Call Dr. Kuroki! Yes.

Let me illustrate this with one of the most devilish data structures ever invented, which is a Red Black tree.

But over here, some light might hit the ground.

Moreover, we still don't have two reds in a row, so we haven't broken invariant number three either.

The trees looked black against the sky.

Pressure can make everything whole again.

There's a black hat caught in the high tree top.

If at most one is red, you'd break the fourth invariant.

Some of those nodes will be black some of those nodes will be red.

So, that's a non example of a red black tree.

So, let's see exactly what I mean. So, let's begin with an observation.

So, what does this buy us? Well, now, let's start thinking about red black trees.

So, it has one child on each side, the three and the seven.

So, that's also very important, although a

In fact, no more than double the absolute minimum that we conceivably have, almost two times log base two of N.

Actress Hitomi Kuroki said on TV she hates dried grapes.

Let's move on to some examples.

I'm searching for is smaller or larger than the element I'm looking at.

So now, red black tree with N nodes.

Here's an example of a Red Black tree.

This is just adding one to both sides and taking the logarithm base two.

You want to accommodate insertions and deletions.

Maybe some of them are red, but in the, in, the maximum case, all of them are black.

So, let's look at an example of a red black tree.

Time permitting, we'll cover just a taste of it in some optional videos.

Well, that's these chains. So, the claim is, even a chain with three nodes can not be a red black tree.

To do that, I took the tree branch and embedded it in black with the Multiply blending mode.

A black node must have red children, and a red node must have black children.

And what's clear about this proof is it's very obvious the role played by this invariants three and four.

They're not super, most of them are not super different from each other.

A Red Black tree is a data structure to represent associative arrays also known as mappings.

So, it's a violation of the fourth invariant, therefore, this would not be a red black tree.

To get an idea just how complicated they are, let's take a look on Wikipedia what they wrote about Red Black trees.

What did he look like?

Let me discuss the second quiz here, in which we're given two scan lines again a left and a right scan line.

So search in Red Black tree is easy but insertion and removal are really complicated.

You do so at the beginning, you do so at the end, and when all of your assertions pass, then you can be sure that your Red Black tree never ever becomes corrupted.

least the number of nodes in a perfectly balanced tree of depth k 1 which is 2 k 1, So, for example, when k 3, it's 2 3 (two cubed) 1, or 7 that's just a basic fact about trees, nothing about red black trees.

Boots, black. Belt, black.

Crows are black.

Small black

Large black

NA

Ah, yes. The Black Cauldron.

Your soul is black.