Mathematics for Data Science 1 - W11_L9: Minimum cost spanning trees | prim’s algorithm

Welcome to Week 11 Lecture 9 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 introduces Prim’s Algorithm, a classic greedy approach for finding the Minimum Cost Spanning Tree (MCST) in weighted, connected graphs. The algorithm grows a spanning tree step by step, at each stage adding the smallest-weight edge that connects the current tree to a new vertex outside it. We work through a detailed example to illustrate the method in action and provide a formal proof of correctness using the minimum separator lemma. The lecture also examines edge cases, such as graphs with equal edge weights, and explains how the algorithm guarantees an optimal solution. 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 #PrimsAlgorithm #MinimumCostSpanningTree #MCST #WeightedGraph #GraphTheory #SpanningTree #GreedyAlgorithm #AlgorithmExplanation #DataStructures #MinimumSeparatorLemma #GraphAlgorithms #ConnectedGraph #TreeAlgorithms #ShortestPath #Optimization #ComputerScience