1. CO4301 – Advanced Games Development Week 5 Walkthrough of Red-Black Tree Insertion
Gareth Bellaby

2. Insert 40
Root, black 40

3. Insert 20
Parent is black
No change 40 20

4. Insert 45
Parent is black
No change 40 20 45

5. Insert 50
Parent is red
Uncle is red 40 20 45 50

6. Colour uncle and parent black
Colour node and grandparent red
Propagate change in rest of tree 40 20 45 50

7. Insert 43
Parent black
No change 40 20 45 43 50

8. Insert 41
Parent red
Uncle red 40 20 45 43 50 41

9. Colour uncle and parent black
Colour node and grandparent red
Propagate change in rest of tree (no further changes) 40 20 45 43 50 41

10. Insert 42 Parent red Uncle black N is a right child Left rotation on P40 20 45 G 43 50 U 41 P
N is a right child
Left rotation on P N 42

11. Effect of left rotation on P40 20 45 43 50 42
Effect of left rotation on P 41

12. Relabel N and P Uncle is black N is left child Right rotation on G G U40 20 45 G 43 50 U P 42
N is left child
Right rotation on G 41 N

13. Effect of right rotation on G40 20 45 42 50 P 41 N 43 G
Effect of right rotation on G U

14. 40 20 45 42 50 P 41 43 G
Swap colours of P and G

15. The tree is still height balanced. 40 20 45 42 50
Examine the tree
The tree is still height balanced.
The number of black nodes is identical for every path to a leaf. 41 43
The values are sort order