Floyd-Warshall Algorithm: Practice and Implementation

Finding the shortest path between all points in a network is a fundamental challenge in computer science, routing, and network design. This course offers a clear, structured way to understand and practice the Floyd-Warshall algorithm through detailed written explanations and hands-on exercises. You will transition from understanding basic graph representations to confidently tracing and coding the Floyd-Warshall algorithm from scratch. By working through realistic graph scenarios, you will develop a deep intuition for dynamic programming and path reconstruction. What you'll learn: - Understand the core concepts of graph theory, adjacency matrices, and edge weights. - Implement the Floyd-Warshall algorithm using modern Python type hints and clean coding standards. - Trace the algorithm step-by-step to calculate all-pairs shortest paths manually and programmatically. - Detect negative cycles within directed graphs and understand their impact on routing. - Analyze the time and space complexity of dynamic programming solutions for graph problems. - Apply path reconstruction techniques to retrieve the actual shortest paths, not just their weights. The course begins with foundational graph definitions and matrix representation before moving into the core dynamic programming mechanics. You will then progress through guided written walkthroughs, analyzing how the distance matrix updates at each iteration. This course is designed for computer science students, self-taught programmers, and developers preparing for technical interviews who have a basic familiarity with programming concepts. No prior advanced algorithm experience is required. Start practicing today to master one of the most elegant graph algorithms in computer science.