Graph Algorithms for Competitive Programming

Succeeding in competitive programming requires more than just knowing how to code; you must understand how to model complex relationships using graph structures. This text-based course guides you from foundational graph concepts to sophisticated traversal and optimization algorithms. You will learn to recognize hidden graph problems and implement highly efficient solutions that pass strict execution time limits. What you will learn: Understand core graph terminology, representation methods like adjacency lists, and fundamental properties; Implement breadth-first search and depth-first search to traverse networks and detect cycles; Apply shortest-path algorithms including Dijkstra, Bellman-Ford, and Floyd-Warshall to optimize routing; Construct minimum spanning trees using Kruskal's and Prim's algorithms; Solve advanced connectivity problems using strongly connected components and topological sorting; Analyze time and space complexity to ensure your algorithms meet competitive programming constraints. This course starts with basic definitions and representations before moving systematically through traversal, shortest paths, and advanced optimization techniques. It is designed for beginner to intermediate programmers who want to build a strong algorithmic foundation for competitive coding. No advanced mathematical background is required to begin.