# Insertion Sort Advanced Analysis in Algorithm | HackerRank Programming Solutions | HackerRank Problem Solving Solutions in Java [💯Correct]

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#### Introduction To Algorithm

The word Algorithm means “a process or set of rules to be followed in calculations or other problem-solving operations”. Therefore Algorithm refers to a set of rules/instructions that step-by-step define how a work is to be executed upon in order to get the expected results.

• It is easy to understand.
• Algorithm is a step-wise representation of a solution to a given problem.
• In Algorithm the problem is broken down into smaller pieces or steps hence, it is easier for the programmer to convert it into an actual program.

`Insertion Sort Advanced Analysis– Hacker Rank Solution`

### Problem:

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  … + .

Example

```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.

insertionSort has the following parameter(s):

• int arr[n]: an array of integers

Returns
– int: the number of shifts required to sort the array

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

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, so there is no need to shift any elements. 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```
`Insertion Sort Advanced Analysis – Hacker Rank Solution`
```import java.io.*;
import java.util.*;

public class Solution {
private static final int MAXVAL = 10000000;
private static int[] array = new int[MAXVAL+1];

public static void main(String[] args) {
/* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
Scanner sc = new Scanner(System.in);
int testCaseCount = sc.nextInt();
for (int i = 0; i < testCaseCount; i++) {
int size = sc.nextInt();
long sum = 0;
Arrays.fill(array, 0);
for (int j = 0; j < size; j++) {
sum += assign(sc.nextInt(), array, j);
}
System.out.println(sum);
}
}
private static int assign(int x, int[] prefixSums, int current) {
update(prefixSums, x);
return current-n;
}

private static int read(int[] prefixSums, int x) {
int nrt=0;
while(x>0) {
nrt += prefixSums[x];
x -= (x&(-x));
}
return nrt;
}

private static void update(int[] prefixSums, int x) {
while(x <= MAXVAL) {
prefixSums[x]++;
x += (x&(-x));
}
}
}``` 