Construction

Construction problems are a common type of question in competitions.

From a formal point of view, the answers to problems often have a certain regularity, so that when the scale of the problem increases rapidly, there is still a chance to get the answer relatively easily.

This requires that when solving problems, you need to think about the impact of the increase in the size of the problem on the answer, and whether this impact can be generalized. For example, when designing a dynamic programming method, consider the impact of transitions from one state to subsequent states.

A very significant feature of construction problems is the high degree of freedom, which means that there may be many ways to construct a question, but there will be a simpler construction method that satisfies the meaning of the question. It seems that the requirements have been relaxed and the questions have become simpler, but in many cases, it is this high degree of freedom that leads to questions without a clear idea and no way to start.

Another feature of construction problems is their flexible form and variety. There is no universal solution or routine that can solve all construction problems, and it is even difficult to find commonalities in problem-solving ideas.