<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 getAllSums(nums):
            n = len(nums)
            sums = [(0,0)]
            print(n)
            for i in range(n):
                for s,k in sums[:(1<<n)]:
                    sums.append((s+nums[i],k+1))
            ans = {k:set() for k in range(n+1)}
            # print(sums)
            for s,k in sums:
                ans[k].add(s)
            return ans

        def _checkSum(nums1,nums2,allSum):
            nums1,nums2 = list(nums1),list(nums2)
            if len(nums1) > len(nums2):
                nums1,nums2 = nums2,nums1
            nums2.sort()
            ans = []
            for num1 in nums1:
                target = allSum/2-num1
                if nums2[0] >= target:
                    ans.append(2*abs(target-nums2[0]))
                    continue
                if nums2[-1] <= target:
                    ans.append(2*abs(target-nums2[-1]))
                    continue
                i,j = 0,len(nums2)-1
                while j-i > 1:
                    k = (i+j)//2
                    if nums2[k] > target:
                        j = k
                    else:
                        i = k
                ans.append(min(2*abs(target-nums2[i]),2*abs(target-nums2[j])))
            return int(min(ans))

                

        n = len(nums)//2
        sumsFirstHalf = getAllSums(nums[:n])
        sumsSecondHalf = getAllSums(nums[-n:])

        ans = abs(sum(nums[:n]) - sum(nums[-n:]))
        for k in range(n+1):
            ans = min(ans,_checkSum(sumsFirstHalf[k],sumsSecondHalf[n-k],sum(nums)))
        return ans


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