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Arithmetic Subarrays

arrayhash tablesorting

Problem Statement

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 ^th 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.

Examples

Example 1
Input: nums = [4,6,5,9,3,7] , l = [0,0,2] , r = [2,3,5]
Output: [true,false,true]
In the 0 ^th query, the subarray is [4,6,5]. This can be rearranged as [6,5,4], which is an arithmetic sequence. In the 1 ^st query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence. In the 2 ^nd 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
🤔
Medium
Difficulty
Topic Info
ModuleDSA
CategoryArray
Sub-topicHash Table
Tags
arrayhash tablesorting
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