Foundations of Algorithms and Data

This unit introduces core algorithmic concepts, basic data representations, and practical problem‑solving techniques using hands‑on coding in Google Colab. Students will learn to implement and analyze sorting and graph algorithms, perform simple vector and matrix computations without third‑party libraries, and compare algorithmic strategies to prepare for more advanced optimization and large‑scale data topics in later units.

Learning Objectives

• Analyze problem statements to design step‑by‑step algorithms, decompose problems into subproblems, and document algorithm behavior and correctness
• Apply Google Colab to implement basic linear algebra operations (vectors and matrices) and core routines (e.g., sort, traversal) without relying on NumPy, measuring runtime and space usage
• Demonstrate implementation and complexity analysis of fundamental algorithms including merge sort, quick sort, breadth‑first and depth‑first graph traversals, and simple search engine indexing concepts
• Evaluate and compare algorithmic strategies (greedy, dynamic programming, randomized, local search, and heuristics) and data‑management techniques (compression, aggregation) to select appropriate approaches for given problem constraints