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In-Degrees and Kahn's Peel
Dependency edges point from prerequisite to dependent — count unmet prerequisites as in-degree, peel the zeros, and a valid order falls out.
Complete codeMultiple choice - 2
Minimum Vertices to Reach All Nodes
In a DAG, the smallest starting set is exactly the in-degree-0 nodes — nothing else can reach them, and everything sits downstream of them.
Complete codeDebugMultiple choiceTrace - 3
Find All Possible Recipes
Kahn's peel with a twist: supplies seed the ready queue, recipe-on-recipe ingredients form the edges, and a recipe cooks only when ALL its ingredients resolve.
Complete codeDebugMultiple choiceTrace - 4
Course Schedule IV
Is course u a prerequisite of course v — even through a chain? Precompute FULL reachability by propagating ancestor sets along topological order, then answer every query with one lookup.
Complete codeMultiple choiceTrace - 5
All Ancestors of a Node in a DAG
Who are v's ancestors? Flip the question: search FORWARD from each source u and stamp u on everything it reaches. Iterate sources 0..n-1 and every list comes out sorted for free.
Complete codeMultiple choiceTrace - 6
Find Eventual Safe States
Safe means EVERY path ends at a terminal — one path into a cycle disqualifies a node. Reverse the graph and run Kahn's peel from the terminals; whatever never gets peeled is on or feeds a cycle.
Complete codeMultiple choiceTrace - 7
Topological Sort CheckpointCheckpoint
No new concepts — carry the peel to unseen ground: package installs, alien alphabets, parallel semesters, and the question of whether an order is the ONLY order.
Code orderMultiple choiceTrace - 8
Topological Sort ReviewReview
Mixed recap of the island: in-degree bookkeeping, the ready-queue rule, what an incomplete peel proves, when to reverse the graph, why topo orders aren't unique, and the O(V+E) price tag.
Complete codeMultiple choice - 9
Boss: Course ScheduleBoss
The island's final test: can every course be finished? Read [a, b] as b BEFORE a — the arrow flows from prerequisite to dependent — then peel with Kahn's. Courses left unpeeled are the cycle's confession.
Complete codeDebugCode orderMultiple choiceTrace
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