Time & Space Complexity Basics: Big O Notation Explained for DSA

What is Time Complexity and Why is it Needed?

Time complexity is not the actual time taken by code to run, as this varies between machines (e.g., old Windows vs. new MacBook).
It is defined as the rate at which time taken increases with respect to the input size.
In interviews, your code is judged by its time and space complexity using Understanding Time and Space Complexity: A Comprehensive Guide to Big O Notation, not by running it on a specific machine.

Big O Notation and the Three Rules

Big O notation (written as O(...)) is used to express time complexity. The number of operations is what goes inside the parentheses, but three rules simplify the process:

1. Always Consider the Worst-Case Scenario

Best case: The minimum time, e.g., a grade code (if-else) that finds a match in the first condition.
Average case: The median time.
Worst case: The maximum time, e.g., the code runs through all conditions before finding a match. This is what matters for scalability.

2. Avoid Constants

Constants become insignificant for large input sizes. For example, if the complexity is 4n3 + 3n2 + 8, and n = 105, the +8 is negligible.
In code, a single operation like int x = 2; is a constant and is ignored compared to loop iterations.

3. Avoid Lower-Order Values

Lower-order terms (like + 3n2 in a 4n3 expression) are dropped because they don't affect the growth rate significantly for large n.

How to Compute Time Complexity: Examples

Example 1: Nested Loop (Both loops run `n` times)

for(i=0; i<n; i++) {
  for(j=0; j<n; j++) {
    // constant time operation
  }
}

Outer loop runs n times.
For each outer iteration, the inner loop runs n times.
Total iterations = n * n = n2 → Time Complexity = O(n2)

Example 2: Inner Loop Depends on Outer Loop Counter

for(i=0; i<n; i++) {
  for(j=0; j<=i; j++) {
    // constant time operation
  }
}

When i=0: inner loop runs 1 time.
When i=1: runs 2 times.
... When i=n-1: runs n times.
Sum of first n natural numbers: n(n+1)/2 = n2/2 + n/2.
After removing constants and lower-order terms → Time Complexity = O(n2) (Exact: O(n2/2 + n/2), but simplified to O(n2)).

Other Notations (For Knowledge, Not Required in Interviews)

Big O (O): Upper bound / worst-case complexity.
Omega (Ω): Lower bound / best-case complexity.
Theta (Θ): Average complexity.

The focus of this course is on using Big O notation for solving coding problems, not on mathematical derivations.

What is Space Complexity?

Space complexity = Auxiliary space + Input space, expressed in Big O notation.
Auxiliary space: Extra space you create to solve the problem (e.g., a new variable c to store a + b).
Input space: Space taken to store the input (e.g., variables a and b).
Just like time complexity, space complexity is expressed in Big O, not in KB/MB.

Crucial Rule: Never Modify the Input

In interviews, never manipulate the given input data (e.g., storing a + b in b itself).
The data might be used elsewhere in a production system.
Always use extra variables or arrays. Using O(2n) space instead of O(n) is acceptable.
If the interviewer explicitly allows modifying the input, you can do so, but explain why you prefer not to.

Bonus: Competitive Programming Guideline

Most coding platforms (LeetCode, Codeforces, GFG) can execute roughly 108 operations per second.
If time limit is 1 second, your code's Big O should be ≤ 108 operations.
For a 2-second limit, aim for ≤ 2 * 108 operations.
For more advanced techniques to optimize your solutions, check out Mastering Two Pointer & Sliding Window Techniques in DSA Interviews.
Use this to choose efficient algorithms.

hey everyone welcome back to the channel I hope you guys are doing extremely well then this lecture we'll be learning

about time complexity and this is the continuation of Strivers A to Z DSA course slash cheat so uh if you remember

in the previous video we have covered all of these green TIG Mark things and this video will be covering the time

complexity learn Basics and then analyze the next steps what does that mean they'll be teaching the basics of pen

complexity what is time complexity how to compute time complexity and all the terms related to it and then eventually

when you go through all the latest steps at every problem that we solve we will be discussing time complexity of every

problem in depth So eventually when you complete all the steps or all the problems you will have a very very good

hold on the time complexity part now in this video I cannot teach you time complexity of uh very complex codes

because you do not know them right so once you learn the complex codes and recursion backtracking we will be

discussing time complexity in depth over here but as of now just let's start with the B6 so the first question what is

time complexity now what why is time complexity required first of all now whenever you're going to an interview

you might end up writing a piece of code right now that code how do how does an

interview judge that code this is where they will analyze the time complexity of the code now they will not they're not

going to take your code run into a machine and see how much time does the machine take and on the basis of that

tell you that your code is right or wrong that is not going to happen this is where something like time complexity

comes in whatever code you are going to write in an interview in every interview they're going to analyze you what is the

time complex team and what is the space complexity and then on the basis of that you will be judged right so whenever you

write a code that might end up taking let's say two seconds on a machine or might end up taking three seconds on a

machine might end up taking five seconds on a machine so the time taken will you call it the time complexity no

you will never call time complexity As Time taken now you might ask but why if a code is taking certain time that

should be its time complexity let's give you a very very easy example to explain why not imagine I take this code

I take this code this can be any code any code I take this code and I run it on two machines one is the old Windows

machine and the other one is the new Macbook machine now I'm sure the old windows

hypothetically might end up taking two second to run that code while the new Macbook which is a lot more in terms of

the like a lot more latest in terms of the configuration might end up taking one second so does it mean

that your code is taking one second or does it mean that your code is taking two second it might happen I bring up

some other machine the next day it might end up taking lesser than one second so depending on the system the code ends up

taking a different time so that is why time complexity cannot be said as time taken because it is dependent on system

it is different dependent on configuration right so this is why that is this is the first point time taken is

never equal to time taken never ever so you might ask if time complexity is not time taken then what is it that is where

I see the definition the rate remember the rate at which the time taken increases

the rate at which the time taken increases with respect to

the input with respect to the input size rather so what does that mean let's explain

this with the help of a graph so again let's take the same example where I'm saying I have a old Windows machine

and I have a new Macbook okay now imagine you are giving the old windows a size 10 just as hypothetical a

size 10 input size and I'm plotting the graph and this is one second

this is two seconds this is three second this is four second this is five second this is 10 input size is 20 30 40.

at 10 input size it might end up taking 2 seconds at 20 it might end up taking 4 at 30 it might end up taking 6 which

will be here so you see the time increasing at some at some Theta angle like it's increasing

at a certain slope so this increase this increase this Theta angle is what you call as the rate of increase this is

what you call the rate of increase okay now let's see the new Macbook

so if I take the new Macbook the 10 might end up taking one second the 20 might end up taking two second

the 40 might end up taking three seconds so it's here here

so this is the read and this Theta is the rate for the new Macbook so I can say the rate at which it increases time

is what you call As Time complexity depending on the input if they are giving you more input it might end up

taking a certain more time so the rate at which the time increases is what is generically referred as time complexity

of Any Given code the next question that might come to your brain is okay if we are saying the time complexity is not

computed in terms of seconds or minutes then how do we how do we write it this is where something like a big O

a bigger notation comes in now in all the interviews that you're going to give or in all the examinations

if you're writing a piece of code they will ask you to analyze the time that is when you do not like you will

not say two seconds no you will say it in terms of bigon notation every piece of code takes time in terms of Vigo

notation what is Big annotation I just give you a prime example so it's like a capital O open parenthesis and a closed

pattern this is what bigo notation is and inside it you write whatever the time is taken inside is you write the

time taken or the hypothetical time which I'll show you how to compute let's take

a very very small example to compute the time complexity of a certain code so imagine I write the for Loop I've

already taught you Loops in the previous video I equal to 1 I lesser than 5 I plus plus

and then I write C out and my name Raj okay so can you tell me what is the Big O of

this this is nothing but the number of steps that this code will take first step is very sure

assigning the second step is comparison the third step is printing right and then you come across and this is your

fourth step and then again you check this is your fifth step and then again you print this is your sixth step so

this is how every step is computed so whatever is the total number of steps that is what you write inside is and

that is what you call as the prime bego notation but you cannot just keep on Counting step one step two step three

step four step five step six step seven that is insane you just cannot keep on manually

counting the steps this is where three rules come in and I'll write the rules the three rules are very simple always

compute time complexity in terms of worst case scenario time complexity to be computed in terms of worst case

scenario why was case I'll explain you the next one is avoid constants avoid constants

the third and the third is avoid lower values so if I have to compute the time

complexity or the Big O of this piece of code let's look at it on a very high level can I say this for Loop is running

for 5K I can at every time what is happening it's like increment

check print increment check print so can I say for every time it's operating price but

every time it is operating three times increment check print five into three can I see this I can so can I say a

total of 15 times that is how you write it you write it as we go of 15 is what you write and this is time complexity it

runs for 15 times but this is a number this is a number you generally do not represent your code

in terms of numbers okay so let's let's change this now can I see this if I change the

statement if I if I probably will change this to lesser than n less than equal to n

now can you say how many times will this Loop run I know one thing this is going to run for we go of n times the loop the

code will run for n times n iteration and at every iteration one two three things will happen

that every iteration three things fella pretty obvious this is what will be the time complexity we go of t n we go of 3n

will be your time so whenever you're saying we go you go to the code and you see how many times

it is running and then you write we go of 3 n as your time complexity does that make sense right okay let's now come

back to the three points that have written always compute time complexity in terms of worst case scenario now

there are three things one is the best case one is the average case

and the other one is the worst case now let's take a snippet of the code and explain you what is best case what is

average case and what is worst case okay let's so this is the snippet of the code now imagine the snippet of the code is

very it states of marks is lesser than 25 print grade D it states of marks is less than 45 print grade C if marks is

lesser than 65 then you go ahead and print Grade B or else you go ahead and print create a so let's talk about the

best case scenario what is baskets when the program

takes the least amount of time so over here can I say if someone gives you an input of marks equal to let's say

10 what will happen this will execute it and grade D will be printed and none of these lines will be

executed none of these like so can I take can I say the number of operations will be just one a check

and a print which is like two operation which is like two operations and I said imagine

if I give you marks equal to 70. so at Max 10 it was we go of 2

operation correct we go off to operation now if I give you marks equal to 70 what will happen

check false check false check false it comes here 3 and

then four can I say four operations were here like one two three and then goes to else somewhere around 4 octave so it

takes four operations so whenever you're analyzing the time complexity will you say that my code runs in week of or will

you say that your code runs in week of four obviously you will say we go for because that might be the worst case

that the computer might encounter when it is given an input so always yes always compute the time complexity in

terms of worst case scenario and if they will ask you the best case you know the best case whatever is the best case like

in this case is the first if statement getting executed which is we go of two operations

so you've got an idea about the best case and the worst case you know what is the average case there's nothing but the

best plus worse and divided by two it's it's the median of it so pretty self-explanatory why

if I give you a question why do we compute it in terms of worst case the answer is again self-explanatory if

you're building a system will you build it for one person or or will you build it for one million

person if given an option if given an option he will say 1 million because you want to build a system which can scale

up you always think of the worst that can happen that is why when I talk about time complexity your code

extreme worst case is what is considered while Computing time complexity now let's talk about constants I'm saying

avoid constants why am I seeing that let's take a shuttle example let's say something like 4 n Cube something like 3

n square plus 8 that's it so over here 4 n q plus 3 n square plus 8 these are

the number of operations that your code is taking hypothetically I do not want to be support I'm just taking a

hypothetical we go expression now imagine if I tell you that the input size n the input size n is somewhere

around 10 to the power 5. right I'm saying 10 to the power 5 is the input size

so when I say 10 to the power 5 and you put that in What will what will it be 10 to the power 15 10 to the power 5 Cube

15 plus 3 n Square that's 3 10 to the power 10 plus 8. tell me a very easy thing

10 degree of 15 plus 10 to the power 10 into Plus 8 will this 8 have any significance in the operations this is

in itself such a huge number if you had eight will it will it matter to them like whatever is standard of 50 I'm not

sure what it is it's a billion trillion whatever more than that I guess with that A Plus 8 does it have a

significant it doesn't if you're earning 1 million and I give you one buck that will not

have any significance that is why we do not consider constants we do not consider constants now in terms of code

imagine I see you something like this int x equal to 2. so this is the modified code

this is the modified code x equal to 2 and then the for Loop so this is one operation it's it's something like n

into three plus one the time complexity updated will be n into 3 plus 1 operation and this is the one operation

so you never ever take this unit operation so you will not consider this you will say no it will still stay as n

into 3 I will avoid constants because whenever the input size is very large those constants have very less

significance got it now let's take the next thing avoid lower values let's take the same example I am saying 10 to the

power of 15 10 to the power 15. if you add 10 to the power 10 to it will it have any significant it won't so adding

10 to the power 10 to 10 to the power 15 10 to the power 15 will have absolutely no significance

it is similar to saying I will add let's say one two thousand

maybe even lesser than that it is similar to actually seeing one two yeah I'm adding one to this much or one

more zero yeah will it have any significance no so adding this one to this one will it have any significance

no the number of operations will be like slightly slightly more because 10 to the power 5 15 in itself is such a huge

number but this is why again certainly very important avoid the lower values which does not change its significance

by much so avoid lower values correct so these are the three points that you will always keep in mind while Computing the

Beagle notation because Vigo notation is what you will be expressing your code in interviews always all the problems that

I'll be solving I'll be telling you about bigo notation only apart from bigot notation there are certain other

terms at Theta notation Omega notation Delphi a lot of other terms in textbooks are they required in

interviews no no one is going to ask you these things no one or just for knowledge let me tell you the bigo

notation is always the highest complex or the worst case complexity remember this worst case complexity or the

highest or generically known as the upper bound complexity it's known as the upper bound the Omega

is the lower Bond as I said the kind of the best case is the lower bound or the lowest Bond or

whatever you can and this is nothing but the average complexity foreign

just a quick disclaimer there are a lot of theoretical stuffs revolving around Biko Theta Omega a lot of limit

derivations but I am not teaching you Theory stuff I'm not teaching you for your semester examinations I am teaching

you for interviews I am preparing you for the DAC coding rounds and they will not be asking it over there they'll be

asking a programming logic you'll have to solve problems don't be asking you tell the formula for big connotation in

limit terms no one is going to ask might be asked in semesters for that you'll find different teachers on YouTube if

you are learning from me you're learning for interviews for coding rounds for problem solving abilities not for your

semester exam so please do not comment that you did not teach the mathematical derivation because that is something

which is not required while problem solving right so you know how to compute picona let's uh do one thing let's

quickly solve some questions okay so the first snippet of the code for which you have to find the time complexity imagine

inside your main you have something like int I equal to zero I lesser than n i plus plus

and for INT J equal to 0 J lesser than n j plus plus and imagine it has a block of code like something a single line of

code and this is your entire snippet of the code okay this is your some block of code

you can consider this to be taking very constant time constant time so this can be avoided

tell me the time complexity you know time complexity will be computed in terms of bigo notation tell me the time

complexity of this particular code pause the video and maybe think about it and then see if you are correct or not so

how do you analyze the time complexity of Snippets of the code it's very simple analyze how's the code

working so if you see the outer loop is starting from I equal to 0 and going till n so it's definitely running for n

times and the inner loop is going from J equal to 0 till n this is also running for n times now if you're a beginner you

might find it a bit difficult so what you will do is you will say at I equal to 0 what is happening let's see

whenever I is 0 what is happening whenever I is 0 it goes inside and J starts its value from 0 and goes till n

and this completes n iterations can I say when I is uh zero J goes from 1 0 1 2 3 dot dot till n can I see that

and then again when the is value increases to one can I say J again goes from 0 1 2 3 because it's inside it it's

reiterating again from zero can I say if I is 2 again it again goes from 0 till n can I say till I is n minus 1 y n minus

1 because it is lesser than n can I say it again goes from 0 till

n minus 1 to be very accurate can I say this so what is happening

every time it is running for n n every time it is running for n and n so can I say it's running for n times first

then for another n times second time then for another end time second and then dot dot dot till end times

how many times is it running can I say it's running for exactly n times so can I say this is nothing but n

into n yes thereby n square is the number of iterations it is taking yes there are

other things as well like increase comparison we usually do not consider which rule avoid lower values if you

remember because 3 into something won't matter that much because you can avoid it so what I can say is it's running for

n Square yeah if you want to consider all these constant operations you can do it that is your wish I usually do not do

it so we go off n square is what is the time complexity of this particular let's say the next

example and try to compute the time complexity of this one so it's like the first Loop is definitely running for n

a second Loop is running from 0 to I so let's analyze slowly and probably

we'll get the time complexity so can I say if I equal to 0 J is nothing but from 0 is only running for 0 can I say

this because when I is 0 J is running for 0 K lesser than equal to 0 it will run for just one time 12. when I becomes

2 what happens J now runs for 0 sorry when I becomes 1 rather and I becomes one what happens J now

runs for zero and one can I say why because I is 1 it's like 0 lesser than one correct nice

can I see if I is equal to 2 what happens J now runs for 0 1 2 so when I at the end becomes n minus 1

what will happen J will be 0 1 2 dot dot n minus one can I see this is how many operations it is taking again I'm

ignoring all these constant operations I'm taking the overall iterations now first time it's one equation next time

it's 2 x m is three four until n so can I say the number of iterations the first time it is one the next time it is two

the next time it is 3 and X7 is 4 so on Del Nitric can I see and do you remember the formula for this particular thing

some of the first and natural numbers simple maths n into n plus 1 whole divided by 2 which is nothing but n

Square by 2 plus n by 2 thereby this is the exact time complex but we

can avoid if you remember the rules constant to be a like the smaller values to be avoided so it'll be like n Square

by 2 so this is the time complexity again if you try to

remove the constants like one by half you can say the time complexity is near about we go of n square but if someone

does ask you the exact time complexity this is the exact time complexity but according to the rules

this is voted boils down to so these were the basics of time complexity okay now next I'll be doing all these

patterns in the next lecture well be writing all the nested for loops and there you can analyze time complexity in

a much better way but eventually all the time complexity terms like login and login n Square n Cube n Square login all

of these things you will see as I proceed with the playlist I do not want to rush you in I just want you to get an

overview of what is time complexity how to think on it how to compute how to avoid terms these things should be

crystal clear to you so I'm assuming the time complexity uh stuff is crystal clear to you they'll now be moving to

something like space complexity again what a space complexity it's the memory

space that your program takes it is the memory space that your program takes in a very very naive term

when I talk about memory space again it will vary from machine to machine so you cannot be dependent on the machine and

that is why again in order to complete base complexity we will be using the bigo notation again

so bigo notation is kind of very very important in all the interviews we go in terms of time we go in terms of the

space so we'll again be using bigger notation and you know the reasons why not in terms of KB MB GB Etc

so what is exactly the definition of space complexity it is nothing but auxiliary space

Plus input space what is auxiliary space

the space that you take to solve the problem the space

that you take to solve the problem input space the space that you take to store the

problem foreign not the problem so let's give a very

very small example in order to explain what is auxiliary space and what is the input space so I'll write a very very

small thing imagine I am taking an input of A and B in Java you know how to take it and C plus plus you know so I'm

assuming I'm taking an input of a uh so I'm not writing any syntax because then it'll be C plus plus or Java

specific I just want you to learn pseudo code and the logic so in Imagine a given input to variably imagine I give an

input to variable B and I am saying c equal to a plus b now I am saying c equal to a

plus b so the auxiliary space that you're using is an extra C variable this is the

auxiliary space why because you're using a c variable in order to solve the problem okay you

cannot use that is okay I am saying if you use any extra variable or extra space to solve the problem that is what

you refer as auxiliary space what about the input space this is one and this is one so both of these can be referred as

input space whereas this can be referred as auxiliary space and combined I can say this is the space complexity or I

can say we go off three over here because you're using three different variables you can

convert them into bytes if you're taking an integer you can convert them into bytes I am not concerned about this in

an interview you will have to say it in terms of bigo of something not in terms of bytes KB MB so for example

if I Define an array of size n it means I'm consuming B go of n size or n space complexity so in an interview if you are

solving a problem which uses an array of size n you say bego of n is the space complexity that I am using as simple as

that now a thing that I want to highlight over here is if you're doing space complexity a lot of times it will

happen is imagine you're given an input to a imagine you're given an input to B and the task is to some add both the

numbers a lot of people say I'll do this b equal to a plus b so the summation of a plus b will be stored in B and I'll

not be using the third variable it is okay to do it is okay but this is something you should avoid it takes

lesser space but in an interview the interviewer will say this method is not done why is it not done this thing in

person in perspective of software engineering imagine you writing a quote for a big MNC and they're giving you

some data they've given you some set of data and they want you to do something on that data and you're like you

manipulate the data over here you change the data you changed B this is why never ever do

anything on the input very very crucial rule in interviews never do anything to the never do anything to the input

unless the interviewer sees anything to the input because data should not be touched you

can do whatever You Wish by taking the data what you cannot do on the data because if you manipulate the data it

has an issue because in software engineering that data might be used in some other place so never ever

manipulate data this might save you a bit of space but the interviewer will end up rejecting you because this is a

very very bad practice so never ever do anything to the input given always take extra variables extra array extra Matrix

it might be tempting that if you use the same input variables you will end up taking less of space but it's it's not a

big concern if you're using bigo of n space like if 2N is used by taking an extra

array it is okay this is okay no one is going to reject if you're using big of 2N instead of B of n if the interview

specifically says do it on the input then you can use them otherwise do not and you can tell that to the interview

you can explain that I do not want to uh I do not want to tamper with the data that is why I'm taking an extra variable

in order to solve this problem keep this in mind forever so this was about the high level idea about space complexity

and the practices you should follow regarding the in-depth knowledge when we solve different problems on different

data structures you will see how I'll be explaining space complexity in terms because the more problems you solve the

space complexity gets into your head in a much much better way so before ending up this lecture in case you are into

competitive programming then remember one thing over there you do not run your codes on your MacBook or your windows

whatever code you write you send it to the server there is a server you send it to the

server everyone sends to the same server and these servers in competitive programming or let's say you're using

lead code or let's say code Studio or let's say gfg any platform if you're using they have their servers and most

of the servers take one second for 10 to the power 8 operations remember this most of the servers most of us are take

one second for roughly 10 to the power 8 operation might be 10 to the power 8 plus something might be 10 to the power

8 minus something but roughly it is 10 to the power 8 operations is what you can execute in one seconds on the server

most of the servers are relatively the same and if they're saying two seconds it doesn't mean 10 to the power 16. it

doesn't it doesn't it means 2 into 25 operations if they're saying five seconds it means 500 to The Power 8

operations do not do 10 to the power 8 to the power of to not a lot of people do that okay so this is something just

keep in your mind because a lot of times you will see time limit one second they'll write it they'll write it in

your uh let's say coding round the time limit given to you is one second

where you should Analyze That the time complexity of your snippet of the code or your entire code should be roughly

big go of 10 to the power 8 operations if in a coding round they are stating time limit one second it means roughly

when you compute the time complexity of your code avoiding constants avoiding lower values it should be because of 10

to the power 8 operations so with this I will be uh completing the step

1.1 guys I hope you have understood everything over here and the next lecture will be about uh do all these

patterns yes I'll be doing all of these patterns each other 22 of them in the next lecture just in case you have one

District time complexity and space complexity in depth we have a ritual on Tiki forward on every lecture if you

understand everything right at the end of the lecture you drop a comment understood in the comment section so

that I get that belief that you guys understanding I get that motivation that I come back and record these videos so

please please do consider dropping the comment understood if you're new to our Channel please please do consider

subscribing to us if you haven't checked out uh Strivers A to Z DSA course the link will be in the description and you

get everything on the description my LinkedIn Instagram Twitter everything you can follow me at any any of these

places and if you are learning online you can always use the hashtag that is over here and with this I'll be wrapping

up this video let's be in some other videos [Music]

Why is time complexity measured in 'rate of growth' rather than actual execution time?

What does the rule 'Avoid Constants' mean when simplifying Big O notation?

How do you calculate the time complexity of nested loops where the inner loop's counter depends on the outer loop?

What is the difference between auxiliary space and total space complexity?

Why should you never modify the input data in an interview setting?

How can I use the '10^8 operations per second' rule to choose an algorithm in competitive programming?

What are Big O, Omega, and Theta notations, and which one matters most in coding interviews?

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This video teaches you how to calculate the time complexity of various loop structures in code, including simple loops, nested loops, and loops with non-standard increments or conditions. Through detailed tracing and analysis, you'll learn to identify Big O notation for O(n), O(n²), and O(√n) complexities, making algorithm analysis straightforward.

How to Write and Analyze Algorithms: Time and Space Criteria

This tutorial explains how to write algorithms using flexible syntax, emphasizing clarity for human understanding over strict programming rules. It also covers the key criteria for analyzing algorithms—time efficiency and space consumption—with a basic example demonstrating constant time and space complexity.

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Time & Space Complexity Basics: Big O Notation Explained for DSA

What is Time Complexity and Why is it Needed?

Big O Notation and the Three Rules

1. Always Consider the Worst-Case Scenario

2. Avoid Constants

3. Avoid Lower-Order Values

How to Compute Time Complexity: Examples

Example 1: Nested Loop (Both loops run `n` times)

Example 2: Inner Loop Depends on Outer Loop Counter

Other Notations (For Knowledge, Not Required in Interviews)

What is Space Complexity?

Crucial Rule: Never Modify the Input

Bonus: Competitive Programming Guideline

Related summaries

Understanding Time and Space Complexity: A Comprehensive Guide to Big O Notation

Algorithm Complexity: Frequency Count Method for Time Space Analysis

Asymptotic Analysis Part 3: Growth Rates & Time Complexity

How to Analyze Time Complexity of Nested Loops and Sequences

How to Write and Analyze Algorithms: Time and Space Criteria

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Time & Space Complexity Basics: Big O Notation Explained for DSA

What is Time Complexity and Why is it Needed?

Big O Notation and the Three Rules

1. Always Consider the Worst-Case Scenario

2. Avoid Constants

3. Avoid Lower-Order Values

How to Compute Time Complexity: Examples

Example 1: Nested Loop (Both loops run n times)

Example 2: Inner Loop Depends on Outer Loop Counter

Other Notations (For Knowledge, Not Required in Interviews)

What is Space Complexity?

Crucial Rule: Never Modify the Input

Bonus: Competitive Programming Guideline

Related summaries

Understanding Time and Space Complexity: A Comprehensive Guide to Big O Notation

Algorithm Complexity: Frequency Count Method for Time Space Analysis

Asymptotic Analysis Part 3: Growth Rates & Time Complexity

How to Analyze Time Complexity of Nested Loops and Sequences

How to Write and Analyze Algorithms: Time and Space Criteria

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Example 1: Nested Loop (Both loops run `n` times)