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Data Structures and Algorithms Design

NPTEL via Swayam

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ABOUT THE COURSE:The modern economy is run by algorithms. This a first-level course to introduce the students to the world of algorithm design, data structures, analysis, and programming. We'll start with the asymptotics notation which captures time and space of algorithms in the worst-case.The basic data structures covered are -- array, list, queue, stack, matrix, tree, heap, set, and graph. The algorithmic paradigms covered are -- induction/recursion, divide-conquer, hashing, greedy-method, and dynamic-programming.In the lectures, the theory will be backed up by numerous practical CS examples. The content is suitable for anyone who is mathematically inclined or computationally curious.INTENDED AUDIENCE: Computer Science & Engineering, Mathematics, Electronics, Physics, & similar disciplines.PREREQUISITES: Very good analytical skills.INDUSTRY SUPPORT: Discrete Optimization, Cryptography/ Cyber Security, Coding theory, Computer Algebra, Symbolic Computing Software, Artificial Intelligence, Learning Software

Syllabus

Week 1: How do clever algorithms look? Introduction
Week 2:Max-sum-subarray in linear-time; Time/Space Complexity and Asymptotics
Week 3:How to write proofs? Super-clever Local-minima in 1D and 2D arrays
Week 4:Abstract Data Structure; Range-minima in 1D array
Week 5:Binary Search Tree (BST) data structure, Height, Balancing
Week 6:LIFO/FIFO, Grid-distance problem; Stack ds, Expression-evaluation
Week 7:BST example: RB tree, Height, Insert, Delete
Week 8:Half-majority, Multiplication, Inversion; Algo.Paradigm: Divide and Conquer
Week 9:BFS, Bipartiteness, DFS; Graph theory and algorithms; DFS tree
Week 10:Articulation points, Biconnectedness; Heap data structure; Dynamic ds
Week 11:Multi-Increment, Range-Min; Set, Disjoint-union, Find; Greedy paradigm
Week 12:I-th-Minima, Median; Dijkstra's algo; Counting sort, Radix sort