Ford's Algorithm for Shortest Paths in Graphs

Graph algorithms form the backbone of modern routing, network optimization, and pathfinding systems. Understanding how to find the shortest path from a single source is a foundational skill for any software engineer or computer science student. This text-only course guides you through Ford's classic algorithm for single-source shortest paths, breaking down complex mathematical concepts into clear, readable explanations and structured code walkthroughs. In this course, you will learn through written explanations, conceptual breakdowns, and step-by-step pseudocode analysis. We will start with the absolute basics of graph representation before diving deep into the mechanics of relaxation, culminating in a complete implementation using modern Python type hints and clean coding practices. What you'll learn: - Understand foundational graph theory concepts, including vertices, directed edges, and path weights. - Master the core mechanics of edge relaxation and distance initialization. - Trace Ford's algorithm step-by-step to see how shortest-path estimates converge. - Detect negative cycles in graphs and understand how they impact pathfinding solutions. - Analyze the time and space complexity of the algorithm to write efficient code. - Implement the algorithm using modern Python structures and clean programming conventions. This course is designed for beginners to graph algorithms, computer science students, and developers looking to strengthen their algorithmic problem-solving skills. No advanced mathematics or prior graph theory knowledge is required. Start reading today to master one of the fundamental building blocks of graph theory.