Review for Exam 2

1
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
• 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
Review for Exam 2

• K-D Trees
• 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 bhk can
  have
• Bottom-up insertion and deletion

7
Review for Exam 2

• B-Trees
• What is a 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)