Data structures: Binary Tree

See complete series on data structures here:
• Data structures
In this lesson, we have discussed binary tree in detail. We have talked about different types of binary tree like "complete binary tree", "perfect binary tree" and "balanced binary tree" and their properties. We have also discussed how cost of operations in a tree may depend upon height of the tree and why we want a tree to be dense and its height to be minimum. Finally, we talked about two possible implementations of binary tree - a) using dynamically created nodes and b) using arrays.
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[@saikumar555]

Felt very sad that the guy who was founder of these courses passed away on June 2014 . in a car accident! but he is alive with his videos!!! RIP !! :(

[@nicolasgoosen5142]

Yes, they're fantastically dense full of info and comprehensive.

[@aakashSky-0]

how do you know this? who is running the channel now, cuz the last video on this channel is 4 years old.... please reply I really wanna know the answers.....

[@findoc9282]

he always live in our heart, never be forgot. Every moment we get inspired in some moment in the future

[@rchtchauhan]

@@qq3801 thanks buddy for this

[@databaseteacher]

sad to hear that. RIP

[@mycodeschool]

Here is the next video - Data structures: Binary Search Tree

[@nishant73391]

+mycodeschool at 13:20 you show the height of the left child of root is 2. The height of left child of 2 is 0 here not 1. so how the height is 2?

[@sambitsarkar6987]

+NISHANT NIKET You are right. The height of the left child of 2 is 1 and not 0. But we are talking about the abs difference between the height of left and right sub tree. So, lheight = 1, Rheight = 1, lheight - Rheight = 0. Hope this helps!!

[@cafafans]

I have been watching this video since 2015 and I never get tired even on this 2019. Thank you so much for this wonderful work.

[@rohithpokala]

@@cafafans me too

[@DOOREO]

mycodeschool ahhhhh.. I see!! *pointer to “the next video”...... GENIUS teachings

[@hariprasadramakrishnan6241]

Awesome explanation.. I have a doubt though.. In the definition of complete binary tree in the video, it says all levels except possibly the last are completely filled, What do u mean by last here? We can have complete binary trees with incomplete last and incomplete last but one levels ...

[@sumanjha3914]

Hi, I need a video on B tree insertion, traversing and deletion

[@Anoopegi]

please give a lecture on avl tree ,threaded trees and graph using link list

[@gaganb.9408]

sir, if we check the height of the node 2, upto subtree it calculates to 2, but if i check the same for one upto subtree then it should be 0, because |1-1|=0, instead of 1? please if you can clear this doubt

[@eshaan7_]

If anyone is having confusion between depth and height, think of the analogy that we measure the 'depth' of sea from it's surface and the 'height' of a person from toe to head. PS: This was taken from a stackoverflow thread.

[@nareshramini1796]

I'm still confused about height and depth of a tree!

[@astagfargamer]

what do you mean!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

[@thewatcherlollol]

stole this right off of Stackoverflow. Credit the person smh.

[@dhruvgaba8516]

Let's imagine an example of a fish swimming in the sea. Here, fish resembles a node, and the height of the fish from the sea bed resembles the height of the node and the depth of the fish from the surface of the sea resembles the depth of the node. Have a look at the diagram below: _ _ _ _ _ _ _ _ _ _ _ _ _ == surface (root node) | | == Depth from the surface of the sea (if there are d no. of edges to get to node x) | ((*)) === Fish Any particular node (x) | | == Height from the bottom of the sea (if there are h no. of edges from the bottom-most leaf) | _ _ _ _ _ _ _ _ _ _ _ _ _ == sea bed (leaves, end of tree)

[@akshaysolanki4340]

Eshaan thanks for sharing

[@learningisjoy8613]

Thanks for your hardwork...you did awesome job that benefit many students like me...Thumbs up and keep on sharing.

[@mycodeschool]

Jamyang Tashi Thans a lot :)

[@sersuplado1354]

J

[@maryjaneponcedeleon4372]

🙌🏻

[@Dhruv-jf1ho]

@@mycodeschool Helped me in 2020

[@anveshreddypinnapareddy3552]

@@Dhruv-jf1ho yeah, always has been 🙌

[@md-ayaz]

Instead of thanking him on comment section. You could white list his channel on Ad-block ( if you are using one).

[@TheOverAndAround]

at 13:04 I am confused how you say the height of left subtree is 1? I thought it was 2. Say node x is the one in red. I watched the previous vid and it says, the height of x is the number of edges in the longest path of x to a leaf. I counted 2? I look at it this way to make it easier. if left subtree has no edge - height = 0 if right subtreee has no edge - height = 0 if left or right subtree has an edge, add up all the edges leading to the deepest leaf node then use your formula diff = | leftsubtree_height - rightsubtree_height |

[@mycodeschool]

Matt Stewart - We are saying height of left and right subtrees. Height is defined as number of edges in some longest path from root to a leaf. For the sub-trees, the root node is not the node marked in red. For left subtree, root node is the left child and for right sub-tree root node is the right child. We need to calculate from root of the respective subtrees. Let me know if this is still not clear to you. Actually, you can calculate the diff, by saying 0 height if there is no child. Actual diff wont change. Lot of people do that. That's ok.. But when we say subtree, we cannot count the node (marked in red here) itself.

[@TheOverAndAround]

mycodeschool thanks so much, that makes sense, I didn't understand where the subtree started.Learning alot from your clear vids.

[@simonetruglia]

Matt Stewart Thanks for the question :)

[@GauravTayal26]

Still not clear. Height of left subtree is 2 and not 1 since there are 2 edges from root of left sub-tree to the leaf while chosing longest path. Please clarify

[@prashanttrar9599]

Height of the left subtree means counting no. of edges starting from the left node and not from the base root itself, maximum no. of edges from left node to the leaf node is 1 hence, height of left subtree is 1. Consider it as a new temporary tree of which base root is the left node and just calculate height of it.

[@chiranjeeveemohapatra]

for node2 at 12:51 , you mentioned diff = |1-(-1) | But Shouldn't it be |2-0| ? Left subtree has height 2 and right as 0... 0 because we still have node 2 and it's not empty node. The difference is 2 anyway.

[@PrabhuGunaDeepakPallikonda]

Exactly my doubt!!! Thank you for confirming !!!

[@yashchandraverma3131]

I click on every ads that you show because you are teaching me well and it is my duty to give some money from ads to you. Thanks mycodeschool.

[@blackflame_]

He passed away..

[@lyfokzz3848]

@@blackflame_ his friend passed away...

[@blackflame_]

@@lyfokzz3848 Whoever he was I owe him for helping me clear my courses

[@lyfokzz3848]

@@blackflame_ yup...some of the real IT/CS people will understand his work!

[@shahriarmim4696]

It's the cofounder Animesh Nayan. And I think he doesn't need anyone's money. And death happened to Late Harsha who was also a managing member of MyCodeSchool. Read this: blog.mycodeschool.com/2013/12/the-story-of-mycodeschool.html?view=classic

[@TheTahlia1988]

I cannot thank you enough for this playlist on Data Structures! Keep up the good work :)

[@sunitsingh5429]

i have a doubt..@13:06 why is the height of the left subtree 1 and not 2? i mean given that height of a node is the maximum path up from a leaf,shouldnt it be 2?

[@theFifthMountain123]

Note the word "subtree". Subtree is the blob after edge from the red node. The blob has 3 nodes total; height of the blob is 1. Thus, height of left subtree is 1.

[@abhinavmishra6648]

theFifthMountain123 Thanks man!

[@theFifthMountain123]

Abhinav Mishra I'm a woman. Not your fault though, typical programmer is a nerdy guy which I'm not.

[@ZeeshanAli-ck3ue]

@@theFifthMountain123 if this is the case that you mentioned above then how did you find difference one at 12:49.AS your both lest and right sub-tree height is one.

[@vrindabv]

anybody watching this in 2019

[@o1-preview]

yup.

[@SanchayGoyal]

yup

[@jill4470]

Even this kind of video has this dumbass question

[@StoreyofGee]

@@jill4470 Hahah so true

[@bakibillah8759]

yeah, i have seen many tutorials and articles but this one seemed to me best

[@sourabhdattawad9244]

Best data structures tutorial around the web. Thanks for enlightening!

[@human-011]

anybody watching in 2018

[@irfanansari6448]

2019

[@tusharthurawa2830]

2019

[@adeboyeoyeniyi9473]

2019 lol

[@deepgagan9015]

2019

[@human-011]

again watching in 2021

[@ishratrhidita9393]

How did you get 1 left child in 13:04 seconds? There are two edges from the left subtree to the leaf.

[@eagerassaultixopi4558]

left subtree is the node left to the node marked in red which has height of 1 where as right subtree is the tree on the right of red marked node which has height of -1 coz it is empty

[@MVK-eo7gg]

@13:08 How is the height of left sub tree -1? I think it should be 2, right?

[@franciscoprin4091]

I'm confused in minute 13:10. The "h_left" should be 2. There are two edges before reach one of leafs in the bottom. Therefore, diff = | h_left - h_right| = | 2 - (-1) | = 3 Could someone clarify this for me, please? (sorry for the grammatical mistake.)

[@abhijitroy4702]

I also thought so.

[@alijafari9576]

Even if the tree is not complete you are still able to use an array. You can use -1 or any invalid number for the children that are missing!

[@mycodeschool]

Ali Jafari That's true !!

[@aditipatil7377]

hats off to u sir ! ur videos r life savers ! helped me alot during my dsa viva !! u r truly great teacher ! :))

[@rajatnarlawar]

u teach very well...finding it easy cuz of u..:)

[@nicolasgoosen5142]

This is an awesome series - even 7 years later!

[@josedubois2295]

You are an amazing teacher thank you so much for helping me understand these topics more completely.

[@akumasdeception]

This is a masterpiece, thank you so much for the job that you're doing!

[@gigachad6844]

Guys there also exists a different version ACBT = Complete Binary Tree of mycodeschool Complete BT = Perfect Binary Tree of mycodeschool While Full/Strict/Proper and Perfect BT all are same.

[@WiseFatOwl]

Thanks a lot for this data structure playlist! A life saver if u ask me.. I know I know i'm pretty late.. but still thanks again!

[@RebeliousSapien]

oh my god this was so helpful. i've read so much content about trees and watched so many videos that always left me even more confused. But THIS ... this was just perfect and extremely well explained. thank you so much for making this video.

[@minhnguyennhat5112]

Thank you very much for your work. This channel is a fucking gold mine!!!

[@premalathak6748]

please teach redblack tree and splay trees.

[@abdal720]

bhai lagta tum pass karwao gey!

[@docuscientifique]

You saved my life :) I love you :)

[@prabaljainn]

GOD BLESS YOUR Soul SIR "Humblefool"

[@renon3359]

Hands down best videos on the net for Data Structure. Awesome work man.

[@TheSteak1984]

Great tutorials. Thank you.

[@eimaisklhros]

damn! i have to get a math revision asap

[@GauravSehrawat8888]

Just too Good.. Awesome concepts . Channel will be popular soon !!

[@vivekk232]

excellent sir....& lots of thanks to help me as such easy language to learn tree...I appreciate u sir

[@premalathak6748]

Thank you so much for wonderful video with the subtitles. Finally,now i can understand what a binary tree is.

[@philtrem]

These videos are fantastic, thanks a bunch!

[@SonuSonu-tk5pk]

why dont u go to ur country and study

[@philtrem]

o.Ô

[@saurabhshah8802]

Haha. What's wrong with you man? Its KZbin. Its free and available to all.

[@victorkiwumulo5712]

Im just watching it in 2024

[@prakrutijani4205]

Excellent even after 5 years..Thank you

[@lorimemontanes8950]

Hi. I am one of your subscriber, been following you for a couple of months. Can i possibly use this as a reference in our class, seems like you do have a very clear way of explaining. Thankyouuu.

[@amankhubani2413]

Hey at 13:23, the height of left subtree should be 2, correct? why have you taken it as 1?

[@qaziahmed9850]

Thanks a lot sir yoh have good job and great effect in this way to help students whose want to increase the knoweldge wd conpect.

[@ashfaqtunio1311]

Excellent! Explained very well. Thanks for these videos

[@VIKASHKUMAR-qt7pk]

thanks to making such a nice tutorial it will covers all necessary information to starting binary tree. thanks again.

[@georgioskyritsis2929]

The best explanation i've ever seen. Thank you!

[@rhinethetauren]

Great lesson. The log stuff threw me off, but I just need to review all that anyway

[@surekasunder5923]

This is a great video. Just had one doubt, i understood we consider height of node as 0 if there are no child nodes and height of tree as -1 if there is no root. However, around 13th minute we considered tree with no child nodes with height -1(instead of 0), also made height of left sub-tree as 1(instead of 2).

[@badxcode]

yeah, I got confused there too. at 13:11 it should be |2-0| = 2 not |1-(-1)| = 2 by his definition. Am I right?

[@AwaraGhumakkad]

2power0 + 2 power1 + 2power2 ........ 2powerh generic would be 2powerh, how come its 2(power h+1) -1 ?

[@anurakboonyaritpanit9129]

thank you mycodeschool for good and free video tutorial. it is a complete data structure. help me understand outside my class.

[@PrashantKumar-qk3ew]

I want to provide a suggestion that when you write at down of the board it gets hidden by the words displaying above it. Mind it please, it will further enhance your work and thanx for providing the best.😊

[@ewanmcdonnell6990]

Thank you for your good explanation.

[@vikashgola287]

So i did the calculations and found that an average computer with a CPU frequency of 3GHz(which can execute 3 billion instructions per second) will take upto 13398978947110 years to execute 2^100 instructions. Crazy alright.

[@ketkidavda8588]

this is awesome !!! youre a very good teacher :) thanks

[@madanmohan5661]

Wouldn't be the diff be, diff = height of left sub tree - right subtree, so -> (2 - 0) = 2. Because left subtree have a max depth or height of 2 and right side we don't have a subtree so it will be 0. So the diff will be = | (2-0) | = 2 not | 1 - (-1) |. Can someone clarify?

[@hiba0090792]

if you sir dont go to heaven i will cause a fuss in the judgment day

[@derrickellerbie4806]

Great video but I would recommend going a little slower. The math is important and I think you went too fast on those parts. Thanks for the good work!

[@fondfrequencies9409]

I watch it at 1.5X bro...and u still want it to be slower??😅

[@saiavinashduddupudi8975]

@mycodeschool A Small Correction:- Maximum no of nodes in a complete binary tree with height h is 2^(no. of levels+1) - 1. In the video it is written as 2^(no of levels) - 1.

[@MuhammadRizkyEkaArlin]

+saiavinash duddupudi i think you are mistaken. No. of levels is equal to height + 1.

[@brexittortoises6129]

Couldnt understand much.. Seemed to be read out from a page.Helpful for quick revision, but not for understanding.

[@RM-lb7xw]

Implementation of binary trees using Arrays is only possible for Perfect Binary Trees, right? Not Complete Binary Trees?

[@shahriarmim4696]

6:20 the sum of powers of 2 is one less than the next powers of 2, in particular 2^0 + 2^1 + ... + 2^n = 2^(n+1) - 1.

[@ductive]

12:00 I think if we say that height of a tree is the number of nodes on the longest downward path minus 1. we would avoid this possible confusion.

[@ravitejachatti4711]

how the balanced binary tree is calculated

[@Dylanbforthree]

Awesome videos, keep up with adding the captions please!!! Makes it so easy to follow along, great tutorial!

[@noaht.8928]

If you compare it with the big o sheet then your explanation are not correct. Deletion with Linked list is O(1) bigocheatsheet.com/

[@sampannapokhrel]

At 13:15. wouldn't it be 2-(-1) = 3 as the height difference. As I could see 2 edges from that to the leaf node.

[@VisualMASM]

Great video. However, it's missing a huge piece of completing the explanation of trees. In your example, you are showing node 2 with 3 children. It would have been much more helpful to show how a generic tree is implemented in C/C++ then jumping right away to a binary tree explanation. For example, node 2 has 3 children. How would you implement a tree with nodes that have more than 2 children? You would have to show the dynamic nature of how to manage x number of children. This would have been much more helpful and would have completed the explanation of trees than jumping to binary trees.

[@Kovai-Siva]

Great videos. Thanks a lot. But having one question, in the last few minutes in video you are talking abt the binary tree implementation using arrays. You have told that the link identify equation 2i+ 1 and 2i + 2 is valid only for complete binary tree but example you have taken is perfect binary tree. Now i am confused whether the equation holds good for perfect or complete binary tree. In case of complete binary tree there can be empty links, if that is the case how we will identify the links. Please clarify.

[@mycodeschool]

Hi Siva, You can always put some value for NULL for empty links. Like lets say, you will put "-1" as value to mean NULL. So, as such, any binary tree and not just complete binary tree can be stored in an array, the only thing is that you will waste a lot of memory. In complete binary tree, only the last level may be unfilled. With this formula, we will not need extra space in the array for NULL links in case of complete binary tree. If 2i or 2i+1 is outside the range of array, we do not have a child. Just sit with this and think for some time.

[@Kovai-Siva]

Thanks for your response. Got it.

[@harin.g6806]

perfect . Thank you very much.

[@Omar_Muhammad]

Thanks, a lot.

[@MdRumanHossain]

Have your own blog/site on programming sir,. if then please link.

[@saikumarnallagangula]

thank you so much for the videos. I have never thought that I would learn DataStructures with so ease. Really loved each and every video(content, concepts and the way of teaching). Eagerly waiting for other Concepts of DataStructure and Specially Trees and Graphs. Hope you would continue with many more.

[@ajaytillu]

rey bujji chadavalekapothunnam ra

[@bharathirv8479]

Can u plz upload video for binary tree delete operation. Not binary search tree.

[@techno_bob]

Dude height means no.of edges from node to the farthest leaf node??? But you are taking height as 1 from root to its child. is it correct?

[@gunjankumar3068]

height of subtree of node not node itself

[@pramodaravind]

can someone explain me why only we can have left nodes to the leaf node of tree as possible and why cant for right nodes and still call it a complete binary tree?

[@JeshOrquina]

Do you have any tutorials on threaded binary trees? Is there any possibility you could make one? I have trouble understanding it in class and your tutorials have been very useful to me so it would be great if you could make one. Thanks!

[@vjkumk]

seems i need to learn algebra to understand those Log :(.. lost after 7.22

[@The_new_age_code]

in the minut 9:00, why the min-height is log2(n) and maximum is n-1?

[@chetanbhardwaj5088]

the no. of nodes in a perfect binary tree with height h will be =(2^h)-1......not (2^h+1)-1......or ...........the no. of nodes of a perfect binary tree with max LEVEL m will be = 2^0+2^1+2^2......+2^m.......

[@asishraz6173]

Lots and lots of information in just one video. Thank you so much for your effort and dedication towards sharing this valuable piece of information. Keep up the great work.

[@suman6327]

Some definitions / references : stackoverflow.com/questions/2603692/

[@PepeTostado]

How would you reccomend me to learn this? because I'm having a hard time processing it, thanks in advance.

[@abhilashbss9059]

fantastic work .... very easy n smooth take over

[@dilrubakose]

You are such an amazing person thanks a lot :)

[@ivandrofly]

14:16 representing BST (binary search tree) as array

[@pb6785-k3m]

Considering an empty AVL tree and successive insertion of 1,2,3,4,5 and 6 into it, which of the following is the post-order traversing of the final AVL tree? A: 1,3,2,5,6,4 B: 1,3,6,2,5,4 C: 3,1,2,6,5,4 D: 1,3,2,6,5,4 My ans is A...Sir, Please reply close answer

[@utsargapokharel8709]

one question friends, shouldn't a complete binary tree also be a strict binary tree? it is otherwise in the video

[@tejaswininandan7025]

Ur videos r awesome.......... But one simple request........can u plz put that subtitles little down coz we can't see what is written on bottom of the board

[@toufiq-ul-alam6475]

suddenly parent child becomes nodes and leaves and etc....why... why cannot you stick to root, branch, leaf? making so many relationships and later not using them at all?

[@sonnybrown4758]

I was with you until half way through the video lol

[@hitesh123ism]

Best lecture on a binary tree so far.

[@yalmazkhan2974]

Question : What do you mean by complete binary tree at 5:18, Do you mean that all L0 - L2 nodes must have 2 children, or do you mean numerical fulfillment of nodes?

[@pawanBilaspur]

Your Voice is very clear but have some example while explaining this Tree mathematics, also slow down in between,don’t run away with all the lecture

[@PriyojitKharibam]

Can anyone explain almost complete binary tree and difference between almost complete binary tree and complete binary tree??

[@PanZheng]

By definition, a tree is is a UNdirected graph, which means the edges should not have arrows. Good explanations though!

[@KUSHGPATEL]

Can a binary tree also be classified as a generic tree?

[@mxkep]

All your data structures videos are great ! Thank you so much!