<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 __binary_search(self, arr, target):
        l, r = 0, len(arr)
        while l < r:
            mid = (l + r) // 2
            if arr[mid] < target:
                l = mid + 1
            else:
                r = mid
        return l 

    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums) // 2

        total = sum(nums) 
        half = total // 2 
        
        ans = abs(sum(nums[:n]) - sum(nums[n:]))
        for k in range(1, n):
            left = [sum(comb) for comb in combinations(nums[:n], k)]
            right = [sum(comb) for comb in combinations(nums[n:], n-k)]
            right.sort()
            for s1 in left:
                #p = bisect.bisect_left(right, half-s1) 
                p = self.__binary_search(right, half-s1)
                if 0 <= p < len(right):
                    s2 = right[p]
                    left_sum = s1 + s2
                    right_sum = total - left_sum
                    diff = abs(left_sum - right_sum)
                    ans = min(ans, diff) 
        return ans
2797