AVL Trees & Rotations (Self-Balancing Binary Search Trees)

[@TheAntloo]

Hey man just realized I never actually thanked you, I passed my interview and your videos were so much help!!! You are awesome!

[@BackToBackSWE]

great - flourish in life friend

[@DavidVCastro]

@TheAntloo, how many times have you used an AVL Tree in your job of two years? 🙂

[@yonathanmichael1910]

This kid's older brother is one of my little homies from college. Now i'm reviewing algorithms and the little little homie is teaching me. Both impressive young men who are making their families proud.

[@BackToBackSWE]

haha hey

[@WyMustIGo]

Looks like this homie stopped the videos because there is no money in teaching for free. That means he gained wisdom and is using his knowledge to make a profit instead... Homie is getting wise.

[@BackToBackSWE]

Check out the free DSA Mini-Course 👉backtobackswe.com/five-day Table of Contents: Introduction 0:00 - 2:07 Tree Height 2:07 - 3:51 Node Balance 3:51 - 4:21 Balance Calculation Practice 4:21 - 7:32 Breaking The AVL Property 7:32 - 8:32 Rotations 8:32 - 12:52 Right Rotation 12:52 - 15:58 Left-Right Rotation 15:58 - 18:12 Left Rotation 18:12 - 18:50 Right-Left Rotation 18:50 - 19:44 Support Us At backtobackswe.com 19:44 - 20:37 Errors: 0:19 - 1:41 The is not a BST, this is fixed at 1:41. 11:08 NIT: The purple triangle is > y (strictly greater) and > x I hope this helps someone. If there are any mistakes let me know and I'll update the "Errors" section.

[@arjunkashyap8896]

This is the clearest explanation I have seen on Balanced Trees so far. I was trying to learn this topic back in march and I could not find a good resource to understand and I dropped this topic. Now today I picked it back up and I found your video. Thank you so much !! ---> Subscribed

[@BackToBackSWE]

sure!!

[@BoonkiCoC14]

Before i watch the video again gotta let you know, this was hands down the best illustration ideo for AVL trees. The illustrations are easy to follow. Cheers.

[@doublaitmaxim7540]

I have a test tomorrow on binary trees and this video really helped me out so thank you so much! !!

[@BackToBackSWE]

great

[@abhinavsingh4221]

Just few moments ago I was really missing you and your content and now your video is here!! Welcome back buddy :)

[@BackToBackSWE]

hey.

[@rustyshackleford2605]

The clarity of your explanation is astounding. Thanks a bunch!

[@BackToBackSWE]

Haha! thanks. Try out the free mini course on our website - backtobackswe.com/

[@weallgotwoodandnails]

Clear, concise, and invaluable. Thank you for uploading this.

[@BackToBackSWE]

thanks - sure

[@eishkapoor703]

Hey man, don't comment alot but I just wanna thank you for being a big part in me getting an internship. The work you do is invaluable, and I for one really appreciate it. Keep grinding these out, you got a life long sub in me

[@nands4410]

Congratulations Where did you get the internship at

[@yutaitadori7318]

Yeah eger to know @Eish

[@BackToBackSWE]

Congrats mate! Keep hustling

[@shilpag08]

I actually like you being on the frame. Helps to focus more and real lecture feeling

[@BackToBackSWE]

nice

[@ishaansrivastav5732]

Its hard to find a teacher who explains better than you SWE. Also, +1 on the tries tutorials would love that

[@BackToBackSWE]

thanks and ok

[@stevendeng2758]

It's definitely the best course that I've ever seen about AVL tree.

[@BackToBackSWE]

thanks

[@hascuhas]

Thank you, I never understood AVL trees from my university courses. Your explinations made it crystal clear for me.

[@dramallama111]

As always, why is that some guy on youtube can explain these concepts so much better, and in a shorter amount of time than most college professors? It boggles the mind.

[@MoscleBrog]

my god i understood his explaination and i feel fun doing this work it kinda feel like rubiks cube. this channel is a magic of understanding

[@DanielDiaz-rq3ko]

I know this video came out awhile back but if you see this, thank you so much! I just didn't understand it in class and when my professor explained it again to me. You literally made this such an easy concept to get!! Thank you !!!!

[@BackToBackSWE]

Glad it helped!

[@Delinester]

This author explained AVL trees better than our professor in 2 lectures. Thank you!

[@BackToBackSWE]

Happy Holidays 🎉 Thank you for your kind words, Delinester! We'd love to offer you a 40% Off our exclusive lifetime membership just use the code CHEER40 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=CHEER40

[@OktayDerman]

professors are like not-teaching teachers at schools stay away from them, go after assistants.

[@jenweatherwax7113]

Lost me when counting nodes became positive and negative @6:10 ...is it negative when you go right, and positive if left?

[@BackToBackSWE]

Hi, is this referring to balance at a node?

[@jenweatherwax7113]

Back To Back SWE Yes 😂 that is very confusing for me. All the positive 1 and negative 1 values

[@hawadoh]

After spending 12 hours non-stop trying to fix just one bug in my AVL tree (with parent node pointers) I've decided to take a step back and watch this video, and this is so much help! I am going to try again now after eating

[@akshayagarwal2714]

Benyam, you are PRO man! I am fan of your teaching style! Your videos have helped me a lot in my prep. Now I have come back for yet another interview, going though your videos first for a quick learning. May this channel be in everyone's recommendation! KZbin you better be listening! XD

[@BackToBackSWE]

thanks - we are humbled

[@manhalrahman5785]

Thanks I used to hate avl trees a lot because of rotations. But this video fixed it

[@BackToBackSWE]

great.

[@marcocaniglia2047]

awesome video, my professor should watch these before lecturing lmao. Thank you!

[@BackToBackSWE]

lol thanks!

[@svenzanetti5637]

Very clear explanation! Is the tree at 8:30 actually a BST though? Because 0 is to the right of 2...

[@BackToBackSWE]

I think I correct it

[@Rishirajsingh2758]

Hey bro , I have loved your teaching methodology , I have started visualising the algorithms , I love you man thank you so much. Could you try to cover up segment trees if possible

[@BackToBackSWE]

great. and yes.

[@JessPen00]

my professor literally puts me to sleep, thank you so much for this video

[@BackToBackSWE]

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[@adarshsharmanit356]

Welcome Back Brother ...Love from INDIA

[@BackToBackSWE]

love from 'MURICA 🚜🌽

[@adarshsharmanit356]

@@BackToBackSWE Learnt new word "MURICA" LoL

[@BackToBackSWE]

@@adarshsharmanit356 nice

[@thatoneguy9287]

Thank you, it definitely helped alot but still i cant figure how do i determine if i need a left or a right left rotation? Like on what do i have to look to know which to use?

[@WatchM3Fail]

This is the simplest vid I’ve seen on this, thanks!

[@BackToBackSWE]

Glad you liked it!

[@mystica7284]

yo welcome back!!! thanks for helping us. ;)

[@BackToBackSWE]

sure.

[@0x1h0b]

thank god !!.. finally you are back.. good to see you buddy

[@BackToBackSWE]

hey.

[@marcspataru]

I have a really important interview tomorrow. If I remember I’ll come here and update.

[@sexcommunist]

Hey, how was your interview?

[@moosegoose1282]

i exited out my prof zoom lecture to watch this. thank u

[@BackToBackSWE]

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[@KanekiSidibe]

This tutorial is awesome, since there is no dislike button, I just let you know in advance !

[@IStMl]

finally a natural explanation

[@shine0nme135]

absolutely loved the way you explain the concept here thanks a lot this really helps me

[@TrueDetectivePikachu]

right in 6:09 I decided to just pause and get to code to see if I can understand it. I ended up with something not very stable but it works XD Done in Python, I'm not sure if this may be O(n log n), it prolly depends on how bad the tree that is traversing is class Node(object): def __init__(self, data=None): self.data: object = data self.left: Node = None self.right: Node = None def get_height(b: Node): def inner(b: Node): if b is None: return -1 return max(inner(b.left), inner(b.right)) + 1 return abs(inner(b.left) - inner(b.right))

[@TrueDetectivePikachu]

still figuring out how to implement the rotation btw, ended in either a stack overflow or loosing a bunch of nodes along the way

[@gcraneorigami]

Absolutely stellar explanation

[@BackToBackSWE]

thx

[@GeovaniLopesDias]

In english, LR and RL rotations are so intuitive! In Portuguese, I'm struggling to get what the heck a "double left" rotation looks like...

[@cocoarecords]

The legend is back with a new video

[@BackToBackSWE]

I am normal.

[@arrahul316]

Thanks bro....this is a great content. It will be useful if we have an example where we have say 5 or greater number of nodes and left or right right heavy with left->right or right->left rotation explained. Again, many thanks for this content. You just rock.. Another suggestion is whether we could explain some practical applications of each DS/Alg as and when you cover them in each video. Like now I know what is AVL tree's properties-> Self balancing. Now where is this Self balancing mandatory in some real world problems. Yes we could google this out or get from intuition. But it will be good conclusion to any video you present, once you have this explained. Again, just a thought. Not an absolute requirement. Thanks Bro. Have a good one!

[@BackToBackSWE]

sure - ok, and u too

[@kirillzlobin7135]

12:45 How did we fix the balance if the tree became heavy on the other side

[@chrispy808]

Best explanation of this thank you!

[@brainwizard8915]

Wow what a sleek explanation

[@BackToBackSWE]

haha

[@user-zm3uw5ij9r]

please do a video on explaining the red black tree.....and comparision of red black tree and avl tree

[@BackToBackSWE]

maybe.

[@jkim5118]

Welcome back, Ben!

[@BackToBackSWE]

hey.

[@jkim5118]

@@BackToBackSWE Yo Ben, is the discussion section on BTB SWE still active? I've posted some questions on this video.

[@patrickneff7846]

Great explanation. Very clear, thanks.

[@BackToBackSWE]

thanks, glad it helped! There are other codes at - backtobackswe.com/ check it out. Would love some feedback

[@monjasonsteng7861]

Thank you - this was great!

[@gaasong2615]

Thank you so much for the best explanation I ever had.

[@BackToBackSWE]

Amaze! do try our free mini course - backtobackswe.com/

[@sameerplaynicals8790]

11:20 the purple node can't be equal to y, because the insertion condition was, smaller=left, bigger or equal to=right.

[@polycoder]

which program does he use for writing?

[@satheshbm92]

Look who's back :) Great as usual Ben

[@BackToBackSWE]

hey.

[@meloth01]

short and precise thank you

[@manojrajasekar6035]

Yayy ! Welcome BACK Ben !

[@BackToBackSWE]

hey.

[@niklotios]

Can you please explain why you inserted the nodes the way you did in the examples about rotations? Or show me a video of the information that I am missing. Thanks a lot!!

[@BackToBackSWE]

what is confusing i can explain

[@niklotios]

@@BackToBackSWE no worries I just hadn't understood the insertion in a binary search tree. I learned it and have passed the exam now. Thanks a lot!!

[@youareunderarrest.3173]

I kind of miss him shouting near that white board. Welcome back. ✌️

[@BackToBackSWE]

hey.

[@_7__716]

Not clear to me how the rotation fixes the balance. Isn't it still imbalanced just on the other side of the root?

[@_7__716]

At 12:46

[@tmusic591]

"We have looked at binary search trees before" I deliberately clicked on the Video in the Playlist marked as #1. Which is the video that I actually should start with? Is there a sorted playlist regarding topics? I appears to me that every video sais "we did X before" and I wonder where I should actually start.

[@BackToBackSWE]

You could explore the entire set of video content on DSA by getting a full fledged subscription on the Back To Back website - backtobackswe.com/pricing

[@JAIGANESH-gd3qj]

please make a video on boolean parenthesization problem

[@mmaranta785]

Can’t you just make the middle value the root and put the smallest one under it on the left and the largest one under it on the right?

[@ahmedsidi3976]

Thank you thos videos are extremely helpful ! Keep going you're the best

[@BackToBackSWE]

haha! thanks. Give a shot to the free mini course on the website - backtobackswe.com/

[@manhalrahman5785]

Yay Back to back is back

[@BackToBackSWE]

hey.

[@diya9707]

oh wonderful explanation, tysm !!

[@programming2347]

You know, I've been working with btrees for a while and Im not really sure if its necessary to strictly implement these rotations in order to get to an avl tree. Since all what you do in composed rotations is convert them into single rotation cases first to then apply that single rotation step. But what if we just add the unbalance Node to its next subtree. And repeat recursively the wrapper method to balance that new subtree. I mean if you have the case for a BTree like the next one. 2---- | ------------ 12 ----------- | | ---- 6 ---- 15 | | 5 8 *Node 2* (HeadNode) is unbalanced by a factor of 3 Couldnt we just move all the subTree of Node 12 one level up and then add the *Node 2* to that new Resulting Tree. So It would result as: ------------ 7----------- | | ---- 6---- 10 | | ---5 8 | 2 This is balanced Tree already, And now this Tree with Node 7 as the headNode would enter to the balanceTree Method again. To make sure there are no unbalanced nodes after the last change. Its the same Case when you have a Tree Like this: 2---- | 3--- | 5 You just have to take the Node 2 and insert it into the subTree with Node 3 as the HeadNode, So It will became into: --- 3 --- | | 2 5 And then we have the special rotation case: --------- 5 | 3---- | 4 This is a double rotation case, but if you just shift the subTree with Node 3 as HeadNode and insert the Node 5 into that subTree You would already have a single rotation case: 3 ---- | 4 ---- | 5 And if we repeat Sending Node 3 into the BalanceTree Method... SubTree with Node 4 as HeadNode would be already balanced once you do the insertion of Node 3 into it --- 4 --- | | 3 5 I've noticed that in the worst of the cases the new Tree is going to be unbalanced again and you can recursively submit the resulting subtrees untill all the unbalanced nodes are just single rotation cases. But usually with much less steps than implementing the double rotations. Is there any specific or algorithmic reason that makes these 2 special double rotation nodes to be the mandatory way to balance every unbalanced subtree? Or do you think the method Im using would be legit and as effective as the one with the rotations. Im not sure if Im making myself clear with this. But its a simple step to get a balanced Tree. - Just take the unbalance Node and insert it into its child SubTree. (Delegating some of the work to the InsertNode Method) Maybe its a more intuitive solution for me. It just came to my mind watching your video so I wouldn't be able to say that this method has math or algorithm well based basis. So I would be really glad if you tell me like "No dude, there's a problem with that and its..." or whatever. Thank you for your deep explanation

[@Mejayy]

Im literally having my data structures exam in 10 hours and this video is saving my ass

[@BackToBackSWE]

Hope it went amazingg 🎉 Please enjoy a special coupon from us - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=SUB 🚀

[@marilu0007]

I love you, you are my G.O.A.T.!!!!!!

[@BackToBackSWE]

haha! thanks

[@arjay_2002]

Log(n) is faster than N?

[@engineering-ux]

Awesome as always. Ben is Back :)

[@BackToBackSWE]

hey.

[@gustavoandresetticassel6138]

Very nice! Thank you!

[@tsatsralt9112]

hi, i just purchased your platform and i think there is an issue with running a python code. I couldn't find a feedback section, so leaving a comment here

[@BackToBackSWE]

We have had some testing outages and are working to make testing's uptime better. You can contact us at backtobackswe.com/contact and we can chat there if anything else goes awry

[@dibaonguyentat600]

Love this video

[@harsh9558]

Thx a lot!

[@camygiuliani8758]

Very clear thanks!

[@BackToBackSWE]

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

[@Mikaelsag03]

you didnt really explain how i can easily determine when to do a left rotation vs a right left rotation especially for bigger trees

[@supamdeepbains5172]

King's BACK!

[@BackToBackSWE]

I am normal, a civilian

[@dariusvue6714]

Can you make a video about TSP?

[@BackToBackSWE]

maybe

[@siyiyu1916]

Great work!

[@BackToBackSWE]

Thx

[@naveenverma2390]

nice nice you are back

[@BackToBackSWE]

I was always here. Just coding and working on our service most of the time. Found a gap to post something.

[@yashshreeshinde4394]

In this video missed you explaining on white board

[@younesanteur6832]

Nice

[@thevats3731]

you should have told general situation in which R-l rotation and L-R rotation are done

[@varunrao2931]

Bruh looking like Caillou. JK, good shit

[@BackToBackSWE]

it's true.

[@varunrao2931]

@@BackToBackSWE Aside from the fact that you literally have helped me more than any other youtuber. Yeah you kinda do

[@BackToBackSWE]

@@varunrao2931 great.

[@eaglei2505]

i have an exam about his stuff in like 3 hours. lmao. lets goo procrastination gang

[@StrayDogLofi]

Hello Back To Back SWE, Can you do an analysis on Radix sort

[@BackToBackSWE]

You could definitely explore the entire set of video content on DSA by getting a full subscription of B2B SWE - backtobackswe.com/pricing

[@oyuncubirlii]

amazing video!!!

[@BackToBackSWE]

Thank you, means a lot 🎉 You can also check out our free DSA course - backtobackswe.com/

[@ruynobrega6918]

Great video!

[@ruynobrega6918]

Can you tell what software are you using to write on screen?

[@BackToBackSWE]

thanks

[@BackToBackSWE]

GoodNotes (on an iPad)

[@priyamvashi2187]

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 😀

[@seayellow5834]

I actually tried to solve self-balancing all myself, and surprisingly my idea of balancing the tree was exactly the same as rotation!

[@humza4848]

helpful vid dawg

[@mangoofficial527]

thanks

[@-NguyenBuiAnhKhoa]

really appreciate mate

[@BackToBackSWE]

Thank you, means a lot 🎉 You can also check out our free DSA course - backtobackswe.com/

[@mrbam8833]

Great content! My only issue is your handwriting lol Y and X look the same lol

[@shivanibambhaniya5568]

you are good!

[@BackToBackSWE]

Thank You!! Do check out backtobackswe.com/platform/content

[@frankyan8135]

thx

[@mikeexplainsit]

The new Khan Academy

[@MiketheCoder]

420 baby!!

[@BackToBackSWE]

hello friend

[@MiketheCoder]

@@BackToBackSWE Btw Ben, what software/hardware do you use to write on the canvas? I'm give tutorials as well and writing pen and paper is a tiresome for me.

[@Chirag-mb2yd]

I'm no geek but shouldn't we call it imbalance instead of balance, just sayin.

[@BackToBackSWE]

sure

[@nawendusingh2858]

why i only see you in 3 months :(

[@BackToBackSWE]

yo

[@preeeby]

Why subscribe for one video every 3 months?

[@BackToBackSWE]

We post ~2-3 videos a week on backtobackswe.com that are not here, we have an in-browser code workspace (in 4 languages right now), & it is not a subscription. It is only getting better by the day as we add features & content.

[@lwinphyoaung847]

👏

[@BackToBackSWE]

Happy Holidays 🎉 Thanks! We'd love to offer you a 40% Off our exclusive lifetime membership just use the code CHEER40 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=CHEER40