Hello there. Lets talk about graphs and whether they are connected or not or maybe whether they are strongly connected versus weakly connected. We look at undirected graphs first and show what makes a graph connected meaning every node can reach every other node by a path. We add edges and check the connections step by step while also noting subgraphs. Then we switch to directed graphs and explain strongly connected versus weakly connected. Strongly connected follows the edge directions for every path. Weakly connected ignores the directions and checks if the graph would still be connected. Examples show how adding edges changes the status of the graph.

00:00 Introduction to Graph Connectedness
00:01 Drawing Nodes and a Disconnected Graph
01:56 Defining a Connected Graph
03:21 Introducing Subgraphs
04:48 Adding Edges to Create a Connected Graph
06:32 Adding Directions to Create a Directed Graph
08:03 Strongly Connected Versus Weakly Connected
08:34 Removing an Edge to Show Disconnection
09:29 Checking and Achieving Weak Connectivity
11:18 Adding Edges to Create a Strongly Connected Graph
13:20 Confirming the Strongly Connected Graph
13:32 Conclusion
14:17 Outro and Subscribe Request

=-=-=-=-=-=-=-=-=

Thanks for watching!

Find us on other social media here:

• https://www.NeuralLantern.com/social
• Twitter / X: https://x.com/NeuralLantern
• Rumble: https://rumble.com/c/c-3696939
• BitChute: https://www.bitchute.com/channel/pg1Pvv5dN4Gt
• Daily Motion: https://www.dailymotion.com/neurallantern
• Minds: https://www.minds.com/neurallantern/
• Odysee: https://odysee.com/@NeuralLantern:5

Please show your support!

• Buy me a coffee: https://ko-fi.com/neurallantern
• Subscribe + Sharing on Social Media
• Leave a comment or suggestion
• Subscribe to the Blog: https://www.NeuralLantern.com
• Watch the main “pinned” video of this channel for offers and extras

Hello there! Let’s talk about graphs and whether they’re connected or not or maybe whether they’re

strongly connected versus weakly connected versus not connected. You never know.

Okay, so hopefully you’ve seen my previous videos by now where we just talked about the basics of

paper here i’m just going to start drawing a graph remember graphs are nodes and edges where

the nodes are like little t-type data structures that can hold a specific type of value um so i’m

going to say our our nodes hold integers um i think i made that one too small that’s okay

and the edges uh could have weights or maybe not weights at all depending on if you have

a weighted or an unweighted graph so i’m just going to start duplicating my nodes a little bit

going to make a random graph. I need to probably change these values. Technically your graphs

should support duplicate values in the nodes and also the weights, but I don’t want to because

it’s easier to talk about the graph when all the values are distinct. So for starters, we have a

bunch of nodes and they’re not really connected to each other. Is this a valid graph? Yeah it is.

It’s just not a connected graph. So the terminology that we’re going to use for

undirected graphs meaning the edges don’t have direction is going to be connected or not you

know i usually just say a not connected graph or a disconnected graph so just basically like

connected or not connected okay so this is a not connected graph i’m going to say not connected

not cinnamon i’m thinking about food as usual

connected graph why is it not a connected graph well to define what does it mean to be a connected

graph it just means that every single node can find a path to every single other node

in an undirected graph so we can just double check this real fast we can say you know can

node number two find a path to uh you know let me put a question here let’s say we’re going to check

you should be checking all the nodes one by one by one to see if if the node in particular can

first node that can’t do it means the whole graph is not considered connected so you know two it

can’t reach one so that means it’s not a connected graph so this is not a connected graph because one

or more nodes violate the rule of you have to be able to reach every single other node okay so that

means if we want a connected graph we probably just have to start adding edges so I’m going to

go ahead and uh let me let me write the word connected here and then I can like either circle

cross it out. So right now we have no, this is not a connected graph. I’m going to start adding

edges. We’re going to stick with an undirected graph for now. So I’m going to connect two and one

and two and nine, maybe one and 13. Actually, you know what? I’m going to erase this edge

and maybe connect these over here. And the thing is, this is a valid graph that you’re looking at.

it’s just not a connected graph.

Some other terminology I didn’t mention in other videos

is that we can have subgraphs.

We have like a subgraph here and another subgraph here.

Those are basically just two different portions of the same graph

that appear to be connected within themselves.

So those are subgraphs.

You can probably tell right away that this is not a connected graph.

You can double check to be sure.

You know, it’s good to do things the hard way

so you don’t get the wrong answer

when you’re really trying to figure something out.

So let’s look at two.

So let’s look at two. Can two reach one? Yes. So that’s good. Can two reach nine? Yeah,

it just hops to one and then hops to nine. So two can reach one and also nine. That’s good.

Can two reach three? Nope. So this is still not a connected graph.

Okay, I’m going to add one more edge. And then we’ll just check again.

Where do you think I’m going to do it? Maybe if I add, I’ll add a funky edge going from 13 to like

to like nine or something just so it feels a little bit more awkward okay let’s check one by

one by one let me actually get rid of this edge on the previous slide so we can still say that’s

not connected let’s check one by one by one every node must be able to reach every single other

node so I’m gonna look at two and I’m gonna say all right two can it reach one yes can it reach

to nine. So that’s good. Can it reach three? Yeah, it can go from two to one to nine to 13

to three, and then it can reach three. And because we just saw that it went through 13 to reach three,

that means two can reach every single other node. This is going to be more important as a double

check when we have directed graphs in a second. So two is good. So the next thing you want to do is

the next thing you want to do is just move on to some other node and do the exact same process you

know can can nine reach a one yes okay it can reach a one can it reach a two yeah it goes through

the one can it reach the 13 yep can it reach the three yep okay so we just check every single

destination node starting at the node nine but here’s a little bit of a shortcut try to find a

node that is right next to a node that you know can reach everything and if the node in question

that previously connected node, vertex,

then we know that that node in particular is also connected.

So what I’m saying is the one,

instead of checking every single other node in the graph,

which might be really hard

if we have a whole bunch of nodes in our graph,

we’ll just ask, can the one reach the two?

Because if it can, the two can reach everything.

So that means the one actually can reach everything as well.

So the one can reach the two.

So the one is connected to everything.

the three, the three can reach the one and the one can reach everything. I’m doing things the

hard way on purpose just to prove a point. So the three can reach everything. The 13 can reach the

three in one hop. So the 13 can reach everything. The nine, it can reach the one and it can reach

the 13 in one hop. So the nine can also actually reach everything. So that means this is indeed a

the next thing that we’re going to do is add direction to our graph you know we could do like

more examples maybe leave a comment if you want me to do some super extra complicated examples for

just a undirected and connected graph i’m ignoring weight by the way because it doesn’t really matter

for these purposes so let’s upgrade our graph so uh maybe i should put a question mark here

that would have been a good idea we’re just asking you know is it connected or not

And I’m just going to start adding direction to every single edge.

Let’s see if I’m following my notes.

Single node, subgraphs, right?

Well, it wasn’t connected at first and then we started adding.

Okay, so that’s basically okay.

Let’s add direction to every single edge.

So every single edge has to have a direction

or every single edge has to have no direction.

You can’t really mix and match.

So I’m just going to go through every single edge and add a direction like this.

and you know to be fair I think I’ve said this in my other videos an undirected edge is kind of the

same thing as a directed edge going in or two directed edges going in both directions so this

3 and 13 what’s going on with my computer hello this 3 and 13 edge it would have kind of been the

same as just having two edges going in opposite directions so maybe I’ll just do that right now

for this huge weird edge I’m just going to put like an arrow over here instead of totally redrawing

Then I double check that every single edge has a direction so that I have a valid graph.

And now I can ask, is this connected or not?

Actually, when it comes to a directed graph, you don’t really have connected or not anymore.

You have strongly connected versus weakly connected.

Maybe I should just separate these words and then just kind of like move them.

So let’s get rid of this.

to this save this over here move it down so what am i talking about um well first let me remove an

edge real quick i’ll remove this edge right here so now we have two sub graphs in this graph you

can tell for sure if this was an undirected graph it would not be connected but now that we’re

dealing with direction we have to ask is it strongly connected versus weakly so what does

can every node reach every other node if you obey the direction of the edges so that’s clearly not

true there’s no edge at all that even connects this one and nine so it’s definitely not strongly

connected weakly connected on the other hand means if you temporarily ignore the direction

of the edges then could you consider the graph connected so if we pretended that there were no

arrows here would we think that it’s a connected graph if the answer is yes then it’s at least a

So this is not weakly connected because if this was an undirected graph, it’s not even connected at all.

So that sucks.

I’m going to go ahead and add another edge here.

So I’m going to add an edge from 2 to 9.

So the first thing is, oh, sorry, I have to add another edge.

Let me do from 1 to 13 for fun.

So now the first thing is, let’s check to see if this is a strongly connected graph.

node is unreachable by any other node so this is definitely not strongly

connected because all the other nodes would be would have to be able to reach

too alright so first thing you could do just to very quickly check is just look

at every single node and ask is it reachable you know by anything and then

after that you can do things the hard way so it’s not strongly connected what

about weakly connected if we ignore the direction of the graph sorry if we

then yeah, we could reach every single node from every other node. Let’s just double check that

real fast. I’m going to say, you know, the two node, if we’re ignoring direction, can it reach

the one? Yes. Can it reach the 13? Yes. The three? Yes. Can it reach the nine? Yes. So that means the

two node is sort of like weakly connected to every other node in the graph. Do the same thing for the

one node. Previously, we just said, you know, check everything one by one or use a shortcut.

one by one or use a shortcut. So I’m going to use the shortcut. The one node, if we ignore direction

can reach the two nodes. So I’m going to say the one is weakly connected, at least everything else.

I’m not even going to check to see if it’s strongly connected to everything else. I think the answer

is no, but we do the same thing for the 13. The 13 can reach the one pretty fast. The three can

reach the 13. The nine can reach the two. So every single node can weakly reach. That’s not an

a weakly connected graph. Okay, cool. How can we make this a strongly connected graph? Well,

we just have to add a bunch of edges. So that’s what I’m going to do. I’m going to kind of like

look at what is missing here. So we’ll ask the two, can the two reach and let’s obey the direction

of the edges again. Can the two reach the one? Yes. Can the two reach the 13? Yes. Can it reach

Yes, so that means right now the two is strongly connected to everything else.

So we’re on track for a strongly connected graph.

We then look at the one node and we realize that the one node,

it can reach the 13 and the three and it can also reach the nine,

but it can’t reach the two.

That’s one thing that was blocking us last time from saying strongly connected.

So we just have to add another edge if we want this to be a strongly connected graph.

We have to figure out how can we get the one to reach the two.

the 2 we can go through something if we want to that’s fine we can also just

write an edge that just goes back to the 2 but that’s I don’t know that’s kind of

boring I’m gonna make an edge that goes from 1 to 9 and then I’m gonna make an

edge that goes from 9 to 2 so looking at the 1 node it can now reach the 2 if we

go through the 9 so that’s good can the 1 reach the 9 yes can the 1 reach the 13

three yes okay so the one node can now reach every single other node so now we’re a little bit more

on track for a strongly connected graph look at the 13 node can it reach the one node um actually

yes if we go from 13 to 9 and then 2 and then 1 we can reach the one node since we know the one

node is connected to everything else we can now say that the 13 node is connected to everything

13 so i’ll say three is connected to everything the nine node can reach the two node which is

connected to everything so that means the nine node is also connected to everything and at this

point we now have a strongly connected graph it’s not weakly connected it’s stronger than that

any questions um so let’s see we added a bunch of uh edges i think maybe this is actually all we

need to do for this particular video because we’re just going to talk about connectedness

going to talk about connectedness about 15 minutes not too bad all right so i think i’m

going to leave it here drop a comment if you want to do way more complicated examples if you want to

provide me a sample graph that’s awful and i could just i don’t know in the sometime in the future i

could record a video about it um or just let me know your thoughts thank you so much for watching

this video i hope you had a little bit of fun and i hope you learned a little bit of stuff i’m outie

Patowdy.

Alright, let’s see.

I’m going to do this.

Whoa. Can you see that guy in the background?

Oh, shoot.

I’m just kidding.

I set that as the screensaver.

Hey, everybody.

Thanks for watching this video again from the bottom of my heart.

I really appreciate it.

I do hope you did learn something and have some fun.

If you could do me a please, a small little favor,

please subscribe and follow this channel or these videos or whatever it is you do on the current

social media website that you’re looking at right now. It would really mean the world to me and it’ll

help make more videos and grow this community. So we’ll be able to do more videos, longer videos,

better videos, or just I’ll be able to keep making videos in general. So please do me a kindness

and subscribe. You know, sometimes I’m sleeping in the middle of the night and I just wake up

or followed. It just wakes me up and I get filled with joy. That’s exactly what happens every single

time. So you could do it as a nice favor to me or you could you could troll me if you want to just

wake me up in the middle of the night. Just subscribe and then I’ll just wake up. I promise

that’s what will happen. Also if you look at the middle of the screen right now you should see a

QR code which you can scan in order to go to the website which I think is also named somewhere at

the bottom of this video and it’ll take you to my main website where you can just kind of like see

videos i published and the services and tutorials and things that i offer and all that good stuff

and uh if you have a suggestion for uh uh clarifications or errata or just future videos

that you want to see please leave a comment or if you just want to say hey what’s up what’s going on

you know just send me a comment whatever i also wake up for those in the middle of the night i get

i wake up in a cold sweat and i’m like it would really it really mean the world to me i would

it so again thank you so much for watching this video and enjoy the cool

music as as I fade into the darkness which is coming for us all

Thank you.

so

I’m going to go ahead and get started.

so

Yeah, I think I’m good.

Hello there.

Let’s talk about whether a graph is connected or not,

or maybe whether it’s strongly connected or weakly connected or not connected at all.

You never know.

The post Graph Connectedness Explained: Connected Strongly Connected and Weakly Connected appeared first on NeuralLantern.com.

Clear step-by-step explanation of what defines a Binary Search Tree (BST). We build the definition rule-by-rule starting from graphs all the way to the BST ordering property (all left descendants, node, all right descendants). Great first video before learning insert, delete, search, and Big-O.

What is a Binary Search Tree? 00:00
Intro to Graphs and Nodes 00:42
Connected Graph Requirement 03:16
Acyclic Graph – Removing Cycles 04:54
Turning Graph into Tree 07:05
Establishing a Root 07:09
Adding Hierarchy and Levels 09:05
Single Common Ancestor 11:18
Binary Tree Definition 17:30
BST Ordering Property 17:39
Left Subtree Less Than Node 18:29
Fixing Invalid BST Example 20:26
Valid BST Final Check 21:24
In-Order Ascending Order 24:11
Video Summary and Next Steps 25:02
Thanks and Call to Action 25:30

=-=-=-=-=-=-=-=-=

Thanks for watching!

Find us on other social media here:

• https://www.NeuralLantern.com/social
• Twitter / X: https://x.com/NeuralLantern
• Rumble: https://rumble.com/c/c-3696939
• BitChute: https://www.bitchute.com/channel/pg1Pvv5dN4Gt
• Daily Motion: https://www.dailymotion.com/neurallantern
• Minds: https://www.minds.com/neurallantern/
• Odysee: https://odysee.com/@NeuralLantern:5

Please show your support!

• Buy me a coffee: https://ko-fi.com/neurallantern
• Subscribe + Sharing on Social Media
• Leave a comment or suggestion
• Subscribe to the Blog: https://www.NeuralLantern.com
• Watch the main “pinned” video of this channel for offers and extras

hey there let’s talk about binary search trees specifically in this video I want to help you

define and identify what is a binary search tree all the rules that go into determining whether

or not something is a binary search tree so you can you can tell that you’re looking at one or

whether you’re not looking at one we’ll talk about some terminology but keep in mind I’m

going to save searching and sorting and like you know deleting and adding items and a whole bunch

extra stuff, especially the hard stuff for videos that’ll come right after this one.

For now, we’re just going to talk about what is a binary search tree.

So you can see on the screen right here, I hope that we have a binary search tree.

Let’s see.

Can you see that?

Yeah, I think you probably can.

Yeah, I think you can.

This is not drawn quite as well as I would like to draw ours.

I’ll tell you how to do that in a little while.

to do that in a little while but when you draw a tree in a really really nice pretty aligned way

it’s way easier to debug it’s way easier to tell that you’re looking at something that is sorted

and so forth anyway okay so first let’s start off with a graph so this is not a video about graphs

uh i guess i can probably expect that you already kind of know what a graph is at this point in time

and edges. So what do I mean by nodes? Well just imagine there’s like a little circle here

that contains some sort of data. If you know data structures already then

there would be a t-type sitting inside the node. We’ll just call the t-type an integer

and so for our nodes, for our trees, we’re just going to say that they hold integers even though

you know technically speaking in a binary search tree or a graph you could have all sorts of

Okay. So I’m just going to, you know, grab this and sort of like duplicate it and just duplicate it again.

I’m just going to make a bunch of duplicates. Something is definitely wonky about my setup right now.

I think I just upgraded the camera and the CPU is maxed out. I just upgraded the CPU on this computer too.

Oh well. Okay. So we aren’t going to support duplicate values in our binary search tree,

I’m going to say it doesn’t really matter for the graph. Later on, we’ll start making sure there’s

no duplicate data. For now, I think I can probably do that somewhat quickly. Let’s see. So a graph,

you know, for the for our purposes right now, a graph is just basically a collection of nodes and

edges. It could be empty. It could be just nodes. It couldn’t just be edges, it would have an edge

always has to have a node or two connected to it. So we just have like a bunch of nodes inside of

data values this is a valid graph but I’m going to draw some edges randomly here so we’re going

to do this it doesn’t really matter I’m just randomly drawing edges okay actually I should

probably do maybe like one that’s kind of separated okay so this is a graph this is not a binary search

tree so let’s add a bunch of rules let me just pull up my rules real fast here okay so what is

First we’ll start off with the graph like we have here and then we’ll say that the graph must be connected.

What is a connected graph? A connected graph is basically a graph where every single node can find every single other node

or find a path to every single other node only following along edges and only by respecting the direction of edges.

You can see this particular graph is undirected meaning the edges don’t really have a direction to them.

So that means we could travel along in any direction from node to node.

So just as a real quick, you know, I guess like tutorial, I’m going to say is 8 connected to every single other node?

Well, it can find a path to 12 and it can find a path to 33 and it can find a path to 76 and 45.

But it cannot find a path to 99, which means this is not a connected graph.

So that’s the first rule that we have to implement here.

We’re going to say this graph needs to be upgraded or modified so that it will be a connected graph.

start randomly adding edges until this is a connected graph I’m gonna do maybe

like an edge from 99 to 12 there and then now I think this is a connected

graph but let’s double check real fast so connected graph you know what I’m

gonna put graph connectedness in another video to keep this one short for now

check out my other videos if you would like to see whether or not a graph is

but long story short as I just said if every single node can find a path to

every single other node without you know skipping where there is no edge then

it’s connected okay so that’s the first thing the next thing that we need let me

just put the words connected up here we need a connected graph the next thing

that we need is we need an acyclic graph which basically means a graph with no

A cycle is, can you find a path in this graph that starts at one node and ends at the same node without repeating any edges?

So for example, if I was asking, you know, is 76 involved in any cycles?

Well, we could go from 76 to 33 and then 12.

And, you know, we could kind of take 8, 45, 12 again.

But by the time we turn around and try to get back to the 33, we’ve already crossed this edge twice.

so that means the 76 is not involved in any cycles because we cannot find our way back to 76

without repeating an edge so 76 is okay i’m just going to maybe put like a little check box here

and uh you can also tell that the 33 is not involved in any cycles because we go down to

the 76 and then come back up to 33 we already repeated an edge so that’s not valid same thing

again. Same thing for the 34, same thing for the 99. But if you look at the 12 here, we could

actually find a cycle. We could go from the 12 to the 8, and then from the 8 to the 45, and from the

45 to the 12. Now we’re back where we started. We’re at the 12 node again, and we did not repeat

any edges. So this is not a cyclic. This is a cyclic graph. It’s got a cycle. So that’s the

we want to make sure that our graph has no cycles. So, uh, the next rule I’m just going to say is,

is going to be satisfied by me removing some edges at random. So I don’t know, let’s get rid of, uh,

the eight to the 45 connection. See if that works. Um, let’s see. Well, wait a minute. What did I

just do? Something happened here. I just accidentally, oh, I erased too many edges

from the last slide. Okay. Let me add that one back in 33 to 76. That was supposed to be there.

33 to 76 that was supposed to be there.

So now we have an acyclic graph

and we can consider this graph a tree.

The next thing we need to do is add a hierarchy to this tree.

So this is gonna make more sense in a little bit

but for now I’m gonna say,

we’ll imagine a family tree kind of,

it’s not really exactly a family tree

but you know imagine there are parents

and children and grandchildren

and we’ll just try to like,

we’ll try to rank children according to

according to you know when they were born or or how many parents or children

they have you know their descendancy their lineage whatever you want to call

it so I think I’m just gonna maybe move the eight up a little bit so that it’s

on the same rank with the 12 and the 33 so I’m just gonna move these up a little

bit and then redo their connecting lines so I’m gonna do this and that and then

and then we’ll say that the 76 is still a child of the 33.

So I’ll just kind of move it over here.

Or sorry, we never said it was a child.

Now we’re saying it’s a child

because when you go from top to bottom,

imagine like a family tree,

we’ll say we have parents and children.

The children or the descendants are lower.

The ancestors or the parents or the grandparents are higher.

Maybe I want to put this 45 over on the left

so that it’s a child of the 8 node.

And maybe I’ll say that the 99 node

the 99 node is a child of the 12 node. Okay, so eventually this is going to look not exactly like

a family tree because usually in the family tree we have two parents that go to one or more children.

In this type of tree, in eventually our binary tree, we’re going to have one parent that has,

you know, children just by itself, like asexual reproduction. We’re pretending to be bacteria

What was that comedy skit a long time ago, Tiny Elvis?

And he was like, hey, see that protozoa over there?

The thing is huge.

Anyone?

No?

Okay.

So the next rule we need is we must have a rooted tree.

What is a rooted tree?

Actually, let me clean up the lineage real fast, the heritage.

I want to make nodes that have the same level with respect to their ancestors

respect to their ancestors to have the same physical y coordinate the same

physical level so notice how the 99 I just moved it down a little bit because

I wanted it to look like it’s the same you know number of generations lower

than the top row so like with aid it had a child 45 so that’s one level down 33

had a child that’s one level down that’s a 76 and the 12 also one level down

would have been 99 but the 99 was kind of too physically high this will help

will help you debug your binary trees in the future anyway so i’m just going to clean this up right now

and uh now that we have you know parent child relationships we need to look at the most common

ancestor in the whole entire tree or if there is one so notice how uh i guess i’m just kind of using

the word ancestor without explaining it so your ancestors are the people that you’re disappointing

or whatever it is, ancestors came before us, right?

Like my parents are my ancestors.

My grandparents are also my ancestors.

My great-grandparents are also my ancestors.

Going down in the family tree are your descendants.

You know, my children are my descendants.

My grandchildren are my descendants.

My great-grandchildren are my descendants and so forth.

So if you look at the number 34 here,

what is the greatest ancestor that it has?

Well, if you just go up and up and up

until you can’t go up anymore,

up until you can’t go up anymore it’s the 12th so that means the greatest ancestor of at least in

this tree of the 34 is the 12th the 45 the highest you can go is the 8 notice how 8 and 12 and 33 are

siblings there’s not really like a parent-child relationship they’re connected sideways we’ll

eventually get rid of the sideways connections for our binary search trees but for now we have

some siblings and so we actually have three different greatest ancestors in this tree we’ve

tree we’ve got 8 and 12 and 33 and that’s no good so the next rule that we need is we need

one common ancestor for every single other node in the entire tree so I’m going to duplicate this

slide right here and I’m going to say we need to clean this up so we got to choose 8 or 12 or 33

I don’t know I’m just going to maybe say that 8 and it’s 45 are children of the 12 so I’m just

line here arbitrarily so i’m gonna go like that notice how i’m trying to keep the 8 the 99 and

the 76 on the same y coordinate the same level now we have two uh you know greatest ancestors

we need to have only one so i think i’m probably going to say that the 33 and the 76 are going to

become children of the 12 node just for simplicity so i’m going to put this over here i’m going to

i’m gonna like move this over here this is a gross tree but we’ll fix it soon we’ll do that all right

okay okay

okay and then i have to get rid of that little sibling line and then i have to add another line

to say that 33 is a child of 12. okay so now we have a rooted tree what we had before was an

unrooted tree or just like not a rooted tree because there was no root there was no greatest

greatest common ancestor to the entire rest of the tree. But now we can say that 12 is the root

of the tree because it’s the ancestor for all other nodes. I guess even if 12 was by itself,

we could call it a root of tree. It just wouldn’t be a very good example. So I’m going to actually

get rid of the word acyclic here since we already handled that. And I’m going to do,

I’m going to say that 34’s greatest ancestor is 12, 99’s greatest ancestor is 12, 33’s greatest

all the nodes in the tree their greatest ancestor is 12 and it’s common to all of them so now we

have a rooted tree maybe I should type in my doomed I really hope the screen I really hope

the screen cast doesn’t freeze it probably will upgraded the CPU it’s 33 faster than it was before

board so i am still using an old cpu even though it’s new to me dang it i’m gonna have to spend

like 500 okay uh so the next rule is so we have a rooted tree and now let’s rearrange everything

hierarchically which we already kind of did so uh there’s not really much to do here except

we did hierarchical organization

we probably just need to move on to our next rule which is to say that

if our rooted tree is to become a binary tree

then each node in the entire tree

cannot have more than two children

every single node in the entire tree

can have zero or one or two children

if there are three or more anywhere in the entire tree

then it’s not a binary tree

so okay that means you know the 45 is okay

because it has no children

because it has no children. All the rows, all the leaves at the bottom are okay. All these nodes

over here are okay because they just have one child. But the 12 node, the root of the tree,

it’s got three children and that violates the rule. So now we need to rearrange this.

So I think I’m going to just move these numbers down here maybe. Whoops. Maybe move these nodes

descendants of the 33 node. So I’m going to do this.

Okay. So cool. Now we have a binary tree and now we need to rearrange the drawing a little bit.

This is not part of the definition, but this will make it easier to debug your trees. So what I want

to do is make it so that every left descendant of a node appears physically on that node’s left

every right descendant of a node should appear on its right side

or like further to the right on the x-coordinate

so sort of similar to you know like the y-coordinate ranking

but notice how the 12 its left child is 8 and its right child is 33

so that means all the nodes here on the left side you know that come underneath the 8

are left descendants or you could say that they are in the left subtree of the 12.

So, they’re okay because 8 is to the left of 12 and 45 is to the left of 12.

But notice how 33 is a right child of 12 and it’s part of the right subtree.

It’s part of the right descendancy, but it’s physically on the left of 12.

That’s going to be really bad because it’ll be harder to debug our trees later.

So, I’m just going to slide it over without rearranging the tree.

And I usually try to split the difference here.

and then their parent is kind of like physically in the middle that will also help you debug in

the future so i’m going to do this wrong let me get the blue i’m going to do this make sure that

my ranking is still okay not the best most neatest tree and so now i’m going to look at the eight

it’s left subtree or it’s left uh descendancy uh all of those nodes which is just the 45 are

it’s left child 76 is the only thing that’s on the left side in the left subtree so that’s all

right probably the 33 I think it’s still a little lopsided I probably could have you know dragged

it a little bit more to the right but I’m going to leave it so the 33 and the 76 are okay and then

the 99 is a right descendant or it’s part of the right subtree of the 33 so it should be on the

right side it is that’s good the 34 should be on the right side of the 33 because it’s it’s a it’s

It’s part of the right subtree of 33.

It’s part of the right descendancy.

And it should also be on the left side of the 99

because it’s part of the left subtree of the 99.

So, so far, this is okay.

This is not the best drawing.

So now we have a binary tree

and we have kind of drawn it in a slightly good way.

Not super great.

The last rule that we’re going to add here is,

whoops, what happened there?

I’m supposed to do that, yeah.

The last rule we’re going to add is

we must have ordering to our nodes, to the numbers in our nodes. So what do I mean by ordering? Well,

the whole reason that we want a binary search tree, at least usually, is because it’s really,

really fast to search through. This is going to be a tree that we can search through in log time,

which we’ll talk more about in another video. We’ll do time complexities and searching and stuff. But

in order for this to be a super fast tree to search through, we need to be able to

very quickly make a decision. Do we go down and to the left? Do we go down and to the right?

left do we go down into the right and every decision we make should help us eliminate half

of the remaining data set half of the tree at a time every time we go down a level and that’s only

possible if the nodes themselves are ordered so what i’m going to do is say every node that’s on

the left side or let’s say every descendant that’s on the left side of a node should be of a lesser

value than that particular node every node that is on the right side of a node meaning it’s a right

descendant of that node or part of the right subtree of the node should be greater than that

node. Please note that this would not allow us to support duplicate values in our tree.

You could use something like less than or equal to versus greater than if you wanted to support

duplicate values in your tree. You could also change the T type, you know, the template type

to a node from the data you want it to store to a list. So every single node has a list inside of it

and the items in the list are just, you know, the regular values that you wanted. There’s a whole

values that you wanted there’s a whole bunch of different ways you could actually do that

but for now we’re going to see our trees don’t support duplicate values

so okay we don’t support duplicate values but we need you know from left to right

the order needs to look sane and this is kind of why we’re drawing the tree in this special way

we’re trying to make our tree really easy to debug visually so check this out the way we’ve

drawn this every single node has its own x coordinate basically notice how the 12 there’s

nothing underneath it at least not directly underneath it the 33 the 34 all the nodes you

know you can draw a straight line down from the node and it shouldn’t cross over with any other

nodes or edges so that means now that we’ve drawn it this way and we’ve made sure that all the left

descendants are on the left and all the right descendants are on the right we could actually

just scan our eyes from left to right and be sure that we are seeing an increasing order or

Since duplicates aren’t allowed in this tree, we’ll say an increasing order or an ascending order.

So if we start at 45 and then we go to the right, we should see a higher number.

So if we look at 8, 8 is a lower number.

So this violates the ordering rule.

This is not a valid binary search tree.

It’s only a valid binary tree.

So sad.

Okay, so I could, you know, swap the 45 and the 8 or I could just increase the value of the 8 itself.

of the 8 itself, I think it’ll be faster for me to just increase the 8 value. So I’m going to make

it 52 now. So we’ve got 45, 52. Then we go to the right a little bit more. It should also increase.

So 52 should increase. I’m just going to randomly increase it to, you know, 59, let’s say. Then as

we go to the right, we see another number here. It is 76. That already is increased from 59.

So we don’t need, we don’t need to alter that number. Then we go to the right one more time

that because it’s lower than 76 so I’m going to put 87 then when we go to the right one more time

that’s the 34 down here that’s definitely a decrease so we have to increase it now so I’m

going to say 99 how about if I just do 92 yeah so now we have a 92 down here and then if we go

to the right a little bit more there’s the 99 and now we actually have a binary search tree let’s

just double check all the rules first off is this a graph yeah there’s nodes and edges there’s nothing

There’s nodes and edges.

There’s nothing weird happening.

There’s not like a edge floating in the middle of nowhere.

Is this a connected graph?

Yeah, it is.

Because every single node, if you followed, you know, the edges, you know, could find

every single other node.

Like the 45, it could find, you know, the 92 node if it just followed all these edges.

Notice again that these edges have no direction.

There’s no arrows on them.

So we could go up or down in any direction we want.

So that means the 76 can find everything else.

else and so this is a connected graph for sure okay now that we have a

connected graph is this an acyclic graph I don’t know about you but I can’t find

any cycles in the graph right like the 92 it goes out but it doesn’t come back in

same thing for the 76 if we went from the 76 up to the 87 and then took a

right turn we wouldn’t be able to come back towards it without repeating that

same edge so this is definitely an acyclic graph all of the nodes follow

they’re not involved in cycles is this a rooted tree yeah there’s only one common ancestor to the

entire tree it’s the 59 it’s the highest node in the entire tree and it’s common to all other of

all of its descendants um so let’s see i’m going to duplicate this real fast the next thing is

we arranged it hierarchically and we added the terminology of like i think i kind of just like

tried to sneak this one past you but we added the terminology of a left child and a right child

and a right child.

Right? We also added the terminology of a right subtree and a left subtree.

Just to clarify what I mean, what do I mean by a right subtree and a left subtree.

So imagine we’re considering the 59.

If we consider the 59, then the 52 is the root node of the left subtree of the 59 node.

If we consider the 59, then the 87 is the root node of the right subtree of the 59 node.

so the right child is basically the root of the subtree uh in in you know the right child is the

root of a subtree of the right subtree uh i think i’m getting muddled my words here okay

anyway so we have a little bit of terminology uh the 59 is the root node that’s like the

the only node in the entire tree without uh an ancestor or a parent so okay uh then we have a

Note, and the entire tree doesn’t have more than two children.

Notice how the 59 has two children.

That’s fine.

If it was three, that’s way too much.

52 has one.

87 has one.

No, 87 has two children.

99 has one child.

92 has zero children.

So, okay, we’re not violating that rule.

So, we definitely have a binary tree.

And then we, you know, kind of read from left to right.

Let me write down the numbers this time for fun.

physically without kind of like following edges or anything we just scan

our eyes from left to right we can see that we have an ascending list if we

supported duplicates it would be okay to just see a non decreasing list but we

see an increasing list or an ascended list ascending list okay whoops this is

left to right so this is actually a binary search tree and um i don’t know about you but i think i

need to like you know get a snickers or something right now because uh this video has been going on

for longer than i wanted it to go on so we’ve defined a binary search tree in future videos

we’ll talk about how to add nodes into a binary search tree how to build the tree what’s the time

complexity of the tree in various operations deleting nodes from a tree terminology like

terminology like what are these nodes called things like that so anyway thank you so much

for for watching i hope you learned a little bit of stuff and had a little bit of fun

i’ll see you at a later date in time

just kidding

hey everybody thanks for watching this video again from the bottom of my heart i really

appreciate it i do hope you did learn something and have some fun uh if you could do me a please

If you could do me a please a small little favor

Could you please subscribe and follow this channel or these videos or whatever it is you do on the current social media?

It’s a website that you’re looking at right now

It would really mean the world to me and it’ll help make more videos and grow this community

So we’ll be able to do more videos longer videos better videos or just i’ll be able to keep making videos in general

So please do do me a kindness and uh and subscribe

I’m sleeping in the middle of the night and I just wake up because I know somebody subscribed or followed.

It just wakes me up and I get filled with joy.

That’s exactly what happens every single time.

So you could do it as a nice favor to me or you could troll me if you want to just wake me up in the middle of the night.

Just subscribe and then I’ll just wake up.

I promise that’s what will happen.

Also, if you look at the middle of the screen right now, you should see a QR code which you can scan in order to go to the website,

which I think is also named somewhere at the bottom of this video.

and it’ll take you to my main website where you can just kind of like see all the videos

I published and the services and tutorials and things that I offer and all that good

stuff.

And if you have a suggestion for clarifications or errata or just future videos that you want

to see, please leave a comment.

Or if you just want to say, Hey, what’s up?

What’s going on?

You know, just send me a comment, whatever.

I also wake up for those in the middle of the night.

I get, I wake up in a cold sweat and I’m like, it would really, it would really, it

it would really mean the world to me.

I would really appreciate it.

So again, thank you so much for watching this video

and enjoy the cool music

as I fade into the darkness,

which is coming for us all.

Thank you.

The post Binary Search Tree Definition Explained Step by Step appeared first on NeuralLantern.com.