<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 bisect import bisect_right

class Solution:
    def ss_sum(self, arr):
        n = len(arr)
        mapping = defaultdict(list)

        for i in range(1 << n):
            curr_len, curr_sum = 0, 0

            for j in range(n):
                if i & (1 << j) == 0:
                    curr_sum += arr[j]
                    curr_len += 1

            mapping[curr_len].append(curr_sum)

        return mapping

    def minimumDifference(self, nums: List[int]) -> int:
        n = len(nums) // 2
        left_part, right_part = nums[:n], nums[n:]
        left_sums, right_sums = self.ss_sum(left_part), self.ss_sum(right_part)
        full_sum = sum(nums)
        half_sum, ans = full_sum // 2, inf

        for curr_len in left_sums:
            req_len = n - curr_len

            if req_len in right_sums:
                left_subset_sums = left_sums[curr_len]
                right_subset_sums = right_sums[req_len]

                right_subset_sums.sort()

                for curr_sum in left_subset_sums:
                    index = bisect_right(right_subset_sums, half_sum - curr_sum)

                    if index < len(right_subset_sums):
                        ans = min(ans, abs(full_sum - 2 * (curr_sum + right_subset_sums[index])))
                    if index > 0:
                        ans = min(ans, abs(full_sum - 2 * (curr_sum + right_subset_sums[index - 1])))

        return ans
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