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
class Solution {
    public int[] recoverArray(int n, int[] sums) {
        int m = 1 << 30;
        for (int x : sums) {
            m = Math.min(m, x);
        }
        m = -m;
        TreeMap<Integer, Integer> tm = new TreeMap<>();
        for (int x : sums) {
            tm.merge(x + m, 1, Integer::sum);
        }
        int[] ans = new int[n];
        if (tm.merge(0, -1, Integer::sum) == 0) {
            tm.remove(0);
        }
        ans[0] = tm.firstKey();
        for (int i = 1; i < n; ++i) {
            for (int j = 0; j < 1 << i; ++j) {
                if ((j >> (i - 1) & 1) == 1) {
                    int s = 0;
                    for (int k = 0; k < i; ++k) {
                        if (((j >> k) & 1) == 1) {
                            s += ans[k];
                        }
                    }
                    if (tm.merge(s, -1, Integer::sum) == 0) {
                        tm.remove(s);
                    }
                }
            }
            ans[i] = tm.firstKey();
        }
        for (int i = 0; i < 1 << n; ++i) {
            int s = 0;
            for (int j = 0; j < n; ++j) {
                if (((i >> j) & 1) == 1) {
                    s += ans[j];
                }
            }
            if (s == m) {
                for (int j = 0; j < n; ++j) {
                    if (((i >> j) & 1) == 1) {
                        ans[j] *= -1;
                    }
                }
                break;
            }
        }
        return ans;
    }
}