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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

Companies: Google, Adobe

Related Topics:
Array, Sorting

Similar Questions:

Hints:

  • To check if a given sequence is arithmetic, just check that the difference between every two consecutive elements is the same.
  • If and only if a set of numbers can make an arithmetic sequence, then its sorted version makes an arithmetic sequence. So to check a set of numbers, sort it, and check if that sequence is arithmetic.
  • For each query, get the corresponding set of numbers which will be the sub-array represented by the query, sort it, and check if the result sequence is arithmetic.

Solution 1.

// OJ: https://leetcode.com/problems/arithmetic-subarrays
// Author: github.com/lzl124631x
// Time: O(MNlogN)
// Space: O(N)
class Solution {
public:
    vector<bool> checkArithmeticSubarrays(vector<int>& A, vector<int>& L, vector<int>& R) {
        int M = L.size(), N = A.size();
        vector<bool> ans(M);
        for (int i = 0; i < M; ++i) {
            vector<int> tmp;
            for (int j = L[i]; j <= R[i]; ++j) tmp.push_back(A[j]);
            sort(begin(tmp), end(tmp));
            int j = 2, d = tmp[1] - tmp[0];
            for (; j < tmp.size(); ++j) {
                if (tmp[j] - tmp[j - 1] != d) break;
            }
            ans[i] = j == tmp.size();
        }
        return ans;
    }
};