UVALive2363 POJ1005 HDU1065 ZOJ1049 I Think I Need a Houseboat【数学计算】

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原文链接：http://www.cnblogs.com/tigerisland/p/7563691.html

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#c/c++

本文介绍了一个用于预测土地侵蚀年份的算法。该算法基于输入的土地坐标计算出土地开始遭受侵蚀的具体年份。通过使用半圆面积变化来模拟土地侵蚀过程，并结合特定的计算公式，可以准确预测出不同土地位置开始侵蚀的时间。

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I Think I Need a Houseboat

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 104215		Accepted: 45370

Description

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.)

Input

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.

Output

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.”

Sample Input

2
1.0 1.0
25.0 0.0

Sample Output

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

Hint

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.

Source

Mid-Atlantic 2001

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问题链接：UVALive2363 POJ1005 HDU1065 ZOJ1049 I Think I Need a Houseboat。

问题简述：（略）

问题分析：

计算半径的公式为：r^2 = x^2 + y^2

计算半圆面积公式：area = πr^2/2

侵袭年数：year = (int)ceil(area / 50.0)

程序说明：

如果PI=3.1415926，那么UVALive2363会出现WA，精度问题；

如果PI=3.1415926535，那么HDU1065中会出现WA。

简直不可理喻啊！！！

AC通过的C++语言程序如下：

/* UVALive2363 POJ1005 HDU1065 ZOJ1049 I Think I Need a Houseboat */

#include <iostream>
#include <stdio.h>

using namespace std;

const double PI = 3.1415926535;

int main()
{
    int t;
    double x, y;

    cin >> t;
    for(int i=1; i<=t; i++) {
        cin >> x >> y;
        printf("Property %d: This property will begin eroding in year %d.\n", i, int((x*x + y*y) * PI / 100 + 1));
    }
    printf("END OF OUTPUT.\n");

    return 0;
}

转载于:https://www.cnblogs.com/tigerisland/p/7563691.html