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The brute force approach involves iterating over every possible subarray, checking if its length is odd, and then summing its elements. This approach is straightforward but not optimal.
Time Complexity: O(n^3) where n is the number of elements in the array, due to triple nested loops.
Space Complexity: O(1), only a few extra variables are utilized.
1using System;
2
3class Program {
4 static int SumOddLengthSubarrays(int[] arr) {
5 int totalSum = 0, n = arr.Length;
6 for (int start = 0; start < n; ++start) {
7 for (int end = start; end < n; ++end) {
8 if ((end - start + 1) % 2 != 0) {
9 for (int k = start; k <= end; ++k) {
10 totalSum += arr[k];
11 }
12 }
13 }
14 }
15 return totalSum;
16 }
17
18 static void Main() {
19 int[] arr = {1, 4, 2, 5, 3};
20 Console.WriteLine(SumOddLengthSubarrays(arr));
21 }
22}Similar to the Java and C++ implementations, this C# code uses a series of nested loops to process the subarrays, checking for odd lengths and summing them accordingly.
The optimized approach calculates the contribution of each element to the final sum using a mathematical formula. For each element at index i, calculate how many odd-length subarrays it can contribute to, then sum directly based on these contributions.
Time Complexity: O(n), much improved by calculating contributions directly.
Space Complexity: O(1), only a few extra integer variables.
1
This solution computes the contribution of each element to possible odd-length subarrays using a mathematical formula. For each element, calculate how many subarrays include the element, split this into odd/even counts, and then use that to determine its overall contribution to the sum.