<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 lower_bound(self,arr,x):
        low=0
        high=len(arr)-1
        ans=arr[high]
        while low<=high:
            mid = (low+high)//2
            if arr[mid] >=x:
                ans = arr[mid]
                high=mid-1
            else:
                low=mid+1
        return ans


    def minimumDifference(self, nums: List[int]) -> int:
        n=len(nums)
        total = sum(nums)
        N=n//2;
        l=[[] for _ in range(N+1)]
        r=[[] for _ in range(N+1)]
       
        for i in range((1<<N)):
            ele=0
            l_sum=0
            r_sum=0
            for j in range(N):
                if (i&(1<<j))!=0:
                    ele+=1
                    l_sum+=nums[j]
                    r_sum+=nums[N+j]
            l[ele].append(l_sum)
            r[ele].append(r_sum)
        
        for i in range(N):
            r[i].sort()
        
        ans=min(abs(total-2*l[N][0]),abs(total-2*r[N][0]))

        for i in range(1,N):
            for sum_1 in l[i]:
                rem = total//2 - sum_1
                rem_number = N-i
                possible_second_sum = self.lower_bound(r[rem_number],rem)
                ssum=sum_1+possible_second_sum
                ans=min(ans,abs(2*ssum - total))
        return ans




        
4991