<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:
        tot = sum(nums)
        ans = 0
        N = len(nums)
        n = N//2
        
        half = tot//2

        def generate(start,end):
            arr = nums[start:end+1]
            
            csum=0
            subSum=[[] for _ in range(1+len(arr))]
            for mask in range(1,1<<n):
                sz=0
                csum=0
                for i in range(n):
                    if mask&(1<<i)>0:
                        csum+=arr[i]
                        sz+=1
                subSum[sz].append(csum)
            subSum[0].append(0)
            return subSum
                
        

        first = generate(0,n-1)
        second = generate(n,N)
        for s in second:
            s.sort()
        
        # print(first,second)

        ans = float("inf")
        for i in range(n+1):
            for num1 in first[i]:
                rem = half-num1
                
                pos = bisect.bisect_left(second[n-i],rem)
                # print(num1,rem,pos)
                
                if pos>0:
                    ans = min(ans, abs(tot-2*(num1+second[n-i][pos-1])))
                if pos<len(second[n-i]):
                    ans = min(ans, abs(tot-2*(num1+second[n-i][pos])))
                if pos+1<len(second[n-i]):
                    ans = min(ans, abs(tot-2*(num1+second[n-i][pos+1])))

                
                # print(num1, second[n-i],ans)
            
        return ans




        
5503