Binary Search

CODE

Binary Search

Given a sorted array arr[] of n elements, write a function to search a given element x in arr[].

Binary Search: Search a sorted array by repeatedly dividing the search interval in half. Begin with an interval covering the whole array. If the value of the search key is less than the item in the middle of the interval, narrow the interval to the lower half. Otherwise narrow it to the upper half. Repeatedly check until the value is found or the interval is empty.

Recursive implementation of Binary Search

// C program to implement recursive Binary Search

#include <stdio.h>  

// A recursive binary search function. It returns 

// location of x in given array arr[l..r] is present, 

// otherwise -1

int binarySearch(int arr[], int l, int r, int x)

{

   if (r >= l)

   {

        int mid = l + (r - l)/2;

          // If the element is present at the middle 

        // itself

        if (arr[mid] == x)  

            return mid;

         // If element is smaller than mid, then 

        // it can only be present in left subarray

        if (arr[mid] > x) 

            return binarySearch(arr, l, mid-1, x);

          // Else the element can only be present

        // in right subarray

        return binarySearch(arr, mid+1, r, x);

   }

   // We reach here when element is not 

   // present in array

   return -1;

}

int main(void)

{

   int arr[] = {2, 3, 4, 10, 40};

   int n = sizeof(arr)/ sizeof(arr[0]);

   int x = 10;

   int result = binarySearch(arr, 0, n-1, x);

   (result == -1)? printf("Element is not present in array")  : printf("Element is present at index %d",  result);

   return 0;

}

Output :

Element is present at index 3

Iterative implementation of Binary Search

// C program to implement iterative Binary Search

#include <stdio.h>

// A iterative binary search function. It returns

// location of x in given array arr[l..r] if present,

// otherwise -1

int binarySearch(int arr[], int l, int r, int x)

{

    while (l <= r)

    {

        int m = l + (r-l)/2;

        // Check if x is present at mid

        if (arr[m] == x)

            return m;

        // If x greater, ignore left half

        if (arr[m] < x)

            l = m + 1;   

        // If x is smaller, ignore right half

        else

            r = m - 1;

    }   

    // if we reach here, then element was

    // not present

    return -1;

}

  int main(void)

{

    int arr[] = {2, 3, 4, 10, 40};

    int n = sizeof(arr)/ sizeof(arr[0]);

    int x = 10;

    int result = binarySearch(arr, 0, n-1, x);

    (result == -1)? printf("Element is not present in array"): printf("Element is present at index %d",result);

    return 0;

}

Output :

Element is present at index 3