- 描述
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.- 输入
- 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.
- 输出
- For each line of input, output one line with the displacement of the center of the rod in millimeters with 3 digits of precision.
- 样例输入
-
1000 100 0.0001
15000 10 0.00006
10 0 0.001
-1 -1 -1
- 样例输出
-
61.329
225.020
0.000
- 来源
- Waterloo local 2004.06.12
- 这个题目主要的是数学公式。公式搞明白了，直接二分h就可以解决
-
#include <bits/stdc++.h>
#include <algorithm>
using namespace std;
double l,n,c;
int fun(double h) {//z这个计算公式有点复杂，由胡长公式、勾股定理、三角函数推理出来的。
double r=(4*h*h+l*l)/(8*h);//先求出半径
double s=2*r*asin(l/(2*r))-(1+n*c)*l;//带入半径比较弧长
if(s>0)return 1;
else return -1;
}
int main() {
while(cin>>l>>n>>c&&l!=-1) {
double left=0.0,right=(l*1.0)/2;
while(right-left>0.0001) {
double mid=left+(right-left)/2;
if(fun(mid)>0) {
right=mid;
} else left=mid;
}
printf("%.3lf\n",left);
}
return 0;
}
