Worked Examples: Red-Black Trees

These examples are designed to step through the logical process of applying the algorithmic concepts.

Example 1: Black Height

❓ Problem: Max height for bh(x)?

💡 Solution: $h \le 2 bh(x)$. Proof by properties.

Example 2: Rotation

❓ Problem: Right Rotate on x.

💡 Solution: x moves up, parent moves down-right. Subtrees shift.

Example 3: Double Red

❓ Problem: How to fix Red Parent + Red Uncle?

💡 Solution: Recolor both Black, Grandparent Red. Recurse up.

Example 4: Zig-Zag

❓ Problem: Fix Red Parent + Black Uncle (triangle)?

💡 Solution: Rotate to form line, then Rotate + Recolor.

Example 5: Performance

❓ Problem: Worst case Search?

💡 Solution: $2 \log_2 n$.

Example 6: vs AVL

❓ Problem: RB vs AVL?

💡 Solution: AVL more strictly balanced (faster search), RB faster insert/delete.