Introduction

In this article, we will solve the leetcode problem #1630, Arithmetic Subarrays. A sequence of numbers is called arithmetic if it consists of at least two elements, and the difference between every two consecutive elements is the same. More formally, a sequence s is arithmetic if and only if s[i+1] - s[i] == s[1] - s[0] for all valid i.
For example, these are arithmetic sequences: 1, 3, 5, 7, 9 7, 7, 7, 7 3, -1, -5, -9 The following sequence is not arithmetic: 1, 1, 2, 5, 7 You are given an array of n integers, nums, and two arrays of m integers each, l and r, representing the m range queries, where the ith query is the range [l[i], r[i]]. All the arrays are 0-indexed. Return a list of boolean elements answer, where answer[i] is true if the subarray nums[l[i]], nums[l[i]+1], ... , nums[r[i]] can be rearranged to form an arithmetic sequence, and false otherwise.
  1. static void Main(string[] args)
  2. {
  3. var nums = new int[] { 4, 6, 5, 9, 3, 7 };
  4. var l = new int[] { 0, 0, 2 };
  5. var r = new int[] { 2, 3, 5 };
  7. var result = checkArithmeticSubarrays(nums, l, r);
  8. //result is [true, false, true]
  9. //In the 0th query, the subarray is [4,6,5]. This can be rearranged as [6,5,4], which is an arithmetic sequence.
  10. //In the 1st query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence.
  11. //In the 2nd query, the subarray is [5,9,3,7]. This can be rearranged as [3,5,7,9], which is an arithmetic sequence.
  13. nums = new int[] { -12, -9, -3, -12, -6, 15, 20, -25, -20, -15, -10 };
  14. l = new int[] { 0, 1, 6, 4, 8, 7 };
  15. r = new int[] { 4, 4, 9, 7, 9, 10 };
  17. result = checkArithmeticSubarrays(nums, l, r);
  18. //result is [false, true, false, false, true, true]
  19. }

Solution

The hints to solve the problem is as follows,
  1. To check if a given sequence is arithmetic, just check that the difference between every two consecutive elements is the same.
  2. If and only if a set of numbers can make an arithmetic sequence, then its sorted version makes an arithmetic sequence. So to check a set of numbers, sort it, and check if that sequence is arithmetic.
  3. For each query, get the corresponding set of numbers which will be the sub-array represented by the query, sort it, and check if the result sequence is arithmetic.
Here is the C# code for the approach,
  1. static List<bool> checkArithmeticSubarrays(int[] nums, int[] l, int[] r)
  2. {
  3. List<bool> result = new List<bool>();
  4. for (int i = 0; i < l.Length; i++)
  5. {
  6. result.Add(isArithmetic(nums, l[i], r[i]));
  7. }
  8. return result;
  9. }
  11. static bool isArithmetic(int[] nums, int start, int end)
  12. {
  13. List<int> list = new List<int>();
  14. for (int i = start; i <= end; i++)
  15. {
  16. list.Add(nums[i]);
  17. }
  18. list.Sort();
  19. for (int i = 1; i < list.Count; i++)
  20. {
  21. if (list[i] - list[i - 1] != list[1] - list[0])
  22. {
  23. return false;
  24. }
  25. }
  26. return true;
  27. }