Going from AVL trees to Red-Black trees - avl-tree

According to my book, coloring red links that go from nodes of even height to nodes of odd height in an AVL tree gives a (perfectly balanced) 2-3-4 tree, where red links are not necessarily left-leaning.
But I don't get how exactly. When I try it with some examples, I keep getting stuck. Can someone illustrate it for me please?

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Randomly generating a maze in winforms

So for a project I wanted to make a game which involves randomly generating a maze with some space in the middle of the maze with 2 entrances on opposing sides. The objective is for 2 players to spawn on each side of said maze and to make their way into the middle in which they fight. I've thought about a few ways to approach this:
using the graph class in c# to generate a grid of nodes - then generating a path through it
using an array to draw out the grid of nodes - and generating a path through it
In terms of the algorithm, I've decided to go with the recursive backtracking algorithm.
My problem is how would I implement this into either method and how would I be able to apply this to my game ie space in the middle with 2 entrances.
Any other methods for drawing out the maze are also welcome, I'm relatively new to coding so please give pointers.
So far all I've done is design the logic for this algorithm.
Any help is appreciated, Thanks.

Why don't react use red-black tree to shape its model?

Red-black tree is a kind of AVL tree which is widely used in data base for it is efficient in CRUD. Why react do not use it as its virtual DOM tree model? You'd better give me a mathematic proof.
I guess there is a reason that AVL tree is to make searching more quickly, but in UI area, we often concentrate on tree's diff and transform. But another question, is there a kind of data structure can make tree diff and transform more efficient?

Insertion of same elements in Red-Black Tree?

How Red Black Tree will formed if we insert same elements, for example inserting 8,8,8,8,8,8,8 .
If you insert 8,8,8,8,8,8,8 it will be displayed something like below,
because Red-Black Tree follows these properties:
A red-black tree is a balanced binary search tree with the following properties:
Every node is colored red or black.
Every leaf is a NIL node, and is colored black.
If a node is red,
then both its children are black.
Every simple path from a node to a
descendant leaf contains the same number of black nodes.

what is the Balance factor in AVL tree

I'm making presentation for AVL tree, can't understand what is the balance factor.
please give me the link or any thing that I can understand graphically how height of an AVL tree's height effect
If I understood your question correctly.
Difference between the height of the left sub tree and right sub tree is the balance factor of an AVL tree.when the factor is 1,0, or -1 the tree is balanced otherwise unbalanced .
Play with AVL tree applet to get some intuition on this
See this link for Balance Factor

ExtJS4: Find tree node by screen coordinate or HTML element

In my web application I work with ExtJS4 and I use an Ext.tree.Panel. For a custom drag and drop implementation I need to find the tree node by its screen coordinates.
Is there a way to find a tree node by its screen coordinate? Or is it possible to find it via its HTML element?
Thanx in advance...
It would be not very efficient to seek node by coordinates as the only way to find the node by coordinates is to walk over all nodes.
Finding node by HTML element seems like more logical approach to me. Extjs4 tree utilizes the view. So you can try the view.getRecord method:
var node = tree.view.getRecord(htmlEl);
I haven't tried this code but it should work provided you passed correct htmlEl.
One part of your question has already been answered.
If you really need to get HTML element (use it only as last resort) by screen coordinates, then you will need document.elementFromPoint.
Extra info and quirks here: http://www.quirksmode.org/blog/archives/2010/06/more_ie9_goodne.html

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