And there's a whole range of compounds that they do use.

The traveling wave reactor is another form of a liquid metal fast breeder reactor.

These challenges are not insurmountable, by any means.

Food allergies and food sensivities are far more common than we realize.

So what we're able to do with this information is boil it down to hot spots, 4,000 deployments, a huge herculean task, 2,000 tags in an area, shown here for the first time, off the California coast, that appears to be a gathering place.

And of course buildings have their shapes.

Being solemn is easy.

Sleep with it tonight. Is this all yours?

Lucky for us we don't have to think about it.

Originally, we tried the full reactors.

It's hard to keep track of these things.

And there are a lot of other problems with that.

It is hard to see the sights of Tokyo in a few days.

So, now we're in a good position to finally define this notion of NP completeness that I mentioned in the beginning of the unit.

I know this is hard.

He needed only to push himself up a little, and it fell by itself.

I found it difficult to understand what he was saying.

So this is from spelling correction data.

So my questions are very simple have the hearing reports really been lost?

No, they are full of misery.

Extra hard land, right?

First of all, if you can, don't fight the patent, fight the infringement.

In point of fact it is difficult to foresee the destiny of people.

It was difficult to carry out the plan.

I find it difficult to express my meaning in words.

Life, which has English words in it, and so it's often difficult to know where the movie name starts and ends.

A computer file could just be a big list of numbers.

It is difficult for me to understand him.

Well, I hope to change that in less than three minutes.

Well, coming out of the research labs just now, for our generation, is the possibility to do that.

And these are very unstudied sounds because they're hard to measure.

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.

It is difficult for him to buy a car.

I think that makes sense.

So that's also, that's equal to a, to 1 over log base x to a.

Mountaineering is attractive especially to young people because it is accompanied with hardships and adventures.

This first section, the select , this is basically what we're selecting.

We have trouble feeding, providing fresh, clean water, medicines, fuel for the six and a half billion.

Instead of circumstances, outcomes.

This will mean that growing food will become difficult.

It represents an amount of digital information, which is uncomfortable to store, transport, or analyze.

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.

It's extremely hard to move from one planet to another.

It is difficult to solve this problem.

Hard