# Binary Search in C++

The binary search in the C++ programming language will be discussed. By continually halves the array and then seeking specified items from a half array; binary search is a technique for finding supplied elements from a sorted array. And so on until the perfect match is found. Only sorted data structures are supported. The binary search algorithm has an O time complexity (log n).

### Algorithm

The algorithm for performing a binary search in C++ is as follows:

• As a search key, start with the middle member of the whole array.
• Return an index of the search key if the value of the search key is equal to the item.
• Alternatively, if the search key's value is smaller than the item in the interval's middle, limit the interval to the bottom half.
• Otherwise, limit it to the upper half of the page.
• Check the value from the second point until the interval is empty or the value is discovered.
``````beg = 0 ;
end = size - 1 ;
while ( beg < = end )
{
// calculate mid value
mid = ( beg + end ) / 2 ;
/* if the specified element is found at mid index, terminate the process and return the index. */
// Check middle element is equal to the defined element.
If ( arr [ mid ] = = num )
{
return mid + 1 ;
}
else if ( arr [ mid ] > num )
{
end = mid - 1 ;
}
else if ( arr [ mid ] < num )
{
Beg = mid + 1 ;
}
}
// If the element does not exist in the array, return -1.
Return -1 ;
``````

### In C++ follow these steps to execute a binary search:

Step 1: Declare the variables and sort all of the items in an array (ascending or descending).

Step 2: Split the array element listings into halves.

Step 3: Now compare the target items to the array's centre member. Return the location of the middle element and finish the search if the target element's value matches that of the middle element.

Step 4: If the target element is less than the middle element, we look for it in the array's lower half.

Step 5: If the target element is larger than the centre element, we must look for it in the array's greater half.

Example 1: Using the binary search, locate the provided integer from a sorted array:

Let's use the C++ programming language to create a program that uses the binary search to discover a certain integer from a sorted array.

``````#include < iostream >
#include < bits/stdc++.h >
#include < stdio >
#include < stdlib >
#include < conio.h >
using namespace std ;
int main ( )
{
// declaration of the variables and array
int arr [ 100 ] , st , mid , end , i , num , tgt ;
cout << " Define the size of the array: " << endl ;
cin >> num ; // get size
// enter only sorted array
cout << " enter the values in sorted array either ascending or descending order: " << endl ;
// use for loop to iterate values
for ( i = 0 ; i < num ; i++ )
{
cout << " arr [ " << i << " ] = " ;
cin >> arr [ i ] ;
}
// initialize the starting and ending variable's values
st = 0 ;
end = num - 1 ; // size of array ( num ) - 1
// define the item or value to be search
cout << " Define a value to be searched from sorted array: " << endl ;
cin >> tgt ;
// use while loop to check 'st', should be less than equal to 'end'.
while ( st < = end )
{
// get middle value by splitting into half
mid = ( st + end ) / 2 ;
/* if we get the target value at mid index, print the position and exit from the program. */
if ( arr [ mid ] == tgt )
{
cout << " element is found at index " << ( mid + 1 ) ;
exit ( 0 ) ;  // use for exit program the program
}
// check the value of target element is greater than the mid element' value
else if ( tgt > arr [ mid ] )
{
st = mid + 1 ; // set the new value for st variable
}
// check the value of target element is less than the mid element' value
else if ( tgt < arr [ mid ] )
{
end = mid - 1 ; // set the new value for end variable
}
}
return 0 ;
}
``````

OUTPUT:

``````Define the size of the array:
10
enter the values in sorted array either ascending or descending order:
Arr [ 0 ]  = 12
Arr [ 1 ]  = 24
Arr [ 2 ]  = 36
Arr [ 3 ]  = 48
Arr [ 4 ]  = 50
Arr [ 5 ]  = 54
Arr [ 6 ]  = 58
Arr [ 7 ]  = 60
Arr [ 8 ]  = 72
Arr [ 9 ]  = 84
Define a value to be searched from sorted array:
50
element is found at index 5
……………………………………………………………………..
Process executed in 2.22 seconds
Press any key to continue.
``````

Explanation:

In the above example of a program in C++, search for a element in a sorted array. First we find the middle element and then comparing our element or key with the middle element if the key is les then middle element then we bring the end pointer from last element to mid+1 and performing the procedure again till we find the element or the key.

Example 4: Another type of iterative function program for binary search in C++:

``````#include < bits/stdc++.h >
#include < stdio >
#include < stdlib >
#include < vector >
#include < iostream >
using namespace std ;
int binarySearch ( vector < int > v , int To_Find )
{
int lo = 0 , hi = v.size ( ) - 1 ;
int mid ;
// This below check covers all cases , so need to check
// for mid = lo - ( hi - lo ) / 2
while ( hi - lo > 1 ) {
int mid = ( hi + lo ) / 2 ;
if ( v [ mid ] < To_Find ) {
lo = mid + 1 ;
}
else {
hi = mid ;
}
}
if ( v [ lo ] == To_Find ) {
cout << "Found"
<< " At Index " << lo << endl ;
}
else if ( v [ hi ] == To_Find ) {
cout << "Found"
<< " At Index " << hi << endl ;
}
else {
}
}
int main ( )
{
vector < int > v = { 1 , 3 , 4 , 5 , 6 } ;
int To_Find = 1 ;
binarySearch ( v , To_Find ) ;
To_Find = 6 ;
binarySearch ( v , To_Find ) ;
To_Find = 10 ;
binarySearch ( v , To_Find ) ;
return 0 ;
}
``````

OUTPUT:

``````Found At Index 0
Found At Index 4
……………………….
Process executed in 2.22 seconds
Press any key to continue.
``````

Explanation

In the above example of a program in C++, we have used vector instead of array and using to_find function but using while loop and using mid pointer as we have discussed which is created by initializing lo pointer at index 0 and hi at index n-1, where n is the length of the vector. If the element which we want to find is the element which is present at the middle element, then middle element is our element or the key.

Example 3: A program that uses a user-defined function to execute a binary search.

``````/* program to find the specified element from the sorted array using the binary search in C++. */
#include < iostream >
using namespace std ;
/* create user-defined function and pass different parameters:
arr [ ] - it represents the sorted array;
num variable represents the size of an array;
tgt variable represents the target or specified variable to be searched in the sorted array. */
int bin_search ( int arr [ ] , int num , int tgt )
{
int beg = 0 , end = num – 1 ;
// use loop to check all sorted elements
while ( beg < = end )
{
/* get the mid value of sorted array and then compares with target element. */
int mid = ( beg + end ) / 2 ;
if ( tgt = = arr [ mid ] )
{
return mid ; // when mid is equal to tgt value
}
// check tgt is less than mid value, discard left element
else if ( tgt < arr [ mid ] )
{
end = mid – 1 ;
}
// if the target is greater than the mid value, discard all elements
else {
beg = mid + 1 ;
}
}
// return -1 when target is not exists in the array
return -1 ;
}
int main ( )
{
// declaration of the arrays
int arr [ ] = { 5 , 10 , 15 , 20 , 25 , 30 , 37 , 40 } ;
int tgt = 25 ; // specified the target element
int num = sizeof ( arr ) / sizeof ( arr [ 0 ] ) ;
// declare pos variable to get the position of the specified element
int pos = bin_search ( arr , num , tgt ) ;
if ( pos ! = 1 )
{
cout << " element is found at position " << ( pos + 1 ) << endl;
}
else
{
cout << " element is not found in the array" << endl ;
}
return 0 ;
}
``````

OUTPUT:

``````element is found at position 5
……………………………………………
Process executed in 2.22 seconds
Press any key to conitinue.
``````

Explanation

We defined an array arr [ ] = { 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 } in the preceding program, and then we supplied number '25' as the number to seek from the sorted array using the binary search method. As a result, we write the bin search ( ) user-defined function, which searches the supplied integer and returns the message "Element is located at position 5". The bin search ( ) method returns "Element not found in the array" if the number is not specified in the array.

Example 4: Using the recursion function, discover the requested element:

Let's look at an example of utilizing the binary search within the recursion function to see if the provided element is found in the sorted array.

``````/* find the specified number using the binary search technique inside the recursion method. */
#include < iostream >
#include < bits/stdc++.h >
#include < stdlib >
#include < stdio >
using namespace std;
// define a function
int binary_search ( int [ ] , int , int , int ) ;
int main ( )
{
// declaration of the variables
int i , arr [ 100 ] , tgt , num , ind , st , end ;
cout << " Define the size of an array: " ;
cin >> num ;
cout << " enter " << num << " elements in ascending order: " << endl ;
// use for loop to ieterate the number
for ( i = 0 ; i < num ; i++ )
{
cout << " arr [ " << i << " ] = " ;
cin >> arr [ i ] ;
}
// define the element to be search
cout << " \n enter an element to be searched in ascending array: " ;
cin >> tgt ;
// ind define the index number
ind = binary_search ( arr , 0 , num - 1 , tgt) ;
// check for existemce of the specified element
if ( ind = = 0 )
cout << tgt << " is not available in the array-list" ;
else
cout << tgt << " is available at position " << ind << endl ;
return 0 ;
}
// function defnition
int binary_search ( int arr [ ] , int st , int end , int tgt )
{
int mid ;
// check st is greater than end
if ( st > end )
{
return 0 ;
}
mid = ( st + end ) / 2 ; // get middle value of the sorted array

// check middle value is equal to target number
if (arr [ mid ] == tgt )
{
return ( mid + 1 ) ;
}
// check mid is greater than target number
else if ( arr [ mid ] > tgt )
{
binary_search ( arr , st , mid - 1 , tgt ) ;
}
// check mid is less than target number
else if ( arr [ mid ] < tgt )
{
binary_search ( arr , mid + 1 , end , tgt ) ;
}
}
``````

OUTPUT:

``````Define the size of an array: 10
Arr [ 0 ] = 2
Arr [ 1 ] = 4
Arr [ 2 ] = 5
Arr [ 3 ] = 8
Arr [ 4 ] = 12
Arr [ 5 ] = 13
Arr [ 6 ] = 27
Arr [ 7 ] = 36
Arr [ 8 ] = 49
Arr [ 9 ] = 51
enter an element to be searched in ascending array: 12
12 is available at position 6.
…………………………………………………………………………………
Process executed in 2.22 seconds
Press any key to continue.
``````

Explanation

We input all items of an array in ascending order in the aforementioned software, and then define a number as the target element, which is '12,' which is found from a sorted array using the binary search method. As a result, we develop the binary search () user-defined function, which searches an array for the given element's location and returns the specific element accessible at that point. It also returns 0 if the element isn't found in the sorted array.