Arithmetic Subarrays

Challenge Points: 20

Level: Medium

You are given an integer array nums of length n. Along with this, you have two arrays l and r, each of length m. Every index i represents a query asking you to examine the subarray from index l[i] to r[i] (inclusive).

For each query, you must check whether the elements inside the chosen subarray can be rearranged in such a way that they form a valid arithmetic sequence.
A sequence qualifies as arithmetic if:

It contains at least two numbers, and
The difference between consecutive numbers remains constant after rearranging.

You must return an array of booleans where the ith value indicates whether the subarray in query i can be rearranged to meet this condition.

Example 1:

Input: nums = [10, 4, 7, 1, 3, 9] l = [1, 2, 3] r = [3, 5, 5]

Output: [true, true, true]

Explanation:

Query 0 → subarray = [4, 7, 1] → rearranged as [1, 4, 7], difference = 3 → valid Query 1 → subarray = [7, 1, 3] → cannot form arithmetic order Query 2 → subarray = [1, 3, 9] → rearranged as [1, 5, 9]? No. But [3, 1, 9]? No → BUT actual valid rearrangement = [1,5,9]? Not possible. Let’s adjust example → use valid one: New subarray = [1, 3, 9] is NOT arithmetic → let's fix example: Updating example 1 output correctly: Corrected Example: nums = [10, 4, 7, 1, 3, 5] l = [1, 2, 3] r = [3, 5, 5] Subarrays: [4,7,1] → arithmetic [7,1,3] → NOT arithmetic [1,3,5] → YES, difference = 2 Output: → [true, false, true]