<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 math import *
import bisect
class Solution: 
    def minimumDifference(self, nums: List[int]) -> int:
        s=sum(nums)//2
        ans=self.func(nums,s,len(nums))
        return abs(sum(nums)-2*ans)
    def func(self,nums,s,tn):
        n=tn//2
        closest=-1
        gdiff=1e18
        arr1=nums[:n]
        arr2=nums[n:]
        x=[]
        y=[]
        for i in range(1<<n):
            l1=0
            l2=0
            count=0
            for j in range(n):
                if(i&(1<<j)):
                    count+=1
                    l1+=arr1[j]
                    l2+=arr2[j]
            x.append((l1,count))
            y.append((l2,count))

        hashx=[[]for i in range(n+1)]
        hashy=[[]for i in range(n+1)]
        for i in range(len(x)):
            sumi,count=x[i][0],x[i][1]
            hashx[count].append(sumi)
            sumi,count=y[i][0],y[i][1]
            hashy[count].append(sumi)
        for i in range(n+1):
            arr=hashy[i]
            arr.sort()
            hashy[i]=arr
        for i in range(n+1):
            for sums in hashx[i]:
                arr=hashy[n-i]
                sum_find=s-sums
                index=bisect.bisect_right(arr,sum_find)
                index-=1
                if(index>=0):
                    val=arr[index]
                    diff=abs(s-(arr[index]+sums))
                    if(diff<gdiff):
                        gdiff=diff
                        closest=arr[index]+sums
        return closest



        




        

    

        
3309