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Key breakthrough points in some OI problems

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This post is translated from Chinese into English through AI.View Original
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The document discusses key insights for solving specific competitive programming problems (P8817, P8818, P8819). 1. For P8817, it mentions that a graph with edge weights of 1 can be processed in O(n) using BFS. It also highlights the importance of determining certain points (a, d) early on. 2. P8818 emphasizes the need for classification in problem-solving. 3. P8819 suggests that conditions for counterattacks can be transformed into a scenario where all points have an out-degree of 1. It notes that maintaining out-degrees can be challenging, so it can be converted to in-degrees. However, in-degrees only meet necessary conditions, not sufficient ones, implying the need for randomness in understanding solutions.

This is more like a record than an explanation#

P8817#

  1. For a graph with edge weights of 1, BFS can achieve O(n)

  2. a and d can be easily determined, so determine them first

P8818#

  1. Classification discussion

P8819#

  1. The conditions for counterattacks can be transformed into all points having an out-degree of 1

  2. Out-degree is difficult to maintain, transform it into in-degree

  3. In-degree can only satisfy necessity, but cannot satisfy sufficiency—randomness (understand through the solution)

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