<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>

from collections import defaultdict
class Solution:
    def ub(self, arr, t):
        n = len(arr)
        l = 0
        r = n - 1
        mid = 0
        while l <= r:
            mid = (l + r) // 2
            if arr[mid] <= t:
                l = mid + 1
            else:
                r = mid - 1

        return mid

    def minimumDifference(self, nums: List[int]) -> int:
        def getSum(arr, n):
            d = defaultdict(list)
            for i in range(1 << n):
                sz = temp = 0
                for j in range(n):
                    if (i & (1 << j)): 
                        sz += 1
                        temp += arr[j]

                d[sz].append(temp)
            return d

        N = len(nums)
        n = N // 2
        S = sum(nums)
        s = S // 2

        l = getSum(nums[:n], n)
        r = getSum(nums[n:], n)

        for key in r.keys(): r[key].sort()

        res = float("inf")
        for key in l.keys():
            rn = n - key
            for numl in l[key]:
                req_r = s - numl
                iu = self.ub(r[rn], req_r)
                il = iu - 1
                p1a, p1b = numl + r[rn][iu], numl + r[rn][il]

                res = min(res, abs(p1a - (S - p1a)))
                res = min(res, abs(p1b - (S - p1b)))

        return res


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