# Arithmetic Subarrays

## 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 - s 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 };
6.
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.
12.
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 };
16.
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.     {
7.     }
8.     return result;
9. }
10.
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.     {