Lecture 14

Midterm review

Notes:

This materials is just meant to give you an idea of important topics. You are still responsible for learning from the following materials:

• Class notes
• Reading assignments
• Review questions
• Material covered in recitation
• Assignments and our assignment solutions

In order to prepare for the midterm, I suggest that after learning the material, you try answering the review questions and homework/recitation assignments.

Important topics

C++

• Use guards in header files
• Implement, use, and compile template functions and classes
• Remember that templates go in header files, and don't compile these files
• Deep copy in classes with dynamically allocated data -- copy constructor, assignment (avoid self copy), destructor
• Using using namespace std;
• Use common STL containers (list, vector, deque, stack, and queue, apart from string) and operations, such as: push_front, push_back, pop_front, pop_back, front, back, empty, size, begin, and end.
• Declare and use STL iterators, increment (++) them, and compare with end()
• IO: File IO, output to stdout, and read from stdin
• Command line arguments

Vectors

• Implement simple vector features: push_back, pop_back, operator[], (push_front, and pop_front)
• Use simple STL vector features
• Remember to expand the vector when necessary
• Time complexity of common vector operations
• Implement algorithms to perform binary search and insertion into a sorted vector.

Linked lists

• Implement simple features of singly and doubly linked lists: push_front, push_back, pop_front, and pop_back
• Implement simple features of self-organizing lists, in particular, a search method that also performs a self-organization (the self organization scheme may be different from those discussed in class)
• Given a sequence of operations, draw the state of the final doubly linked list, singly linked list, or self-organizing linked list
• Time complexity of common singly and doubly linked list operations
• Use simple STL list features

Complexity analysis

• You may need to use the formula for the sum of the first n positive integers, and approximations to the sum of their powers too
• You may need to use the formula for the sum of a geometric series
• Remember that alogan = n
• Prove big-O properties, such as O(f1 + f2) = O(max{f1, f2})
• Show that f(n) = O(g(n)) using the definition (that is, finding c and N), or using properties
• Perform average case analysis, given a probability distribution for the input
• Perform amortized analysis
• Explain how amortized analysis is different from average case analysis
• Derive tight bounds for sums using integration (I will probably not ask a question on this in the midterm; however you should know a good approximation to Sumni=1 ik for a constant k)
• Derive time complexity for algorithms or nested loops
• Given the time taken by an algorithm on a small input size, and its time complexity, determine the time taken by that algorithm on a larger input size
• Give the time complexities of common set operations, when using doubly or singly linked lists, vectors, or sorted vectors, to represent sets

Deque

• Given a sequence of operations, show the state of the deque implemented in class, remembering to expand it when necessary, and copy as done in class
• Implement common operations on a deque, implemented using an array or a vector: push_front, push_back, pop_front, pop_back, size, empty, and operator[]
• Use simple STL deque features
• Time complexity of common operations on a deque

Stacks and queues

• Given a sequence of operations, show the state of a stack or a queue, and that of its underlying implementation
• Implement common operations on stacks and queues, using some other suitable container: push, pop, front, top, size, and empty
• Use simple STL stack and queue features
• Time complexity of common operations on stacks and queues
• Given a problem, write pseudo-code that uses stacks or queues to solve it

Applications

• Given an application, give the time complexities of relevant operations using different containers, and suggest a suitable one

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Last modified: 21 Feb 2008