<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
import bisect

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums) // 2
        all_sum = sum(nums)
        
        # Generate all possible sums of all possible combinations for the first and second half of the array
        first_half_sums = [[] for _ in range(n + 1)]
        second_half_sums = [[] for _ in range(n + 1)]
        
        for i in range(2**n):
            count = bin(i).count('1')
            curr_sum = 0
            for j in range(n):
                if (i & (1 << j)) != 0:
                    curr_sum += nums[j]
            first_half_sums[count].append(curr_sum)
            
            curr_sum = 0
            for j in range(n):
                if (i & (1 << j)) != 0:
                    curr_sum += nums[n + j]
            second_half_sums[count].append(curr_sum)
            
        # Sort the second half sums to use binary search
        for i in range(n + 1):
            second_half_sums[i].sort()
        
        # Initialize the result with a large number
        res = float('inf')
        
        # Iterate over all combinations to find the minimum difference
        for i in range(n + 1):
            for first_half_sum in first_half_sums[i]:
                # Use binary search to find the closest sum in the second half
                idx = bisect.bisect_left(second_half_sums[n - i], all_sum / 2 - first_half_sum)
                for j in [idx, idx - 1]:
                    if 0 <= j < len(second_half_sums[n - i]):
                        res = min(res, abs(all_sum - 2 * (first_half_sum + second_half_sums[n - i][j])))
        
        return res
5796