Review for Exam 2 Topics covered (since exam 1): –Splay Tree –K-D Trees –RB Tree –Priority Queue and Binary Heap –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

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 –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

–Binary heap 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 Review for Exam 2

B-Trees –What is a 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(log M 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, pointer, data element, and disk block Review for Exam 2