1630 Arithmetic Subarrays - Medium

Problem:

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

Problem Analysis:

• iterate though the subarrays from the zip(l,r) pair

• core logic in is_arithmetic function

• return true for the base case when all element is the same

• else sort the array and find the first delta

• return true if all delta is the same

• Time Complexity

  • O(Q * N * log N) where Q is the number of queries (length of l or r) and N is the maximum length of the subarrays.
    • The solution involves iterating through each specified subarray and, for each subarray, performing sorting operations (O(N * log N)) inside the is_arithmetic function.

• Space Complexity:

  • O(N) for the sorted subarrays created inside the is_arithmetic function.
    • The space complexity is mainly due to the sorting operation inside the is_arithmetic function. The additional variables (is_arithmetic, arr, delta) use constant space.

Solutions:

class Solution:
    def checkArithmeticSubarrays(self, nums: List[int], l: List[int], r: List[int]) -> List[bool]:
        def is_arithmetic(arr):
            if len(set(arr)) == 1:
                return True

            arr.sort()
            delta = arr[1] - arr[0]
            return all(y - x == delta for x, y in zip(arr, arr[1:]))

        return [is_arithmetic(nums[left:right+1]) for left, right in zip(l, r)]

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