1588. Sum of All Odd Length Subarrays

Problem

Given an array of positive integers arr, return **the sum of all possible *odd-length subarrays* of **arr.

A subarray is a contiguous subsequence of the array.

  Example 1:

Input: arr = [1,4,2,5,3]
Output: 58
Explanation: The odd-length subarrays of arr and their sums are:
[1] = 1
[4] = 4
[2] = 2
[5] = 5
[3] = 3
[1,4,2] = 7
[4,2,5] = 11
[2,5,3] = 10
[1,4,2,5,3] = 15
If we add all these together we get 1 + 4 + 2 + 5 + 3 + 7 + 11 + 10 + 15 = 58

Example 2:

Input: arr = [1,2]
Output: 3
Explanation: There are only 2 subarrays of odd length, [1] and [2]. Their sum is 3.

Example 3:

Input: arr = [10,11,12]
Output: 66

  Constraints:

• 1 <= arr.length <= 100

• 1 <= arr[i] <= 1000

  Follow up:

Could you solve this problem in O(n) time complexity?

Solution (Java)

class Solution {
    public int sumOddLengthSubarrays(int[] arr) {
        int len = arr.length;
        int sum = 0;
        for (int i = 0; i <= len - 1; i++) {
            sum = sum + (((i + 1) * (len - i) + 1) / 2) * arr[i];
        }
        return sum;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).