<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

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums) // 2
        total_sum = sum(nums)
        
        # Split nums into two halves
        left, right = nums[:n], nums[n:]
        
        # Function to get all possible sums of subsets of a given size
        def get_subset_sums(arr):
            n = len(arr)
            subset_sums = {i: [] for i in range(n + 1)}
            for size in range(n + 1):
                for comb in combinations(arr, size):
                    subset_sums[size].append(sum(comb))
            return subset_sums
        
        # Get all possible sums for subsets of each half
        left_sums = get_subset_sums(left)
        right_sums = get_subset_sums(right)
        
        # To minimize the absolute difference, we need to find sums close to total_sum / 2
        target = total_sum // 2
        min_diff = float('inf')
        
        # Sort the right sums for binary search
        for size in right_sums:
            right_sums[size].sort()
        
        # Try to balance left and right sums
        for l_size in range(n + 1):
            for l_sum in left_sums[l_size]:
                r_size = n - l_size
                r_list = right_sums[r_size]
                
                # Binary search to find the closest sum to target - l_sum
                low, high = 0, len(r_list) - 1
                while low <= high:
                    mid = (low + high) // 2
                    current_sum = l_sum + r_list[mid]
                    current_diff = abs(total_sum - 2 * current_sum)
                    min_diff = min(min_diff, current_diff)
                    
                    if current_sum < target:
                        low = mid + 1
                    else:
                        high = mid - 1
        
        return min_diff

# Example usage:
# solution = Solution()
# print(solution.minimumDifference([3,9,7,3]))  # Output: 2
# print(solution.minimumDifference([-36,36]))  # Output: 72
# print(solution.minimumDifference([2,-1,0,4,-2,-9]))  # Output: 0
5650