Solving All-Pairs Shortest Paths with Johnson's Algorithm in Python

Finding the shortest path between every single pair of nodes in a network is a fundamental challenge in computer science, crucial for routing, logistics, and network analysis. This text-based course guides you through the foundational concepts of graph theory, building up to the implementation of Johnson's algorithm. You will learn how to combine Dijkstra's and Bellman-Ford algorithms to solve the all-pairs shortest path problem efficiently, even in graphs with negative edge weights, while writing clean, modern Python code. What you'll learn: - Understand the core principles of graph representation, edge weights, and path optimization. - Implement the Bellman-Ford algorithm to detect negative cycles and compute initial node potentials. - Apply Dijkstra's algorithm efficiently using priority queues for single-source shortest paths. - Combine these techniques to execute Johnson's algorithm for all-pairs shortest paths. - Write clean, structured Python code using modern type hints and dataclasses for graph nodes. - Test your algorithm implementations using structured test cases to ensure accuracy. The course starts with essential graph terminology and basic traversal concepts before diving into step-by-step algorithmic logic. You will progress from simple pathfinding to handling complex scenarios with negative weights, analyzing performance trade-offs along the way. This course is designed for aspiring software engineers, computer science students, and Python developers who want to strengthen their algorithmic problem-solving skills. No advanced mathematical background is required. Start reading today to master one of the most elegant routing algorithms in computer science.