leetcode-problemset/leetcode-cn/originData/find-array-given-subset-sums.json

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        "question": {
            "questionId": "2109",
            "questionFrontendId": "1982",
            "categoryTitle": "Algorithms",
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            "title": "Find Array Given Subset Sums",
            "titleSlug": "find-array-given-subset-sums",
            "content": "<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>\n\n<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>\n\n<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>\n\n<p><strong>Note:</strong> Test cases are generated such that there will <strong>always</strong> be at least one correct answer.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, sums = [-3,-2,-1,0,0,1,2,3]\n<strong>Output:</strong> [1,2,-3]\n<strong>Explanation: </strong>[1,2,-3] is able to achieve the given subset sums:\n- []: sum is 0\n- [1]: sum is 1\n- [2]: sum is 2\n- [1,2]: sum is 3\n- [-3]: sum is -3\n- [1,-3]: sum is -2\n- [2,-3]: sum is -1\n- [1,2,-3]: sum is 0\nNote that any permutation of [1,2,-3] and also any permutation of [-1,-2,3] will also be accepted.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2, sums = [0,0,0,0]\n<strong>Output:</strong> [0,0]\n<strong>Explanation:</strong> The only correct answer is [0,0].\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, sums = [0,0,5,5,4,-1,4,9,9,-1,4,3,4,8,3,8]\n<strong>Output:</strong> [0,-1,4,5]\n<strong>Explanation:</strong> [0,-1,4,5] is able to achieve the given subset sums.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 15</code></li>\n\t<li><code>sums.length == 2<sup>n</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= sums[i] &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
            "translatedTitle": "从子集的和还原数组",
            "translatedContent": "<p>存在一个未知数组需要你进行还原，给你一个整数 <code>n</code> 表示该数组的长度。另给你一个数组 <code>sums</code> ，由未知数组中全部 <code>2<sup>n</sup></code> 个 <strong>子集的和</strong> 组成（子集中的元素没有特定的顺序）。</p>\n\n<p>返回一个长度为 <code>n</code> 的数组<em> </em><code>ans</code><em> </em>表示还原得到的未知数组。如果存在 <strong>多种</strong> 答案，只需返回其中 <strong>任意一个</strong> 。</p>\n\n<p>如果可以由数组 <code>arr</code> 删除部分元素（也可能不删除或全删除）得到数组 <code>sub</code> ，那么数组 <code>sub</code> 就是数组 <code>arr</code> 的一个<strong> 子集</strong> 。<code>sub</code> 的元素之和就是 <code>arr</code> 的一个 <strong>子集的和</strong> 。一个空数组的元素之和为 <code>0</code> 。</p>\n\n<p><strong>注意：</strong>生成的测试用例将保证至少存在一个正确答案。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 3, sums = [-3,-2,-1,0,0,1,2,3]\n<strong>输出：</strong>[1,2,-3]\n<strong>解释：</strong>[1,2,-3] 能够满足给出的子集的和：\n- []：和是 0\n- [1]：和是 1\n- [2]：和是 2\n- [1,2]：和是 3\n- [-3]：和是 -3\n- [1,-3]：和是 -2\n- [2,-3]：和是 -1\n- [1,2,-3]：和是 0\n注意，[1,2,-3] 的任何排列和 [-1,-2,3] 的任何排列都会被视作正确答案。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 2, sums = [0,0,0,0]\n<strong>输出：</strong>[0,0]\n<strong>解释：</strong>唯一的正确答案是 [0,0] 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 4, sums = [0,0,5,5,4,-1,4,9,9,-1,4,3,4,8,3,8]\n<strong>输出：</strong>[0,-1,4,5]\n<strong>解释：</strong>[0,-1,4,5] 能够满足给出的子集的和。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 15</code></li>\n\t<li><code>sums.length == 2<sup>n</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= sums[i] &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
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