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4.4Strongly connected components

Before you start

It helps to have read 3.1 Graph search: BFS and DFS and 3.4 Dynamic programming I. Overall level: Advanced.

Practice: Strongly connected components

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About these problems

Apply, Connect, Reason and Stretch describe difficulty within this topic, not an official contest rating. Open any problem in any order; reading the chapter first is optional.

  1. 1Strong group countCount strongly connected components of a directed graph. Two vertices share a component iff each is reachable from the other.ApplyNot started
  2. 2Mutual reachability deskFor each pair a, b, decide whether there is a directed route from a to b and also a directed route from b to a. Length-zero routes are allowed.ConnectNot started
  3. 3Broadcast startersChoose the smallest number of starting vertices so that every vertex is reachable from at least one chosen vertex in a directed graph. Print that minimum number.ReasonNot started
  4. 4Collect once on a walkEach vertex has a nonnegative reward. A directed walk may start and end anywhere and revisit vertices or edges. Each vertex reward is collected only on its first visit. Find the largest collectible reward.StretchNot started

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