<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>

def ssum(arr):
    n = len(arr)
    
    def helper(idx):
        el = arr[idx]
        if idx == n - 1:
            return set({(arr[idx], 1)})
        # get all sums from idx + 1
        others = helper(idx + 1)
        # for each of others, add ours to it or not.
        res = set({(el, 1)})
        for (su, c) in others:
            res.add((su, c))
            res.add((su + el, c + 1))
        return res
    return helper(0).union(set({(0,0)}))

from bisect import bisect
def partition(arr):
    n = len(arr) // 2
    left = arr[:n]
    right = arr[n:]
    
    lsubs = ssum(left)
    rsubs = ssum(right)
    
    tot = sum(arr)
    closest = tot // 2

    # store right in <count> => list format.
    # TODO: Does sorting help?
    hsh = {}
    for (s, c) in rsubs:
        if c not in hsh:
            hsh[c] = set({})
        hsh[c].add(s)
    
    for c, ar in hsh.items():
        hsh[c] = sorted(ar)
    
    mini = None
    for (s, c) in lsubs:
        if c == n:
            half = s
        else:
            rarr = hsh[n - c]
            ideal = closest - s
            # we need tp get to the closest
            idx = bisect(rarr, ideal)
            if idx == len(rarr) or rarr[idx] > ideal: 
                idx -= 1
            actual = rarr[idx]
            half = s + actual

        other = tot - half
        diff = abs(half - other)
        mini = min(mini, diff) if mini is not None else diff

    return mini

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:
        return partition(nums)
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