All language subtitles for 2 - Growth of Functions English

This is a very important video in the course because this really sets up and gives a foundation for

why we do what we do with algorithm development.

The concept of growth and functions shows how important it is that our algorithms are efficient because

we're going to see here in a minute how fast the numbers grow when we utilize inofficial algorithms.

And so if you don't understand any of the things we're talking about here that's perfectly fine.

You don't have to have mastered everything in order to go through this course but it is really important

to at least understand the high level concepts that this video teaches.

So what we're going to view is something called either Big O complexity or growth of functions and it's

going to show how different functions can affect numbers and how that growth can happen very rapidly.

And the way we're going to do to break down is to first look at the different type of functions that

there are.

So I'm going to go from smallest to greatest and the smallest or most efficient is something called

Order 1

1 and these are all going to be in order.

So the next one is going to be was based two of em and we typically write that just as log and next

one is an followed by an well-based to have an followed by an squared.

And you could technically do things such as in queue or into the fourth after that but we're not going

to do that.

We're going to skip straight ahead and do two to the end and you'll see why I'm here in a minute.

And then the last one is in fact you.

And if you do not know what factorials are just please refer to the video that I did on for factorials

just I did it because not everyone is aware how those were.

But it is important because they are by far the fastest.

And there is something you want to avoid at all costs when developing algorithms to analyze these.

The easiest way is just to insert a number in for them.

So we're going to do is we're going to say that in equal time.

So no reason a special reason why pick that number except for the fact it's very easy to multiply and

it's easy to use exponents with.

So the very first one order of one this one should be.

This one just equals one and I'll put one up top so that everybody knows what that one is and we can

track it and we get put on a chart here in a second.

The next one log in which would actually kill you in this case when we do our substitution log 10 this

one works out to be three point three two.

If you do not know the properties of logarithms.

Just please refer to my video on logs.

It's actually pretty basic.

Some people try to make it more complicated than it is but the basic concepts are pretty easy to get.

OK the next one we are he said n equals 10.

So I'm just to put that right up top.

And so our next one is going to be 10 voicebase 2 of 10.

And with that one equals that to be is thirty three point two two.

So put that up top.

You can see that these numbers are starting to grow and they haven't even gotten started.

Compared to how much they will in a second here.

So the next one is going to be

10 square.

Everyone here knows that a hundred

and the next one is going to be two to three.

And just to get 10 equals 1000 24

and just in case you're wondering I'm not a mouth savant.

I had these multiplication products written down on the sides so I'm not doing these in my head.

Especially this last one.

Ok last one.

Ten factorial.

What does 10 factorial equal.

Well if you work it out it works out to be three million six hundred twenty eight thousand and right

up top here we're just going to sum it up to three million.

So as you can see the growth functions happens very rapidly we go all the way from one right here all

the way to the same number equaling well over three million almost four million really when we get 10

factorial.

So if you're thinking of having an algorithm that seems to work but it happens to be something that

utilizes that has a factorial running time you're never going to be able to run it because there is

no computers on in this planet.

Fast enough of doing that if you have any kind of all.

And so is just something to keep in mind.

Now to see this it also really helps me to really plot it on a graph.

So I'm going to just create a really cool graph right here and we're going to give different colors

to each one.

So for our order of one this is going to be on the very bottom and it grew like that.

So this one is our border one.

OK.

Next one is going to be in blue and this one is going to be our last base too and

something along those lines right there.

It's constant It's constantly increasing.

However it's really nothing that's too crazy.

So in all of these actually our order of I just did it in front of the one but all of these are so order

of log in the next one we're starting grease a little bit more.

And so for this next one we're looking at our order and this one is going to be right here.

And I'm just showing these in order.

This is not drawn to scale.

If this was drawn to scale our log in would actually be much much closer to our order of 1.

But if I did that it would be hard to write.

So just just know this is not drawn to scale.

I'm just showing it because it kind of helps to see exactly how this is broken down.

OK.

After our order and we have our order of analog and we're going to be some more and more in this strange.

You can see it's still palatable but it's definitely starting to increase faster now.

We will get into things a little bit of.

And now we're going to go into the square and square it go look something like this

next

we're going to go into the two to the M

and then each one of these numbers are these points on the graph.

These actually correspond very closely to the numbers up top.

The rate of growth is very similar.

And so for our very last one we're going to go with in fact Turino which is just something like this.

It's as straight up as you can possibly get.

So in fact when.

And there you go.

You have your growth functions.

You can see the order and more important than understanding this or you know being able to explain and

or anything like that unless you're taking this for a college class or something and then you do need

to know it.

However the most important part about this for practical development is just understanding the importance

and having kind of a visual representation of efficiencies of algorithms so you know that if you design

an algorithm that used to be squared so it used to be somewhere on this side of the world with this

kind of performance and you're able to take it and make it a analog and kind of algorithm you've just

done an incredible job and you've been able to make your program much more efficient much more scalable

and much more of an enterprise type product.

So good job if you went through the streets please let me know if you have any questions or any if there's

anything I can do to clarify growth functions just please let me know.