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

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

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)

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

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?

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

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)