<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:
        
        def get_all_subarray_sums(arr):
            levels = defaultdict(list)
            
            def get_sum(idx,cur_sum,n):
                if idx == len(arr):
                    levels[n].append(cur_sum)
                    return
                
                get_sum(idx+1,cur_sum,n)
                get_sum(idx+1,cur_sum+arr[idx],n+1)
                
            get_sum(0,0,0)
            
            return levels
        
        
        nums.sort()
        mid = len(nums)//2
        left = nums[:mid]
        right = nums[mid:]
        right_sum = sum(right)
        
        pair_sums = get_all_subarray_sums(right)
        for k in pair_sums:
            pair_sums[k].sort()
            
        static_left = sum(left)
        total = sum(nums)
        ans = inf
        n = len(left)
        goal = total//2
        
        def get_answer(referring_arr,left_sum,right_sum_gain):
            nonlocal right_sum
            nonlocal static_left
            target = goal + right_sum_gain - static_left
            idx = bisect_left(referring_arr,target)
            if idx == len(referring_arr):
                idx -=1
            best_diff = inf
            if idx > 0:
                bisect_left_sum = referring_arr[idx-1] + left_sum
                bisect_right_sum = right_sum - referring_arr[idx-1] + right_sum_gain
                best_diff = abs(bisect_left_sum-bisect_right_sum)
                
            bisect_left_sum = referring_arr[idx] + left_sum
            bisect_right_sum = right_sum - referring_arr[idx] + right_sum_gain
            best_diff = min(best_diff,abs(bisect_left_sum-bisect_right_sum))
            
            
            return best_diff
        

        
        def calculate_given_mask(mask):
            
            nonlocal static_left
            nonlocal total
            nonlocal pair_sums
            nonlocal right_sum
            nonlocal goal
            
            
            left_sum = static_left
            cnt = 0
            right_sum_gain = 0
            
            for idx,val in enumerate(bin(mask)[2:]):
                if val == "1":
                    left_sum -= left[idx]
                    right_sum_gain += left[idx]
                    cnt +=1

            referring_arr = pair_sums[cnt]
            
            return get_answer(referring_arr,left_sum,right_sum_gain)
            
        
        
        for combo in range(2**n):
            cur_ans = calculate_given_mask(combo)
            ans = min(ans,cur_ans)
              
        return ans
3748