Leetcode problem 124 - Arithmetic Subarrays

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

/**
 * @param {number[]} nums
 * @param {number[]} l
 * @param {number[]} r
 * @return {boolean[]}
 */
var checkArithmeticSubarrays = function (nums, l, r) {
  let result = [];
  for (let i = 0; i < l.length; i++) {
    const subArray = nums.slice(l[i], r[i] + 1);
    subArray.sort((a, b) => a - b);

    let isArithmetic = true;
    for (let k = 2; k < subArray.length; k++) {
      if (subArray[k] - subArray[k - 1] !== subArray[1] - subArray[0]) {
        isArithmetic = false;
        break;
      }
    }
    result.push(isArithmetic);
  }

  return result;
};

The time complexity of this solution is O(n _ m _ log m), where n is the length of the l and r arrays and m is the average length of the subarrays. This is because for each subarray, we are sorting it which takes O(m * log m) time complexity.

The space complexity is O(m) where m is the average length of the subarrays. This is because we are creating a new subarray for each subarray in the input.

Overall, the time complexity is dominated by the sorting step for each subarray, making it O(n _ m _ log m), and the space complexity is O(m).