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
#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
#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