We want to show that some problems in NP hard we got some problem, we have to show that we can reduce some other NP hard problem to it.

That's a problem difficult to solve.

Now that we've talked about reduction, we can revisit that definition and say a problem X is NP hard if we can reduce some other NP hard problem to it, what that really means is we can use a solution to problem X to solve some NP hard problem, that means that solving X has to be at least as hard as the NP hard problem making it therefore NP hard.

We always begin with the hardest problems.

I am confronted with a difficult problem.

Doctors have a difficult problem.

They fell into the difficult problems.

Our teacher will give us difficult problems.

This algorithm is known to converge to a locally optimal clustering of data ponts.

It is difficult to solve this problem.

Same for mid air. Multiply 3 up to 6.

The problem was beset with difficulties.

I think that makes sense.

So there, we got it right.

That's an epic win. This is a gamer on the verge of an epic win.

Let me see if I can make it a little bit clearer.

Excellent work!

We can just reduce SAT to it and then we're done, but at this point now, there's actually a huge number of problems that are known to be NP hard.

They also have the highest rate of homicide, the fourth lowest life expectancy in the world, and sits within the biggest HlV epidemic in the world.

Clearly a complex problem, but is it complicated?

It is difficult, indeed.

We maximized the posterior probability of data logarithmic is a monotonic function, and I put a minus sign over here so the optimization problem becomes a minimization problem.

Please calculate once again using Bayes rule these posteriors.

When you have a database in production that has thousands or millions of users, this can be really painful.

Patients are dying every day because we don't have enough of those organs to go around.

Many countries are having difficulties in the economic sphere.

But we'll keep doing it, and we'll solve more and more difficult problems.

Now, what kinds of questions can we ask to do inference about?

This problem is a real challenge.

Now I'm finally going to make, as my final quiz, a really challenging question for you.

And h of x is equal to 5x. Now I'm going to give you a tough problem.

Who is going to pay for it?

That's a matter of prime importance.

This is a matter of capital importance.

It costs about 10 dollars a piece to go and take a disk and put it online, if you're doing things in volume.

Developing countries suffer from difficulties of fiscal problems.

Do they have a common cold?

We'll talk about parcing which is good enough now to be used in lots of applications, and machine translation usable on the web.

They talked about feeling better understood by their friends and family.

Let's do one more.

It is your commonplace, featureless crimes which are really puzzling, just as a commonplace face is the most difficult to identify.

The most severe problem at present is that of over population.

If you managed to figure all that out, that's really impressive.

So let me divert for a second as we're going to identify the problems, the challenges, the behavioral challenges, that prevent people from saving.

Now we are going to have a quiz to see that you understand while loops, as well as break.