Finding Longest Paths in Directed Acyclic Graphs

Graph algorithms can feel intimidating, but Directed Acyclic Graphs (DAGs) offer unique mathematical properties that make complex pathfinding problems surprisingly elegant to solve. Understanding how to find the longest path in a DAG is a fundamental computer science skill with massive real-world applications in scheduling, critical path analysis, and project management. This text-only course guides you from the absolute basics of graph theory to writing clean, modern code that finds the longest path in any DAG. You will transition from visualizing nodes and edges to confidently implementing topological sorts and modifying shortest-path algorithms to solve optimization problems. In this course, you will: Understand the fundamental properties of Directed Acyclic Graphs (DAGs) and weighted digraphs; Learn how topological sorting forms the foundation for linear-time DAG algorithms; Apply shortest-path algorithms by modifying edge weights to find the longest path; Build step-by-step algorithms using modern Python type hints and clean data structures; Analyze real-world scenarios such as critical path method (CPM) scheduling and task dependencies; Practice your skills with written exercises and code walkthroughs that reinforce core algorithmic logic. You will start with core definitions and structural rules of graphs before moving into topological ordering. From there, you will explore the relationship between shortest and longest paths, culminating in practical algorithmic implementations. This course is designed for beginner programmers, computer science students, and self-taught developers who want to strengthen their algorithmic thinking. No advanced mathematical background is required, though a basic understanding of programming logic is helpful. Start reading today to demystify graph optimization and add essential pathfinding algorithms to your developer toolkit.