Binary Search

Binary Search is a searching algorithm that is used to find the position of an element in a sorted array.

Sorted means array stored in increasing order or decreasing order.

Binary means (divide and conquer)

• Bi => Two
• n => n
• ary => array

FORMULA

• start=mid+1
• mid = (start+end)/2
• end=mid-1

Example 3:

#include <iostream>
using namespace std;
int main() {

    int number[10] = {10,20,30,40,50,60,70,80,90,100};

    int key;
    cout<<"Enter Number do you want to search: ";
    cin>>key;

    int start=0;
    int end=9;

    while(start<=end)
    {
       int mid = (start + end) / 2;

       if(key==number[mid])
       {
           cout<<"Element found at: "<<mid;
           break;
       }
       else if(key>number[mid])
       {
           start = mid + 1;
       }
       else
       {
           end = mid - 1;
       }
    }
    return 0;
}

Output :

Which number do you want to search: 100
Element found at: 9

Explanation :

Declare array that name has number and size of array is 10 stored value is {10,20,30,40,50,60,70,80,90,100} datatype of array is int.
Declare key variable, datatype is int.
Print message Enter Number do you want to search using cout.
store value in key variable using cin object.
initialize start varible store value is 0.
initialize another end variable store value is 9.
start while and check condition (start<=end).
check this formula mid = (start + end) / 2;.
check if(key==number[mid]) and print Element found at: using cout and print mid variable.and break statements.
check next condition else if(key>number[mid]) start = mid + 1. this condition is false then execute else condition. end = mid - 1.