- Practice
- Algorithms
- Sorting
- Insertion Sort Advanced Analysis

# Insertion Sort Advanced Analysis

# Insertion Sort Advanced Analysis

Insertion Sort is a simple sorting technique which was covered in previous challenges. Sometimes, arrays may be too large for us to wait around for insertion sort to finish. Is there some other way we can calculate the number of shifts an Insertion Sort performs when sorting an array?

If is the number of elements over which the element of the array has to shift, then the total number of shifts will be ... + . For example, consider the array .

```
Array Shifts
[4,3,2,1]
[3,4,2,1] 1
[2,3,4,1] 2
[1,2,3,4] 3
Total shifts = 1 + 2 + 3 = 6
```

**Function description**

Complete the *insertionSort* function in the editor below. It should return an integer that represents the number of shifts required to sort the given array.

insertionSort has the following parameter(s):

*arr*: an array of integers

**Input Format**

The first line contains a single integer , the number of queries to perform.

The following pairs of lines are as follows:

- The first line contains an integer , the length of .
- The second line contains space-separated integers .

**Constraints**

**Output Format**

Print lines containing the number of shifts for each query.

**Sample Input**

```
2
5
1 1 1 2 2
5
2 1 3 1 2
```

**Sample Output**

```
0
4
```

**Explanation**

The first query is already sorted, therefore there's no need to shift any element. In the second case, it will proceed in the following way.

```
Array: 2 1 3 1 2 -> 1 2 3 1 2 -> 1 1 2 3 2 -> 1 1 2 2 3
Moves: - 1 - 2 - 1 = 4
```