<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)//2
        left_part = nums[:n]
        right_part = nums[n:]
        total = sum(nums)

        #all from left, all from right sums
        min_diff = abs(sum(left_part) - sum(right_part))

        def get_sums(arr):
            sums = {}
            for i in range(1, len(arr)):#create a subset of i length from arr
                combination = list(itertools.combinations(arr, i))
                sums[i] = [sum(x) for x in combination]
                sums[i].sort()
            return sums

        def binarySearch(arr, val):
            left = 0
            right = len(arr)-1
            while left < right:
                mid = (left+right)//2

                if arr[mid] == val:
                    return arr[mid]
                elif arr[mid] < val:
                    left = mid + 1
                elif arr[mid] > val:
                    right = mid
            
            #if lower value is closer
            if abs(arr[right-1] - val) <= abs(arr[right] - val):
                return arr[right-1]
            else:
                return arr[right]


        #stores all subsets of len i to n in each half
        left_sums = get_sums(left_part)
        right_sums = get_sums(right_part)
        # print(left_sums)
        # print(right_sums)

        for key, value in left_sums.items():
            #select subset from left with len key + select subset from right with len n-key 
            for l_subset in value:
                half_sum = binarySearch(right_sums[n-key], total//2 - l_subset)
                # print(total//2 - l_subset, half_sum, l_subset)
                half_sum += l_subset
                min_diff = min(min_diff, abs((total-half_sum) - (half_sum)))
        return min_diff
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