HDU1065 I Think I Need a Houseboat 【数学递推】

I Think I Need a Houseboat

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 9530    Accepted Submission(s): 2733

Problem 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.”



Notes:



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.

 

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. 

题意：给定一个从原点開始且中心在原点的半圆，每天以50mile^2的速度向外扩充。给你一个点。求第几天扩充的半圆能覆盖到它。

题解：这题最先開始想到的思路是模拟，可是考虑到模拟太耗时间又认为这题应该能找到规律，然后就拿着笔在演草纸上画了出来，规律是pi/2*(r[n]^2 - r[n-1]^2)=100; r[1]^2 = 100 / pi; r[n]表示第n天半圆覆盖的半径，这明显是一个等差数列，得到r[n]^2 = 100*n/pi;然后就该直接用公式了~

#include <stdio.h>

int main()
{
    int t;
    double x, y;
    scanf("%d", &t);
    for(int i = 1; i <= t; ++i){
        scanf("%lf%lf", &x, &y);
        printf("Property %d: This property will begin eroding in year %d.\n",
            i, int((x*x + y*y) * 3.1415926 / 100 + 1));
    }
    printf("END OF OUTPUT.\n");
    return 0;
}