 So now let's look at a little bit more of a complex step, something like a for loop. We would still come in and do some of the same analysis. You see, with a for loop, this first portion right here, this int i, our initialization if you will, that gets its own sort of classification of t in equaling 1. It's one action solely of creating that i. Now, if we look over at this comparison, remember this is how we sort of determine how many times we go through the loop. I see I'm going to actually have to do this comparison since right now I have it at 10. I'm going to need to do this comparison 10 times. All right, well, that's its own t of n. Now this i++, if you are familiar with Java syntax, that means that we're going to plus i once. Now here's where things can get a little questionable. You see, a lot of people think that because I have that i, I need to look at it and I have to access some memory. And they say, oh, that's a 1 in this. Not true. You see, because I've actually already created the i and it's already loaded up from memory sort of in my instruction, I actually don't have to access i a second time here. And what that means is this iteration, if we thought about it, is going to happen 10 times as well. Now, the astute of you might be noticing that this is not how many times I go through my for loop. You see, I would go through and i would equal 0, 1, 2, 3, up until 10. And when it reached 10, it would exit out. You see, so that's actually its own additional step. So we would actually classify the fact that I'm exiting my loop to be its own as well. So if we came in and once again, if we think about the idea of adding all of these t of n's that I've created, here, that's not an arrow. That, there we are. And this one right here, we see that I got a 10, plus a 10, plus one, plus one, creating t of n, 22. But okay, we're still looking at things from sort of numerical perspective. What if I don't know 10? So let's actually kind of take a look at that. Let's say for example, I came in and I still made my for loop the same way I would always do it. I'd come in with my i, set it equal to 0, i is less than, I'm going to call it just some value, some val. I don't know what that val is. It could be anything. It could be really, you know, 20, 200, 200 billion. It doesn't actually matter. So just like we said before, this section right here is still a 1. Me, sort of, I'm going to say this exit, I'm going to call that the exit, that's still a 1 as well. However, this and this, these two operations have changed. Because like I said, I have some value. And some value could be 20, 200, or that many. Okay, I'll stop. So all right, well I can't just magically put in a number here and just play the guessing game. So what we do when we're looking at run times is then we basically assign this type of operation an in. We would say that this is perfectly valid. I don't know how much it is, but I know it's going to be some number that's dependent sort of on, in this case, an in. The same thing actually happens over here as well because i++ we're going to continue to iterate through i until we hit some val. So as a result, just like before, we would classify that as in as well. So if we look at sort of any for loop and we remove the idea of knowing what this is, we create suddenly this t of in. Ah, look at that number. So I still have my one, I still have my other one, and I now have an in, I have another in, and so as a result what we're going to get is a t of in of 2n plus 2.