<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, nums: List[int]) -> int:
        # bit mask
        # sum = a + b, a < b: minimize b - a
        # => a <= sum / 2: minimize sum / 2 - a
        targetSum = int()
        accSum = 0
        for num in nums:
            targetSum += num
            accSum += num
        targetSum /= 2
        n = len(nums)
        maxLeftSum = -1_000_000_000
        ###################################################
        def generateSum(nums: List[int]) ->  List[List[int]]:
            n = len(nums)
            sumByNumBits = [[] for _ in range(n+1)]
            for mask in range(0, 1 << n):
                curSum = 0
                numBits = 0
                for i in range(0, n):
                    if (mask >> i) & 1:
                        curSum += nums[i]
                        numBits += 1
                sumByNumBits[numBits].append(curSum)
            for i in range(0, n+1):
                sumByNumBits[i].sort()
            return sumByNumBits
        ###################################################
        leftSum = generateSum(nums[:int(n/2)])
        rightSum = generateSum(nums[int(n/2):])
        for leftNumBits in range(0, len(leftSum)):
            rightNumBits = int(n/2) - leftNumBits
            leftPointer = 0
            rightPointer = len(rightSum[rightNumBits]) - 1
            while leftPointer < len(leftSum[leftNumBits]):
                while rightPointer >= 0 and \
                rightSum[rightNumBits][rightPointer] + leftSum[leftNumBits][leftPointer] > targetSum:
                    rightPointer -= 1
                
                if rightPointer >= 0:
                    maxLeftSum = max(maxLeftSum, rightSum[rightNumBits][rightPointer] + leftSum[leftNumBits][leftPointer])
                leftPointer += 1
                
        return abs((accSum - maxLeftSum) - maxLeftSum)
4406