That's a problem difficult to solve.

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.

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.

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.

We always begin with the hardest problems.

The problem was beset with difficulties.

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

It is difficult, indeed.

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.

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?

So there, we got it right.

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.

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.

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.

The sum of the Yis, is a particularly challenging question.

Hard

It's So

The general problem of detecting that two phrases or sentences mean the same thing the paraphrase tasks still quite hard.

Clearly a complex problem, but is it complicated?

And now you've put in front of me the one thing, the one thing that is gonna make this unbearable.

clutchy?

Then you simplify it, and you'll see that you can keep using rules until you get to a much simpler answer.

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

The birth rate is not the only problem we're facing.

Another problem has arisen.

The problem perplexed him.

Another problem has come up.

I'm at my wit's end with this difficult problem.

The problem is how we cope with the present difficulties.

So I'll have to find out the hard way.

I go around the world to speak, and people ask me questions about the challenges, my moments, some of my regrets.

This problem seems difficult.

Same for mid air. Multiply 3 up to 6.

look nutty and horrible like this.