Arithmetic Subarrays

Problem Description

You are given an array of integers, nums, and two arrays representing range queries. Each query specifies a subarray, and the task is to determine if that subarray can be rearranged to form an arithmetic sequence.

Key Insights

• A sequence is arithmetic if the difference between consecutive elements is constant.
• To check if a subarray can be rearranged into an arithmetic sequence, sort the subarray and check the differences between consecutive elements.
• If the sorted subarray has at least two elements, it can potentially form an arithmetic sequence, provided all differences are the same.

Space and Time Complexity

Time Complexity: O(m * k log k), where m is the number of queries and k is the maximum length of any subarray. Space Complexity: O(k), for storing the subarray during processing.

Solution

To solve the problem, we will follow these steps:

1. For each query, extract the specified subarray from the main array.
2. Sort the subarray to ensure that we can easily check the differences between consecutive elements.
3. Calculate the difference between the first two elements of the sorted subarray.
4. Iterate through the sorted subarray and check if all consecutive differences are equal to the initial difference.
5. If they are, the subarray can be rearranged into an arithmetic sequence; otherwise, it cannot.

The algorithm primarily uses sorting, which allows us to efficiently check the required condition.

Code Solutions