Partition Array Into Two Arrays to Minimize Sum Difference
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2000-2099/2035.Partition%20Array%20Into%20Two%20Arrays%20to%20Minimize%20Sum%20Difference/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2000-2099/2035.Partition%20Array%20Into%20Two%20Arrays%20to%20Minimize%20Sum%20Difference/images/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>
Bit Manipulation; Array; Two Pointers; Binary Search; Dynamic Programming; Bitmask; Ordered Set
func minimumDifference(nums []int) int {
	n := len(nums) >> 1
	f := make([][]int, n+1)
	g := make([][]int, n+1)
	for i := 0; i < (1 << n); i++ {
		s, cnt := 0, 0
		s1, cnt1 := 0, 0
		for j := 0; j < n; j++ {
			if (i & (1 << j)) != 0 {
				s += nums[j]
				cnt++
				s1 += nums[n+j]
				cnt1++
			} else {
				s -= nums[j]
				s1 -= nums[n+j]
			}
		}
		f[cnt] = append(f[cnt], s)
		g[cnt1] = append(g[cnt1], s1)
	}

	for i := 0; i <= n; i++ {
		sort.Ints(f[i])
		sort.Ints(g[i])
	}
	ans := 1 << 30
	for i := 0; i <= n; i++ {
		for _, a := range f[i] {
			left, right := 0, len(g[n-i])-1
			b := -a
			for left < right {
				mid := (left + right) >> 1
				if g[n-i][mid] >= b {
					right = mid
				} else {
					left = mid + 1
				}
			}
			ans = min(ans, abs(a+g[n-i][left]))
			if left > 0 {
				ans = min(ans, abs(a+g[n-i][left-1]))
			}
		}
	}
	return ans
}

func abs(x int) int {
	if x > 0 {
		return x
	}
	return -x
}