- Merge Sort: Counting Inversions

# Merge Sort: Counting Inversions

# Merge Sort: Counting Inversions

In an array, , the elements at indices and (where ) form an inversion if . In other words, inverted elements and are considered to be "out of order". To correct an inversion, we can swap adjacent elements.

**Example**

To sort the array, we must perform the following two swaps to correct the inversions:

Given an array , return the number of inversions to sort the array.

**Function Description**

Complete the function *countInversions* in the editor below.

countInversions has the following parameter(s):

*int arr[n]:*an array of integers to sort

**Returns**

*int:*the number of inversions

**Input Format**

The first line contains an integer, , the number of datasets.

Each of the next pairs of lines is as follows:

- The first line contains an integer, , the number of elements in .
- The second line contains space-separated integers, .

**Constraints**

**Sample Input**

```
STDIN Function
----- --------
2 d = 2
5 arr[] size n = 5 for the first dataset
1 1 1 2 2 arr = [1, 1, 1, 2, 2]
5 arr[] size n = 5 for the second dataset
2 1 3 1 2 arr = [2, 1, 3, 1, 2]
```

**Sample Output**

```
0
4
```

**Explanation**

We sort the following datasets:

- is already sorted, so there are no inversions for us to correct.

We performed a total of swaps to correct inversions.