Topics for Park's CMSC 341 Midterm 2:

1. Review: Proof by Induction
2. Review: Binary Search Tree (BST) vs. plain binary tree
   • Traversal: inorder, preorder, postorder
   • searching for specified value
   • finding MinValue and MaxValue
3. Amortized cost:
   • You should be able to explain why growing a vector by doubling it each time is amortized O(1) per insertion (this was covered in class multiple times)
4. AVL Trees
   • Purpose of this struct
     • AVL tree is a BST--allows fast search
     • Balanced nature allows fast operations
   • Structural properties of AVL tree
     • Is a BST
     • Balanced: heights of the children of node can differ by at most 1
     • Overall height is O(log n)
   • Insertion, deletion operations:
     • Trinode retructuring:
       • You should be able to sketch out effects of single and double rotations
   • Performance of AVL tree
     • O(?) for: search, insertion, deletion
5. Splay Trees
   • Purpose of this struct
     • Splay tree is a BST
     • Minimizes average cost of operations
     • However, does not guarantee specific performance of any single operation
   • Structural properties of splay tree
     • Again, is a BST
     • Not strictly balanced after any given operation, though
     • Most-recently accessed value is at top
   • Purpose of splaying
     • Are splay trees balanced?
     • Why do we do splaying?
   • When are items splayed
   • What item is splayed
   • The zig, zig-zig, and zig-zag operations
   • Performance properties of splay tree
     • Cost of splaying: amortized cost
       • Any single operation can be expensive (O(n))
       • You only have to understand general concept of "amortized cost" of splay trees, not details: not responsible for proving anything
     • Advantage of splay trees for frequently-accessed items
6. Red-Black Trees
   • Purpose of this struct
     • R-B tree is a BST--allows fast search
     • Balanced nature allows fast operations
   • Structural properties of a R-B tree
     • Know the 4 properties of R-B trees--IMPORTANT!
     • Definition of "black depth"
     • Bounds on true height of R-B tree O(log n)
     • Balanced: black depth of all leaves is same
   • Insertion operation:
     • You should understand basic operation: search, followed by converting dummy leaf to a new internal value node (what color?)
     • Concept of "double red"
     • Fixing double red: restructuring vs. recoloring You should be able to sketch out basics of both
   • Deletion operation:
     • Need to be able to describe basic strategy
     • What a "double black" is, how it arises
     • You do NOT need to memorize the complex 3-case strategy for resolving double black!
   • Performance of R-B tree
     • O(?) for: search, insertion, deletion
7. Priority Queues, Heaps
   • Operations and behavior of "priority queue" ADT
     • Difference from regular queue ADT
     • Various ways to implement a priority queue (list, sorted list, tree, etc.)
   • Purpose of the heap struct
   • Structural properties of heap
     • Conceptual model as a complete binary tree (but not a BST!)
     • Implementation of a heap as an array
   • Min heap vs max heap
   • Insertion in a heap
     • where to initially insert new element
     • "Bubbling up"
   • Deletion from a heap
     • Where to find min (max) element in a min heap (max heap)
     • How to delete
     • "Bubbling down"
   • Performance of heaps tree
     • O(?) for: search, insertion, deletion
   • True MinMax heap
     • What it is--high level description
     • How to find the min, max
     • Do not need to know anything about implementation
8. Hash Tables
   • Purpose of this struct
   • Structural properties of hash tables
     • Bucket array
     • Hash function
     • Load factor
   • Hash functions
     • Difference between key and index
     • Should be able to describe some simple hash functions
   • Collisions
     • What collisions are
     • Chaining solution
     • Open addressing (probing) solutions:
       • Linear probing
       • Quadratic probing
       • Double hashing
     • Probing and Clustering
     • Probing and lazy deletion
   • Performance of hash tables
     • O(?) for: search, insertion, deletion of min (max)

Not all of these will be be specifically asked about on the exam, but you are responsible for knowing it.