Time Limit: 1000MS | Memory Limit: 30000K | |
Total Submissions: 15285 | Accepted: 4071 |
Description
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
Output
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
推出来公式算不出来,算不出来就枚举答案,由于题目说的扩张不会超过L的一半,所以在 [ 0 , L/2 ] 这个区间找答案
这是推出两个公式
r=(L*L+4*h*h) / (8*h)
S= 2*r*arcsin(L/2/r)
二分出的答案,带入上面两个公式,算出S'与题目中L'=(1+n*C)*L比较
#include <iostream>
#include <string.h>
#include <algorithm>
#include <math.h>
#include <stdio.h>
using namespace std;
#define esp 1e-6
double s,n,c,mid;
void erfen(double l,double r)
{
if(r-l>=esp)
{
mid=l+(r-l)/2;
double r=(s*s+4*mid*mid)/8/mid;
double ss=2*asin(s/2/r)*r;
if(ss>(1+n*c)*s)
{
erfen(l,mid);
}
else
{
erfen(mid,r);
}
}
}
int main()
{
double l,r;
while(~scanf("%lf%lf%lf",&s,&n,&c))
{
if(s==-1 && n==-1 && c==-1)
break;
l=0.00;
r=s/2;
erfen(l,r);
printf("%.3f\n",mid);
}
return 0;
}