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
logo
Events
Attend free live masterclass hosted by top tech professionals
New
Scaler
Explore Offerings by SCALER

Time Complexity

Go to Problems

Level 1

Jump to Level 2

Level 2

Jump to Level 3

Level 3

Jump to Level 4

Level 4

Jump to Level 5

Level 5

Jump to Level 6

Level 6

Jump to Level 7

Level 7

Jump to Level 8

Level 8

Be a Code Ninja!

Relevance of time complexity

Lets assume we ask 2 interviewees A and Bto write a program to detect if a number N >= 2 is prime.

A number is prime if it is divisible by exactly 2 distinct positive numbers 1 and the number itself. 
https://www.mathsisfun.com/prime-composite-number.html

A comes up with the following code :

 i = 2 
 while i < N
   if N is divisible by i
      N is not prime
   add 1 to i   

B comes up with the following code :

i = 2
while i <= square root of N
  if N is divisible by i 
    N is not prime
  add 1 to i

For now, lets assume that both codes are correct. 

Now, B claims that his code is much better as it takes much less time to check if N is prime. 

Lets look into why that is the case.

Lets assume that the operation N is divisible by i takes 1 ms. 

Lets look at few examples on time taken :

Example 1 :

N = 1000033 ( Prime number ) 
Time taken by A's program = 1 ms * number of divisions
                          = 1 ms * 1000033
                          = approximately 1000 seconds or 16.7 mins. 

Time taken by B's program = 1ms * number of divisions 
                          = 1ms * square root of 1000033
                          = approximately 1000ms = 1 second. 

Example 2 :

N = 1500450271 ( Prime number ) 
Time taken by A's program = 1 ms * number of divisions
                          = 1 ms * 1500450271
                          = approximately 1000000 seconds or 11.5 days 

Time taken by B's program = 1ms * number of divisions 
                          = 1ms * square root of 1500450271
                          = approximately 40000ms = 40 seconds.

As you can see B’s program is significantly faster even though both methods of solving the problem are correct. 

This is where time complexity of programs comes in, which is a measure of how efficient ( or quick ) a program is for large inputs. 

In first case, time taken is directly proportional to N, whereas in second case it is directly proportional to square root of N. In later slides, we will look into how we can formalize it into time complexity notations.

Serious about Learning Programming ?

Learn this and a lot more with Scaler Academy's industry vetted curriculum which covers Data Structures & Algorithms in depth.

This topic has only Multiple Choice Questions

Jump to subsequent topics to solve code problems.

Time Complexity Problems

Basic primer
Problem Score Companies Time Status
LOOP_CMPL 20 2:43
NESTED_CMPL 20
1:10
NESTED_CMPL2 30
1:25
CHOOSE4 50
0:57
Math
Problem Score Companies Time Status
WHILE_CMPL 50
1:31
NESTED_CMPL3 80 3:56
LOOP_CMPL2 80
2:43
GCD_CMPL 150
4:13
Compare functions
Problem Score Companies Time Status
CHOOSE3 50
1:39
CHOOSE1 50
1:43
CHOOSE2 80
2:23
Function calling itself
Problem Score Companies Time Status
REC_CMPL1 80
6:58
REC_CMPL2 80
6:25
REC_CMPL3 150
4:39
Amortized complexity
Problem Score Companies Time Status
AMORTIZED1 100
3:03
Excel at your interview with Masterclasses Know More
Certificate included
What will you Learn?
Free Mock Assessment
Fill up the details for personalised experience.
All fields are mandatory
Current Employer *
Enter company name *
Graduation Year *
Select an option *
1993
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
Phone Number *
OTP will be sent to this number for verification
+91 *
+91
Change Number
Phone Number *
OTP will be sent to this number for verification
+91 *
+91
Change Number
Graduation Year *
Graduation Year *
1993
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
*Enter the expected year of graduation if you're student
Current Employer *
Company Name *
Please verify your phone number
Edit
Resend OTP
By clicking on Start Test, I agree to be contacted by Scaler in the future.
Already have an account? Log in
Free Mock Assessment
Instructions from Interviewbit
Start Test