It grows less slowly asymptotically.

It's just a linear function asymptotically.

Asymptotically, this won't change. It's again 3, 3, 3, and 3.

And, asymptotically, the number of quadratic features grows roughly as order n squared, where n is the number of the original features,

In other words, from an asymptotic standpoint, in this algorithm, we'll run the same worse case asymptotically then check both of the boxes.

Things are close to Euclidean and therefore the counts will be a asymptotically going to the straight line with the slope we just derived.

like the first K elements but we basically have them at that point and K is smaller than n so asymptotically that's the whole running time.

In the beginning maybe weird things happen, but once we get out far enough asymptotically in the limit as things get really big, f(n) lies between c2g(n) and c1g(n).

We're trying to figure out what the running time is asymptotically Θ for selection and insertion as a function of n and K and then we can substitute in the value of K.

In fact, there's some cases very good algorithms and you see that they're all polynomially bounded, so there's some polynomial in n and m that actually is larger asymptotically than all of these.

Here as well as in the other plots, all of the curves are really close together at very low redshifts, when things that are asymptotically Euclidean. So that's the distances, what about the look back time?

So, in the last century, OK, people debated about whether this expansion of space would continue forever whether it would slow down, you know, will be slowing down, but continue forever slow down and stop, asymptotically stop or slow down, stop, and then reverse, so it starts to contract again.

With the very long list that were wanting to tap values of, you might as well just sort the whole thing. n, well what happens with n? n where look we're comparing n log n to n( n) which is n³ ². n³ ² is asymptotically larger than n log n so we're still better off just sorting the whole list.