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Course Overview

To learn about properties of algorithm and how to design an algorithm discuss asymptotic notations, Design and measure time complexity analysis of searching, sorting and Graph traversal algorithms. Make comparison of different type of algorithm likes Linear, Quadratic, Polynomial and Exponential, Describe how greedy approach facilitate solving the problem. Discuss Divide and Conquer approach for solving the problem

BLOCK 1 : Introduction to Algorithm

Unit1 : Basics of an Algorithm

Definition and Example of an algorithm, Characteristics of an algorithm, Steps in Designing of Algorithms, Growth of function, Recurrence, Problem Formulation (Tower of Hanoi),Substitution Method, Iteration Method, Master Method

Unit 2 : Asymptotic Bounds

Asymptotic Notations, Concept of efficiency of analysis of an algorithm Comparative efficiencies of algorithms: Linear, Quadratic, Polynomial and Exponential

Unit 3 : Analysis of simple Algorithms

Euclid’s algorithm for GCD, Horner’s Rule for polynomial evaluation, Simple Matrix (n x n) Multiplication, Exponent evaluation e.g. an, Searching, Linear Search, Sorting, Bubble sort, Insertion Sort, Selection sort.

BLOCK 2 : Design Techniques

Unit 1 : Greedy Technique

Elements of Greedy strategy, Activity Selection Problem ,Continuous Knapsack Problem, Coin changing Problem, More Examples

Unit 2 : Divide and Conquer Approach

General Issues in Divide and Conquer, Binary Search, Merge Sort, Quick Sort, Integer Multiplication, More Examples

Unit 3 : Graph Algorithm

Representation of Graphs, Adjacency Matrix, Adjacency List, Depth First Search and Examples, Breadth First Search and Examples.

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