HBC234840[SCOI2009]游戏,背包问题,动态规划,数论,递推Machining Disc Rotors题解 （edwardisaworkerforalumin）

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Suppose the operation panel for him is a Euclidean plane with the coordinate system. Originally the mould is a disc whose centre coordinates is. i-th mechanical arm is a circle whose centre coordinate is. .In order to obtain the highly developed product, it is guaranteed that the affected areas of any two mechanical arms share no intersection and no one has an affected area containing the whole original mould.Your task is to determine the diameter of the residual mould. Here the diameter of a subset, which may not be convex, over the Euclidean plane is the supremum of distances between every two points in the subset. Here is an illustration of the sample.

Edward is a worker for Aluminum Cyclic Machinery. His work is to control the mechanical arms to cut out some parts of the mould material. Here is a brief introduction to his work. Suppose the operation panel for him is a Euclidean plane with the coordinate system. Originally the mould is a disc whose centre coordinates is (0,0) (0,0) and of radius R R. Edward controls nn different mechanical arms to cut out and erase those all of the mould within their affected areas. The affected area of the i i-th mechanical arm is a circle whose centre coordinate is (x_i,y_i) (x i ​ ,y i ​ ) and of radius r_i r i ​ . In order to obtain the highly developed product, it is guaranteed that the affected areas of any two mechanical arms share no intersection and no one has an affected area containing the whole original mould. Your task is to determine the diameter of the residual mould. Here the diameter of a subset, which may not be convex, over the Euclidean plane is the supremum (i. e. the least upper bound) of distances between every two points in the subset. Here is an illustration of the sample.

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标签： HBC234840[SCOI2009]游戏 背包问题 动态规划 数论 递推Machining Disc Rotors题解