POJ 题目1905 Expanding Rods(二分,数学几何)
2015-05-13 18:50
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Expanding Rods
Description
![](http://poj.org/images/1905_1.jpg)
When a thin rod of length L is heated n degrees, it expands to a new length L'=(1+n*C)*L, where C is the coefficient of heat expansion.
When a thin rod is mounted on two solid walls and then heated, it expands and takes the shape of a circular segment, the original rod being the chord of the segment.
Your task is to compute the distance by which the center of the rod is displaced.
Input
The input contains multiple lines. Each line of input contains three non-negative numbers: the initial lenth of the rod in millimeters, the temperature change in degrees and the coefficient of heat expansion of the material. Input data guarantee that no rod
expands by more than one half of its original length. The last line of input contains three negative numbers and it should not be processed.
Output
For each line of input, output one line with the displacement of the center of the rod in millimeters with 3 digits of precision.
Sample Input
Sample Output
Source
Waterloo local 2004.06.12 http://blog.csdn.net/lyy289065406/article/details/6648562 ac代码
Time Limit: 1000MS | Memory Limit: 30000K | |
Total Submissions: 12827 | Accepted: 3311 |
![](http://poj.org/images/1905_1.jpg)
When a thin rod of length L is heated n degrees, it expands to a new length L'=(1+n*C)*L, where C is the coefficient of heat expansion.
When a thin rod is mounted on two solid walls and then heated, it expands and takes the shape of a circular segment, the original rod being the chord of the segment.
Your task is to compute the distance by which the center of the rod is displaced.
Input
The input contains multiple lines. Each line of input contains three non-negative numbers: the initial lenth of the rod in millimeters, the temperature change in degrees and the coefficient of heat expansion of the material. Input data guarantee that no rod
expands by more than one half of its original length. The last line of input contains three negative numbers and it should not be processed.
Output
For each line of input, output one line with the displacement of the center of the rod in millimeters with 3 digits of precision.
Sample Input
1000 100 0.0001 15000 10 0.00006 10 0 0.001 -1 -1 -1
Sample Output
61.329 225.020 0.000
Source
Waterloo local 2004.06.12 http://blog.csdn.net/lyy289065406/article/details/6648562 ac代码
#include<stdio.h> #include<math.h> const double eps=1e-5; int main() { double l,n,c,s; while(scanf("%lf%lf%lf",&l,&n,&c)!=EOF) { if(l<0&&n<0&&c<0) break; double low=0,high=0.5*l,mid; s=(1+n*c)*l; while(high-low>eps) { mid=(high+low)/2; double r=(4*mid*mid+l*l)/(8*mid); if(2*r*asin(l/(2*r))<s) low=mid; else high=mid; } printf("%.3lf\n",mid); } }
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