<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, A: List[int]) -> int:
        s=sum(A)
        target=s//2
        l=len(A)
        arr1=A[:l//2]
        arr2=A[l//2:]

        

        def helper(i,curr,ct,req,arr):
            nonlocal st
            if ct==req:
                st.add(curr)
                return 
            if i>=l//2:
                return 
            helper(i+1,curr+arr[i],ct+1,req,arr)
            helper(i+1,curr,ct,req,arr)

        
        res=float('inf')
        for i in range(l//2+1):
            st=set()
            helper(0,0,0,i,arr1)
            l1=sorted(st)
            st=set()
            helper(0,0,0,l//2-i,arr2)
            l2=sorted(st)
            ans=float('inf')
            print()
            # print(l1)
            # print(l2)
            for j in l1:
                find=target-j
                left=0
                r=len(l2)-1
                while left<=r:
                    mid=(left+r)//2
                    ans=min(ans,abs(target-j-l2[mid]))

                    if l2[mid]>find:
                        r=mid-1
                    else:
                        left=mid+1

            s1=target-ans
            s2=s-s1
            
            
            res=min(res,abs(s1-s2))
        return res



        





        
            
17800