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

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

Pre-requisites Discrete Structures Data Structures

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

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

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.

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.

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

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.

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

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

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.

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.

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.

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

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

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

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

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

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]

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

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