<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:
        n, target = len(A) // 2, sum(A) // 2
        lft, rgt = A[:n], A[n:]
        l_iter, r_iter = [(0, 0)], [(0, 0)] # (No. of numbers, sum)
		
		# Build Lft and Rgt
        for a in lft:
            cur = []
            for pre_num, pre_sum in l_iter:
                cur.append((pre_num, pre_sum))
                cur.append((pre_num + 1, pre_sum + a))
            l_iter = cur[:]
        for a in rgt:
            cur = []
            for pre_num, pre_sum in r_iter:
                cur.append((pre_num, pre_sum))
                cur.append((pre_num + 1, pre_sum + a))
            r_iter = cur[:]
            
        r_dic = collections.defaultdict(list)
        for num, s in r_iter:
            r_dic[num].append(s)
        for key in r_dic.keys():
            r_dic[key] = sorted(r_dic[key])
            
        ans = float('inf')
		
		# Iterate over Lft and binary search for the closet half sum in Rgt.
        for num, s in l_iter:
            key = n - num
            idx = bisect.bisect_right(r_dic[key], target - s)
            if idx > 0:
                ans = min(ans, target - s - r_dic[key][idx - 1])
            if idx < len(r_dic[key]):
                ans = min(ans, r_dic[key][idx] - target + s)
                
        return ans * 2 + sum(A) % 2
        
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