The document describes implementing and testing three sorting algorithms - insertion sort, heapsort, and shellsort - on arrays of 1,000 and 10,000 elements. It provides code samples to perform each algorithm and print the number of comparisons and item movements for analysis. The sorting algorithms are tested on sample arrays and the sorted output is displayed.

1. Write a program to implement and test the following sorting
algorithms to sort an array: Insertion sort. Shellsort Heapsort
Test your program on a list of 1,000 elements and on a list of
10,000 elements. You need to print the number of comparisons
and the number of item movements for each sorting algorithm.
Solution
A) INSERTION SORT :
#include<iostream>
using namespace std;
void INSERTION_SORT(int [],int );
int main()
{
char ch;
do
{
int n;
cout<<"Enter the no. of elements in the array"<<endl;
cin>>n;
int a[n];
cout<<"Enter the elements in the array"<<endl;
for(int i=1;i<=n;i++)
{

2. cin>>a[i];
}
INSERTION_SORT(a,n);
cout<<"::::Sorted Output:::"<<endl;
for(int k=1;k<=n;k++)
{
cout<<a[k]<<" ";
}
cout<<endl<<"Press 'y' or 'Y' to continue!!!";
cin>>ch;
}while(ch=='y'||ch=='Y');
return 0;
}
void INSERTION_SORT(int a[],int n)
{
int key,i,j;
for(j=2;j<=n;j++)
{
key=a[j];
i=j-1;
while((i>0)&&(a[i]>key))
{
a[i+1]=a[i];
i=i-1;
}

3. a[i+1]=key;
}
}
B ) HEAP SORT :
#include <iostream>
using namespace std;
// To heapify a subtree rooted with node i which is
// an index in arr[]. n is size of heap
void heapify(int arr[], int n, int i)
{
int largest = i; // Initialize largest as root
int l = 2*i + 1; // left = 2*i + 1
int r = 2*i + 2; // right = 2*i + 2
// If left child is larger than root
if (l < n && arr[l] > arr[largest])
largest = l;
// If right child is larger than largest so far
if (r < n && arr[r] > arr[largest])
largest = r;
// If largest is not root
if (largest != i)
{
swap(arr[i], arr[largest]);
// Recursively heapify the affected sub-tree
heapify(arr, n, largest);

4. }
}
// main function to do heap sort
void heapSort(int arr[], int n)
{
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// One by one extract an element from heap
for (int i=n-1; i>=0; i--)
{
// Move current root to end
swap(arr[0], arr[i]);
// call max heapify on the reduced heap
heapify(arr, i, 0);
}
}
/* A utility function to print array of size n */
void printArray(int arr[], int n)
{
for (int i=0; i<n; ++i)
cout << arr[i] << " ";
cout << " ";
}
// Driver program

5. int main()
{
int arr[] = {12, 11, 13, 5, 6, 7};
int n = sizeof(arr)/sizeof(arr[0]);
heapSort(arr, n);
cout << "Sorted array is ";
printArray(arr, n);
}
C )SHELL SORT :
#include<iostream.h>
#include<constream.h>
void read(int a[10],int n)
{
cout<<"reading ";
for(int i=0;i<n;i++)
cin>>a[i];
}
void display(int a[10],int n)
{
for(int i=0;i<n;i++)
cout<<a[i]<<"t";
}
void shellsort(int a[10],int n)
{
int gap=n/2;

6. do
{
int swap;
do
{
swap=0;
for(int i=0;i<n-gap;i++)
if(a[i]>a[i+gap])
{
int
t=a[i];
a[i]=a[i+gap];
a[i+gap]=t;
swap=1;
}
}
while(swap);
}
while(gap=gap/2);
}
void main()
{
int a[10];

7. int n;
clrscr();
cout<<"enter n ";
cin>>n;
read(a,n);
cout<<"before sorting ";
display(a,n);
shellsort(a,n);
cout<<" after sorting ";
display(a,n);
getch();
}