1588. Sum of All Odd Length Subarrays.md

1588. Sum of All Odd Length Subarrays

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the first one in Biweekly Contest 35.

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Difficulty : Easy

Related Topics : Array

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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

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Solution

• mine
  • Java
    • Runtime: 1 ms, faster than 88.25%, Memory Usage: 37.3 MB, less than 68.44% of Java online submissions

      // O(N^2)time
      // O(N)space
      public int sumOddLengthSubarrays(int[] arr) {
          int res = 0;
          int n = arr.length;
          int[] sum = new int[n + 1];
          for(int i = 0; i < n; i++){
              sum[i + 1] = sum[i] + arr[i];
          }
          for (int i = 0; i < n; i++){
              for (int j = 1; i + j <= n; j += 2) {
                  res += sum[i + j] - sum[i];
              }
          }
          return res;
      }
      

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