All-Pairs Shortest Paths: Implementing Johnson's Algorithm in C++

Finding the shortest paths between all pairs 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 step-by-step through the mechanics of graph algorithms, showing you how to combine Dijkstra's and Bellman-Ford's methods into the highly efficient Johnson's algorithm using modern C++. What you'll learn: - Understand core graph theory concepts, including directed graphs, edge weights, and path optimization. - Analyze the mechanics of Dijkstra's and Bellman-Ford algorithms and how they handle negative edge weights. - Implement Johnson's algorithm from scratch using clean, modern C++ patterns. - Detect negative cycles in a graph to prevent infinite loops in pathfinding. - Apply reweighting techniques to transform graphs with negative edges into non-negative equivalents. - Optimize your code for performance using efficient data structures like priority queues. You will start with foundational graph definitions and algorithmic complexity before progressing to step-by-step code implementations and debugging strategies. This course is designed for beginner to intermediate programmers and computer science students who want a clear, conceptual understanding of advanced graph algorithms without complex math prerequisites. Start reading to master one of the most elegant graph algorithms in computer science.