DFS Components and Reachability
Follow adjacency as deeply as needed to decide reachability, enumerate components, or aggregate each component. The goal is to exhaust a region, not to minimize travel distance.
Free · First family
Traversal and connectivity
The first family and its related problems are fully open.
Patterns
BFS Connectivity Traversal
Use a FIFO queue to exhaust reachable regions without recursion risk, while leaving room to record levels, parents, or component labels.
Grid Flood Fill
Treat a matrix as an implicit graph and consume the maximal region connected to a seed, supporting recoloring, area, boundary-touch, and enclosure analysis.
Topological Sort / Indegree Elimination
Turn prerequisites into an executable order by repeatedly removing tasks with no unfinished predecessors; detect directed cycles and support execution layers or DAG DP.