<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>

from collections import defaultdict
from itertools import combinations
import bisect
class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        n=len(nums)//2
        half=sum(nums)//2
        full=sum(nums)
        left,right=nums[:n],nums[n:]
        left_sum,right_sum=self.generateSubsetSum(left),self.generateSubsetSum(right)
        ans=abs(sum(left)-sum(right))
        for j in range(1,n):
            left_dict=left_sum[j]
            right_dict=right_sum[n-j]
            right_dict_new=sorted(right_dict)
            for x in left_dict:
                needed_val=half-x
                pos=bisect.bisect_left(right_dict_new,needed_val)
                if 0<=pos<len(right_dict_new):
                    left_val=x+right_dict_new[pos]
                    right_val=full-left_val
                    ans=min(ans,abs(left_val-right_val))
        return ans
    def generateSubsetSum(self,nums):
        d={}
       
        for i in range(1,len(nums)+1):
            sums=[]
            for j in combinations(nums,i):
                sums.append(sum(j))
            d[i]=sums
        return d
1407