Binary Search Algorithm – Iterative and Recursive Implementation

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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). 

Binary Search Algorithm

What is Binary Search Algorithm?

Binary search is a search algorithm used to find the position of a target value within a sorted array. It works by repeatedly dividing the search interval in half until the target value is found or the interval is empty. The search interval is halved by comparing the target element with the middle value of the search space.

Conditions to apply Binary Search Algorithm in a Data Structure

To apply Binary Search algorithm:

• The data structure must be sorted.
• Access to any element of the data structure should take constant time.

Binary Search Algorithm

Below is the step-by-step algorithm for Binary Search:

• Divide the search space into two halves by finding the middle index “mid”. 
• Compare the middle element of the search space with the key. 
• If the key is found at middle element, the process is terminated.
• If the key is not found at middle element, choose which half will be used as the next search space.
  • If the key is smaller than the middle element, then the left side is used for next search.
  • If the key is larger than the middle element, then the right side is used for next search.
• This process is continued until the key is found or the total search space is exhausted.

Binary Search Visualizer

How does Binary Search Algorithm work?

To understand the working of binary search, consider the following illustration:

Consider an array arr[] = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91}, and the target = 23.

How to Implement Binary Search Algorithm?

The Binary Search Algorithm can be implemented in the following two ways

• Iterative Binary Search Algorithm
• Recursive Binary Search Algorithm

Given below are the pseudocodes for the approaches.

Iterative Binary Search Algorithm:

Here we use a while loop to continue the process of comparing the key and splitting the search space in two halves.

// C++ program to implement iterative Binary Search
#include <bits/stdc++.h>
using namespace std;

// An iterative binary search function.
int binarySearch(int arr[], int low, int high, int x)
{
    while (low <= high) {
        int mid = low + (high - low) / 2;

        // Check if x is present at mid
        if (arr[mid] == x)
            return mid;

        // If x greater, ignore left half
        if (arr[mid] < x)
            low = mid + 1;

        // If x is smaller, ignore right half
        else
            high = mid - 1;
    }

    // If we reach here, then element was not present
    return -1;
}

// Driver code
int main(void)
{
    int arr[] = { 2, 3, 4, 10, 40 };
    int x = 10;
    int n = sizeof(arr) / sizeof(arr[0]);
    int result = binarySearch(arr, 0, n -