So here's two exercises.

So this first one that I just showed is the number of recursive calls in

Quicksort, and the other one is average number of exchanges.

And it shows a little facility in

dealing with the recurrences of the way that I talked about, by following

through the way that I did other things people can get this exercise solved.

And in the next one, it's about this idea of a parameter that I talked about.

In practice what we do is recognise the quick sort is not going to be first with

small range, so we should switch to a method even simpler for

penal rays than that insertion sort.

So what threshold value we going to use, are we going to use different a different

sorting method when file gets less than 100 or less than five or what .And so

what this exercise shows is a way to parameterize that threshold.

Do the math.

And then figure out the best value of the parameter.

And again, that's the importance of having a mathematical model.

And it's a poster child for

this concept that comes up often in the analysis of algorithm.

We have some degree of freedom.

And we capture that in the math and

with the math model we can figure out the optimal value and

that translates right back to practice so that's those two exercises.

So in summary if for the next lecture if people would take a look at the book

cites to just become familiar with what's in there and bookmark them so

you can get back to them and then start learning to use some of the software.

If you are not to comfortable with your programming environment.

We have imputed a few some familiarity.

We have prettY simple programming model.

And I'll be describing codes in terms of those models.

It's not an absolute requirement, but a lot of people might find it interesting

to, when working with the code that I'm presenting, to run experiments and

do other things.

So that's all described in the algorithm fourth edition books.

And it's pretty easy to download our model.

And to be using our code.

We have hundreds and hundreds of students do it every year here at Princeton.

Most of them are only 19 or 20.

So I think a lot of the people taking this course have the experience maturity to

be able to run programs this way.

Another thing is tech, as I said nowadays the best way to communicate mathematics,

it turns out to be is using tech and there is plenty of tools available.

So that you can write up assignments either in tech

using tech shop or some similar tool or you can actually do it in HTML.

The way I did for the books.

It was less than a year ago I set on this project, I never imagined I'd be able to

get the math in the books as easily so people can do assignments that way too.

And maybe the discussion groups will tell us.

I'm sure there'll be a great amount of discussion about the best way to do this.