<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 typing import List
from itertools import combinations
import bisect

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums) // 2
        total_sum = sum(nums)
        target = total_sum // 2
        
        def generate_sums(arr):
            n = len(arr)
            sums = [[] for _ in range(n + 1)]
            for r in range(n + 1):
                for comb in combinations(arr, r):
                    sums[r].append(sum(comb))
            return sums
        
        # Split nums into two halves
        first_half = nums[:n]
        second_half = nums[n:]
        
        # Generate sum of all subsets for both halves
        first_half_sums = generate_sums(first_half)
        second_half_sums = generate_sums(second_half)
        
        # Sort each list of sums for the second half
        for i in range(n + 1):
            second_half_sums[i].sort()
        
        min_diff = float('inf')
        
        # Try every possible partition
        for i in range(n + 1):
            for s1 in first_half_sums[i]:
                # We want to find s2 such that s1 + s2 is closest to target
                s2_target = target - s1
                j = n - i
                
                # Use binary search to find the closest sum in second_half_sums[j]
                idx = bisect.bisect_left(second_half_sums[j], s2_target)
                
                # Check the closest sum at idx
                if idx < len(second_half_sums[j]):
                    s2 = second_half_sums[j][idx]
                    current_diff = abs(total_sum - 2 * (s1 + s2))
                    min_diff = min(min_diff, current_diff)
                
                # Check the closest sum just before idx
                if idx > 0:
                    s2 = second_half_sums[j][idx - 1]
                    current_diff = abs(total_sum - 2 * (s1 + s2))
                    min_diff = min(min_diff, current_diff)
        
        return min_diff

# Example usage:
# sol = Solution()
# print(sol.minimumDifference([3,9,7,3]))  # Output: 2
# print(sol.minimumDifference([-36,36]))  # Output: 72
# print(sol.minimumDifference([2,-1,0,4,-2,-9]))  # Output: 0
18900