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Course Schedule — Cycle Detection BFS/DFS
Determine if you can finish all courses given prerequisites. Equivalent to detecting a cycle in a directed graph using BFS (Kahn) or DFS coloring.
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Course Schedule II — Topological Order
Return a valid course order given prerequisites. Kahn's BFS topological sort outputs nodes in processing order — that is the valid schedule.
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Graph Valid Tree — Cycle + Connected Check
Check if n nodes and edges form a valid tree: must be connected and acyclic. Exactly n-1 edges, all connected via BFS/DFS or Union-Find.
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Connected Components — Union-Find / BFS
Count connected components in an undirected graph. Union-Find or BFS both give O(V+E) solution.
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Redundant Connection — Union-Find Cycle Detection
Find the edge that creates a cycle in an undirected graph that started as a tree. Process edges with Union-Find; the first edge whose endpoints share a root is redundant.
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