Graphs

Graph problems are about modeling relationships first, then choosing the traversal or relaxation rule. Say what the nodes are, what the edges mean, whether the graph is directed/weighted, and what visited state prevents repeated work.

Mental Model

• BFS: shortest path by number of edges or level-order expansion.
• DFS: connected components, reachability, cycle checks, and backtracking over paths.
• Topological sort: prerequisites and directed acyclic dependency order.
• Union-Find: dynamic connectivity and component merging.
• Dijkstra / MST: weighted routing or minimum connection cost.

Diagram

Problem List

Start with 200. Number of Islands, 133. Clone Graph, 207. Course Schedule, 261. Graph Valid Tree, and 743. Network Delay Time.