Algorithm is the central concept of computer science. Whole of computer science can be thought of as revolving around the concept of algorithm - the machines are designed and fabricated to execute algorithms; the programming languages are defined to describe algorithms so that the machines can understand and execute programs written in programming languages; the foundation/theory of Computer Science is the study of the limits of algorithmic methods, i.e., the study tells whether a particular task is accomplishable by a computer or not, etc. Hence, the study of the Design and Analysis of Algorithm has to be an essential part of any Computer Science/Engineering curriculum. Even if, software for solving all types of problems may become available in the future and the user/student may not be required to write an algorithm to solve any problem, still training the students in the skills of designing and analyzing the algorithms will remain essential, because these constitute the fundamental skills for solving problems with computers. It is like teaching of geometry to instill in students the skills of logical reasoning. The objectives of the Course is to make the students aware of and well-groomed in the use of the tools & Techniques of designing and analyzing algorithms.
Example of an Algorithm Problems and Instances Characteristics of an Algorithm Problems, Available Tools & Algorithms Building Blocks of Algorithms Outline of Algorithms
Unit 2: Some pre-rquisites and Asymptotic BoundsSome Useful Mathematical Functions & Notations Mathematical Expectation Principle of Mathematical Induction Concept of Efficiency of an Algorithm Well Known Asymptotic Functions & Notations
Unit 3 : Basics of AnalysisAnalysis of Algorithm ─ Simple Example Well Known Sorting Algorithms Best-Case and Worst-Case Analyses Analysis of Non-Recursive Control Structures Recursive Constructs Solving Recurrences
General Issues in Divide-And Conquer Integer Multiplication Binary Search Sorting Finding the Median Matrix Multiplication Exponentiation
Unit 2 : Graphs AlgorithmsExamples Traversing Trees Depth-First Search Breadth-First Search Best-First Search & Minimax Principle Topological Sort
Unit 3 Models for Executing Algorithms –I: FARegular Expressions Regular Languages Finate Automata
Unit 4 : Models for Executing Algorithms –II PDFA & CFGFormal Language & Grammer Context Free Grammer(CFG) Pushdown Automata (PDA)
Prelude to Formal Definition Turing Machine: Formal Definition and Examples Instantaneous Description and Transition Diagram Some Formal Definitions Observations Turing Machine as a Computer of Functions
Unit 2 : Algorithmically Unsolvable ProblemsDecidable And Undecidable Problems The Halting Problem Reduction to Another Undecidable Problem Undecidable Problems for CFL Other Undecidable Problems
Unit 3 : Complexity of AlgorithmsNotations for the Growth Rates of Function
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