COMSATS Institute of Information Technology, Lahore
M. A. Jinnah Campus, Defence Road, Off Raiwind Road, Lahore
Tel: 042-5321090, 042-9203101, Fax: 042-9203100
Semester Course Plan and Course Outline
Design and Analysis of Algorithms
Study Program
Semester
Course Code
Course Title
Instructor
Credit Hour
Pre-Requisite(s)
Total Lectures
Lecture Duration
BCS
Fall 2012
CSC-201
Design and Analysis of Algorithms
Dr. Muhammad Umair
3
Data Structure, Discrete Mathematics,
Statistics
30
90 minutes
Basic Information
Course Statement
It is an introductory course to the design and analysis of algorithms. It covers
mainly asymptotic analysis of time complexity, Proofs of correctness,
Algorithms and advanced data structures for searching and sorting lists,
graph algorithms, numeric algorithms, and string algorithms.
Course Objectives
This course focuses on the complexity and correctness of algorithms:
big oh, big omega, and big theta notations, recurrence relations and
their solutions, and worst, average and amortized analysis of
algorithms with examples. Basic and advanced data structures for
searching, sorting, and graph algorithms.
This course places emphasis on complexity analysis, sorting, graph
theory and problem-solving strategies. Comparison of various sorting
and graph algorithms, with focus on complexity and space versus
time trade-offs is made. A special effort is made to formulate and
design algorithms and use of approximate algorithms where the
problem cannot be solved by an exact algorithm
COMSATS Institute of Information Technology, Lahore
M. A. Jinnah Campus, Defence Road, Off Raiwind Road, Lahore
Tel: 042-5321090, 042-9203101, Fax: 042-9203100
Learning Outcome
On successful completion of this course unit students will:
1. Understand the general notion of complexity classes, P and
NP, completeness and hardness, and the relationships between
classes by reduction. You will also have seen how to show
tasks are NP-complete
2. Be able to develop, and reason about the correctness and
performance, of algorithms for string searching and for
calculating over graphs
3. Have studied a range of distributed and probabilistic
algorithms, understand the key issues involved, and be able to
use distributed and probabilistic techniques to develop
algorithms.
COMSATS Institute of Information Technology, Lahore
M. A. Jinnah Campus, Defence Road, Off Raiwind Road, Lahore
Tel: 042-5321090, 042-9203101, Fax: 042-9203100
Course Outline
Design and Analysis of Algorithms
Week #
1
2
3
4
5
Topics/Contents
Basic Mathematic & Introduction to Algorithms: Reading Material, What is an
Algorithm? Its role in computing, Its Implementation Domain, Data structure &
Techniques, Hard Problems, Algorithm as Technology, Efficiency, Algorithms & other
technologies.
Algorithm Analysis: Introduction to Algorithm analysis, Bench marks for analysis,
Selection Sort and its analysis, Complexity Classes, Big – O Notation, Experimental
and mathematical proof for Selection Sort.
Analyzing the Algorithms, RAM model, Analysis of Insertion Sort, Worst & Average
Case analysis, Order of Growth.
Growth of Functions: Asymptotic notations,  - notation, O – notation,  - notation,
Asymptotic notation in equations and inequalities, o – notation,  - notation,
comparison of functions, Standard notations & common function
Designing of Algorithms: Loop Invariants and the correctness, Incremental Approach,
Divide and conquer approach, Its use in Merge Sort, Analysis of Merge Sort,
Recurrences, Its Technicalities, The Substitution Method, Subtleties, Avoiding pitfalls,
Changing Variables.
Designing of Algorithms: The Recursion – Tree Method, Its implementation and use.
Different cases of Recursion Tree Method. The Master Method, The Master Theorem &
its use, Revision of Course for First Sessional
First Sessional
6
7&8
9&10
11
Application of Analysis & Design Techniques: Heaps, Heap Sort, Maintaining Heap
Property, Building a Heap, The Heap Sort Algorithm, Priority Queues
Application of Analysis & Design Techniques: Sorting and order Statistics, Structure
of data, Why sorting is used? Different Sorting Techniques, Quick sort, Description of
Quick Sort, Performance of Quick Sort, worst, average & best cases, Analysis of quick
sort, Worst-case analysis.
Application of Analysis & Design Techniques: Sorting in Linear Time, Lower Bounds
for sorting, Decision – tree model, Tracking and implementation of Counting Sort, Its
analysis, tracking and implementation of Radix Sort & Bucket Sort with their analysis.
Hash Table & Hashing: Hashing, Direct – address table, Hash Tables, Collision,
Resolution by chaining, and Analysis of hashing with chaining, Hash functions, The
division method, and Multiplication method, Universal Hashing, Designing a universal
class of hashing functions. Revision of Course for Second Sessional
Second Sessional
12
13
Hashing & Binary Search Tree: Open Addressing, Linear probing, Quadratic probing,
Double Hashing, Analysis of open – address hashing. What is Binary Search Tree?
Querying a Binary Search Tree, Insertion and Deletion of Binary Search Tree.
Dynamic Programming: Assembly – line scheduling, fastest way through the factory,
recursive solution, computation of the fastest time, construction of fastest way, Matrix –
chain Multiplication, optimal parenthesization, recursive solution, optimal cost
calculation, construction of optimal solution.
COMSATS Institute of Information Technology, Lahore
M. A. Jinnah Campus, Defence Road, Off Raiwind Road, Lahore
Tel: 042-5321090, 042-9203101, Fax: 042-9203100
Week #
14,15
16,17
Topics/Contents
Dynamic Programming: Basic elements of dynamic programming, Longest Common
Subsequence (LCS), Optimal Binary Search tree, Analysis & construction of optimal
solution.
Greedy Algorithms: Activity – selection problem, recursive & iterative greedy
algorithm, Elements of the greedy strategy, greedy choice property, Optimal
substructure, greedy versus dynamic programming. Huffman Codes, prefix code,
Construction of Huffman code, and Correctness of Huffman’s algorithm.
Recommended Text Book(s)
Sr.
No.
1
2
3
Book
Introduction to Algorithms
Algprithms
Author(s)
Edition
Thomas H. Cormen
Robert Sedgewick
2nd
2nd
Supplementary Reading(s)
Sr.
No.
1
2
Book
Author(s)
Compared to What? An Introduction to
the Analysis of Algorithms
The Design and Analysis of Computer
Algorithms
G.J.E Rawlins
Alfred V. Aho
Edition