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This lecture covers the concept of finding the shortest path in directed graphs, focusing on the algorithmic approach to solve the problem efficiently. The instructor explains the process step by step, from defining the problem to implementing the solution using directed edges. Various scenarios and optimizations are discussed, such as handling negative costs and determining the maximum cost path. The lecture also delves into NP-complete problems related to finding the shortest path. Additionally, the lecture explores the concept of minimum cost walk and its application in solving optimization problems in directed graphs.