1. Red-Black Tree Rotations

2. Red-Black Diagrams
The diagrams which follow show the rotations and recoloring for each “case” for Bottom-Up Insertion, Top-Down Insertion and Bottom-Up Deletion.
Bear in mind that each case has a left-right symmetrical twin which is not shown here.

3. S Bottom-Up Insertion Case 0 - X is the root Color it BlackG G
Recolor P, G, U Move X up to G Move to another case
Case 1 – U is Red U U P P X
Case 2 -Uncle is black. X and P are opposite children G P U X X
Zig-Zag Rotation G P
Recolor X and G S S U
Case 3 – Uncle is Black X and P are both left (right) children G P U P
Rotate P around G G X X
Recolor P and G S U S S

4. Bottom-Up Deletion

5. Top Down Insertion Case 1 – P is Black Recolor X, Y and ZG
Case 2 – P is red and P and X are both left (right) children G P P U
Recolor X, Y, Z, P, G P U
Rotate P around G G X X S X S Y Z Y Z S U Y Z G X
Case 3 – P is red and P and X are opposite children G
Recolor X,Y,Z X U G P U
Recolor X, G P
Rotate X around P P Z
Rotate X around G S X S S Y Z U Y Y Z