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

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?

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

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

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

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