The Ultimate Big O Notation Tutorial (Time & Space Complexity For Algorithms)

[@geraldcerna516]

I think this is one of those videos that will really keep you up rather than making you want to go to sleep. It's not boring. And the explanations are so lit.

[@BackToBackSWE]

thanks!

[@dontfollowme4057]

You're lit.

[@umbraemilitos]

@@BackToBackSWE Your channel is excellent. Thank you for your educational content.

[@JasonOgasian]

The way the camera moves and the speaker is acting makes it feel like someone is about to bust in and erase all his whiteboards at any moment 😂 Great video!

[@BackToBackSWE]

Hahahaha that was the case. 2nd video I ever did

[@naskavian7041]

This is the Blair Witch Project of Big O :)

[@BackToBackSWE]

Table Of Contents: (I want to redo this video, the video is overexposed in lighting) Messing Around 0:00 - 0:17 Big O Introduction 0:17 - 0:43 O(n^2 )Bounding Example 0:43 - 1:33 Upper Bounding 1:33 - 1:51 The O(n) Mistake 1:51 - 2:38 Notating min() & max() 2:38 - 2:56 O(1) "Constant time" 3:07 - 3:46 O(log(n)) 3:46 - 5:43 O(n) "Linear time" 5:43 - 6:30 O(n * log(n)) 6:32 - 8:09 O(n^2) 8:09 - 9:09 O(2^n) "Exponential time" 9:09 - 9:40 O(n!) "n-factorial" 9:40 - 10:55 Considering Tradeoffs 11:01 - 11:34 Why To Optimize Time 11:34 - 11:58 Space Complexity 12:02 - 14:38 DO. NOT. GUESS. 14:44 - 15:40 Leveraging Our Complexities 15:40 - 16:30 Wrap Up 16:30 - 16:59 HUGE IDEA. Time complexity must be at least the space complexity. If you deduce a complexity and this does not happen then something is wrong. This is because to use space we must use time (space is tightly bound to the time that it takes to use it). Due to this relationship, space ALWAYS has at least a loose lower bound on time if not very close. I will make a part 2 to this video to expand with nuances like this in complexity theory.

[@igo1071]

Back To Back SWE excellent explanation God bless🙏🏼

[@BackToBackSWE]

thanks

[@bakor-org]

Simply the best explanation on the whole internet. I really like how he points out what he has done wrong in the past so we don't do the same. Thank you. :)

[@BackToBackSWE]

thanks - he is here

[@victorariasvanegas7407]

This is the kind of video by which people like me, who are introducing to this world, will buy access to your platform, never stop making them, excellent explanation bro, I finally understood this concept.

[@BackToBackSWE]

haha, well nice

[@andrewgray3112]

THE BEST, CLEAREST BIG-O VIDEO BREAKDOWN YOU WILL FIND ON KZbin!!! Thank you so much for making this, it has really helped me understand things better!

[@TimothySusanto]

Finally an introduction to Big O that actually makes sense!! Thank you.

[@BackToBackSWE]

sure

[@ReBufff]

Out of the ones I checked out, this actually explains WHAT the concept is before jumping into some arbitrary code. Thanks!

[@BackToBackSWE]

Glad to hear that

[@BackToBackSWE]

Subscribe to our DSA course with a flat 30% discount for some amazing content b2bswe.co/3HhvIlV

[@jorossbarredo]

Dude, this video introduction to Big O is what I needed! Blessing from the gods!

[@BackToBackSWE]

nice

[@brAzzi64]

Never seen that many whiteboards before.

[@BackToBackSWE]

yeah

[@joacortez3423]

This video is one of the most complete and engaging i have seen

[@MTKClassy]

From the bottom of my heart, thank you so much for the gold knowledge

[@BackToBackSWE]

Thank you, glad you liked it 😀 Do check out backtobackswe.com/platform/content and please recommend us to your family and friends 😀

[@lien-chinwei4815]

Thank you for the first 11 min presenting solid examples related to each big Oh. Fantastic work.

[@BackToBackSWE]

hey

[@kainguyen4259]

Wow bro you really kill the n * log (n) part. Thank you!

[@BackToBackSWE]

sure

[@MrJaddamo]

Ben, you are the MAN. I wish I could attend a Bootcamp taught entirely by you. I go to Columbia and it's extremely difficult to keep up with the speed at which the curriculum is taught. Your videos really help create a baseline of understanding.

[@BackToBackSWE]

haha, I am but a man, a lot of videos left to make

[@user-gp8fr1nd3w]

oh my god same I got to Columbia now. Were you doing data structures?

[@dizhang3157]

thank you soooo much!!! seeing you so passionately talking about this encourages me to learn more about it. great great work

[@BackToBackSWE]

haha nice

[@zihangjin9186]

Thank you! It helps me (a beginner) get a brief understanding of all those concepts in such an easy way.

[@georgesmith9178]

Thanks for the tutorial - thumbs-up given. The most important comment you made was toward the end of the video: it is impressive to state the space-time complexity. For interviews, it always helps to create an air of authority, regardless of how practical it would be to write production code that relies on the what you are being tested, which in all likelihood you never will :)

[@BackToBackSWE]

thx

[@syedrizvi2687]

Love your energy bro! Thank you for your great explanations to so many concepts

[@muhammadfaisalhyder4012]

To be honest, this is by far the best one! now please make a vid where you go through actual code, I am talking about actual code, not some rubbish nested for loops just to print the name or number. That will help in practically applying these concepts.

[@BackToBackSWE]

ok

[@tathagatnegi5923]

Great video❣️ Helped me alot I have watched many videos on big O notation but no1 has ever explained it in this easy and simple manner Great job sir👍❣️

[@BackToBackSWE]

great and thanks

[@pavithravenkatesan7216]

Very simple to understand. The teaching method is unique and efficient :) Thanks a lot for doing this :)

[@BackToBackSWE]

sure

[@lazymacs2823]

Nerd: "you can't buy time" RTX3090: allow me to introduce myself

[@BackToBackSWE]

lmaooo

[@azuboof]

What an amazing lad. Hope he reaches heights. thanks for the clear explanation

[@BackToBackSWE]

Thank you, appreciate it 😄 Also check out our Free 5 Day DSA Interview Prep Mini-Course - backtobackswe.com/ 🎉

[@anuchechi9917]

wow! It is the ultimate Big O notation tutorial. Awesome work, please keep doing the same. Thanks a lot.

[@BackToBackSWE]

thx

[@Ashmole3]

Your videos have been really helpful to me and it seems like some of the things that trip me up sometimes also tripped you up as well.

[@VictorGarcia-si8wy]

"We can buy memory, but we can't buy more time." That's some deep stuff right there.

[@gauravbhisikar6381]

Thanks you My all doubt about algorithmic complexity is now cleared🙂

[@BackToBackSWE]

nice

[@rohantohaan8684]

Prepping for Fall hiring season. Botta watch/learn from your videos

[@BackToBackSWE]

great. welcome to the party.

[@044_karan8]

This is the best video on big Oh.. I also like ur style bro

[@BackToBackSWE]

thanks

[@alpavaidya412]

Very good explanation...unlike other videos I can relate to ur teaching cause u stress on the points which u urself found difficult to understand

[@BackToBackSWE]

thanks and great

[@sbv5220]

I am glad you didnt use a potato to record this, instead you opted for a bowl of jello. I was dizzy at times, but overall. Great content!

[@soverby5]

I just love these videos, the presentation style really resonates with me. Great job.

[@BackToBackSWE]

thx

[@noahpineda3419]

I love this channel. I wish I could like videos multiple times haha.

[@BackToBackSWE]

haha nice

[@SumitSahoo]

Simplest explanation of Big O period.

[@BackToBackSWE]

hello

[@SumitSahoo]

@@BackToBackSWE hello world :)

[@Elidangerfield1111]

My god im so glad I found this channel.

[@BackToBackSWE]

hey - ben

[@rtr0spct210]

5:59 really helped things click for me, thanks!

[@srikarvoleti8950]

Clear and precise. If I get an A on my final tomorrow, I'll dedicate it to you.

[@BackToBackSWE]

ok

[@moddatrucka]

Good Explanation! A camera tripod would have helped though :)

[@BackToBackSWE]

this was my second video ever jeez guys

[@123Azns]

amazing!!! Better than stackoverflow, and professors that taught me.

[@BackToBackSWE]

haha, I'm working on redoing this video. It is badly exposed.

[@123Azns]

Back To Back SWE hahah could you give more examples in the new vid?

[@BackToBackSWE]

@@123Azns yeah. it will be amazing.

[@AlphaZeroOmega]

Studying the behavior and complexity of algorithm can be super confusing, especially considering mathematics is involved and not all developers are well schooled beyond basic algebra. This is a pretty good introduction in my opinion, to get your head around the basics.

[@BackToBackSWE]

thx, old video tho

[@AlphaZeroOmega]

@@BackToBackSWE Hey, at least the info is still good.

[@Series0Tubes]

Again, I love these videos. Thank you very much!

[@BackToBackSWE]

Sure!

[@peejaylero3467]

So very proud of this video. I love it! I was just thinking today after about 6 years of higher education in the US (undergrad and grad), I've never had a black lecturer/instructor. Never! Not even outside of my CS classes. Thank you for this :)

[@stpetar213]

Great explanation! Thank you.

[@BackToBackSWE]

sure

[@shanthanreddy2524]

could u make another video with a detailed explanation for the space complexity ? Thanks, Sai

[@BackToBackSWE]

yes

[@allierobinson9914]

Thanks for making this interesting presentation! I love your energy!

[@BackToBackSWE]

sure and thanks!

[@ibrahimk6729]

Great video, interview bytes at last on (15:43) was really impressive..

[@jknair0]

I just felt like i watched video at 2x speed. so much useful content in so less time.

[@xiuwenzhong7375]

very good explanation, watch your video everyday on my train to office is my habits now.

[@BackToBackSWE]

wow, that is so cool, I'm flattered

[@rahil_rehan]

In O(n) complexity, when it is 3*n the linear graph line doesn't become sterper but shifts up 3 units. Great explanation!

[@BackToBackSWE]

What? Can you timestamp it? Multiplication by a constant factor makes a line steeper. Shifting up is addition.

[@rahil_rehan]

@@BackToBackSWE Yeah! Sorry, I was just confused between multiplication and addition on functions. You again made it clear. Thanks alot!

[@simoneckerstorfer4174]

Thanks for this video!

[@BackToBackSWE]

sure!

[@rogersteele2835]

Great video it really clarifies Big O in relation to the search types

[@BackToBackSWE]

ye

[@abigailgonzalez7857]

This is the best explanation! thank you so much!

[@BackToBackSWE]

sure

[@angeloliwanag2619]

This video is GOATED

[@BackToBackSWE]

yes

[@stannikolov]

Watching this was fun. Thank you!

[@BackToBackSWE]

Thank You, Glad you liked it. Do check out backtobackswe.com/platform/content and please recommend us to your family and friends :)

[@emekatimothyiloba699]

Thanks. You are a great teacher

[@ramizrizwan3057]

Such a great and helpful video. You explained this sos well

[@powerhouse5424]

Thanks for saving my life!

[@mahakshmalhotra7634]

Amazing explanation!! great job!!

[@BackToBackSWE]

thanks

[@Mona19_05]

the best explanation of big O thanks! camera wasn't stable enough :/

[@BackToBackSWE]

ik, 2nd video we ever made

[@DanielSColao]

Thanks for uploading videos like this!

[@AshishSingh-753]

Hey your are best content creator

[@BackToBackSWE]

no u

[@rahulpadalkar6237]

Is the triangular work @ 8:45 a graph of number of comparisons (y) vs index (x) ? That's how you would get a triangle imo. Also from what i know about work (from physics) work is calculates as the area under the graph. Since it is a right angle triangle, we can calculate the area as 1/2 * base * height which equals n^2/2 which then gives us the complexity of n^2.

[@BodySnatchers-v5f]

A tripod is a portable three-legged frame or stand used as a platform for supporting the weight and maintaining the stability of some other object. In photography, a tripod is used to support, stabilize and elevate a camera, a flash unit, or other photographic equipment. Tripods are available in various sizes and materials and can be purchased from many retailers such as Amazon and Best Buy.

[@kushalchawla4395]

🤣exactly my feeling right now while suffering from a headache after watching this.

[@BugattiVeyron1]

Subscribed you did a good job explaining the material thanks

[@BackToBackSWE]

yuh, welcome

[@trmnatr21]

Holy shit. It makes sense. Didn’t expect that. Thanks lol.

[@BackToBackSWE]

nice

[@DataVids]

very helpful thanks for making this video.

[@BackToBackSWE]

sure thanks for watching

[@leo71648]

It forms what it look like a triangle--> Didn't understand this point for O(n2), how it formed a triangle?

[@meyringvanderwalt72]

Love this guy! Keep it up!

[@BackToBackSWE]

ur name is cool

[@MAliRamazani]

Very good! I just wish the video footage wasn't shaky!

[@BackToBackSWE]

Glad it was helpful and sorry about the footage! 😄 Also check out our FREE DSA Interview Prep Mini-Course - backtobackswe.com/ 🎉

[@momenaboessa]

That was AWESOME ✌🏻👨‍💻🔥🔥🔥🔥

[@HN-if9qt]

At 8:34, how did you go from 3 comparisons of an array to form a triangle?

[@BackToBackSWE]

I dont remember

[@gvartchanel144]

Great explanation, thank you

[@BackToBackSWE]

sure

[@abdullahclementabdulshekur6736]

very clear and on point

[@BackToBackSWE]

Happy Holidays! Really glad to help 🎉 Do you know about the BacktoBackSWE 5 Day Free Mini Course? Check it out here - backtobackswe.com/

[@bluejprogramming184]

Sir, can we say O(log(n)) means "half of n or half of the common runtime" of the algorithm? So, if anyone asks that what is O(n*log(n)), we can say its O(n*(n*1/2)) which is O(1/2*n^2) and drop the constant which becomes O(n^2)?? Means O(n*log(n)) = O(n^2)???

[@gianm1064]

Amazing content!

[@yashwanthnerella9935]

The clarity!

[@BackToBackSWE]

thanks

[@올롱볼롱]

do you have any book recommendation to study this subject?

[@BackToBackSWE]

Just the internet

[@thesickbeat]

Try "Data structures and problem solving using Java" by Mark Allen Weiss. The concepts transfer to other languages too.

[@leonelhernandez6027]

Hi mate, have you seen the Berlekamp-Massey algorithm? The time complexity is defined as O(n^2), where n is the input data. Can I asume the same space complexity?

[@BackToBackSWE]

No I haven't :/

[@leonelhernandez6027]

No worries. I was doing this analysis and basically the time complexity can be calculated according to biggest tasks involved, where n^2 steps are taken. When calculating the space complexity is a different story because, I was mainly considered the vectors that I used, in my case 4.

[@kidpesto]

This man doesn't use dots for bullet points he uses transmutation circles

[@ahmedboutaraa8771]

i never thought that big O is so easy till now

[@BackToBackSWE]

ye

[@SaiKumar-vo2ek]

which language is best for DS&A? Please respond to my question

[@ahmedboutaraa8771]

@@SaiKumar-vo2ek I think it depends on your goal, if you want to get into competitive programming then C++ might be a good option. otherwise use a high-level language like python, ruby, or javascript where you don't have to worry about the lengthy syntax, and implement your own DS on top the existing one. NOTE: I'm not an expert so take with a grain of salt and do your own research.

[@jonasmaoh1371]

Doesnt that make nlogn then 8 times 3 making it 24 as complexity????

[@user-vq6yi7se2r]

Great one!!!!!!!!!

[@derreck3424]

Very low production quality, but high quality content. Thank you :)

[@BackToBackSWE]

hahahahaha, you found my 2nd video ever

[@EllAntares]

I dunno, there is nothing better than white\blackboard explanation XD

[@jerrywu5797]

Talking about time complexity, it's great to watch your video and do some further study on it because it's almost a basic skill during interviews. At least from my previous interview experience, both facebook and bloomberg interviewers were willing to know if I could accurately state time & space complexity. Highly recommend Cracking the Code Interview Chapter VI. Big O, where you would deeply understand the practical ways of solving this issue. The answer here clearly explained how we should calculate time complexity for the recursion calls: stackoverflow.com/questions/43298938/space-complexity-of-recursive-function

[@BackToBackSWE]

Nice, thank you for sharing.

[@nolan412]

new WhizBangArray(n) # picks the best container type for n

[@nolan412]

"They don't OOP!?"

[@nolan412]

Come on lazy iterator! 😜

[@nolan412]

I got the job!

[@mareshbm2731]

thanks a lot brother.......n im your new subscriber!

[@BackToBackSWE]

welcome

[@ericfricke4512]

I like this dude.

[@BackToBackSWE]

I like u

[@mistermomo2904]

8:08 woah woah... no need to get personal

[@BackToBackSWE]

old video - sorry if I said something weird

[@mistermomo2904]

@@BackToBackSWE lmao no u just said an O notation of n^2 was innefficient i cant do better >:

[@ben17449]

Insertion Sort is O(n) I believe not O(n^2) could have just heard it wrong though

[@BackToBackSWE]

wut

[@vinodphalke2121]

Awesome teaching & white board also

[@BackToBackSWE]

Thank you, glad you liked it 😀 Do check out backtobackswe.com/platform/content and please recommend us to your family and friends 😀

[@yizhangchen7409]

Thank you!

[@BackToBackSWE]

sure

[@KyzylMartan]

Cool! Great job, thank you!

[@BackToBackSWE]

sure

[@jwilliams8210]

Nice job!

[@BackToBackSWE]

thanks

[@mdrsoooow]

dude i love you

[@marlhex6280]

Bruh I need more practice on this! What can I do?

[@bhishma620]

Subscribed ❣️✨

[@cocoarecords]

revisiting thanks !!

[@BackToBackSWE]

nice

[@aiinque]

thanks a lot!!!♥

[@BackToBackSWE]

sure

[@ythalorossy]

Thanks for share it

[@BackToBackSWE]

thanks

[@bmack7536]

This is my question besides all this, plain English plain Math. int x = 3; right? O.K. what "operators" create more complexity? Do 2 operators on 1 line square the time? Each variable has a size in memory, int, char, float. so in PEMDAS notation per operator what creates complexity? I think I will make my own channel. thanks anyway for the try.