subroutine

A subroutine called countdown takes an input x.

The contents of the four registers are preserved by the called subroutine.

So let me remind you, the pseudo code of the merge subroutine, here it is.

First, let me just tell you the pseudo code, leaving aside exactly how the merging subroutine is implemented.

We didn't talk about the number of steps that it take to do a print statement if there's a subroutine, but we're going to call it one for the print statement plus however many steps it takes to execute the subroutine call.

The simplest type of question is the same question we ask with an ordinary subroutine or function in a programming language.

Then, we've got a subroutine called path (G, V₁,V₂) and what that does is it takes graph G, a start node,

So the upshot is that the running time of the merge subroutine, given an array of M numbers, is at most four M plus two.

The key question you recall was how many lines of code does merge sort require to correctly sort the input array, not just this subroutine.

Here's that subroutine again just copied over, and I'd like you to answer the question what is the running time of this little i with the mean.

Now I don't expect anyone to be impressed with this rather crude upper bound, the number of lines of code that the merge subroutine needs to finish, to execute.

We saw this philosophy at work very early on in our analysis of merge sort. When we discussed the number of lines of code that the merge subroutine requires.

So, we wrote that subroutine down in pseudocode, and we gave it analysis of 4m plus two on the number of lines of code executed, given an input of

First there is a recursive call so we're not counting that, second there is another recursive call again we're not counting that a little j and then third we just invoke the merge subroutine.

J. And we know that the merge subroutine, when given an input, given an array of size, N over two to the J, will execute almost six times that many number of lines of code.

And we're going to define a subroutine mean that takes a list and initializes total to 0, runs through all the elements in the list adding up their values, and then returning the total divided by the length.