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

# Time Complexity

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

### Time Complexity Of A Computer Program

#### What is Time complexity and What is its need?

Let us take one example, suppose your friend picked a number between 1 to 1000 and he told you to guess the number. If your guess is correct he will tell you that it is correct, otherwise, if your guess is bigger than his number he would tell you that it's 'too big and if it is smaller than his number then he would tell you that it is ‘too small. Here are some ways by which we could find the number.

• We can guess each number from 1 to 1000, and see if it is correct.
• We can pick the middle number, if he says ‘too big’ then we know for sure that the number is on the left side so we can discard the right side, similarly if he says ‘too small’ we can discard the left side. We can repeat the same process until he says it's correct.

#### Which way do you think is better?

As you might have guessed correctly, the 2nd way is actually way better than the first way. In the worst case, the 1st way would take 1000 guesses before we get the correct number ( if the number is 1000 ), while the 2nd way would only take 10 guesses in the worst case ( this is because at every guess we discard one of the halves).

Later you would see that the time complexity of the first way is O(n) and that of the second way is O(logn).

As we saw from the above example there can be multiple approaches to solving the same problem. The same applies to computer programming. For every approach (algorithm) the time taken, amount of space used, and computational power might be different. Therefore there has to be a way by which we can distinguish these different approaches (algorithms) and choose the one which is the most efficient.

In this article, we are going to speak about how we can choose the best algorithm based on the time taken by an algorithm to execute. But how do we compare the algorithms which are written in two different languages, running on two different machines? This is exactly why the concept of time complexity was introduced. But what is time complexity?

By definition, Time complexity is the time taken by an algorithm/program to run as a function of the length of the input.

Why is it so important?

• It can clearly distinguish between two different algorithms based on their efficiency.
• It’s independent of the machine on which the algorithm is run.
• We can get a direct correlation with the length of the input.

It’s important to note here that time complexity doesn’t really measure the actual time taken by an algorithm to run ( Since that kind of depends on the programming language, processing power etc.). It calculates the execution time of an algorithm in terms of the algorithms and the inputs.

## Time Complexity Problems

0/4
Basic primer
0/4
Math
0/3
Compare functions
0/3
Function calling itself
0/1
Amortized complexity
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 you graduated from
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