Find Array Given Subset Sums
<p>You are given an integer <code>n</code> representing the length of an unknown array that you are trying to recover. You are also given an array <code>sums</code> containing the values of all <code>2<sup>n</sup></code> <strong>subset sums</strong> of the unknown array (in no particular order).</p>

<p>Return <em>the array </em><code>ans</code><em> of length </em><code>n</code><em> representing the unknown array. If <strong>multiple</strong> answers exist, return <strong>any</strong> of them</em>.</p>

<p>An array <code>sub</code> is a <strong>subset</strong> of an array <code>arr</code> if <code>sub</code> can be obtained from <code>arr</code> by deleting some (possibly zero or all) elements of <code>arr</code>. The sum of the elements in <code>sub</code> is one possible <strong>subset sum</strong> of <code>arr</code>. The sum of an empty array is considered to be <code>0</code>.</p>

<p><strong>Note:</strong> Test cases are generated such that there will <strong>always</strong> be at least one correct answer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3, sums = [-3,-2,-1,0,0,1,2,3]
<strong>Output:</strong> [1,2,-3]
<strong>Explanation: </strong>[1,2,-3] is able to achieve the given subset sums:
- []: sum is 0
- [1]: sum is 1
- [2]: sum is 2
- [1,2]: sum is 3
- [-3]: sum is -3
- [1,-3]: sum is -2
- [2,-3]: sum is -1
- [1,2,-3]: sum is 0
Note that any permutation of [1,2,-3] and also any permutation of [-1,-2,3] will also be accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, sums = [0,0,0,0]
<strong>Output:</strong> [0,0]
<strong>Explanation:</strong> The only correct answer is [0,0].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 4, sums = [0,0,5,5,4,-1,4,9,9,-1,4,3,4,8,3,8]
<strong>Output:</strong> [0,-1,4,5]
<strong>Explanation:</strong> [0,-1,4,5] is able to achieve the given subset sums.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 15</code></li>
	<li><code>sums.length == 2<sup>n</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= sums[i] &lt;= 10<sup>4</sup></code></li>
</ul>
Array; Divide and Conquer
func recoverArray(n int, sums []int) []int {
	m := -slices.Min(sums)
	rbt := redblacktree.NewWithIntComparator()
	merge := func(key int, value int) {
		if v, ok := rbt.Get(key); ok {
			nxt := v.(int) + value
			if nxt == 0 {
				rbt.Remove(key)
			} else {
				rbt.Put(key, nxt)
			}
		} else {
			rbt.Put(key, value)
		}
	}
	for _, x := range sums {
		merge(x+m, 1)
	}
	ans := make([]int, n)
	merge(ans[0], -1)
	ans[0] = rbt.Left().Key.(int)
	for i := 1; i < n; i++ {
		for j := 0; j < 1<<i; j++ {
			if j>>(i-1)&1 == 1 {
				s := 0
				for k := 0; k < i; k++ {
					if j>>k&1 == 1 {
						s += ans[k]
					}
				}
				merge(s, -1)
			}
		}
		ans[i] = rbt.Left().Key.(int)
	}
	for i := 0; i < 1<<n; i++ {
		s := 0
		for j := 0; j < n; j++ {
			if i>>j&1 == 1 {
				s += ans[j]
			}
		}
		if s == m {
			for j := 0; j < n; j++ {
				if i>>j&1 == 1 {
					ans[j] = -ans[j]
				}
			}
			break
		}
	}
	return ans

}