Question

Write a complete C++ program that analyzes the following sorts by keeping track of how long they take to sort arrays of longS of size 5000, 10000, and 100000, as well as the number of swaps and comparisons they take in doing so:

Insertion sort

Selection sort

Quick sort

shell sort(using gaps of n/2, n/4, n/8, ..., 1) for 20, the gaps would be 10, 5, 2, and 1

shell sort(using gaps based on 2^k + 1, but starting at 1) for 20, the gaps would be 17, 9, 5, 3, and 1

Specifications:

ask the user for the size of the array to be sorted and validate that number accordingly

your gap arrays will not need to hold more than 20 elements

when generating random numbers for the arrays, just use rand(); do not use %

the only things that should be printed are the times, swaps, and comparisons for each sort

use the same numbers for each sort. To do this, keep a master array and then copy the values from the master array to the array to be sorted before you run each sort (do not have more than two large arrays)

in order to keep track of the numbers of swaps and comparisons, you will need to do the following: declare variables of type long long (2 words) in the main that will store the swaps and comparisons, pass these variables as reference parameters to each of your sort functions, and increment these variables when appropiate within your sort functions

Answer 1

Solution=> Please do comment in case of any query.

1. Insertion Sort:- Please do read all the comments in the Program.

Output:-

Proram:-

#include<iostream>
#include <stdio.h>
#include<stdlib.h>
using namespace std;
int no_swap;
int comp;
//used for swapping the elements
void swap(int *x,int *y)
{
  
int temp=*x;
*x=*y;
*y=temp;
}

//this function sort the array using Insertion Sort Algorithm
void Insertion(long array[],int n)
{
long temp;
int j;
for (int i = 1; i < n; i++) {
j = i;
comp++;
while ((j > 0) && (array[j - 1] > array[j])) {
if(array[j-1]>array[j]){
comp++;
}
temp = array[j - 1];
array[j - 1] = array[j];
array[j] = temp;
j--;

no_swap++;//increment swap variable when actually swap is done
}}
}
int main()
{
int n;
cout << "Enter the number of elements: "<<endl;
cin >> n;
long A[n]; //create an array with given number of elements

for(int i = 0; i<n; i++) {
A[i]=rand();
}

cout<<"Array Before Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");

Insertion(A,n);

cout<<"Array After Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");
cout<<"Total No. of comparisions :"<<comp<<endl;
cout<<"Total No. of swaps :"<<no_swap<<endl;
return
0;
}

Selection sort:-  Please make sure to read all the comments in the program.

Program:-

#include<iostream>
#include <stdio.h>
#include<stdlib.h>
using namespace std;
int no_swap;
int comp;
//used for swapping the elements
void swap(long *x,long *y)
{
  
long temp=*x;
*x=*y;
*y=temp;
}

//this function sort the array using Selection Sort Algorithm
void SelectionSort(long A[],int n)
{
int i,j,k;

for(i=0;i<n-1;i++)
{
for(j=k=i;j<n;j++)
{
comp++;
if(A[j]<A[k])
k=j;
}
swap(&A[i],&A[k]);
no_swap++;
}
}

int main()
{
int n;
cout << "Enter the number of elements: "<<endl;
cin >> n;
long A[n]; //create an array with given number of elements

for(int i = 0; i<n; i++) {
A[i]=rand();
}

cout<<"Array Before Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");

SelectionSort(A,n);

cout<<"Array After Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");
cout<<"Total No. of comparisions :"<<comp<<endl;
cout<<"Total No. of swaps :"<<no_swap<<endl;
return
0;
}

Quick Sort:-  Please read all the comments in the program.

Program:-

#include<iostream>
#include <stdio.h>
#include<stdlib.h>
using namespace std;
int no_swap;
int comp;
//used for swapping the elements
void swap(long *x,long *y)
{
  
long temp=*x;
*x=*y;
*y=temp;
}
//Parition function of quicksort
int partition(long A[],int l,int h)
{
int pivot=A[l];
int i=l,j=h;

do
{

do{i++; comp++;}while(A[i]<=pivot);

do{j--; comp++;}while(A[j]>pivot);

if(i<j){
swap(&A[i],&A[j]);
no_swap++;
}}while(i<j);

swap(&A[l],&A[j]);
no_swap++;
return j;
}

//Funtion for sorting the array using quicksort
void QuickSort(long A[],int l,int h)
{
int j;

if(l<h)
{
j=partition(A,l,h);
QuickSort(A,l,j);
QuickSort(A,j+1,h);
}
}
int main()
{
int n;
cout << "Enter the number of elements: "<<endl;
cin >> n;
long A[n]; //create an array with given number of elements

for(int i = 0; i<n; i++) {
A[i]=rand();
}

cout<<"Array Before Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");

QuickSort(A,0,n);

cout<<"Array After Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");
cout<<"Total No. of comparisions :"<<comp<<endl;
cout<<"Total No. of swaps :"<<no_swap<<endl;
return
0;
}

Shell Sort :- Please make sure to read all the comments in the program.

Program:-

#include<iostream>
#include <stdio.h>
#include<stdlib.h>
using namespace std;
int no_swap;
int comp;

// Sorting of array using Shell sort
void ShellSort(long A[],int n)
{
int gap,i,j,temp;

for(gap=n/2;gap>=1;gap/=2)
{
for(i=gap;i<n;i++)
{
temp=A[i];
j=i-gap;

while(j>=0 && A[j]>temp)
{comp++;
A[j+gap]=A[j];

j=j-gap;
}
A[j+gap]=temp;
no_swap++;
comp++;

}
}

}

int main()
{
int n;
cout << "Enter the number of elements: "<<endl;
cin >> n;
long A[n]; //create an array with given number of elements

for(int i = 0; i<n; i++) {
A[i]=rand();
}

cout<<"Array Before Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");

ShellSort(A,n);

cout<<"Array After Sorting"<<endl;
for(int i=0;i<n;i++)
printf("%d ",A[i]);
printf("\n");
cout<<"Total No. of comparisions :"<<comp<<endl;
cout<<"Total No. of swaps :"<<no_swap<<endl;
return
0;
}

Hope you will like the answer.

Thanks.