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

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