Toxophily

Toxophily

Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 500 Accepted Submission(s): 317

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.
We all like toxophily.

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?

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.

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.
Technical Specification

1. T ≤ 100.
2. 0 ≤ x, y, v ≤ 10000.

Output

For each test case, output the smallest answer rounded to six fractional digits on a separated line.
Output "-1", if there's no possible answer.

Please use radian as unit.

Sample Input

3
0.222018 23.901887 121.909183
39.096669 110.210922 20.270030
138.355025 2028.716904 25.079551

Sample Output

1.561582
-1
-1

题目大意：给出苹果的坐标x，y，及飞镖的速度v

                   求站在（0，0）时要射中苹果飞镖与x轴的夹角最小是多少

题解：先用三分法分出一个角使得飞镖到达y方向的最大值，与苹果的Y位置比较，再用二分法求出最小的角度

       此答案来自：http://blog.youkuaiyun.com/xieshimao/article/details/6662144

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#define PI acos(-1.0)
#define G 9.8
#define eps 1e-12
using namespace std;
double X,Y,v,sita;
double cal(double x)
{
    double t;
    t=X/(v*cos(x));
    return v*sin(x)*t-0.5*G*t*t;
}
double triplediv()
{
    int i;
    double mid1,mid2,left,right,h1,h2;
    left=0,right=0.5*PI;
    while(right-left>eps)
    {
    mid1=(2*left+right)/3;
    mid2=(left+2*right)/3;
    h1=cal(mid1);
    h2=cal(mid2);
    if(h1>h2)
     right=mid2;
    else
     left=mid1;
    }
    sita=left;
    return cal(left);
}
void doublediv(double maxy)
{
    int i;
    double left,right,mid,h;
    left=0,right=sita;
    while(right-left>eps)
    {
        mid=(left+right)/2;
        h=cal(mid);
        if(h>Y)
          right=mid;
        else
          left=mid;
    }
    printf("%.6lf\n",left);
}
int main()
{
    int t;
    double maxy;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lf%lf%lf",&X,&Y,&v);
        maxy=triplediv();
        if(maxy<Y)
         printf("-1\n");
        else
         doublediv(maxy);

    }
    return 0;
}