1. Final Exam Review
COP4530

2. A high-level summary of what we learned
Algorithm analysis
Data structures
Vector, List, Deque
STL sequence containers
Stack, Queue, Priority queues
STL adaptor containers
Set and map (multiset, multimap)
Hashing tables (unordered_set, unordered_map)
STL associative containers
Trees
set and map in STL implemented using binary search tree
Graphs (not covered)
Available in Boost
Algorithms
Various algorithms associated with data structures
Various sorting algorithms
DFS/BFS, infix to postfix conversion, postfix evaluation
Graph algorithms (not covered)

3. f(n) is asymptotically
Big “O” Notation
f(n) =O(g(n))
If and only if
there exist two constants c > 0 and n0 > 0,
such that f(n) < cg(n) for all n >= n0
iff  c, n0 > 0 | 0 < f(n) < cg(n)  n >= n0
cg(n)
f(n)
f(n) is asymptotically
upper bounded by g(n) n0

4. f(n) is asymptotically
Big “Omega” Notation
f(n) = (g(n))
iff  c, n0 > 0 | 0 < cg(n) < f(n)  n >= n0
f(n)
cg(n)
f(n) is asymptotically
lower bounded by g(n) n0

5. Big “Theta” Notation f(n) = (g(n)) c2g(n) f(n) f(n) has the
iff  c1, c2, n0 > 0 | 0 < c1g(n) < f(n) < c2g(n)  n >= n0
c2g(n)
f(n)
f(n) has the
same long-term
rate of
growth as g(n)
c1g(n) n0

6. C++ Standard Template Library (STL)
Template based
Generic programming
One definition works for all types (proper type)
Containers – data structures
vector, list, deque, priority_queue, set, map, unordered_set, unordered_map, …
Algorithms
Sorting algorithms, and many others
Iterators – to access elements of the containers
Encapsulating difference among distinct data structures
Common interface for generic algorithms

7. Generic programming basics
How to write template classes
Also template function
Iterators
Const Iterators
Unidirectional vs. bidirectional iterators

8. STL Container implementation
Data members (member variables)
Constructors
Destructor
Methods
Iterators
Overloaded operators
The Big five – copy and move assignment operators, copy and move constructors, destructor

9. Basic STL Containers Vector List Familiarity
Similar to array in operation
Index-referenced elements (random element access)
RESIZABLE
First-class objects
List
Linked list – one element points to next one
Singly/Doubly linked list
STL List implemented as DOUBLY LINKED
STL forward_list is singly linked
Familiarity
Use of basic operations
Implementation of each container

10. Double Ended Queues Deque Operations on a Deque
How is it different from Vector?
Deque Implementation
Using a circular array
Locating the front and the back positions of the deque
Calculating the size of the deque
Accessing the ith element in the deque
How a deque should be implemented if we maintain an explicit size member variable?
In particular, member functions front, push_front, pop_front

11. Stack ADT Basic Operations Implementation Common uses of Stack
First In, Last Out
Implementation
Using an Adaptor Class
Common uses of Stack
Depth first search
Evaluation of postfix expressions
Conversion from infix to postfix expressions
Matching brackets
Function calls
Recursion

12. Queue ADT Basic operations Implementation Common uses of Queue
First In, First Out
Implementation
Using an Adaptor Class
Common uses of Queue
Breadth first search
Buffers
Simulations
Producer-Consumer Problems

13. Depth First Search How does it work
How to use stack for conducting DFS
DFS algorithm implementation

14. Breadth First Search How does it work
How to use queues for conducting BFS
BFS algorithm implementation

15. Positional Containers
Definition?
Examples?
Also called sequential containers in STL terms

16. Trees – Basic Theory Definitions Tree, Rooted Tree
Depth/Height of Vertex
Depth/Height of Tree.
Descending Path
Parent, Child, Sibling, Ancestor, Descendant
Root, Leaf

17. Tree Implementation Structure of a node
Linking the children and siblings with constant space for a Node.

18. Generic Tree traversals
Preorder traversal
Postorder traversal
Levelorder traversal
Inorder traversal for binary trees

19. Binary trees Definition Structure representation
Complete Binary Tree
Structure representation
Relation between number of nodes n and height H of a complete binary tree
Levelorder traversal
How to compute the height of a tree?
Vector representation of a complete binary tree

20. Binary Search Tree Not the same as a binary tree
Also known as Totally Ordered Tree
Finding an element
Finding the smallest element
Finding the largest element
Search complexity
Best case, Worst case, Average case
BST implementation
Recursive implementation of tree operations such as insert and delete

21. BST Anomalies Why BST may not necessarily be balanced?
Insertion of element
In sorted order
Or even mostly sorted order
Deletion Bias
Why does it arise?
Simple ways to overcome the bias.

22. AVL trees Definition of AVL trees Implementation of AVL trees
Building AVL trees by inserting/deleting elements

23. M-ary Trees Definition Implementation Usefulness? M-ary tree
Complete M-ary tree
Implementation
Usefulness?

24. M-ary Search Trees Not the same as M-ary Trees Representation
Search process

25. B-Trees B = Balanced Conditions for M-ary tree to be called a B-tree
Inserting a value
Inserting at a non-full leaf
Inserting at a full leaf
When to split a non-leaf node
When to split the root
Deletion
Combining leaves, non-leaves
Borrowing leaves from neighborhood
When does the height of the tree grow? Reduce?

26. Associative Containers
Generic Associative Containers
Unimodal vs. Multimodal associative containers
Sets
Regular set vs. Multi-set
Maps
Regular maps vs. Multi-maps

27. Hash Tables Basic principles of using hash tables
Designing a hash table
Choosing a Hash Function
Conflict Resolution Strategy
Hash functions
Properties of a good hash function

28. Conflict Resolution Strategies
Separate Chaining
Linear Probing
Quadratic Probing
Double Hashing
Rehashing

29. Priority Queue What is it? When is it useful? Operations
Push, pop, top, clear, empty
Implementation
Adaptor class: can use linked lists, Binary Search Trees, B-Trees, Heaps

30. Heaps Notion of partially ordered trees
Heap = partially ordered complete binary tree
Vector representation of Heap
Implementing different operations
Push heap
Pop heap
Build heap
Given a sequence of numbers, building a heap
Insertion and deletion

31. Sorting Different sorting techniques Bubble sort Insertion sort
Algorithm details
Best-case, worst-case and average case complexity of each
Especially for the recursive algorithms
Bubble sort
Insertion sort
Shell sort
Heap sort
Merge sort
Quick sort
Pivoting strategy
Partitioning strategy
Recursion

32. Graph algorithms Representations of Graphs Topological sorting
Shortest-path algorithms
Unweighted version
Weighted version