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1{2  "id": 2241,3  "name": "recover-the-original-array",4  "difficulty": "Hard",5  "link": "https://leetcode.com/problems/recover-the-original-array/",6  "date": "2021-12-19",7  "task_description": "Alice had a **0-indexed** array `arr` consisting of `n` **positive** integers. She chose an arbitrary **positive integer** `k` and created two new **0-indexed** integer arrays `lower` and `higher` in the following manner: `lower[i] = arr[i] - k`, for every index `i` where `0 <= i < n` `higher[i] = arr[i] + k`, for every index `i` where `0 <= i < n` Unfortunately, Alice lost all three arrays. However, she remembers the integers that were present in the arrays `lower` and `higher`, but not the array each integer belonged to. Help Alice and recover the original array. Given an array `nums` consisting of `2n` integers, where **exactly** `n` of the integers were present in `lower` and the remaining in `higher`, return _the **original** array_ `arr`. In case the answer is not unique, return _**any** valid array_. **Note:** The test cases are generated such that there exists **at least one** valid array `arr`. **Example 1:** ``` **Input:** nums = [2,10,6,4,8,12] **Output:** [3,7,11] **Explanation:** If arr = [3,7,11] and k = 1, we get lower = [2,6,10] and higher = [4,8,12]. Combining lower and higher gives us [2,6,10,4,8,12], which is a permutation of nums. Another valid possibility is that arr = [5,7,9] and k = 3. In that case, lower = [2,4,6] and higher = [8,10,12]. ``` **Example 2:** ``` **Input:** nums = [1,1,3,3] **Output:** [2,2] **Explanation:** If arr = [2,2] and k = 1, we get lower = [1,1] and higher = [3,3]. Combining lower and higher gives us [1,1,3,3], which is equal to nums. Note that arr cannot be [1,3] because in that case, the only possible way to obtain [1,1,3,3] is with k = 0. This is invalid since k must be positive. ``` **Example 3:** ``` **Input:** nums = [5,435] **Output:** [220] **Explanation:** The only possible combination is arr = [220] and k = 215. Using them, we get lower = [5] and higher = [435]. ``` **Constraints:** `2 * n == nums.length` `1 <= n <= 1000` `1 <= nums[i] <= 109` The test cases are generated such that there exists **at least one** valid array `arr`.",8  "test_case": [9    {10      "label": "Example 1",11      "input": "nums = [2,10,6,4,8,12]",12      "output": "[3,7,11] "13    },14    {15      "label": "Example 2",16      "input": "nums = [1,1,3,3]",17      "output": "[2,2] "18    },19    {20      "label": "Example 3",21      "input": "nums = [5,435]",22      "output": "[220] "23    }24  ],25  "constraints": [26    "2 * n == nums.length",27    "1 <= n <= 1000",28    "1 <= nums[i] <= 109",29    "The test cases are generated such that there exists at least one valid array arr."30  ],31  "python_template": "class Solution(object):\n    def recoverArray(self, nums):\n        \"\"\"\n        :type nums: List[int]\n        :rtype: List[int]\n        \"\"\"\n        ",32  "java_template": "class Solution {\n    public int[] recoverArray(int[] nums) {\n        \n    }\n}",33  "metadata": {34    "func_name": "recoverArray"35  }36}