<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) // 2
        total = sum(nums)
        goal = total // 2

        def dfs(nums):
            ans = {(0, 0)}
            
            for num in nums:
                ans |= {(num + j[0], j[1] + 1) for j in ans}
            
            arr = []

            for i in range(n-1):
                arr.append([])

            length = 0
            
            for val, idx in ans:
                if idx != 0 and idx != n:
                    arr[idx-1].append(val)
                    
            return arr
            
        arr1 = dfs(nums[:n])
        arr2 = [sorted(arr) for arr in dfs(nums[n:])]

        halfSum = sum(nums[:n])

        min_diff = abs((total - halfSum) - halfSum)

        for i in range(len(arr1)):
            for j in range(len(arr1[i])):
                target = goal - arr1[i][j]
                
                idx = bisect.bisect_left(arr2[n-i-2], target)
                
                minDiff = math.inf
                value = math.inf
                
                if idx<len(arr2[n-i-2])and abs(target - arr2[n-i-2][idx]) < minDiff:
                        minDiff = abs(target - arr2[n-i-2][idx])
                        value = arr2[n-i-2][idx]
                if idx>0 and abs(target - arr2[n-i-2][idx-1]) < minDiff:
                        minDiff = abs(target - arr2[n-i-2][idx-1])
                        value = arr2[n-i-2][idx-1]
                
                halfSum = arr1[i][j] + value
                min_diff = min(min_diff, abs((total - halfSum) - halfSum))
                
        return min_diff
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