poj 1905 Expanding Rods(木杆的膨脹)【數學計算+二分枚舉】

標籤：

                                                                                                          Expanding Rods

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 13516		Accepted: 3484

Description

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 0.000115000 10 0.0000610 0 0.001-1 -1 -1

Sample Output

61.329225.0200.000

題目：可以這樣理解，給你一根木杆，夾在某物體之間。現在木杆會受熱膨脹，膨脹增長，在兩端物體的擠壓下就會變彎曲，如所示。
從一根直的木杆變到彎曲的木杆，兩種狀態下，木杆中間位置的高度差是多少？

解法全在上面的圖片中！

代碼：

#include <stdio.h>#include <string.h>#include <stdlib.h>#include <ctype.h>#include <math.h>#include <iostream>#include <string>#include <stack>#include <algorithm>#define eps 1e-5using namespace std;int main(){    // L‘=(1+n*C)*L    double L, n, c;    while(scanf("%lf %lf %lf", &L, &n, &c)!=EOF)    {        if(L<0 && n<0 && c<0) break;        double low=0.0;        double high=0.5*L;        double mid;        double s=(1.0+n*c)*L;        double R;        while(high-low>eps){            mid=(low+high)/2.0;            R = (4*mid*mid+L*L)/(8*mid);//化簡成一次除法 減小精度誤差            if(2*R*asin(L/(2*R)) < s)                low=mid;            else                high=mid;        }        printf("%.3lf\n",mid);    }    return 0;}

 

poj 1905 Expanding Rods(木杆的膨脹)【數學計算+二分枚舉】