1. Design and Analysis of Algorithms
Lecture # 1
Muhammad Nasir
Department of Computer Science
COMSATS University Islamabad,
Lahore Campus

2. About the Course Purpose:
A brief introduction to Design and Analysis of Algorithms
Lab or Programming Course: Math Course:
No No
Textbook:
Introduction to Algorithms,
second edition by Thomas H. Cormen

3. Pre-requisites
Discrete Structures
Data Structures

4. Course Evaluation Assignments Quizzes Term Projects / Reports S1 exam
Final exam

5. Class Expectations Come to lectures on time and participate
Keep up with reading material
Complete assignments, projects, etc on time
Submit clean, organized, and to the point reports

6. Key to Success Attendance Effort Consistency
Pay attention to lectures and keep extra notes
Ask questions
Effort
Do homework on your own. It’s ok to ask others but make your own effort.
Consistency
Keep up with reading, and homework.

7. Plagiarism Policy
According to this policy, a student's submitted work must be the student's own. In this course, this policy will be applied to all work submitted for grade including exams, quizzes, homework, and projects.

8. Algorithm
The word Algorithm comes from the name of the muslim author Abu Ja’far Mohammad ibn Musa al-Khowarizmi.

9. Introduction Algorithm:
A computer algorithm is a detailed step-by- step method for solving a problem by using a computer.
An algorithm is a sequence of unambiguous instructions for solving a problem in a finite amount of time.
An Algorithm is well defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values as output.

10. Introduction sorting algorithms & Searching algorithms Algorithm:
Most basic and popular algorithms are
sorting algorithms & Searching algorithms

11. Introduction Algorithms and Programming:
good understanding of algorithms is essential for a good programming
Unlike a program, an algorithm is a mathematical entity, which is independent of a specific
programming language, machine, or compiler.
Algorithm design is all about the mathematical
theory behind the design of good programs

12. Introduction Algorithms and Data Structures
Efficient Algorithms require efficient Data Structures and vice versa
Why Study Data Structures and Algorithms?
For good algorithm design
To be really complete algorithm designer, it is important to be aware of programming and machine issues as well
They have various applications like databases, operating system, computer graphics , compilers and computer networks etc.
a good understanding of algorithm design is a central element to a good understanding of computer science and good programming.

13. Course Outline Course will consist of four major sections:
The first is on the mathematical tools necessary for the analysis of algorithms. This will focus on asymptotic,
summations, recurrences.
The second element will deal with one particularly important algorithmic problem: sorting a list of numbers. We will show a number of different strategies for sorting, and use this problem as a case-study in different techniques for designing and analyzing algorithms.

14. Course Outline
The third one will deal with a collection of various algorithmic problems and solution techniques. Dynamic programming, greedy algorithms, graphs etc.
Finally, a very brief introduction to the theory of NP- completeness. NP-complete problem are those for which no efficient algorithms are known, but no one knows for sure whether efficient solutions might exist.

15. Criterion for Analyzing Algorithms
To design good algorithms, we must agree on the criterion for measuring the algorithms
The emphasis is on the design of efficient algorithms

16. Criterion for Analyzing Algorithms
Computational resources required an algorithm
Running time
Memory/space required
An algorithm which requires less amount of running time and memory space will be called an efficient algorithm

17. Model of Computation
Our analysis will be independent of the variations in:
Machine hardware
Operating system
Compiler
Programming language etc
Algorithms need to understood by the people not machines

18. Model of Computation
Ideally this model should be a reasonable abstraction of a standard generic single- processor machine
We will call this machine as Random Access Machine

19. Random Access Machine (RAM)
A Random Access Machine (RAM) is an ideal machine with
Infinite large memory
Executes one instruction at a time (no parallelism)
Each instruction performs some basic operations on two values in memory

20. Basic RAM operations Basic operations include
Assigning a value to a variable
Performing basic arithmetic operation (+, -, *, /) on any size of integer values
Accessing an element of an Array like array[100]

21. An Important Assumption
Each basic operation takes same constant time to execute
There is no difference between performing addition or multiplication on any size of the values

22. Running Time Analysis Criteria
Worst case analysis
Maximum running time over all (legal) inputs of size n
Average case analysis
average running time over all inputs of size n
Best case analysis
Running time over the best case input of size n
We always look for the worst case running time