1. Topics covered (since exam 1):
Review for Exam 2
Topics covered (since exam 1):
Splay Tree
K-D Trees
RB Tree
B-Tree
Priority Queue and Binary Heap
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 Splay tree
Definition (a special BST: balanced in some sense)
Rationale for splaying: amortized performance
Splay operation (bottom up)
Rotation
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?

3. K-D Trees Review for Exam 2 What K-D trees are used for
Multiple keys
Range queries
How K-D trees differ from the ordinary BST
levels
Be able to do insert and range query/print
Limitations
Hard to do deletion
Difficult to balance

4. 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
When and what to rotate and recolor

5. 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)
Internal and external nodes
M and L (half full principle), especial requirement for root
Why need B-tree
Useful/advantageous only when external storage accesses required and why?
Height O(logM N), 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

6. PQ and Heap Binary heap Heap operations (implemented with array)
Definition: CBT with a partial order (heap order)
Why it is good for PQ
Heap operations (implemented with array)
findMin, deleteMin, insert
percolateUp (for insertion), percolateDown (for deletion)
Heap construction (heapify),
Heap sort
Time performance of these operations
Leftist tree and leftist heap
Why we need this?
Definition (npl: null path length)
Meld operations and applications
insert, deletMin, heap construction