<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
    summ = sum(nums)
    goal = summ // 2
    lNums = nums[:n]
    rNums = nums[n:]
    ans = abs(sum(lNums) - sum(rNums))
    lSums = [[] for _ in range(n + 1)]
    rSums = [[] for _ in range(n + 1)]

    def dfs(A: List[int], i: int, count: int, path: int, sums: List[List[int]]):
      if i == len(A):
        sums[count].append(path)
        return
      dfs(A, i + 1, count + 1, path + A[i], sums)
      dfs(A, i + 1, count, path, sums)

    dfs(lNums, 0, 0, 0, lSums)
    dfs(rNums, 0, 0, 0, rSums)

    for lCount in range(n):
      l = lSums[lCount]
      r = rSums[n - lCount]
      r.sort()
      for lSum in l:
        i = bisect_left(r, goal - lSum)
        if i < len(r):
          sumPartOne = summ - lSum - r[i]
          sumPartTwo = summ - sumPartOne
          ans = min(ans, abs(sumPartOne - sumPartTwo))
        if i > 0:
          sumPartOne = summ - lSum - r[i - 1]
          sumPartTwo = summ - sumPartOne
          ans = min(ans, abs(sumPartOne - sumPartTwo))

    return ans
1992