Data Structures and Algorithms Design

Overview

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

• Course Introduction
Overview of Algorithms and Data Structures
Importance and Applications in Modern Economy
• Asymptotic Notation
Big O, Big Ω, and Big Θ Notations
Analyzing Time and Space Complexity
• Basic Data Structures
Arrays and Lists
Stacks and Queues
Matrices
Trees
Binary Trees
AVL Trees
Binary Search Trees
Heaps
Min-Heaps and Max-Heaps
Heap Sort
Sets
Operations and Implementations
Graphs
Representation (Adjacency Matrix/List)
Traversal Algorithms (DFS, BFS)
• Algorithmic Paradigms
Induction and Recursion
Mathematical Induction
Recursive Algorithms
Divide and Conquer
Merge Sort
Quick Sort
Fast Exponentiation
Greedy Method
Principles and Strategies
Applications: Kruskal’s and Prim's Algorithms
Dynamic Programming
Memoization vs. Tabulation
Classic Problems: Knapsack, Fibonacci Sequence
Hashing
Hash Functions
Collision Resolution Techniques
• Practical Applications and Examples
Real-world Scenarios in Computer Science
Case Studies and Problem Solving
• Course Review and Industry Applications
Review of Key Concepts
Application in Discrete Optimization, Cryptography, AI, etc.
Future Directions and Exploration in Algorithm Design

Taught by

Prof. Nitin Saxena

Subjects

Computer Science