# Binary Search (Recursive and Iterative) in C Program

Binary Search is a search algorithm that is used to find the position of an element (target value ) in a sorted array. The array should be sorted prior to applying a binary search.

Binary search is also known by these names, logarithmic search, binary chop, half interval search.

## Working

The binary search algorithm works by comparing the element to be searched by the middle element of the array and based on this comparison follows the required procedure.

Case 1 − element = middle, the element is found return the index.

Case 2 − element > middle, search for the element in the sub-array starting from middle+1 index to n.

Case 3 − element < middle, search for element in the sub-array starting from 0 index to middle -1.

## ALGORITHM

Parameters inital_value , end_value

Step 1 : Find the middle element of array. using ,
middle = initial_value + end_value / 2 ;
Step 2 : If middle = element, return ‘element found’ and index.
Step 3 : if middle > element, call the function with end_value = middle - 1 .
Step 4 : if middle < element, call the function with start_value = middle + 1 .
Step 5 : exit.

The implementation of the binary search algorithm function uses the call to function again and again. This call can be of two types −

• Iterative
• Recursive

Iterative call is looping over the same block of code multiple times ]

Recursive call is calling the same function again and again.

## PROGRAM TO IMPLEMENT BINARY SEARCH USING ITERATIVE CALL

### Example

Live Demo

#include <stdio.h>
int iterativeBinarySearch(int array[], int start_index, int end_index, int element){
while (start_index <= end_index){
int middle = start_index + (end_index- start_index )/2;
if (array[middle] == element)
return middle;
if (array[middle] < element)
start_index = middle + 1;
else
end_index = middle - 1;
}
return -1;
}
int main(void){
int array[] = {1, 4, 7, 9, 16, 56, 70};
int n = 7;
int element = 16;
int found_index = iterativeBinarySearch(array, 0, n-1, element);
if(found_index == -1 ) {
printf("Element not found in the array ");
}
else {
printf("Element found at index : %d",found_index);
}
return 0;
}

### Output

Element found at index : 4

## PROGRAM TO IMPLEMENT BINARY SEARCH USING RECURSIVE CALL

### Example

Live Demo

#include <stdio.h>
int recursiveBinarySearch(int array[], int start_index, int end_index, int element){
if (end_index >= start_index){
int middle = start_index + (end_index - start_index )/2;
if (array[middle] == element)
return middle;
if (array[middle] > element)
return recursiveBinarySearch(array, start_index, middle-1, element);
return recursiveBinarySearch(array, middle+1, end_index, element);
}
return -1;
}
int main(void){
int array[] = {1, 4, 7, 9, 16, 56, 70};
int n = 7;
int element = 9;
int found_index = recursiveBinarySearch(array, 0, n-1, element);
if(found_index == -1 ) {
printf("Element not found in the array ");
}
else {
printf("Element found at index : %d",found_index);
}
return 0;
}

### Output

Element found at index : 3