Practice
Resources
Contests
Online IDE
New
Free Mock
Events New Scaler
Practice
Improve your coding skills with our resources
Contests
Compete in popular contests with top coders
Events
Attend free live masterclass hosted by top tech professionals
New
Scaler
Explore Offerings by SCALER

## Binary Search

Last Updated: Nov 17, 2023
Go to Problems
Binary Search
Complete all the problems in this Topic to unlock a badge
Completed
Go to Problems
Contents

# Binary Search Algorithm

### How does Binary Search Work?

Binary search works by repeatedly dividing the array into two halves that can contain the given target element, till the search area is limited to just one element. The necessary condition for binary search to work is the array needs to be sorted

### Binary Search Example:

Given a sorted array, find if element 2 is present in the array.

Step 1: The given array:

Step 2: Consider two pointers, low = 0 and high = N - 1, where N is the size of the array.

Step 3: Find the mid, i.e. mid = (low + high) / 2. Here, mid = (0 + 6) / 2 = 3.

Step 4: Now, check for three conditions:

• Compare if A[mid] = 2
• Compare if A[mid] > 2
• Compare if A[mid] < 2
• It can be observed that, A[mid] = 9, which is > 2, therefore, we shift, high = mid - 1.

Step 5: If A[mid] < 2, shift low = mid + 1.

Step 6: Repeat Steps 3 to Step 5, until the search area is limited to just one element i.e. low = high.

Step 7: The value 2 is found.

### Binary Search Implementations

Binary Search can be implemented in mainly two ways:

• Recursive method
• Iterative method

Let us first discuss the Recursive method.

### Recursive Method

``````
int bSearch(int arr[], int left, int right, int target) {
if (right >= left) {
int mid = left + (right - left) / 2;

if (arr[mid] == target)
return mid;

if (arr[mid] > target)
return binarySearch(arr, left, mid - 1, target);

return binarySearch(arr, mid + 1, right, target);
}
return -1;
}``````
``````
class BinarySearch {
int bSearch(int arr[], int left, int right, int target) {
if (right >= l) {
int mid = l + (r - l) / 2;

if (arr[mid] == target)
return mid;

if (arr[mid] > target)
return binarySearch(arr, left, mid - 1, target);

return binarySearch(arr, mid + 1, r, x);
}
return -1;
}
}
``````
``````
def bSearch(arr, left, right, target):
if right >= left:

mid = left + (right - left) // 2

if arr[mid] == target:
return mid

elif arr[mid] > target:
return binarySearch(arr, left, mid-1, target)

else:
return binarySearch(arr, mid + 1, right, target)

else:
return -1

``````

Time Complexity :

• Best Case Complexity : O(logN)
• Average Case Complexity : O(logN)
• Worst Case Complexity : O(logN)

### Iterative Method

``````
int bSearch(int arr[], int left, int right, int target) {
while (left <= right) {
int m = left + (right - left) / 2;

if (arr[m] == target)
return m;

if (arr[m] < target)
left = m + 1;

else
right = m - 1;
}

return -1;
}

``````
``````
class BinarySearch {
int bSearch(int arr[], int left, int right, int target)
{
int left = 0, right = arr.length - 1;
while (left <= right) {
int m = left + (right - left) / 2;

if (arr[m] == target)
return m;

if (arr[m] < target)
left = m + 1;

else
right = m - 1;
}
return -1;
}
}
``````
``````
def bSearch(arr, left, right, target):
while left <= right:

mid = left + (right - left) // 2

if arr[mid] == target:
return mid

elif arr[mid] < target:
left = mid + 1

else:
right = mid - 1

return -1

``````

Time Complexity :

• Best Case Complexity : O(logN)
• Average Case Complexity : O(logN)
• Worst Case Complexity : O(logN)

Walkthrough Examples :

0/2
Examples

## Binary Search Problems

0/6
Simple binary search
0/6
0/2
Search step simulation
0/2
Sort modification
Topic Bonus
Bonus will be unlocked after solving min. 1 problem from each bucket

## Video Courses By

View All Courses
Excel at your interview with Masterclasses Know More
Certificate included
What will you Learn?
Free Mock Assessment
Fill up the details for personalised experience.
Phone Number *
OTP will be sent to this number for verification
+91 *
+91
Change Number
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
*Enter the expected year of graduation if you're student
Current Employer
Company Name
College/University Name
Job Title
Job Title
Software Development Engineer (Backend)
Software Development Engineer (Frontend)
Software Development Engineer (Full Stack)
Data Scientist
Android Engineer
iOS Engineer
Devops Engineer
Support Engineer
Research Engineer
Engineering Intern
QA Engineer
Co-founder
SDET
Product Manager
Product Designer
Backend Architect
Program Manager
Release Engineer