<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>

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums)

        left = nums[:n//2]
        right = nums[n // 2:]
        
        
        

        def sub(nums):
            n = len(nums)
            arr = [[] for _ in range(n + 1)]
            for m in range(1 << n):
                cur = 0
                size = 0
                k = 0
                temp = m
                while temp:
                    if temp & 1 == 1:
                        cur += nums[k]
                        size += 1
                    k += 1
                    temp >>= 1
                arr[size].append(cur)
            return arr

        
        

        arr1 = sub(left)
        arr2 = sub(right)
        for i in arr2:
            i.sort()

        res = inf
        tsum = sum(nums)

        for i in range(len(arr1)):
            for val in arr1[i]:
                j = n // 2 - i
                rem = tsum / 2 - val
                index = bisect_left(arr2[j], rem)
                if index < 0:
                    index = -(index + 1)
                
                if index < len(arr2[j]):
                    res = min(res, abs(tsum - 2* val - 2 * arr2[j][index]))
                if index > 0:
                    res = min(res, abs(tsum - 2 * val - 2 * arr2[j][index - 1]))
        return res
5576