Implementing the Bellman-Ford Algorithm for Shortest Paths

Graph algorithms are fundamental to network routing, map navigation, and financial modeling, but standard algorithms fail when negative edge weights are introduced. Understanding how to handle these complex scenarios is a crucial skill for any software engineer or computer science student. This text-based course guides you through the foundational theory of graph representations and the mechanics of the Bellman-Ford algorithm. You will transition from understanding basic node-and-edge structures to writing robust, production-ready algorithm implementations that can detect negative cycles. What you'll learn: - Understand foundational graph representation concepts, including adjacency lists and edge lists. - Apply the concept of edge relaxation to systematically calculate shortest paths. - Implement the Bellman-Ford algorithm using modern Python with type hints and clean structure. - Detect negative weight cycles to prevent infinite loops in your pathfinding logic. - Analyze the time and space complexity of the algorithm to evaluate its performance. - Practice writing unit tests with pytest to verify the correctness of your pathfinding code. We begin with key terminology and graph representations, step through the logic of distance relaxation, and finish by writing and testing a complete, modern Python implementation. This course is designed for beginner to intermediate programmers and computer science students; basic familiarity with Python is helpful but no advanced graph theory knowledge is required. Start reading today to master this essential graph algorithm and write cleaner, more efficient code.