<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:
        
        def fn(arr):
            ans = defaultdict(list)
            ans[0].append(0)
            for x in arr:
                temp = defaultdict(list)
                for k, y in ans.items():
                    temp[k] += y
                    for x2 in y:
                        temp[k + 1].append(x + x2)
                ans |= temp
            for i in range(len(arr) + 1):
                ans[i].sort()
            return ans
        
        n = len(nums)
        s1 = fn(nums[:n // 2])
        s2 = fn(nums[n // 2:])
        res = float('inf')
        total = s1[n // 2][0] + s2[n // 2][0]
        for k, arr in s1.items():
            arr2 = s2[n // 2 - k]
            # minimise (total - x - y) - (x + y)
            # total - 2x - 2y
            # 2y = total - 2x
            for x in arr:
                idx = bisect_left(arr2, (total - 2 * x) // 2)
                if idx > 0:
                    res = min(res, abs(total - 2 * x - 2 * arr2[idx - 1]))
                if idx < len(arr2):
                    res = min(res, abs(total - 2 * x - 2 * arr2[idx]))
                # for y in arr2:
                #     added = x + y
                #     diff = total - added - added
                #     res = min(res, abs(diff))

        return res
1626