W4_L8: Longest path in DAGs

Welcome to Week 4 Lecture 8 of the course "Programming, Data Structures and Algorithms using Python" by Prof. Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pa... Video Overview This lecture delves into the Longest Path Problem in Directed Acyclic Graphs (DAGs) and its practical applications in scheduling and dependency management. We explore how the longest path is closely related to Topological Sorting, allowing us to determine the minimum time or critical path required to complete a sequence of dependent tasks. The lecture demonstrates how to efficiently compute the longest path in linear time O(m + n) using a modified topological sort algorithm. Finally, we discuss why this problem becomes significantly more complex in graphs that contain cycles, emphasizing the importance of acyclicity in efficient computation. 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/stud... #DAG #DirectedAcyclicGraph #LongestPath #TopologicalSort #GraphAlgorithms #Scheduling #Prerequisites #Algorithm #DataStructures #ComputerScience #GraphTheory #LinearTime #MinimumTime #Diameter #GraphDiameter #CriticalPath #TaskScheduling #IITMadras #PythonProgramming #DataStructuresAndAlgorithms