Pattern 15

Topological Sort

Order nodes in a DAG such that every directed edge goes from earlier to later. Use BFS (Kahn's algorithm) with in-degree tracking or DFS with a finish-time stack.

Time

O(V + E)

Space

O(V + E)

Recognize it when

Task scheduling with prerequisites
Course prerequisites / build order
Detect cycles in directed graph

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Questions — ordered by difficulty

#207Medium

Course Schedule

Determine if you can finish all courses given their prerequisites (detect cycle in directed graph).

graphtopological-sortbfs

#210Medium

Course Schedule II

Return the order in which to take courses to finish all of them.

graphtopological-sortbfs

#310Medium

Minimum Height Trees

Find all roots that minimize the height of the resulting tree.

graphtopological-sorttree

#269Hard

Alien Dictionary

Given a sorted dictionary of an alien language, determine the order of characters.

graphtopological-sortbfs