Question

IN C++

Write a program to find the number of comparisons using binarySearch and the sequential search algorithm as follows:
Suppose list is an array of 1000 elements.

3 Search list for some items as follows:
a. Use the binary search algorithm to search the list. (You may need to modify the algorithm given in this chapter to count the number of comparisons.)
b. Use the binary search algorithm to search the list, switching to a sequentialsearch when the size of the search list reduces to less than 15. (Use the sequential search algorithm for a sorted list.)
Print the number of comparisons for Questions 3a and b. If the item is found in the list, then print its position.

Answer 1

a.

#include <iostream>

using namespace std;

//binary search algorithm
int binarySearch(int arr[], int min, int max, int target)
{
//in every recursive call we are comparing the element three time
//compare one
  
if (max >= min)
{
//Compute guess as the average of max and min
int guess = (max+min)/2;

//compare two
if (arr[guess] == target)
{

  cout<<endl<<"The item found at location: "<<guess<<endl;
return guess;
}
  
//compare three
if (arr[guess] > target)
return 3+binarySearch(arr, min, guess - 1, target);

return 3+ binarySearch(arr, guess + 1, max, target);
}
  
return 1;
}

//function to sort an array
void bubbleSort(int a[], int size)
{
//outer for loop
for(int i=0;i<size;i++)
{
//inner for loop
for (int j=0;j<size;j++)
{
if(a[i]<a[j])
{
//swap the values
int temp = a[i];
a[i]=a[j];
a[j] = temp;
}
}
}
}

int main()
{
//array declaration
int arr[1000];
  
//fill array with random number
for(int i=0; i<1000; i++)
{
//fill with random number
arr[i] = rand()%1000;
}
  
//method calling
bubbleSort(arr,1000);
  
//display the result
cout<<endl<<"The number of comparison in binary search = "<<binarySearch(arr,0, 1000, 800);
  
return 0;
}

OUTPUT:

The number of comparison in binary search = 31

b.

#include <iostream>

using namespace std;

//function to find an element using sequential search
int sequentialSearch(int arr[], int size, int target)
{
int countNumCom = 0;
for(int i=0; i<size; i++)
{
countNumCom++;
if(arr[i] == target)

{

  cout<<endl<<"The item found at location: "<<i<<endl;
return i;

}
}
  
return countNumCom;
}

//binary search algorithm
int binarySearch(int arr[], int min, int max, int target)
{
//in every recursive call we are comparing the element three time
//compare one
  
//if the size of the array is less than 15 then sequential search
if((max-min) <15)
{
int smallArr[max-min];
for(int i=0; i<(max-min); i++)
smallArr[i] = arr[min++];
  
int count = sequentialSearch(smallArr, (max-min), target);
  
return count;
}
if (max >= min)
{
//Compute guess as the average of max and min
int guess = (max+min)/2;

//compare two
if (arr[guess] == target)
{

  cout<<endl<<"The item found at location: "<<guess<<endl;
return guess;
}
  
//compare three
if (arr[guess] > target)
return 3+binarySearch(arr, min, guess - 1, target);

return 3+ binarySearch(arr, guess + 1, max, target);
}
  
return 1;
}

//function to sort an array
void bubbleSort(int a[], int size)
{
//outer for loop
for(int i=0;i<size;i++)
{
//inner for loop
for (int j=0;j<size;j++)
{
if(a[i]<a[j])
{
//swap the values
int temp = a[i];
a[i]=a[j];
a[j] = temp;
}
}
}
}

int main()
{
//array declaration
int arr[1000];
  
//fill array with random number
for(int i=0; i<1000; i++)
{
//fill with random number
arr[i] = rand()%1000;
}
  
//method calling
bubbleSort(arr,1000);
  
//display the result
cout<<"The number of comparison in sequential search = "<<sequentialSearch(arr, 1000, 800);
cout<<endl<<"The number of comparison in binary search = "<<binarySearch(arr,0, 1000, 800);
return 0;
}

OUTPUT:

The number of comparison in sequential search = 1000
The number of comparison in binary search = 25