Hello everyone ! In this lesson, we will introduce

you to an interesting data structure that has got its application in a wide number of

scenarios in computer science and this data structure is tree. So, far in this series,

we have talked about what we can call linear data structures. Array, Linked List, stack

and queue, all of these are linear data structures. All of these are basically collections of

different kinds in which data is arranged in a sequential manner. In all these structures

that I am showing here, we have a logical start and a logical end and then an element

in any of these collections can have a next element and e previous element. So, all in

all we have linear or sequential arrangement. Now, as we understand, these data structures

are ways to store and organize data in computers. For different kinds of data, we use different

kinds of data structure. Our choice of data structure depends upon a number of factors.

First of all, its about what needs to be stored. A certain data structure can be best fit for

a particular kind of data. Then, we may care for the cost of operations. Quite often, we

want to minimize the cost of most frequently performed operations. For example, lets say

we have a simple list and we are searching for an element in the list most of the time.

Then, we may want to store the list or collection as an array in sorted order, so we can perform

something like binary search really fast. Another factor can be memory consumption.

Sometimes, we may want to minimize the memory usage and finally we may also choose a data

structure for ease of implementation, although this may not be the best strategy. Tree is

one data structure that’s quite often used to represent hierarchical data. For example,

lets say we want to show employees in an organization and their positions in organizational hierarchy,

then we can show it something like this. Lets say this is organization hierarchy of some

company. In this company, John is CEO and john has two direct reports – Steve and Rama.

Then Steve has 3 direct reports. Steve is manager of Lee, Bob and Ella. They may be

having some designation. Rama also has two direct reports. Then Bob has two direct reports

and then Tom has 1 direct report. This particular logical structure that I have drawn here is

a Tree. Well, you have to look at this structure upside down and then it will resemble a real

tree. The root here is at top and we are branching out in downward direction. Logical representation

of tree data structure is always like this. Root at top and branching out in downward

direction. Ok, so tree is an efficient way of storing and organizing data that is naturally

hierarchical, but this is not the only application of tree in computer science. We will talk

about other applications and some of the implementation details like how we can create such a logical

structure in computer’s memory later. First I want to define tree as a logical model.

Tree data structure can be defined as a collection of entities called nodes linked together to

simulate hierarchy. Tree is a non-linear data structure. Its a hierarchical structure. The

topmost node in the tree is called root of the tree. Each node will contain some data

and this can be data of any type. In the tree that I am showing in right here data is name

of employee and designation. So, we can have an object with two string fields one to store

name and another to store designation. Okay, so each node will contain some data and may

contain link or reference to some other nodes that can be called its children. Now I am

introducing you to some vocabulary that we use for tree data structure. What I am going

to do here is , I am going to number these Nodes in the left tree. So, I can refer to

these Nodes using these numbers. I am numbering these nodes only for my convenience. its not

to show any order. Ok, coming back, as i had said each node will have some data. We call

fill in some data in these circles. It can be data of any type. it can be an integer

or a character or a string or we can simple assume that there is some data filled inside

these nodes and we are not showing it. Ok, as we were discussing, a node may have link

or reference to some other nodes that will be called its children. Each arrow in this

structure here is a link. Ok, now as you can see, the root node which is numbered 1 by

me and once again this number is not indicative of any order. I could have called the root

node number 10 also. So, root node has link to these two nodes numbered 2 and 3. So, 2

and 3 will be called children of 1 and node 1 will be called parent of nodes 2 and 3.

I’ll write down all these terms that I am talking about. We mentioned root, children

and parent. In this tree, one is a parent of , 1 is parent of 2 and 3. 2 is child of

1. And now, 4 , 5 and 6 are children of 2. So, node 2 is child of node 1, but parent

of nodes 4, 5 and 6. Children of same parent are called sibling. I am showing siblings

in same color here. 2 and 3 are sibling. Then, 4, 5 and 6 are sibling, then 7,8 are sibling

and finally 9 and 10 are sibling. I hope you are clear with these terms now. The topmost

node in the tree is called root. Root would be the only node without a parent. And then,

if a node has a direct link to some other node, then we have a parent child relationship

between the nodes. Any node in the tree that does not have a child is called leaf node.

All these nodes marked in black here are leaves. So, leaf is one more term. All other nodes

with at least one child can be called internal nodes. And we can have some more relationships

like parent of parent can be called grand-parent. So, 1 is grand-parent of 4 and 4 is grand-child

of 1. In general, if we can go from node A to B walking through the links and remember

these links are not bidirectional. We have a link from 1 to 2, so we can go from 1 to

2, but we cannot go from 2 to 1. When we are walking the tree, we can walk in only one

direction. OK, so if we can go from node A to node B, then A can be called ancestor of

B and B can be called descendant of A. Lets pick up this node numbered 10. 1, 2 and 5

are all ancestors of 10 and 10 is a descendant of all of these nodes. We can walk from any

of these nodes to 10. Ok, let me now ask you some questions to make sure you understand

things. What are the common ancestors of 4 and 9? Ancestors of 4 are 1 and 2 and ancestors

of 9 are 1,2 and 5. So, common ancestors will be 1 and 2. Ok, next question. Are 6 and 7

sibling? Sibling must have same parent. 6 and 7 do not have same parent. They have same

grand-parent. one is grandparent of both. Nodes not having same parent but having same

grandparent can be called cousins. So, 6 and 7 are cousins. These relationships are really

interesting. We can also say that node number 3 is uncle of node number 6 because its sibling

of 2 which is father of 6 or i should say parent of 6. So, we have quite some terms

in vocabulary of tree. Ok, now I will talk about some properties of tree. Tree can be

called a recursive data structure. We can define tree recursively as a structure that

consists of a distinguished node called root and some sub-trees and the arrangement is

such that root of the tree contains link to roots of all the sub-trees. T1, T2 and T3

in this figure are sub-trees. In the tree that I have drawn in left here, we have 2

sub-trees for root node. I am showing the root node in red, the left sub-tree in brown

and right sub-tree in yellow. We can further split the left sub-tree and look at it like

node number 2 is root of this sub-tree and this particular tree with node number 2 as

root has 3 sub-trees. i am showing the three sub-trees in 3 different colors. Recursion

basically is reducing something in a self similar manner. This recursive property of

tree will be used everywhere in all implementation and usage of tree. The next property that

I want to talk about is – in a tree with n nodes, there will be exactly n-1 links or

edges. Each arrow in this figure can be called a link or an edge. All nodes except the root

node will have exactly 1 incoming edge. If you can see, I’ll pick this node numbered

2. There is only one incoming link. This is incoming link and these three are outgoing

links. There will be one link for each parent-child relationship. So, in a valid tree if there

are n nodes, there will be exactly n-1 edges. One incoming edge for each node except the

root. Ok, now i want to talk about these two properties called depth and height. Depth

of some node X in a tree can be defined as length of the path from root to Node X. Each

edge in the path will contribute one unit to the length. So, we can also say number

of edges in path from root to X. The depth of root node will be zero. Lets pick some

other node. For this node, numbered 5, we have 2 edges in the path from root. So, the

depth of this node is 2. In this tree here, depth of nodes 2 and 3 is 1. Depth of nodes

4,5,6,7 and 8 is 2 and the depth of nodes 9, 10 and 11 is 3. Ok, now height of a node

in tree can be defined as number of edges in longest path from that node to a leaf node.

So, height of some node X will be equal to number of edges in longest path from X to

a leaf. In this figure, for node 3, the longest path from this node to any leaf is 2. So,

height of node 3 is 2. Node 8 is also a leaf node. I’ll mark all the leaf nodes here. A

leaf node is a node with zero child. The longest path from node 3 to any of the leaf nodes

is 2. So, the height of Node 3 is 2. Height of leaf nodes will be 0. So, what will be

the height of root node in this tree. We can reach all the leaves from root node. number

of edges in longest path is 3. So, height of the root node here is 3. We also define

height of a tree. Height of tree is defined as height of root node. Height of this tree

that I am showing here is 3. Height and depth are different properties and height and depth

of a node may or may not be same. We often confuse between the two. Based on properties,

trees are classified into various categories. There are different kinds of trees that are

used in different scenarios. Simplest and most common kind of tree is a tree with this

property that any node can have at most 2 children. In this figure, node 2 has 3 children.

I am getting rid of some nodes and now this is a binary tree. Binary tree is most famous

and throughout this series, we will mostly be talking about binary trees. The most common

way of implementing tree is dynamically created nodes linked using pointers or references,

just the way we do for linked list. We can look at the tree like this. in this structure

that I have drawn in right here, node has 3 fields. one of the fields is to store data.

Lets say middle cell is to store data. The left cell is to store the address of the left

child. And the right cell is to store address of right child. Because this is a binary tree,

we cannot have more than two children. We can all one of the children left child and

another right child. Programmatically, in C or C++, we can define a node as a structure

like this. We have three fields here – one to store data, lets say data type is integer.

I have filled in some data in these nodes. So, in each node, we have 3 fields. We have

an integer variable to store the data and then we have 2 pointers to Node, one to store

the address of the left child that will be the root of the left sub-tree and another

to store the address of the right child. We have kept only 2 pointers because we can have

at most 2 children in binary tree. This particular definition of Node can be used only for a

binary tree. For generic trees that can have any number of children, we use some other

structure and I’ll talk about it in later lessons. In fact, we will discuss implementation

in detail in later lessons. This is just to give you a brief idea of how things will be

like in implementation. Ok, so this is cool. We understand what a tree data structure is,

but in the beginning we had said that storing naturally hierarchical data is not the only

application of tree. So, lets quickly have a look at some of the applications of tree

in computer science. First application of course is storing naturally hierarchical data.

For example, the file system on your disc drive, the file and folder hierarchy is naturally

hierarchical data. its stored in the form of tree. Next application is organizing data,

organizing collections for quick search, insertion and deletion. For example, binary search tree

that we’ll be discussing a lot in next couple of lessons can give us order of log N time

for searching an element in it. A special kind of tree called Trie is used , is use

to store dictionary. Its really fast and efficient and is used for dynamic spell checking. Tree

data structure is also used in network routing algorithms and this list goes on. We’ll talk

about different kinds of trees and their applications in later lessons. I’ll stop here now. This

is good for an introduction. In next couple of lessons, we will talk about binary search

trees and its implementation. This is it for this lesson. Thanks for watching !

Do you know how to create ctree with excel I have added my dataset but when I click build it fails to work. Any help appreciated

Short, accurate and Comprehensive

Great video sir!!

Hello,

Is an Ordered Tree always a Positional Tree? Or are there Ordered Trees that are not Positional Trees?

Thank you for captioning the video and making it accessible

Yarr hindi me video bna leta to thodi …hindi medium ke students bhi sikh lete . Kya yrr

Thanks 🇸🇦

Best one so far

Thank you Sir for your efforts

Thank you so much for the video, really cool and easy to understand.

Good one

U can complete the vedio in less time .. about 10 minutes u were repeating unnecessarly … But the vedio was good

Thank you. I love your lectures!

Owsm sir…….!!!um totally speechless about ua oll de lectures that i had watched….!!! keep it up sir… n tnkui so mch…..!!!

always learn from video lectures.thanks.

very nicely explained

Thanks man! you just made my day

subscribed

Very good for visual leaners. Thanks a lot!!

Make videos on Hash Tables as well, we all are having a lot of problems in it.

super video

Thank you.

excellent

nice video,I do not understand the high terminotogy, would you explain it to me?

Nice!

Superb

amazing explanation! you guys rock!

You are a great man…. Nice explanation. Now, I can understand book easily.

best explanation of theory of tree, very useful for examination point of view

Super

Lifesaver !!

Do you have implementation videos in Python as well?

we all need a teacher like him…. thank you so much sir…. you have made Data Structures very interesting to learn…. Not all HEROES wear capes and he is the perfect example of it

never heard the terms cousin and uncle in context of tree relationships

Kkkkk horrible

wow this is very good

OMG!! Explained everything that my lecturer taught in 12 hours of stupid boring lecture.

C++ Binary tree file download https://dadanp4.blogspot.com/2018/07/algoritma-ii.html?m=1

nice sr..plzz make vdos on design and analises of algoriths

Stop scrolling down and keep watching the Video

Your website is not working. Please look into it.

thank u sir

amazing and funny

nice video

Why is this tree and not family?

Bro, you are doing an awesome job here, I would like to know which software you used to make the presentation.

Hi, It seems a mistake, In Binary tree, the right node is always bigger than left node.. The Root node 2 has right node as 1 and left node as 4

saviour♥♥♥

So … height of 7 is 1 ?

Awesome video, but I think this channel is dead. Can't find new videos.

This is an excellent video. You explain it very well. I had to rewind several times because I'm easily distracted, but I have definitely learned. Thank you so much for your efforts.

well explained

Awesome , to the point explanation . Your videos make even hardest topic very easy to understand .

It was really good the way you explained in simplest way tysm for this lesson 🤟

Excellent sirThank you so much, I had a class today, in which I came to know about Binary Tree, and your video helped alot to know to what it is.

1.25x, save your time, thank me later

must avoid subtitle

the best explanation ever

nice explanation….sounds best @ 1.25x

Very nice, and it is not boring….

tnkw

Your voice is ❤❤

he is confident in his sayings

😃🎉

I feel like touching your feet (Gurudev)

bu ne mk

AMAZING video, thanks!

Thanks

This video is super awesome. Tomorrow i will be sitting data structure exam.

pq só indiano q faz video de programação nessa porra!?

Awesome

Thanx to you, COMPUTER SCIENCE is a sweet dream than a nightmare.

I am really greatful to you sir

Normally I don't comment but I'm so happy that I finally found a person who explains everything structurally and in understandable way. Thank you a lot! <3

great explanation liked it

Akash chopra 😂😂

How can i write a note on a tree in simple words?

Super bhayaa. Gud information so useful to me. Tq so much bhayaa

Common ancestors of 4&9 is 2.

I am unable to visit your website.It says bay gateway

Amazing explaination!!!!!

awesome explanations

Nice explanation sir .keep the good work going.

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.

Sir.

.pls… Can you give an explanation to a question

Woah grandparents, cousins, uncle….the whole goddamn family tree

I love this family thing

Although I don't like your accent, your explanation is the best!

Very Good!

U are simply awesome

God wanted you in heaven so he called you there early. RIP dude

Watching this in 2019.

The only channel that comes to mind when recommending data structures and algorithms

Nice and clear!

Can you make one video on B-Tree code or hashing code (program c/c++)?

thanx

I am just following your lecture instead of my university lectures bc these are way better than my university lectureres…..Thank you..Keep Sharing

Not like mr.srinivas..!!😏

this is an amazing course my man thanks …