1. CS 3610 Midterm Review

2. Analysis of time complexity
Iterative algorithms
Sum up individual components
Recursive algorithms
The time complexity is commonly expressed as a recursive equation
We can solve it be repeated replacements

3. Analysis of time complexity
Worst case cost
Best case cost
Average case
\big-O, \big-Omega, \big-Theta notations

4. Big-O, big-Omega, big-Theta
Definitions
Proof

5. STL (C++98) overview Three basic components of the STL:
Containers, iterators, and algorithms
Basic concepts of sequence containers: vector, deque, list
Functionalities
Basic operations
Basic concepts of iterators

6. Recursions
Recursive definitions, recursive algorithms and recursive functions
the base case and the general case of a recursive definition
how to design recursive algorithms
Examples: Fibonacci number, tower of Hanoi, etc.

7. Recursions Recursion vs. iteration The concept of backtracking
Efficiency issue, general-purpose conversion (won’t show up in the exam)
Simple conversions (may show up)
The concept of backtracking
Examples; understand the procedure.
Similarity and difference w.r.t. depth-first search.

8. Generic Trees Definitions Terminology
Root + disjoint subtrees
Terminology
Height, degree of a node, degree of a tree, level of a node,
Left child/right sibling representation

9. Binary trees
Properties (# of leaf nodes, max # of nodes at certain level, max # of nodes for certain height)
Complete vs. full binary trees
Array representation of complete binary trees
Linked representation of binary trees

10. Binary tree traversals
Different orders
Inorder
Preorder
Postorder
Level-order (won’t show up)

11. Recursion vs. iteration
Recursive programs,
Calculate the number of leave nodes, height of a binary tree, etc.
Inorder, preorder, postorder traversals
The iterative version
Inorder, preorder, postorder

12. Binary search trees Basic operations: Complexities of the operations
Search, insertion, deletion,
finding the minimum, finding the maximum, inorder traversal.
Complexities of the operations

13. AVL trees Basic operations: Balance a tree after insertion
Definition; balance factor
Search, insertion, deletion,
finding the minimum, finding the maximum, inorder traversal.
Balance a tree after insertion
Single rotation; when to happen, how to do it?
Double rotation; when to happen, how to do it?

14. Heap Heap (Max-heap vs. Min-heap) Complexities
Heap property, representation, height, indexes
Operations on heaps: insertion (bubble up), Delete-max (bubble down), build a heap (bottom up)
heap-sort
Complexities

15. B-trees m-way search trees: generalization of binary search trees
Definition of b-trees
Search a key in a b-tree
Insert a new key in a b-tree
May need to split a node, and move up the median key to the parent
Delete a key in a b-tree
May need rotation & merge

16. Structure of the exam Definitions/basic properties (20-30%)
Operations on certain inputs (20-30%)
Code analysis (20-30%)
Code writing (20-30%)
Other