Recursive Binary Search Algorithm

Complexity Analysis of Binary Search Algorithm:

Create a recursive function and compare the mid of the search space with the key. And based on the result either return the index where the key is found or call the recursive function for the next search space.

Implementation of Recursive Binary Search Algorithm:

C++

#include <bits/stdc++.h>
using namespace std;

// A recursive binary search function. It returns
// location of x in given array arr[low..high] is present,
// otherwise -1
int binarySearch(int arr[], int low, int high, int x)
{
    if (high >= low) {
        int mid = low + (high - low) / 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, low, mid - 1, x);

        // Else the element can only be present
        // in right subarray
        return binarySearch(arr, mid + 1, high, x);
    }
}

// Driver code
int main()
{
    int arr[] = { 2, 3, 4, 10, 40 };
    int query = 10;
    int n = sizeof(arr) / sizeof(arr[0]);
    int result = binarySearch(arr, 0, n - 1, query);
    (result == -1)
        ? cout << "Element is not present in array"
        : cout << "Element is present at index " << result;
    return 0;
}

// C program to implement recursive Binary Search
#include <stdio.h>

// A recursive binary search function. It returns
// location of x in given array arr[low..high] is present,
// otherwise -1
int binarySearch(int arr[], int low, int high, int x)
{
    if (high >= low) {
        int mid = low + (high - low) / 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, low, mid - 1, x);

        // Else the element can only be present
        // in right subarray
        return binarySearch(arr, mid + 1, high, x);
    }

    // We reach here when element is not
    // present in array
    return -1;
}

// Driver code
int main()
{
    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;
}

Java

// Java implementation of recursive Binary Search
class BinarySearch {

    // Returns index of x if it is present in arr[low..
    // high], else return -1
    int binarySearch(int arr[], int low, int high, int x)
    {
        if (high >= low) {
            int mid = low + (high - low) / 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, low, mid - 1, x);

            // Else the element can only be present
            // in right subarray
            return binarySearch(arr, mid + 1, high, x);
        }

        // We reach here when element is not present
        // in array
        return -1;
    }

    // Driver code
    public static void main(String args[])
    {
        BinarySearch ob = new BinarySearch();
        int arr[] = { 2, 3, 4, 10, 40 };
        int n = arr.length;
        int x = 10;
        int result = ob.binarySearch(arr, 0, n - 1, x);
        if (result == -1)
            System.out.println(
                "Element is not present in array");
        else
            System.out.println(
                "Element is present at index " + result);
    }
}
/* This code is contributed by Rajat Mishra */

Python

# Python3 Program for recursive binary search.


# Returns index of x in arr if present, else -1
def binarySearch(arr, low, high, x):

    # Check base case
    if high >= low:

        mid = low + (high - low) // 2

        # If 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
        elif arr[mid] > x:
            return binarySearch(arr, low, mid-1, x)

        # Else the element can only be present
        # in right subarray
        else:
            return binarySearch(arr, mid + 1, high, x)

    # Element is not present in the array
    else:
        return -1


# Driver Code
if __name__ == '__main__':
    arr = [2, 3, 4, 10, 40]
    x = 10
    
    # Function call
    result = binarySearch(arr, 0, len(arr)-1, x)
    
    if result != -1:
        print("Element is present at index", result)
    else:
        print("Element is not present in array")

// C# implementation of recursive Binary Search
using System;

class GFG {

    // Returns index of x if it is present in
    // arr[low..high], else return -1
    static int binarySearch(int[] arr, int low, int high, int x)
    {
        if (high >= low) {
            int mid = low + (high - low) / 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, low, mid - 1, x);

            // Else the element can only be present
            // in right subarray
            return binarySearch(arr, mid + 1, high, x);
        }

        // We reach here when element is not present
        // in array
        return -1;
    }

    // Driver code
    public static void Main()
    {

        int[] arr = { 2, 3, 4, 10, 40 };
        int n = arr.Length;
        int x = 10;

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

        if (result == -1)
            Console.WriteLine(
                "Element is not present in arrau");
        else
            Console.WriteLine("Element is present at index "
                              + result);
    }
}

// This code is contributed by Sam007.

Javascript

// JavaScript program to implement recursive Binary Search

// A recursive binary search function. It returns
// location of x in given array arr[low..high] is present,
// otherwise -1
function binarySearch(arr, low, high, x){
    if (high >= low) {
        let mid = low + Math.floor((high - low) / 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, low, mid - 1, x);

        // Else the element can only be present
        // in right subarray
        return binarySearch(arr, mid + 1, high, x);
    }

    // We reach here when element is not
    // present in array
    return -1;
}

let arr = [ 2, 3, 4, 10, 40 ];
let x = 10;
let n = arr.length
let result = binarySearch(arr, 0, n - 1, x);
(result == -1) ? console.log( "Element is not present in array")
               : console.log("Element is present at index " +result);

PHP

<?php
// PHP program to implement
// recursive Binary Search

// A recursive binary search
// function. It returns location
// of x in given array arr[low..high] 
// is present, otherwise -1
function binarySearch($arr, $low, $high, $x)
{
if ($high >= $low)
{
        $mid = ceil($low + ($high - $low) / 2);

        // If the element is present 
        // at the middle itself
        if ($arr[$mid] == $x) 
            return floor($mid);

        // If element is smaller than 
        // mid, then it can only be 
        // present in left subarray
        if ($arr[$mid] > $x) 
            return binarySearch($arr, $low, 
                                $mid - 1, $x);

        // Else the element can only 
        // be present in right subarray
        return binarySearch($arr, $mid + 1, 
                            $high, $x);
}

// We reach here when element 
// is not present in array
return -1;
}

// Driver Code
$arr = array(2, 3, 4, 10, 40);
$n = count($arr);
$x = 10;
$result = binarySearch($arr, 0, $n - 1, $x);
if(($result == -1))
echo "Element is not present in array";
else
echo "Element is present at index ",
                            $result;
                          
?>

Output

Element is present at index 3

Binary Search Algorithm – Iterative and Recursive Implementation

Binary Search Algorithm is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log N).

Recursive Binary Search Algorithm

Binary Search Algorithm – Iterative and Recursive Implementation

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