2122. Recover the Original Array
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 indexi
where0 <= i < n
higher[i] = arr[i] + k
, for every indexi
where0 <= 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
.
Solutions
Solution 1
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