I Think I Need a Houseboat

Posted 2021-01-29 jingwenxing

Problem(问题)：

• Fred Mapper is considering purchasing some land in Louisiana to build his house on. In the process of investigating the land, he learned that the state of Louisiana is actually shrinking by 50 square miles each year, due to erosion caused by the Mississippi River. Since Fred is hoping to live in this house the rest of his life, he needs to know if his land is going to be lost to erosion.

• After doing more research, Fred has learned that the land that is being lost forms a semicircle. This semicircle is part of a circle centered at (0,0), with the line that bisects the circle being the X axis. Locations below the X axis are in the water. The semicircle has an area of 0 at the beginning of year 1. (Semicircle illustrated in the Figure.)

• Fred Mapper正考虑购买路易斯安那州的一些土地来建造他的房子。 在调查土地的过程中，他了解到，由于密西西比河造成的侵蚀，路易斯安那州实际上每年缩小50平方英里。 由于弗雷德希望在他的余生中住在这所房子里，他需要知道他的土地是否会因腐蚀而失去。

• 经过更多的研究，弗雷德得知失去的土地形成了一个半圆形。 该半圆是以（0,0）为中心的圆的一部分，其中将圆将二等分为X轴。 X轴下方的位置在水中。 半圆在第1年开始时的面积为0.（图中所示的半圆）

Input(输入格式)：

• The first line of input will be a positive integer indicating how many data sets will be included (N). Each of the next N lines will contain the X and Y Cartesian coordinates of the land Fred is considering. These will be floating point numbers measured in miles. The Y coordinate will be non-negative. (0,0) will not be given.

• 第一行输入将是一个正整数，表示将包含多少数据集（N）。 接下来的N行中的每一行都将包含Fred正在考虑的陆地的X和Y笛卡尔坐标。 这些是以英里为单位测量的浮点数。 Y坐标将是非负的。 （0,0）将不会给出。

Output(输出格式)：

• For each data set, a single line of output should appear. This line should take the form of: “Property N: This property will begin eroding in year Z.” Where N is the data set (counting from 1), and Z is the first year (start from 1) this property will be within the semicircle AT THE END OF YEAR Z. Z must be an integer. After the last data set, this should print out “END OF OUTPUT.”

• 对于每个数据集，应出现一行输出。 此行应采用以下形式：“属性N：此属性将在Z年开始侵蚀。”其中N是数据集（从1开始计算），Z是第一年（从1开始），此属性将在 年末的半圆Z. Z必须是整数。 在最后一个数据集之后，这应该打印出“END OF OUTPUT”。

Sample Input(输入样例)：

2
1.0 1.0
25.0 0.0

Sample Output(输出样例)：

Property 1: This property will begin eroding in year 1.
Property 2: This property will begin eroding in year 20.
END OF OUTPUT.

Hint(提示)：

1、No property will appear exactly on the semicircle boundary: it will either be inside or outside.
2、This problem will be judged automatically. Your answer must match exactly, including the capitalization, punctuation, and white-space. This includes the periods at the ends of the lines.
3、All locations are given in miles.

1，在半圆边界上不会出现任何属性：它将在内部或外部。
2，将自动判断此问题。 您的答案必须完全匹配，包括大小写，标点符号和空格。 这包括行尾的句点。
3，所有地点均以英里为单位。