How to Efficiently Count Inversions in an Array Using Modified Merge Sort in C#?
Could someone explain I keep running into I'm working on a project in C# where I need to count the number of inversions in an array. An inversion is defined as a pair of indices (i, j) such that i < j and array[i] > array[j]. I know that a brute force method would take O(n^2) time, which won't work for larger arrays. I've read that I can use a modified merge sort to achieve this in O(n log n) time. I've tried implementing the merge sort but I keep running into issues when trying to count the inversions during the merge step. Here's what I have so far: ```csharp class MergeSortWithInversions { static int MergeAndCount(int[] array, int left, int mid, int right) { int[] leftArray = new int[mid - left + 1]; int[] rightArray = new int[right - mid]; // Copy data to temporary arrays Array.Copy(array, left, leftArray, 0, mid - left + 1); Array.Copy(array, mid + 1, rightArray, 0, right - mid); int i = 0, j = 0, k = left, inversions = 0; while (i < leftArray.Length && j < rightArray.Length) { if (leftArray[i] <= rightArray[j]) { array[k++] = leftArray[i++]; } else { array[k++] = rightArray[j++]; inversions += (mid + 1) - (left + i); } } while (i < leftArray.Length) { array[k++] = leftArray[i++]; } while (j < rightArray.Length) { array[k++] = rightArray[j++]; } return inversions; } static int MergeSortAndCount(int[] array, int left, int right) { int inversions = 0; if (left < right) { int mid = (left + right) / 2; inversions += MergeSortAndCount(array, left, mid); inversions += MergeSortAndCount(array, mid + 1, right); inversions += MergeAndCount(array, left, mid, right); } return inversions; } } ``` When I run this code, it seems to count the inversions correctly for small arrays, but I start noticing issues with larger datasets. Specifically, I'm working with an `IndexOutOfRangeException` when the array size gets significantly larger. I've made sure that the left and right indices are set correctly, but I suspect there might be an off-by-one behavior or an scenario with how I'm handling the temporary arrays. Can anyone offer insights or corrections to guide to resolve this? Also, are there any best practices I should be aware of when implementing this algorithm in C#? Any ideas what could be causing this? This is happening in both development and production on Windows 10. Has anyone dealt with something similar? My development environment is Debian. Has anyone else encountered this?