Swayam Central

# Design and analysis of algorithms

By Prof. Madhavan Mukund   |   Chennai Mathematical Institute
This course will cover basic concepts in the design and analysis of algorithms.
• Asymptotic complexity, O() notation
• Sorting and search
• Algorithms on graphs: exploration, connectivity, shortest paths, directed acyclic graphs, spanning trees
• Design techniques: divide and conquer, greedy, dynamic programming
• Data structures: heaps, union of disjoint sets, search trees
• Intractability
INTENDED AUDIENCE: Students in BE/BTech Computer Science, 2nd/3rd year.
PRE-REQUISITES: Exposure to introductory courses on programming and data structures.
INDUSTRY SUPPORT: This course should be of value to any company working in the area of software services and products.

Learners enrolled: 17090

### SUMMARY

 Course Status : Ongoing Course Type : Elective Duration : 8 weeks Start Date : 26 Aug 2019 End Date : 18 Oct 2019 Exam Date : 17 Nov 2019 Category : Computer Science and Engineering Level : Undergraduate
This is an AICTE approved FDP course

### COURSE LAYOUT

Week 1
Module 1: Introduction
Module 2: Examples and motivation
Module 3: Examples and motivation

Module 4: Asymptotic complexity: informal concepts
Module 5: Asymptotic complexity: formal notation
Module 6: Asymptotic complexity: examples
Assignments MCQ/Fill in blanks (unique answer)

Week 2
Module 1: Searching in list: binary search
Module 2: Sorting: insertion sort
Module 3: Sorting: selection sort
Module 4: Sorting: merge sort
Module 5: Sorting: quicksort
Module 6: Sorting: stability and other issues
Assignments MCQ/Fill in blanks, programming assignment

Week 3
Module 1: Graphs: Motivation
Module 2: Graph exploration: BFS
Module 3: Graph exploration: DFS
Module 4: DFS numbering and applications
Module 5: Directed acyclic graphs
Module 6: Directed acyclic graphs
Assignments MCQ/Fill in blanks, programming assignment

Week 4
Module 1: Shortest paths: unweighted and weighted
Module 2: Single source shortest paths: Dijkstra
Module 3: Single source shortest paths: Dijkstra
Module 4: Minimum cost spanning trees: Prim’s algorithm
Module 5: Minimum cost spanning trees: Kruskal’s Algorithm
Module 6: Union-Find data structure
Assignments MCQ/Fill in blanks, programming assignment

Week 5
Module 1: Divide and conquer: counting inversions
Module 2: Divide and conquer: nearest pair of points
Module 3: Priority queues, heaps
Module 4: Priority queues, heaps
Module 5: Dijstra/Prims revisited using heaps
Module 6: Search Trees: Introduction
Assignments MCQ/Fill in blanks, programming assignment

Week 6
Module 1: Search Trees: Traversals, insertions, deletions
Module 2: Search Trees: Balancing
Module 3: Greedy : Interval scheduling
Module 4: Greedy : Proof strategies
Module 5: Greedy : Huffman coding
Module 6: Dynamic Programming: weighted interval scheduling
Assignments MCQ/Fill in blanks, programming assignment

Week 7
Module 1: Dynamic Programming: memoization
Module 2: Dynamic Programming: edit distance
Module 3: Dynamic Programming: longest ascending subsequence
Module 4: Dynamic Programming: matrix multiplication
Module 5: Dynamic Programming: shortest paths: Bellman Ford
Module 6: Dynamic Programming: shortest paths: Floyd Warshall
Assignments MCQ/Fill in blanks, programming assignment

Week 8
Module 1: Intractability: NP completeness
Module 2: Intractability: reductions
Module 3: Intractability: examples
Module 4: Intractability: more examples
Module 5: Misc topics
Module 6: Misc topics
Assignments MCQ/Fill in blanks

Nil

### INSTRUCTOR BIO

Prof. Madhavan Mukund studied at IIT Bombay (BTech) and Aarhus University (PhD). He has been a faculty member at Chennai Mathematical Institute since 1992, where he is presently Distinguished Professor, Deputy Director and Dean of Studies. His main research area is formal verification. He has active research collaborations within and outside India and serves on international conference programme committees and editorial boards of journals.

He has served as President of both the Indian Association for Research in Computing Science (IARCS) (2011-2017) and the ACM India Council (2016-2018). He has been the National Coordinator of the Indian Computing Olympiad since 2002. He served as the Executive Director of the International Olympiad in Informatics from 2011-2014.

In addition to the NPTEL MOOC programme, he has been involved in organizing IARCS Instructional Courses for college teachers. He is a member of ACM India's Education Committee. He has contributed lectures on algorithms to the Massively Empowered Classroom (MEC) project of Microsoft Research and the QEEE programme of MHRD.

### COURSE CERTIFICATE

• The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
• The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
• Date and Time of Exams: 17th November 2019, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
• Registration url: Announcements will be made when the registration form is open for registrations.
• The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
• Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE
• Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
• Exam score = 75% of the proctored certification exam score out of 100
• Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75
• If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
• Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras. It will be e-verifiable at nptel.ac.in/noc.
• Only the e-certificate will be made available. Hard copies are being discontinued from July 2019 semester and will not be dispatched