And the first one we're going to focus on is called the Divide and Conquer algorithm design paradigm.

What makes it, if anything, better than much simpler non divide and conquer algorithms, like say, insertion sort?

On the design side, we'll get more experience applying the divide and conquer paradigm to further problems. See you then.

Conquer your desktop!

Okay? So we'll get a win, first sorting in Divide and Conquer, and Merge Sort is the algorithm that realizes that benefit.

You don't need to know say, the divide and conquer paradigm, if all you need to do is sort 100 numbers.

I shall conquer this.

And that Our forces, they surely must conquer.

And a year after that, we did conquer it.

Conquer your fear and claim the treasure you seek.

We're gonna conquer, and we're gonna kick some. Understood?

I will conquer the new America.

To conquer a history for myself.

The idea of divide and conquer is that you can break a problem into roughly equal size sub problems, solve the sub problems separately, and combine the results.

My wish is to conquer this mountain.

In English, fear is something we conquer.

How can the god conquer his doubts?

And it will allow us to analyze lots of different recursive algorithms, lots of different Divide and Conquer algorithms, including the integer multiplication algorithm that we discussed in an earlier segment.

I divide by 1.05, and then I divide by 1.05 again.

You must conquer your fear of the dark.

You must conquer your fear of the dark.

You should try to conquer your smoking habit.

I don't want to rule or conquer anyone.

Divide

Divide.

You divide by 1.05 there, and then you divide by 1.05 again.

So if you divide 0.2 here and you divide by 0.2 here.

Divide these just like that, and then divide these just like that.

In this state nothing is going to conquer you.

Tanks and planes may defeat the troops but they cannot conquer the people.

So let's divide the numerator by 3 and divide the denominator by 3.

So divide the numerator by 3, and let's divide the denominator by 3.

But if we use this non trivial Divide and Conquer approach, or non obvious approach, we'll get a, as we'll see, a much better running time than this quadratic dependence on the input.

That there's really a fabrication and an instrumentation divide bigger than the digital divide.

And I want to divide that by, I don't know, let's divide it by,

Alexander the Great went on to conquer the known world

We all thought then that somebody wanted to conquer us.

So we could divide 21 by 7. And we can divide so let me make the numerator and we can divide the denominator by 7.

And Merge Sort is still today's the, perhaps the, most transparent application of the Divide and Conquer paradigm, ... ... that will exhibit very clear what the paradigm is, what analysis and challenge it presents, and what kind of benefits you might derive.

In particular, we'll be substantiating the claim that the recursive divide and conquer merge sort algorithm is better, has better performance than simpler sorting algorithms that you might know, like insertion sort, selection sort, and bubble sort.

In the upcoming lectures I'll provide you with the tools to not only precisely understand and answer this question but more generally to predict the running times of an entire genre of divide and conquer algorithms, like

We could divide the 3 by 3 and get 1, and divide the 18 by 3, and get 6.

If all you need to do is sort arrays of size 1500 you really don't need to know Divide and conquer or anything else we'll talk about that's a pretty trivial problem on modern computers.

Divide its length and breadth by ten.

Divide the numerator and denominator by 5.