<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:

    # O((N/2)^2 2^(N/2))
    def generateSubsetSum(self,nums: List[int]) -> List[int]:  #-> O(2^(N/2)log2(2^N/2)) -> N/2*2^(N/2)
        d = {}
        for i in range(1,len(nums)+1):
            sums = []
            for j in combinations(nums,i):
                sums.append(sum(j))
            sums.sort()
            d[i] = sums
        return d

    def minimumDifference(self, nums: List[int]) -> int: #-> generate = 2*( n/2* 2^n/2)+ sort= ( n/2* 2^n/2) + calc = ( n/2* 2^n/2)
        # -> N*(2^(N/2))
        N = len(nums)
        n = N//2
        total = sum(nums)
        half_sum = total//2
        left,right = nums[:n], nums[n:]
        left_sums, right_sums = self.generateSubsetSum(left), self.generateSubsetSum(right)
        ans = abs(sum(left)-sum(right))
        for i in range(1,n):
            for j in range(len(left_sums[i])):  #-> for every 2^N/2 -> log2(2^N/2) -> N/2*(2^N/2)
                target = half_sum - left_sums[i][j]
                idx = bisect_left(right_sums[n-i], target)
                for q in [idx, idx-1]:
                    if 0 <= q < len(right_sums[n-i]):
                        left_half = left_sums[i][j] + right_sums[n-i][q]
                        right_half = total - left_half
                        ans = min(ans, abs(left_half - right_half))
        return ans


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