# 1630. Arithmetic Subarrays

## Description

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.

Example 1:

Input: nums = [4,6,5,9,3,7], l = [0,0,2], r = [2,3,5]
Output: [true,false,true]
Explanation:
In the 0th query, the subarray is [4,6,5]. This can be rearranged as [6,5,4], which is an arithmetic sequence.
In the 1st query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence.
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.

Example 2:

Input: nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10], l = [0,1,6,4,8,7], r = [4,4,9,7,9,10]
Output: [false,true,false,false,true,true]


Constraints:

• n == nums.length
• m == l.length
• m == r.length
• 2 <= n <= 500
• 1 <= m <= 500
• 0 <= l[i] < r[i] < n
• -105 <= nums[i] <= 105

## Solutions

• class Solution {
public List<Boolean> checkArithmeticSubarrays(int[] nums, int[] l, int[] r) {
List<Boolean> ans = new ArrayList<>();
for (int i = 0; i < l.length; ++i) {
}
return ans;
}

private boolean check(int[] nums, int l, int r) {
Set<Integer> s = new HashSet<>();
int n = r - l + 1;
int a1 = 1 << 30, an = -a1;
for (int i = l; i <= r; ++i) {
a1 = Math.min(a1, nums[i]);
an = Math.max(an, nums[i]);
}
if ((an - a1) % (n - 1) != 0) {
return false;
}
int d = (an - a1) / (n - 1);
for (int i = 1; i < n; ++i) {
if (!s.contains(a1 + (i - 1) * d)) {
return false;
}
}
return true;
}
}

• class Solution {
public:
vector<bool> checkArithmeticSubarrays(vector<int>& nums, vector<int>& l, vector<int>& r) {
vector<bool> ans;
auto check = [](vector<int>& nums, int l, int r) {
unordered_set<int> s;
int n = r - l + 1;
int a1 = 1 << 30, an = -a1;
for (int i = l; i <= r; ++i) {
s.insert(nums[i]);
a1 = min(a1, nums[i]);
an = max(an, nums[i]);
}
if ((an - a1) % (n - 1)) {
return false;
}
int d = (an - a1) / (n - 1);
for (int i = 1; i < n; ++i) {
if (!s.count(a1 + (i - 1) * d)) {
return false;
}
}
return true;
};
for (int i = 0; i < l.size(); ++i) {
ans.push_back(check(nums, l[i], r[i]));
}
return ans;
}
};

• class Solution:
def checkArithmeticSubarrays(
self, nums: List[int], l: List[int], r: List[int]
) -> List[bool]:
def check(nums, l, r):
n = r - l + 1
s = set(nums[l : l + n])
a1, an = min(nums[l : l + n]), max(nums[l : l + n])
d, mod = divmod(an - a1, n - 1)
return mod == 0 and all((a1 + (i - 1) * d) in s for i in range(1, n))

return [check(nums, left, right) for left, right in zip(l, r)]


• func checkArithmeticSubarrays(nums []int, l []int, r []int) (ans []bool) {
check := func(nums []int, l, r int) bool {
s := map[int]struct{}{}
n := r - l + 1
a1, an := 1<<30, -(1 << 30)
for _, x := range nums[l : r+1] {
s[x] = struct{}{}
if a1 > x {
a1 = x
}
if an < x {
an = x
}
}
if (an-a1)%(n-1) != 0 {
return false
}
d := (an - a1) / (n - 1)
for i := 1; i < n; i++ {
if _, ok := s[a1+(i-1)*d]; !ok {
return false
}
}
return true
}
for i := range l {
ans = append(ans, check(nums, l[i], r[i]))
}
return
}

• function checkArithmeticSubarrays(nums: number[], l: number[], r: number[]): boolean[] {
const check = (nums: number[], l: number, r: number): boolean => {
const s = new Set<number>();
const n = r - l + 1;
let a1 = 1 << 30;
let an = -a1;
for (let i = l; i <= r; ++i) {
a1 = Math.min(a1, nums[i]);
an = Math.max(an, nums[i]);
}
if ((an - a1) % (n - 1) !== 0) {
return false;
}
const d = Math.floor((an - a1) / (n - 1));
for (let i = 1; i < n; ++i) {
if (!s.has(a1 + (i - 1) * d)) {
return false;
}
}
return true;
};
const ans: boolean[] = [];
for (let i = 0; i < l.length; ++i) {
ans.push(check(nums, l[i], r[i]));
}
return ans;
}


• class Solution {
public bool Check(int[] arr) {
Array.Sort(arr);
int diff = arr[1] - arr[0];
for (int i = 2; i < arr.Length; i++) {
if (arr[i] - arr[i - 1] != diff) {
return false;
}
}
return true;
}

public IList<bool> CheckArithmeticSubarrays(int[] nums, int[] l, int[] r) {
List<bool> ans = new List<bool>();
for (int i = 0; i < l.Length; i++) {
int[] arr = new int[r[i] - l[i] + 1];
for (int j = 0; j < arr.Length; j++) {
arr[j] = nums[l[i] + j];
}
}
return ans;
}
}


• impl Solution {
pub fn check_arithmetic_subarrays(nums: Vec<i32>, l: Vec<i32>, r: Vec<i32>) -> Vec<bool> {
let m = l.len();
let mut res = vec![true; m];
for i in 0..m {
let mut arr = nums[l[i] as usize..=r[i] as usize].to_vec();
arr.sort();
for j in 2..arr.len() {
if arr[j - 2] - arr[j - 1] != arr[j - 1] - arr[j] {
res[i] = false;
break;
}
}
}
res
}
}