Binary Tree Bootcamp: Full, Complete, & Perfect Trees. Preorder, Inorder, & Postorder Traversal.

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Back To Back SWE

5 жыл бұрын

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Full Binary Tree: Every node (besides children) has exactly 2 children (the maximum children a node can have in a binary tree).
Complete Binary Tree: Every level, except possibly the last, is completely filled, and all nodes are as far left as possible.
Perfect Binary Tree: All interior nodes have two children and all leaves have the same depth or same level. Perfect binary trees are both full and complete.
Preorder Traversal: node left right
Inorder Traversal: left node right
Postorder Traversal: left right node
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Пікірлер: 728
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
Table of Contents: A Quick Message 0:00 - 0:31 What We Are Going To Do 0:31 - 0:52 Full Binary Trees 0:52 - 1:38 Complete Binary Trees 1:38 - 2:14 Perfect Binary Trees 2:14 - 3:18 Let's Discuss The 2 Fundamental Traversals 3:18 - 3:42 How To Know Which Traversal Is Which 3:42 - 5:05 Think of Recursion Like This. 5:05 - 5:33 Preorder Traversal Walkthrough 5:33 - 11:15 Inorder Traversal Walkthrough 11:15 - 14:25 We Realize That This Is A Special Tree 14:25 - 15:07 Postorder Traversal Walkthrough 15:07 - 18:59 Briefly Addressing Time Complexity 18:59 - 19:22 Wrap Up 19:22 - 19:40 At 1:42 I meant that binary heaps are complete binary trees with the heap ordering property. Not that a complete binary tree is always a heap. The code for the traversals is in the description. All recursive and basically the same function. We will do iterative and O(1) space traversals soon.
@2WARDEN2
@2WARDEN2 4 жыл бұрын
The ToC and video itself are perfect! The quality of information is phenomenal, I'm glad I kept digging for pre/in/post order examples until I found this! Thanks for taking the time to create this!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
ye, for the internet yo
@bonniwanamaker6296
@bonniwanamaker6296 5 жыл бұрын
This guy is an amazing teacher.
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
i try :*)
@connerjensen8170
@connerjensen8170 4 жыл бұрын
Yeah for real I love his enthusiasm
@SquidBeats
@SquidBeats 2 жыл бұрын
Jesus Christ is God and is the only way. Hell is real whether you believe it or not
@JossinJax
@JossinJax 4 жыл бұрын
Omg writing "lnr" at each node really clear this up for me. Thank you!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice
@oasishusband5260
@oasishusband5260 3 жыл бұрын
Ikr I loved that!
@Parthsean
@Parthsean 2 жыл бұрын
I am a software engineer for 2 years and I didn't know that. Let me go sell my degree ...
@alexandergonzalez5975
@alexandergonzalez5975 4 жыл бұрын
This channel is a shiny gem among a sea of low quality CS channels. Please keep it up.
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
haha, what a statement
@andrews2945
@andrews2945 3 жыл бұрын
*Ocean of low quality CS channels
@swimmingbyrd6283
@swimmingbyrd6283 4 жыл бұрын
Showing these traversal with a "n" saved my lllliiiifffffeeee!!!!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
yuh
@Moitaytay
@Moitaytay 4 жыл бұрын
I've gotta say; I've worked at Amazon and Lyft, where you'd think people have their fundamentals down like crazy, but they can't explain simple topics like these. You, sir, have the gift of teaching. Thanks for your help!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
sure
@prashmokk6659
@prashmokk6659 2 жыл бұрын
This video was amazing. I don't really comment on videos, but I had to express my appreciation to you for creating this. I got an interview about a month ago and this was the first of many videos I watched of yours while I was preparing. This past week I found out that I got the job and you were a big part of that. I'm not sure if you'll see this, but I hope you know that your videos have helped me and many others. Please continue to make awesome informational content like this!
@sunnypatel1784
@sunnypatel1784 3 жыл бұрын
Your reaction to the cutting and the stomping sounds cracked me up! Great content man! You just got yourself a subscriber.
@MM-lo9tk
@MM-lo9tk 3 жыл бұрын
I always assumed this was a super complicated topic and have been putting it off as long as possible. You just made it so simple and easy to understand. Thank you. I think I just found my new favorite channel!
@travissimelane1847
@travissimelane1847 2 ай бұрын
I don't know how to thank you. You have saved me hours of reading a Data Structures Textbook 3 times just to get this concept. Very thankful. Please do not stop your great work
@crewelghoul
@crewelghoul 4 жыл бұрын
I've been struggling with data structures and algorithms, and this really made things a lot clearer, thank you so much!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
great and sure
@MikeChaseJr
@MikeChaseJr 4 жыл бұрын
This is amazing. One of the better CS videos. I love how you ask questions to test our understanding as we watch!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
ye
@fanifyeyev
@fanifyeyev 3 жыл бұрын
I have watched dozens of similar videos, I can tell you, this guy is amazing. The way he provides the material is unbelievable, so motivated, so much energy, so much positive things can be felt.
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
thanks - this guy
@yannickwessidjam2036
@yannickwessidjam2036 Жыл бұрын
Wow! the best video I have ever seen!. I have been trying to understand this for so long. No one really explained it in a format that made sense to me. This makes so much sense!. Thank you !!!
@juliannafotheringham7101
@juliannafotheringham7101 2 жыл бұрын
This is the most fantastic, clear video I have ever seen on DFS traversals, thank you so much my dear angel!
@gloriawang7493
@gloriawang7493 10 ай бұрын
thank you for such a high-quality video. your explanation of "each node needs to execute the same policy" makes a ton of sense! never have i understood traversal so clearly until your video!
@backup2ramdisk
@backup2ramdisk Жыл бұрын
WOW. Watched a bunch of videos by different people on traversals, everyone else just mumbles on and on "print this, skip this and print that" without explaining why, and you're THE ONLY ONE who actually explains the whole recursion thing in detail. THANK YOU SO MUCH!
@andreysantos6660
@andreysantos6660 5 жыл бұрын
Man, I wasn't being able to understand tree transversals properly until I've seen your explanation. Thanks a lot! Now I understand!
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
nice!
@faridashaikh1015
@faridashaikh1015 2 жыл бұрын
lnr at every node just made things so clear for me .....This is just amazing!!!
@birbx3r354
@birbx3r354 3 жыл бұрын
I struggled with data structures and algorithms for 4 years. Watching your vids has helped me finally understand what's actually going on in layman's terms. Thank you so much for making these videos and keep it up!
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
ye, great
@mattdoestechstuff
@mattdoestechstuff 3 жыл бұрын
This was really helpful. My university lecturer did a terrible job explaining this, but you managed to do it so succinctly and clear. Thank you!
@iulia6707
@iulia6707 3 жыл бұрын
this helped me a bunch for my collage exam, thank you!
@alexbowen3381
@alexbowen3381 4 жыл бұрын
Thank you so much for this video!! I'm an MIS major and a former CS major and after a so many CS courses a 20 minute video by you finally made me understand traversals! You are great at explaining these concepts and I look forward to binging more of your lessons as I brush up for some SWE interviews
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice thx
@WorldOfPersianDoc
@WorldOfPersianDoc 3 жыл бұрын
to the point and straight! thank you! in preparing for my qualifying PhD exam and i just arrive after work and come to starbucks to study! i dont have enough time to read allthings in book carefully so thats the reason this video save much more time for me! tnx again! :)
@nitingupta1591
@nitingupta1591 3 жыл бұрын
The best traversal video till now. You teach using first principles. Hats off !
@haylydo8376
@haylydo8376 4 жыл бұрын
I never comment on videos I see, but this one has to be the exception, because this is by far the best video I have seen on this topic. It cleared up so much confusion, and gave me tools to use along the way. Thank you!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
Nice to hear. Thanks and sure
@mhaland2775
@mhaland2775 Жыл бұрын
I have looked at so many videos to understand this. This is the first video that made me understand it:) The recursive way of thinking was really helpful to understand this
@BackToBackSWE
@BackToBackSWE Жыл бұрын
thank you! Means a lot
@drodskate
@drodskate 5 жыл бұрын
This is exactly what I needed! Thank you so much! You have no idea how hard the summer quarter has been with the lack of explanation.
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice - happy 4 u
@manojchoudhary6146
@manojchoudhary6146 3 жыл бұрын
I don't know who's those people who dislike such informative video. Great efforts, keep doing.
@marilu0007
@marilu0007 3 жыл бұрын
The only person with charisma to teach Data Structures, I love it! (mosh is also good but you are pure gold)
@johnisdoe
@johnisdoe 4 жыл бұрын
This video is VERY helpful in understanding recursion. I honestly brute forced recursion and never thought of it that way. As someone mentioned in the comments, this channel is a one-in-a-million!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
great
@samarth319
@samarth319 5 жыл бұрын
Amazing content and teaching!! Gained so much knowledge in 20 mins than i could in my whole semester!! Please continue making such quality content on DS&Algo!! Thank you Ben.
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice
@dennisdouglas5941
@dennisdouglas5941 4 жыл бұрын
Honestly, You did a wonderful job explaining this content! It was fun, easy to follow and understand! 5 Stars! I did watch all of it, and I shall continue too watch all your videos! You rocked it!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice thx
@iaminhridoy5871
@iaminhridoy5871 Жыл бұрын
To be honest, you way of teaching is as clear as crystal, loved it ...
@bufdud4
@bufdud4 2 жыл бұрын
Wow, I was struggling to visualize recursion for months. This cleared it up for me! Thank you!
@BackToBackSWE
@BackToBackSWE 2 жыл бұрын
Amaze! Try our 5 day free mini course for some fascinating content - backtobackswe.com/
@ScottShaulis
@ScottShaulis 10 ай бұрын
Quality breakdown. Simplified, easy to understand. Much gratitude! Man, even very easy means of memorization. Fantastic.
@OTlesuh
@OTlesuh 3 жыл бұрын
I never understood this in class, however after this video I've learned how to correctly implement it and view it from a conceptual standpoint. Great video!
@t1910j
@t1910j 3 жыл бұрын
Absolutely well explained. I am watching this before my google interview tomorrow. Thanks a lot! Subscribed!
@danielbee3697
@danielbee3697 Жыл бұрын
best explaining I've seen so far. Thank you so much!!!
@dansteryoo
@dansteryoo 4 жыл бұрын
a lot of channels would have taken shortcuts to fast-forward or just breeze by each node explanation because it might feel redundant.. but man so thankful you understand repetition is an important part of education.
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
sure
@xMysticWolf
@xMysticWolf 3 жыл бұрын
Dude, you just made it so simple to understand, thank you so much! You're an amazing teacher, I get it now
@bartlomiejdrozd2357
@bartlomiejdrozd2357 4 жыл бұрын
Great stuff my friend! Way you use NLR, LRN, NRL is simply beautiful. Few minutes and I got to understand how binary trees are traversed! Thank you!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
ye - great - sure
@caleboke2771
@caleboke2771 3 жыл бұрын
Using LNR as the call stack just help me understood how binary trees work in general. Thumbs up man
@Elias_90
@Elias_90 Жыл бұрын
best explanation ive heard, very intuitive (I've previously gone through the topic in two separate modules and didnt really get it so this was great help)
@srinadhp
@srinadhp 3 жыл бұрын
The way you explained the recursion is class apart!!! Also how to identify pre/in/post order. Hats off. Will now search for your video on graphs! Hope you have it. Keep posting!
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
thanks and ok
@patrid0
@patrid0 3 жыл бұрын
I have never commented on a KZfaq channel before, but you sir, are an amazing teacher. 🤗 Thank you so much, lots of praise for you from the Namibia University of Science & Technology!
@konekoshoujo
@konekoshoujo 2 жыл бұрын
Bachelors in CS, 3 YOE and this is the firs time I understood recursive tree traversal! thank you!!
@tajahouse4678
@tajahouse4678 3 жыл бұрын
This is AMAZING! And I laughed so hard at *LOUD CUTTING NOISE*! (Probably means I need to come out of my office for a bit lol) I for sure will be using this content for preview of whatever I am learning. Great work!
@naveenantony3924
@naveenantony3924 2 жыл бұрын
had a basic understanding before, your explanation sealed it for me, also patched up a concept i missed..Keep going 👍👍
@ftedg
@ftedg 5 жыл бұрын
A channel like yours pushing quality CS videos is really really in need... Thank you so much for your efforts. Most of what's on youtube is low-quality Indian content (no hate). Again thank you so much and please dont stop! I would recommend some videos on Algorithm designs like divide and conquer, greedy method etc.
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
Haha, well I think my videos are "ok". I just want to do them and if it helps someone then all the better. If it completely goes over someone's head then that is fine too. Also, I think a table of contents in any instructional video longer than 4 minutes is key. Everyone comes to a teaching with different levels of preparedness and precontext. And in regards to the Algorithms stuff...we will do plenty of that just give it time since I have a long content list to cover. Those topics are in the list.
@soumyajeet7809
@soumyajeet7809 5 жыл бұрын
Lma4a Well i agree, that there's a lot of Indian content but u can't classify everything generally as low quality. I mean, since there are so many Indian channels, there's a good chance that the videos posted are not that good but there're some legit channels that if u learn from u definitely won't be disappointed. Instead u'll thank me later. See the videos on the channel "mycodeschool" and u'll know.
@huilingyan3981
@huilingyan3981 4 жыл бұрын
I do have seen good quality Indian content videos. The thing is that as a non-native English speaker, i always have to spend extra time understanding what they said lol
@emilyhao9272
@emilyhao9272 4 жыл бұрын
@@soumyajeet7809 Disagree. All of the content I encountered have been a waste of time. What's even more frustrating is some often switch between English and other languages, highly confusing for the viewer. Just make two videos or stick with one language and subtitle it.
@soumyajeet7809
@soumyajeet7809 3 жыл бұрын
@@emilyhao9272 Here are some Indian KZfaq channels that offer their videos only in English and the quality of content is excellent. You should have a look at these. If you still find these a waste of your time, try learning from books or other channels. 1. Edureka 2. Intellipaat 3. Simplilearn 4. ProgrammingKnowledge 5. Mycodeschool 6. codebasics 7. TutorialsPoint India ltd
@Gyokuru7928
@Gyokuru7928 5 жыл бұрын
Best channel out there. They way you explain things, it really shows how you yourself experienced learning these topics. And Im glad to have found this channel. Big ups from Germany.
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
Thanks! Germany is sweet!
@huaqian3654
@huaqian3654 2 жыл бұрын
You explanation to recursion is amazing!
@josephwong2832
@josephwong2832 3 жыл бұрын
The way this guy walks through these examples is crystal clear.
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
ye - this guy
@maxstanley1818
@maxstanley1818 3 жыл бұрын
two years later, hands down best traversal video on youtube.com. I don't know why schools do not use the nlr rule
@dantedt3931
@dantedt3931 3 жыл бұрын
One of the best explanations for Binary Trees.Subscribed!
@gansaikhanshur4934
@gansaikhanshur4934 2 жыл бұрын
Who's watching this in 2022. This guys know how to teach!!! Thank you!
@shenzheng2116
@shenzheng2116 3 жыл бұрын
I am a math student targeting for a data science career And I have to say this is the BEST computer science video I have even seen! Just AMAZING!
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
thx
@connerjensen8170
@connerjensen8170 4 жыл бұрын
Awesome! Thanks for this video. I was just attempting a leet code problem where I had to traverse a binary tree and I was pretty lost. You're a great teacher!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
sure and thanks
@speedsanti
@speedsanti 3 жыл бұрын
It’s hard to keep up and stay motivated with online classes, so I started slacking off in my data structures class. Thanks to you, I feel like I’ve caught up and I feel ready for my midterm on wednesday 😼
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
great
@Moonev_Fantasy
@Moonev_Fantasy 3 жыл бұрын
Really sweet explaination with humoristic slices) It's gorgeous. Thank you!)
@darkhorse621
@darkhorse621 4 жыл бұрын
High quality and informative content. A must for conceptual clarity and interview prep. Thanks a lot for all the work !
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
sure
@raphk1040
@raphk1040 4 жыл бұрын
you're amazing. I just started learning data structures in C and this is one of the best explanations i've found of binary trees..
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
Nice
@harrietread1749
@harrietread1749 3 жыл бұрын
This was very helpful for my A-Level CS, thank you
@wanyi8761
@wanyi8761 3 жыл бұрын
this is absolutely fire finally understanding tree traversal thanks mate
@Danny1905
@Danny1905 4 жыл бұрын
Awesome. I came from a great CS book I'm reading and the chapter I'm right now touched this topic, so I came here for more info and wow. You helped me to understand it so much better! Keep it up! This channel is awesome
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
thanks
@matthewpourroy1342
@matthewpourroy1342 5 ай бұрын
BY FAR the BEST explanation ever, thank you!!
@arjay_2002
@arjay_2002 3 жыл бұрын
Thank you. 20 mins well spent!
@ruthylevi9804
@ruthylevi9804 2 жыл бұрын
this is exactly what I was looking for, thank you!! top notch explanations
@xxlhara
@xxlhara 3 жыл бұрын
man, you've got some intense energy, i love it.
@debanjanasantra6724
@debanjanasantra6724 3 жыл бұрын
half way through the explanation and really loved the nlr for each node! Hopefully now I can try to write logic on my own for tree problems. Fingers crossed!
@AndrewDaniele87
@AndrewDaniele87 3 жыл бұрын
first time I ever subscribed to a channel after watching just 1 video, you have a great teaching style!
@chahalpawanpreet
@chahalpawanpreet 3 жыл бұрын
Superb job clipping this all together
@sipwhitemocha
@sipwhitemocha 2 жыл бұрын
Love your enthusiasm pal. Thanks for great video
@frozen_tortus
@frozen_tortus 3 жыл бұрын
Absolute hat's down. The teaching style is unique and I love it.
@diveruzumaki5556
@diveruzumaki5556 2 жыл бұрын
after three years I finally understand tree traversal properly T_T , THANK YOU
@persnlassname7137
@persnlassname7137 4 жыл бұрын
Thanks to your channel... It really changed on how I see the traversal works, I understand it better and I hope I can pass my midterm exam on this topic. Thanks dude
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice!
@baranturkan9589
@baranturkan9589 2 жыл бұрын
Dude I wanna say that you are really impressive. This subject really made me confused but with your teaching style that shit became more understandable. Thx so much.
@ichinnorovtuguldur3627
@ichinnorovtuguldur3627 4 жыл бұрын
I like how he teaches it so passionately. It was super helpful! awesome!!!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
thx - and great
@zb2747
@zb2747 Жыл бұрын
Straight to the point and great breakdown - thank you!
@huseyincandayan7947
@huseyincandayan7947 4 жыл бұрын
Amazing video. Spot on teaching. Thank you very much.
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
sure.
@rayaneyahiaoui4174
@rayaneyahiaoui4174 4 жыл бұрын
Your videos are great man. I love your explanations and your examples. They're concise and straight to the point. Keep them coming buddy!!
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
ok
@viniciuspedroso5923
@viniciuspedroso5923 2 жыл бұрын
Finally a decent explanation on tree traversal, thank u
@elimart345
@elimart345 3 жыл бұрын
OMG thank you for breaking this down. I was really confused before this video.
@ocholol
@ocholol 4 ай бұрын
Your channel is carrying me in my CS class rn, tyty.
@carinacarollomalinao7451
@carinacarollomalinao7451 3 жыл бұрын
Sir, thank you very much for this video! Wherever you are, I hope you are safe and feeling well. You made me analyze this in the simplest way possible! I am very grateful to you sir. Thank you so much!
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
thx
@jonathongreenlinger4282
@jonathongreenlinger4282 5 жыл бұрын
Dude, this is seriously so helpful. You explained it well and got right to the point. Keep it up
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
sure
@jonathanluo0
@jonathanluo0 Жыл бұрын
5:24 explain very well on nlr (Preorder) traversal on each node, plus recursion in general
@rushawncampbell7284
@rushawncampbell7284 2 жыл бұрын
I had to subscribe, your explanation is on point, clear, easy to follow.
@apurbapanja1693
@apurbapanja1693 3 жыл бұрын
Thank you Benyam. The way you teach and explain is really awesome. I've really learned a lot from you. This video is special for "lnr" concept. Thank you again.
@mariavic822
@mariavic822 2 жыл бұрын
you make this lesson so EASY to understanddd... thank you!!!!!!
@belledecena199
@belledecena199 Жыл бұрын
Thanks to you! I am able to submit my project because of your video!
@arkster00
@arkster00 5 жыл бұрын
Hey. Just wanted to thank you for the content. You're clear and concise in your explanation which helps a lot.
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
hey, thanks
@pranavmedhi3237
@pranavmedhi3237 4 жыл бұрын
All videos on this channel make my concepts Crystal clear
@BackToBackSWE
@BackToBackSWE 4 жыл бұрын
nice
@sohamkar876
@sohamkar876 5 жыл бұрын
This was just what I needed! Thank you so much for all you do.
@BackToBackSWE
@BackToBackSWE 5 жыл бұрын
This is what I do
@MatthewSeligman
@MatthewSeligman 2 жыл бұрын
This explains tree traversal and recusion so clearly! Truly appreciate you sharing this information!
@BackToBackSWE
@BackToBackSWE 2 жыл бұрын
Thank you, glad you liked it 😀 Do check out backtobackswe.com/platform/content and please recommend us to your family and friends 😀
@anto1756
@anto1756 3 жыл бұрын
thanks for making the recursion so detailed. I really struggle with that concept
@sasbazooka
@sasbazooka Жыл бұрын
I'm a Sr. Software Development Engineer who got here without ever taking any CS courses, and now I am hurting for that. This dude here is giving me the exact info I need to fill in the blanks. Bravo dude!
@BackToBackSWE
@BackToBackSWE Жыл бұрын
Thank you, appreciate it 😄 Also check out our Free 5 Day DSA Interview Prep Mini-Course - backtobackswe.com/ 🎉
@reinasama904
@reinasama904 Жыл бұрын
The quality of this material is beyond what we deserve THANK YOU SIR
@thomasl863
@thomasl863 3 жыл бұрын
Turn this one up! You're a great speaker and break down concepts so well.
@BackToBackSWE
@BackToBackSWE 3 жыл бұрын
thx
@brucewayne3141
@brucewayne3141 3 жыл бұрын
I study CS at an Ivy League school and I didn't learn shit from my professor's lectures. Your videos are literally saving my grade cuz my final is tomorrow. Thank you.
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