum)
                    if diff < min_diff:
                        min_diff = diff
                
                # Check sums2_list[idx - 1]
                if idx > 0:
                    s2 = sums2_list[idx - 1]
                    total_selected_sum = s1 + s2
                    diff = abs(2 * total_selected_sum - total_sum)
                    if diff < min_diff:
                        min_diff = diff
        
        return int(min_diff)

19000