{"id":9256,"date":"2021-12-26T06:04:34","date_gmt":"2021-12-26T14:04:34","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=9256"},"modified":"2021-12-26T06:10:17","modified_gmt":"2021-12-26T14:10:17","slug":"leetcode-2122-recover-the-original-array","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/hashtable\/leetcode-2122-recover-the-original-array\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 2122. Recover the Original Array"},"content":{"rendered":"\n

Alice had a 0-indexed<\/strong> array arr<\/code> consisting of n<\/code> positive<\/strong> integers. She chose an arbitrary positive integer<\/strong> k<\/code> and created two new 0-indexed<\/strong> integer arrays lower<\/code> and higher<\/code> in the following manner:<\/p>\n\n\n\n

  1. lower[i] = arr[i] - k<\/code>, for every index i<\/code> where 0 <= i < n<\/code><\/li>
  2. higher[i] = arr[i] + k<\/code>, for every index i<\/code> where 0 <= i < n<\/code><\/li><\/ol>\n\n\n\n

    Unfortunately, Alice lost all three arrays. However, she remembers the integers that were present in the arrays lower<\/code> and higher<\/code>, but not the array each integer belonged to. Help Alice and recover the original array.<\/p>\n\n\n\n

    Given an array nums<\/code> consisting of 2n<\/code> integers, where exactly<\/strong> n<\/code> of the integers were present in lower<\/code> and the remaining in higher<\/code>, return the original<\/strong> array<\/em> arr<\/code>. In case the answer is not unique, return any<\/strong> valid array<\/em>.<\/p>\n\n\n\n

    Note:<\/strong> The test cases are generated such that there exists at least one<\/strong> valid array arr<\/code>.<\/p>\n\n\n\n

    Example 1:<\/strong><\/p>\n\n\n\n

    Input:<\/strong> nums = [2,10,6,4,8,12]\nOutput:<\/strong> [3,7,11]\nExplanation:<\/strong>\nIf arr = [3,7,11] and k = 1, we get lower = [2,6,10] and higher = [4,8,12].\nCombining lower and higher gives us [2,6,10,4,8,12], which is a permutation of nums.\nAnother valid possibility is that arr = [5,7,9] and k = 3. In that case, lower = [2,4,6] and higher = [8,10,12]. \n<\/pre>\n\n\n\n
    Example 2:<\/strong><\/p>\n\n\n\n
    Input:<\/strong> nums = [1,1,3,3]\nOutput:<\/strong> [2,2]\nExplanation:<\/strong>\nIf arr = [2,2] and k = 1, we get lower = [1,1] and higher = [3,3].\nCombining lower and higher gives us [1,1,3,3], which is equal to nums.\nNote that arr cannot be [1,3] because in that case, the only possible way to obtain [1,1,3,3] is with k = 0.\nThis is invalid since k must be positive.\n<\/pre>\n\n\n\n
    Example 3:<\/strong><\/p>\n\n\n\n
    Input:<\/strong> nums = [5,435]\nOutput:<\/strong> [220]\nExplanation:<\/strong>\nThe only possible combination is arr = [220] and k = 215. Using them, we get lower = [5] and higher = [435].\n<\/pre>\n\n\n\n
    Constraints:<\/strong><\/p>\n\n\n\n
    • 2 * n == nums.length<\/code><\/li>
    • 1 <= n <= 1000<\/code><\/li>
    • 1 <= nums[i] <= 109<\/sup><\/code><\/li>
    • The test cases are generated such that there exists at least one<\/strong> valid array arr<\/code>.<\/li><\/ul>\n\n\n\n
      Solution: Try all possible k<\/strong><\/h2>\n\n\n\n
      Sort the array, we know that the smallest number nums[0] is org[0] – k, org[0] + k (nums[0] + 2k) must exist in nums. We try all possible ks. k = (nums[i] – nums[0]) \/ 2.<\/p>\n\n\n\n
      Then we iterate the sorted nums array as low, and see whether we can find low + 2k as high using a dynamic hashtable.<\/p>\n\n\n\n
      Time complexity: O(n2<\/sup>)
      Space complexity: O(n)<\/p>\n\n\n\n
      \n
      C++<\/h2>\n
      \n\n
      \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  vector recoverArray(vector& nums) {\n    const int n = nums.size();\n    sort(begin(nums), end(nums));\n    unordered_map m;\n    for (int x : nums) ++m[x];\n    \n    auto check = [&](int k) -> vector {      \n      vector ans;\n      unordered_map cur(m);\n      for (int x : nums) {\n        if (cur[x] == 0) continue;\n        --cur[x];\n        if (--cur[x + 2 * k] < 0) return {};\n        ans.push_back(x + k);\n      }\n      return ans;\n    };\n    for (int i = 1; i < n; ++i) {\n      if (nums[i] == nums[0] || (nums[i] - nums[0]) & 1) continue;\n      const int k = (nums[i] - nums[0]) \/ 2;\n      vector ans = check(k);\n      if (!ans.empty()) return ans;\n    }\n    return {};\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
      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 <=…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[70],"tags":[217,82,31],"class_list":["post-9256","post","type-post","status-publish","format-standard","hentry","category-hashtable","tag-hard","tag-hashtable","tag-math","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9256","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=9256"}],"version-history":[{"count":3,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9256\/revisions"}],"predecessor-version":[{"id":9260,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9256\/revisions\/9260"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=9256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=9256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=9256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}