I'll show it to you just for completeness' sake.

The motion vector, just for completeness, will just be 0, 0, 0, 0.

These gadgets come up a lot in NP completeness proofs.

In class, we keep brushing against Turing completeness, and it turns out that languages like

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.

One more property of the algorithms to consider is the property of completeness, meaning if there is a goal somewhere, will the algorithm find it?

Finally, just for completeness, let me write out the formula for the Gaussian distribution so the property of x and I'll sometimes write this instead of p of x, I'm going to write this as p of x semicolon Mu comma sigma squared.

This leads to a lack of completeness, which means there might be solutions to the navigation problem that this algorithm doesn't capture, but it does give us correctness.

I wanted to kind of express the notion of NP completeness and give you a chance to play with that a little bit, and in the homework, we're going to look at that in a little bit more depth.

Once you spend enough time designing algorithms to solve specific problems you start to realize that some problems don't seem to allow for efficient solutions. Unit Six covers the concept of NP Completeness. It doesn't actually give us a way to solve these problems any faster, but it does give us a pretty good indication when it might be okay to stop looking for an exact answer.

Dotti For, for, for

For you. For me. For everybody.

For... For what?

...for... for... whatever.

Thanks for, uh, for fighting for us.

On the one hand, our need for security, for predictability, for safety, for dependability, for reliability, for permanence.

For Turkey, For Europe

'For you, for me'

For journey, for travel.

For me! For Aksinya!

For better, for worse.

For... for the murder?

For Gondor! For Gondor!

For hours... For days...

For what? For us.

For real? For real.

This is a day for curiosity and for scepticism, for openness and for critical thinking, for inspiration and for action.

We know that for Alzheimer's, for Parkinson's, for Huntington's.

For our lands, for our families, for our freedoms.

Thanks for waiting for me.

'for you' is 'for me'

For ourselves or for others.

for this gesture for humanity.

For Rome, or for you?

For Narnia and for Aslan!

For beauty, not for taste.

She worked for us for...

For you and for Sangala.

M for Mary, for marriage.

This is for freedom. For what? For freedom ! And this is for the martyr.

For A, it's 0.1 for X and 0.9 for Y.

For B, it's 0.8 for X and 0.2 for Y.

Cheers for her, cheers for her... three cheers for her!

Could be used for anything, for performances, films, for installations.

One for You, one for Moses, and one for Elijah.