acm_Toxophily

题目：

Problem Description

The recreation center of WHU ACM Team has indoor billiards, Ping Pang, chess and bridge, toxophily, deluxe ballrooms KTV rooms, fishing, climbing, and so on.<br>We all like toxophily.<br><br>Bob is hooked on toxophily recently. Assume that Bob is at point (0,0) and he wants to shoot the fruits on a nearby tree. He can adjust the angle to fix the trajectory. Unfortunately, he always fails at that. Can you help him?<br><br>Now given the object's coordinates, please calculate the angle between the arrow and x-axis at Bob's point. Assume that g=9.8N/m. <br>

 

Input

The input consists of several test cases. The first line of input consists of an integer T, indicating the number of test cases. Each test case is on a separated line, and it consists three floating point numbers: x, y, v. x and y indicate the coordinate of the fruit. v is the arrow's exit speed.<br>Technical Specification<br><br>1. T ≤ 100.<br>2. 0 ≤ x, y, v ≤ 10000. <br>

 

Output

For each test case, output the smallest answer rounded to six fractional digits on a separated line.<br>Output "-1", if there's no possible answer.<br><br>Please use radian as unit. <br>

 

Sample Input

  
  

   
   3<br>0.222018 23.901887 121.909183<br>39.096669 110.210922 20.270030<br>138.355025 2028.716904 25.079551<br>
  
  

 

Sample Output

  
  

   
   1.561582<br>-1<br>-1<br>
  
  
  
  


  
  
  
  


  
  
  
  


  
  
  
  

   
   题意：给你一个坐标，和初速度，从（0，0）开始，求出射中时的最小角度。。
  
  

想法：先求出最大值，然后二分。。

代码：

#include <iostream>
#include <iomanip>
#include<algorithm>  
#include<cmath>
using namespace std;
const double g=9.8;
const double pi=acos(-1);
const double eps=1e-10;  
double X,Y,v,sita;  
double cal(double x)  
{  
    double t,a;  
    t=X/(v*cos(x));  
    a=v*sin(x)*t-0.5*g*t*t;
    return a;
}  
double triplediv()  
{   
    double mid1,mid2,l,r,h1,h2;  
    l=0;
    r=0.5*pi;  
    while((r-l)>eps)  
    {  
        mid1=(2*l+r)/3;  
        mid2=(l+2*r)/3;  
        h1=cal(mid1);  
        h2=cal(mid2);  
        if(h1>h2)  
          r=mid2;  
        else  
          l=mid1;  
    }  
    sita=l;  
    return cal(l);  
}  
void doublediv(double maxy)  
{  
    int i;  
    double l,r,mid,h;  
    l=0;
    r=sita;  
    while((r-l)>eps)  
    {  
        mid=(l+r)/2;  
        h=cal(mid);  
        if(h>Y)  
          r=mid;  
        else  
          l=mid;  
    }  
    cout<<setprecision(6)<<fixed<<l<<endl;  
}  
int main()  
{  
    int t;  
    double maxy;  
    cin>>t;  
    while(t--)  
    {  
        cin>>X>>Y>>v;
        maxy=triplediv();  
        if(maxy<Y)  
         cout<<"-1"<<endl;  
        else  
         doublediv(maxy);  
    }  
    return 0;  
}

感想：没想到还需要用到物理知识。。挺新奇。。