1. Topics covered (since exam 1, excluding PQ):
Review for Exam 2
Topics covered (since exam 1, excluding PQ):
General rooted trees
Binary Search Trees (BST)
K-D Trees
Splay Tree
RB Tree
B-Tree
For each of these data structures
Basic idea of data structure and operations
Be able to work out small example problems
Prove related theorems
Asymptotic time performance
Advantages and limitations
comparison

2. Review for Exam 2 General rooted tree Binary trees Definition
Internal and external nodes
Height and depth, path length
Tree storage methods and their nodes
Binary trees
Full, complete and perfect binary trees and their properties
4 different orders of tree traversals

3. Review for Exam 2 BST Definition
Basic operations and their implementations
find,
findMin,
findMax
insert,
remove,
makeEmpty
Time performance of these operations
Problems with unbalanced BST (degeneration)

4. K-D Trees Review for Exam 2 What K-D trees are used for
Multiple keys
How K-D trees differ from the ordinary BST
levels
Be able to do insert and range query/print

5. Review for Exam 2 Splay tree
Definition (a special BST: balanced in some sense)
Rationale for splaying (data locality)
Splay operation
Root
without grandparent
with grandparent: zig-zag and zig-zig
When to splay (after each operation)
What to splay with find/insert/delete operations
Amortized time performance analysis: what does O(m log n) mean?

6. Review for Exam 2 RB tree Definition: a BST satisfying 5 conditions
Every node is either red or black.
Root is black
Each NULL pointer is considered to be a black node
If a node is red, then both of its children are black.
Every path from a node to a NULL contains the same number of black nodes.
Theorems leading to O(log n) worst case time performance
Black height
min and max # of nodes a RB tree with bh=k can have
Bottom-up insertion and deletion

7. Review for Exam 2 B-Trees What is a B-tree Why need B-tree
Special M-way search tree (what is a M-way tree)
Interior and exterior nodes
M and L (half full principle), especial requirement for root
Why need B-tree
Useful/advantageous only when external storage accesses required
Why so?
Height O(logM N), so are performances for find/insert/remove
B-tree operations
search
insert (only insert to nonempty leaf, split, split propagation)
Remove (borrow, merge, merge propagation, update ancestors’ keys )
B-tree design (determining M and L based on the size of key, data element, and disk block)