We're looking at the same basic setup as the last time.

We start off with a set of n nodes, then we create a graph on half of the nodes recursively.

So what's the running time of this going to be?

Once again, we can think about this as happening in a kind of recursion tree.

The last couple of triple integrals we did we integrated with respect to z first.

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N plus 1's are there?

We now know how deep. It's log n.

One is getting and removing the min and the other one is inserting new elements into the heap.

Let me say a little bit about that now.

Now the recurrence relation has this form..

We have a graph with 1 node, it's going to have 0 edges, by the way that this generation process happens.

Alright, so next we're going to look at some recursively generated graphs.

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So, let's start off with a really simple example. So, here is some pseudo Python for generating a graph with n nodes.

level.

The whole thing is a heap. We made a heap. Woohoo!

Here's our last random graph of this unit.

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