Mathematics for Data Science 1 - W10_L5: Depth-first search (DFS)

Welcome to Week 10 Lecture 5 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture explores Depth-First Search (DFS), a fundamental graph traversal algorithm. Unlike Breadth-First Search (BFS), which explores level by level, DFS dives deep along a single path until it can go no further, then backtracks. We explain how DFS uses a stack to keep track of suspended vertices and introduce DFS numbering, which tracks both visit and finish times. These concepts allow us to uncover important structural properties of graphs, including articulation points (cut vertices) and bridges, which play a critical role in graph connectivity. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #DepthFirstSearch #DFS #GraphTraversal #Algorithms #DataStructures #Stack #GraphTheory #ComputerScience #ArticulationPoints #CutVertices #Bridges #GraphAlgorithms #DFSNumbering