<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)

        # 1. divide the array in 2 parts
        left = nums[ : n//2]
        right = nums[n//2 : ]

        # 2. generate all possible sums from both halves
        def generate_sums(nums):
            sums = []
            n = len(nums)
            for i in range(n+1):
                combos = [sum(combo) for combo in list(combinations(nums, i))]
                sums.append(combos)
            return sums

        all_left_sums = generate_sums(left)
        all_right_sums = generate_sums(right)

        totsum = sum(nums)
        half_sum = totsum // 2

        # initial mindiff being the entire left half minus the entire right half
        mindiff = abs(sum(left) - sum(right))

        for k in range(1, n//2):
            left_sums = all_left_sums[k]
            right_sums = all_right_sums[n//2 - k]

            # sort the right half of the array
            right_sums.sort()
            for ele1 in left_sums:
                
                # find index of the element in right half that gets you closest to 
                # achieving the half_sum of the array
                idx = bisect_left(right_sums, half_sum - ele1)
                for pos in [idx-1, idx]:
                    if 0 <= pos < len(right_sums):
                        
                        # alright cool, ele2 is now the element that, when added to ele1
                        # gives you almost the same val as half_sum
                        ele2 = right_sums[pos]

                        # this means that ele1 + ele2 is the sum of one of the many 'n' 
                        # length partitions of nums. We can use this partition to find
                        # the other sum and then get the min absolute difference
                        first_part = ele1 + ele2
                        second_part = totsum - first_part
                        mindiff = min(mindiff, abs(first_part - second_part))
        return mindiff
21500