UVA 10668 Expanding Rods

Problem A: Expanding Rods

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.

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.

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

Output for sample input

61.329
225.020
0.000


二分法：二分高度H，计算出H对应的L弧长来推出答案 弧长根据补出一个园三角函数推出弧长即可

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <string>
#include <map>
#include <vector>
#include <set>
#include <queue>
#include <stack>
#include <cctype>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MAXN 10000+10
#define INF 1<<30
int MOD;
double l, n, c;

double getL(double h){
    double R = l*l/(8*h)+h/2;
    return asin(l/(2*R))*(2*R);
}

int main (){

    while(scanf("%lf%lf%lf",&l, &n, &c) != EOF){
        if(l < 0 && n < 0 && c < 0)
            break;
        double L = 0, R = l/2;
        double tar = (1+n*c)*l;
        for(int i = 0; i < 100; i++){
            double mid = (L+R)/2;
            if(getL(mid) < tar)
                L = mid;
            else
                R = mid;
        }
        printf("%.3lf\n",L);
    }
    return 0;
}