"Rotations" are what actually keep a red-black tree balanced. Every time one branch of the tree starts to get too long, we will "rotate" those branches to keep the tree shallow. A shallow tree is a healthy (fast) tree!
A properly-ordered tree pre-rotation remains a properly-ordered tree post-rotation
Rotations are O(1) operations
When rotating left:
The "pivot" node's initial parent becomes its left child
The "pivot" node's old left child becomes its initial parent's new right child
Here's the process of a "left rotation":
Assignment
Now that we can add users to our new Red Black Tree, we need to add the rotation functionality that will keep it balanced and running fast!