#graphs
7 articles
Graphs: Everything Is Connected
Graphs model maps, social networks, and dependencies. Learn how nodes and edges work, how to represent them, and what BFS and DFS unlock.
Union-Find (Disjoint Set Union)
Union-Find (disjoint set union) answers 'are these two nodes connected?' in near-constant time. Master path compression, union by rank, and Kruskal's MST.
Graphs
Learn the graph data structure: adjacency lists vs matrices, BFS and DFS traversal, and the grid-as-graph reframe that cracks whole problem categories.
Topological Sort
Order the nodes of a DAG so every edge points forward — the algorithm that drives build systems, package managers, course schedulers, and anything else that lives and dies by dependency ordering.
Shortest Paths (Dijkstra, Bellman-Ford, BFS)
Pick the right shortest-path algorithm: BFS for unweighted graphs, Dijkstra for non-negative weights, Bellman-Ford for negative edges — with every gotcha.
DFS Patterns
Depth-first search is the backbone of cycle detection, flood fill, path enumeration, and clone graph — master the visited-set template, the 3-color trick, and when to reach for DFS over BFS.
BFS Patterns
Queue-driven level-by-level traversal and why breadth-first search is the only guaranteed way to find shortest paths in unweighted graphs. Templates, traps, and four worked problems.