1. CS-2852 Data Structures LECTURE 11 Andrew J. Wozniewicz Image copyright © 2010 andyjphoto.com

2. CS-2852 Data Structures, Andrew J. Wozniewicz Agenda Binary Search Trees – Removing Data

3. CS-2852 Data Structures, Andrew J. Wozniewicz Removing Data Arguably, the most complex algorithm of the course! Find the node to be deleted – If it doesn’t exist: exit Leaf (Terminal) Node: – Remove the parent’s reference to deleted node Non-Leaf Node: – Find the child to replace the deleted node – THREE scenarios…

4. Remove: Case 1 Removed Node has no right child – Left child replaces removed remove(8)

5. Remove: Case 1 Removed Node has no right child – Left child replaces removed remove(8) – Find node to remove – Has no right child ?

6. Remove: Case 1 Removed Node has no right child – Left child replaces removed remove(8) – Find node to remove – Has no right child – Promote left child

7. Remove: Case 2 Removed right child has no left – Right child replaces removed remove(6)

8. Remove: Case 2 Removed right child has no left – Right child replaces removed remove(6) – Find node to remove – Node right has no left

9. Remove: Case 2 Removed right child has no left – Right child replaces removed remove(6) – Find node to remove – Node right has no left – Promote right child

10. Remove: Case 2 Removed right child has no left – Right child replaces removed remove(6) – Find node to remove – Node right has no left – Promote right child

11. Remove: Case 3 Removed right child has left child – Right child’s left-most child replaces removed remove(6)

12. Remove: Case 3 Removed right child has left child – Right child’s left-most child replaces removed remove(6) – Find node to remove – Node on right has left – Find right’s leftmost child – Promote leftmost child

13. Remove: Case 3 Removed right child has left child – Right child’s left-most child replaces removed remove(6) – Find node to remove – Node on right has left – Find right’s leftmost child – Promote leftmost child

14. Remove: Case 3 Removed right child has left child – Right child’s left-most child replaces removed remove(6) – Find node to remove – Node on right has left – Find right’s leftmost child – Promote leftmost child

15. Remove: Case 3 Removed right child has left child – Right child’s left-most child replaces removed remove(6) – Find node to remove – Node on right has left – Find right’s leftmost child – Promote leftmost child

16. CS-2852 Data Structures, Andrew J. Wozniewicz Summary Binary Search Trees – Removing Data

17. Questions? Image copyright © 2010 andyjphoto.com