<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
        total=sum(nums)
        leftDict,rightDict={0:[0]},{0:[0]}
        for i in range(1,2**n):
            bitLen=0
            leftSum=rightSum=0
            for j in range(n):
                if (i & (1<<j))>0:
                    bitLen+=1
                    leftSum+=nums[j]
                    rightSum+=nums[n+j]
            if bitLen not in leftDict: leftDict[bitLen]=[]
            if bitLen not in rightDict: rightDict[bitLen]=[]
            leftDict[bitLen].append(leftSum)
            rightDict[bitLen].append(rightSum)
        ans=float('inf')
        for leftLen in leftDict:
            rightLen=n-leftLen
            sortedLeft=sorted(leftDict[leftLen])
            sortedRight=sorted(rightDict[rightLen])
            i,j=0,len(sortedRight)-1
            while i<len(sortedLeft) and j>=0:
                s=sortedLeft[i]+sortedRight[j]
                rem=total-s
                ans=min(ans,abs(s-rem))
                if s<total/2: i+=1
                else: j-=1
        return ans
            
            
3675