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56 lines
2.8 KiB
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<p>Alice had a <strong>0-indexed</strong> array <code>arr</code> consisting of <code>n</code> <strong>positive</strong> integers. She chose an arbitrary <strong>positive integer</strong> <code>k</code> and created two new <strong>0-indexed</strong> integer arrays <code>lower</code> and <code>higher</code> in the following manner:</p>
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<ol>
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<li><code>lower[i] = arr[i] - k</code>, for every index <code>i</code> where <code>0 <= i < n</code></li>
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<li><code>higher[i] = arr[i] + k</code>, for every index <code>i</code> where <code>0 <= i < n</code></li>
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</ol>
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<p>Unfortunately, Alice lost all three arrays. However, she remembers the integers that were present in the arrays <code>lower</code> and <code>higher</code>, but not the array each integer belonged to. Help Alice and recover the original array.</p>
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<p>Given an array <code>nums</code> consisting of <code>2n</code> integers, where <strong>exactly</strong> <code>n</code> of the integers were present in <code>lower</code> and the remaining in <code>higher</code>, return <em>the <strong>original</strong> array</em> <code>arr</code>. In case the answer is not unique, return <em><strong>any</strong> valid array</em>.</p>
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<p><strong>Note:</strong> The test cases are generated such that there exists <strong>at least one</strong> valid array <code>arr</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,10,6,4,8,12]
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<strong>Output:</strong> [3,7,11]
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<strong>Explanation:</strong>
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If arr = [3,7,11] and k = 1, we get lower = [2,6,10] and higher = [4,8,12].
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Combining lower and higher gives us [2,6,10,4,8,12], which is a permutation of nums.
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Another valid possibility is that arr = [5,7,9] and k = 3. In that case, lower = [2,4,6] and higher = [8,10,12].
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,1,3,3]
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<strong>Output:</strong> [2,2]
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<strong>Explanation:</strong>
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If arr = [2,2] and k = 1, we get lower = [1,1] and higher = [3,3].
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Combining lower and higher gives us [1,1,3,3], which is equal to nums.
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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.
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This is invalid since k must be positive.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [5,435]
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<strong>Output:</strong> [220]
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<strong>Explanation:</strong>
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The only possible combination is arr = [220] and k = 215. Using them, we get lower = [5] and higher = [435].
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>2 * n == nums.length</code></li>
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<li><code>1 <= n <= 1000</code></li>
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<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>
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<li>The test cases are generated such that there exists <strong>at least one</strong> valid array <code>arr</code>.</li>
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</ul>
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