# C++ Program to Compare Binary and Sequential Search

Binary Search and Sequential or Linear Search both are used in computer programming to search an element. The time complexity of Binary Search is O(log(n)) and Sequential Search is O(n).

## Algorithm

Begin
Algorithm for Binary Search:
BinarySearch() function with ‘arr’ the array of data and ‘n’ the number of values, start and end index, iteration count and element to be searched in the argument list.
Increment iteration counter and compare the item value with the a[mid].
If item < a[mid] choose first half otherwise second half to proceed further.
Return iteration value on successful search.
End

## Example Code

#include<iostream>
using namespace std;
int BinarySearch(int a[], int start, int end, int item, int iter) {
int i, mid;
cout<<"\niteration "<<iter+1;
iter++;
mid = start + (end-start+1)/2;
if(item > a[end] || item < a[start] || mid == end) {
return iter;
} else if(item == a[mid]) {
cout<<"\n item found at "<<mid<<" index.";
return iter;
} else if(item == a[start]) {
cout<<"\n item found at "<<start<<" index.";
return iter;
} else if(item == a[end]) {
cout<<"\n item found at "<<end<<" index.";
return iter;
} else if(item > a[mid])
BinarySearch(a, mid, 9, item, iter);
else
BinarySearch(a, start, mid, item, iter);
}
int LinearSearch(int a[], int n, int item) {
int i;
for(i = 0; i < n; i++) {
cout<<"\niteration "<<i+1;
if(a[i] == item) {
cout<<"\n item found at "<<i<<" index.";
return i+1;
}
}
}
int main() {
int n, i, B, L, a[10]={2, 7, 14, 24, 26, 35, 38, 41, 49, 53};
cout<<"\nEnter the element to be searched: ";
cin>>n;
cout<<"\n\n\t\t\tBinary Search :";
B = BinarySearch(a, 0, 9, n, 0);
cout<<"\n\n\t\t\tLinear Search :";
L = LinearSearch(a, 10, n);
if(L > B)
cout<<"\n\nBinary search is better for this search.";
else if(L < B)
cout<<"\n\nLinear search is better for this search.";
else
cout<<"\n\nBoth are equally efficient for this search.";
return 0;
}

## Output

Enter the element to be searched: 7
Binary Search :
iteration 1
iteration 2
iteration 3
iteration 4
item found at 1 index.
Linear Search :
iteration 1
iteration 2
item found at 1 index.
Linear search is better for this search.
Enter the element to be searched: 53
Binary Search :
iteration 1
item found at 9 index.
Linear Search :
iteration 1
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
iteration 10
item found at 9 index.
Binary search is better for this search.
Enter the element to be searched: 1
Binary Search :
iteration 1
Linear Search :
iteration 1
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
iteration 10
Binary search is better for this search.