# 1630. Arithmetic Subarrays

#### Medium

***

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`

```python
class Solution:
    def checkArithmeticSubarrays(self, nums: List[int], l: List[int], r: List[int]) -> List[bool]:
        result = []
        for index in range(len(l)):
            result.append(self.checkArithmetic(nums[l[index]: r[index]+1]))
        return result
    
    def checkArithmetic(self, nums: List[int]) -> bool:
        nums.sort()
        for index in range(2, len(nums)):
            if nums[index] - nums[index-1]  == nums[index-1] - nums[index-2]:
                continue
            else:
                return False
        return True
```