1588. Sum of All Odd Length Subarrays

Difficulty: Easy

Related Topics: Array

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

A subarray is a contiguous subsequence of the array.

Return the sum of all odd-length subarrays of arr.

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

Solution

Language: Python3

class Solution:
    def sumOddLengthSubarrays(self, arr: List[int]) -> int:                    
        rep=0
        for k in range(len(arr)):
            if k==0 or k==len(arr)-1:
                rep+=arr[k]*((len(arr)-1)//2+1)
            else:
                l=k
                r=len(arr)-k-1
                rep+=arr[k]*((l//2+1)*(r//2+1)+((l-1)//2+1)*((r-1)//2+1))   
        return rep