# Leetcode - Arithmetic Subarrays Solution

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 `i`

query is the range ^{th}`[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`

`-10`

^{5}<= nums[i] <= 10^{5}

## Solution in Python

```
class Solution:
@staticmethod
def is_common_difference(nums):
diff = set({})
nums = sorted(nums)
for i in range(1,len(nums)):
diff.add(nums[i]-nums[i-1])
if len(diff)>1:
return False
return True
def checkArithmeticSubarrays(self, nums: List[int], l: List[int], r: List[int]) -> List[bool]:
return [ self.is_common_difference(nums[x:y+1]) for x,y in zip(l,r) ]
```