Topological sort

A topological sort orders the vertices of a directed acyclic graph so that every edge goes from earlier to later. Two standard methods: Kahn's algorithm (repeatedly remove a zero-in-degree node) and DFS post-order (reverse the finish order). If the graph has a cycle, no valid ordering exists.

Reach for it on dependency ordering — build systems, course prerequisites, task pipelines — and as a cycle-detection test on directed graphs (Kahn's leaves nodes unprocessed exactly when there's a cycle).