Graph Algorithms: Solving Shortest Paths with Bellman-Ford

Navigating complex networks requires algorithms that can handle real-world constraints, including negative path weights. While some algorithms fail when negative values are introduced, the Bellman-Ford algorithm provides a robust and reliable solution. This text-based course guides you through the foundational concepts of graph theory, the mechanics of edge relaxation, and the step-by-step implementation of the algorithm. You will learn how to handle negative edge weights, identify negative cycles, and apply these concepts to modern network routing and optimization problems. What you'll learn: * Learn the foundational concepts of graph theory, including vertices, edges, and path weights. * Understand the core concept of edge relaxation and how it iteratively updates path estimates. * Implement the Bellman-Ford algorithm using clean, modern Python code with type hints. * Detect negative cycles in a graph to prevent infinite loops in pathfinding. * Compare Bellman-Ford with Dijkstra's algorithm to choose the right tool for different network scenarios. * Analyze the time and space complexity of the algorithm to write efficient code. You will start with essential terminology and basic graph definitions before stepping through the manual mechanics of the algorithm. From there, you will progress to writing structured code and analyzing practical routing scenarios. This course is designed for beginner programmers, computer science students, and aspiring software engineers who want to build a strong foundation in graph algorithms. No prior algorithm experience is required. Start reading today to master one of the fundamental algorithms of network routing.