Graph Algorithms

Master graph representations, traversals (BFS/DFS), shortest paths, minimum spanning trees, topological sort, and connected components. Graphs are everywhere in software — understanding them transforms how you see systems. Bundler is a graph algorithm. Your Gemfile defines a dependency graph, and bundle install performs topological sort with constraint satisfaction to find a valid resolution. Sidekiq job dependencies form DAGs (directed acyclic graphs). Database foreign key relationships form a graph — and when you run db:migrate, Rails topologically sorts your migrations. If you have ever used acts_as_tree or ancestry gem, you are working with tree structures (special graphs). Understanding graph algorithms helps you design better data models and recognize when a problem is fundamentally a graph problem disguised as a Rails problem.