<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 sortedcontainers import *
class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        # approach
        size = len(nums)
        n = size//2
        total = sum(nums)
        target = total // 2
        # using bit manipulation to pick some elements of array..
        # after picking n elements, we calculate the minimum abs value... and we choose the minimum of all the combinations
        # if we are set with n bits, then we can calculate the abs by abs((total - curr) - curr)
        
        # dp doesn't work

        # meet in the middle to convert 2**n complexity to 2**(n/2)

        left= defaultdict(list)
        right = defaultdict(list)

        for mask in range(2**n):
            l,r = 0,0
            cnt = 0
            for i in range(n):
                if mask & (1<< i):
                    l += nums[i]
                    r += nums[i + n]
                    cnt += 1
            left[cnt].append(l)
            right[cnt].append(r)
        ret = inf
        # print(left, right)
        for k, arr in left.items():
            key = n - k
            comp = right[key]
            comp.sort()
            for first in arr:
                idx = bisect_right(comp, target - first)
                # print(idx, comp)
                if idx != 0:
                    su = first + comp[max(idx-1, 0)]
                    ret = min(ret, abs((total - su) - su))
        
        return ret



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