Inversion count in Array

 Given an array a[]. The task is to find the inversion count of a[]. Where two elements a[i] and a[j] form an inversion if a[i] > a[j] and i < j.




Input: arr[] = {8, 4, 2, 1}

Output: 6

Explanation: Given array has six inversions: (8, 4), (4, 2), (8, 2), (8, 1), (4, 1), (2, 1).


Input: arr[] = {1, 20, 6, 4, 5}

Output: 5

Explanation: Given array has five inversions: (20, 6), (20, 4), (20, 5), (6, 4), (6, 5).


public class InversionCount {

    // Main function to count inversions
    public static int countInversions(int[] arr) {
        return mergeSortAndCount(arr, 0, arr.length - 1);
    }

    // Modified merge sort
    private static int mergeSortAndCount(int[] arr, int left, int right) {
        int count = 0;
        if (left < right) {
            int mid = (left + right) / 2;

            count += mergeSortAndCount(arr, left, mid);
            count += mergeSortAndCount(arr, mid + 1, right);
            count += mergeAndCount(arr, left, mid, right);
        }
        return count;
    }

    // Merge step that also counts inversions
    private static int mergeAndCount(int[] arr, int left, int mid, int right) {
        int[] leftArr = java.util.Arrays.copyOfRange(arr, left, mid + 1);
        int[] rightArr = java.util.Arrays.copyOfRange(arr, mid + 1, right + 1);

        int i = 0, j = 0, k = left, swaps = 0;

        while (i < leftArr.length && j < rightArr.length) {
            if (leftArr[i] <= rightArr[j]) {
                arr[k++] = leftArr[i++];
            } else {
                arr[k++] = rightArr[j++];
                swaps += (leftArr.length - i); // Count inversions
            }
        }

        // Copy remaining elements
        while (i < leftArr.length) {
            arr[k++] = leftArr[i++];
        }
        while (j < rightArr.length) {
            arr[k++] = rightArr[j++];
        }

        return swaps;
    }

    // Test the function
    public static void main(String[] args) {
        int[] arr = {2, 4, 1, 3, 5};
        int count = countInversions(arr);
        System.out.println("Inversion Count = " + count);  // Output: 3
    }
}

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