algorithem for Insertion Sort Advanced Analysis

December 22, 2022

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

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

looking to solve this algorithem

>Solution :

Python program to solve this algorithem:

import math
import os
import random
import re
import sys

def insertionSort1(n, arr):
    target = arr[-1]
    idx = n-2

    while (target < arr[idx]) and (idx >= 0):
        arr[idx+1] = arr[idx]
        print(*arr)
        idx -= 1

    arr[idx+1] = target
    print(*arr)

if __name__ == '__main__':
    n = int(input().strip())

    arr = list(map(int, input().rstrip().split()))

    insertionSort1(n, arr)