Add AVL tree rotation example image; #319

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Expand Up		@@ -43,20 +43,44 @@ The difference between the heights of the left and right subtrees is called the
		If after an insertion or deletion the balance factor becomes greater than 1, then we need to re-balance this part of the AVL tree. And that is done with rotations.

		## Rotations

		Each tree node keeps track of its current balance factor in a variable. After inserting a new node, we need to update the balance factor of its parent node. If that balance factor becomes greater than 1, we "rotate" part of that tree to restore the balance.

	TODO: describe with pictures how these rotations work
	![Rotation0](Images/RotationStep0.jpg)

	For the rotation we're using the terminology:
	* Root - the parent not of the subtrees that will be rotated;
Copy link Member @kelvinlauKL kelvinlauKL Dec 21, 2016 Choose a reason for hiding this comment The reason will be displayed to describe this comment to others. Learn more. typo here - "parent not" should be "parent node" Antondomashnev reacted with thumbs up emoji
	* Pivot - the node that will become parent (basically will be on the Root's position) after rotation;
	* RotationSubtree - subtree of the Pivot upon the side of rotation
	* OppositeSubtree - subtree of the Pivot opposite the side of rotation

	Let take an example of balancing the unbalanced tree using Right (clockwise direction) rotation:

	![Rotation1](Images/RotationStep1.jpg) ![Rotation2](Images/RotationStep2.jpg) ![Rotation3](Images/RotationStep3.jpg)

	The steps of rotation could be described by following:

	1. Assign the RotationSubtree as a new OppositeSubtree for the Root;
	2. Assign the Root as a new RotationSubtree for the Pivot;
	3. Check the final result


	In pseudocode the algorithm above could be written as follows:
	```
	Root.OS = Pivot.RS
	Pivot.RS = Root
	Root = Pivot
	```

	Insertion never needs more than 2 rotations. Removal might require up to log(n) rotations.
	This is a constant time operation - __O(1)__
	Insertion never needs more than 2 rotations. Removal might require up to __log(n)__ rotations.

		## The code

		Most of the code in [AVLTree.swift](AVLTree.swift) is just regular [binary search tree](../Binary Search Tree/) stuff. You'll find this in any implementation of a binary search tree. For example, searching the tree is exactly the same. The only things that an AVL tree does slightly differently are inserting and deleting the nodes.

		> Note: If you're a bit fuzzy on the regular operations of a binary search tree, I suggest you [catch up on those first](../Binary Search Tree/). It will make the rest of the AVL tree easier to understand.

	The interesting bits are in the `balance()` method which is called after inserting or deleting a node.
	The interesting bits are in the `balance()` method which is called after inserting or deleting a node.

		## See also

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@kelvinlauKL kelvinlauKL Dec 21, 2016

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