问题 E: THE TOWER
时间限制: 1 Sec 内存限制: 128 MB Special Judge
提交: 222 解决: 30
[提交] [状态] [命题人:admin]
题目描述
The Tower shows atall tower perched on the top of a rocky mountain. Lightning strikes, setting the building alight， and two people leap frnm the windows, head first and arms outstretched.
It is a scene of chaos and destruction.
There is a cone tower with base center at (0, 0, 0), base radius r and apex (0, 0, h) . At time 0 , a point located at ( x0 ，y0， z0) with velocity （vx,vy,vz）. What time will they collide? Here is the cone tower.
输入
The first line contains testcase number T (T≤1000), For each testcase the first line contains spaceseparated real numbers rand h (1≤r,h≤1000) the base radius and the cone height correspondingly.
For each testcase the second line contains three real numbers x0 ，y0， z0 (0≤|x0|,|y0|,z0≤1000). For each testcase the third line contains three real numbers vx,vy,vx (
). It is guaranteed that at time 0 the point is outside the cone and they will always collide.
输出
For each testcase print Case i: and then print the answer in one line, with absolute or relative error not exceeding 10-6
样例输入
2 1 2 1 1 1 -1.5 -1.5 -0.5 1 1 1 1 1 -1 -1 -1
讯享网
样例输出
讯享网Case 1: 0. Case 2: 0.
（题意：给出一个底部圆圆心为（0，0，0），半径为r，高为h的圆锥，问起始位置为（x0，y0，z0），方向为（vx,vy,vz）的点撞上圆锥的时间。）
（思路：假设相撞的点为（x,y,z）,根据下图的相似三角形，我们可以得出下图中的方程，解方程，加判断即可。）
#include <bits/stdc++.h> using namespace std; double r,h,x,y,z,vx,vy,vz; bool judge(double t) { double xx,yy,zz; xx=x+vx*t; yy=y+vy*t; zz=z+vz*t; if(zz>=0&&zz<=h&&(xx*xx+yy*yy)<=r*r) { return 1; } return 0; } int main(void) { int t; scanf("%d",&t); for(int cas=1;cas<=t;cas++) { scanf("%lf%lf",&r,&h); scanf("%lf%lf%lf%lf%lf%lf",&x,&y,&z,&vx,&vy,&vz); double a,b,c; a=h*h*vx*vx+h*h*vy*vy-r*r*vz*vz; b=2*h*h*vx*x+2*h*h*vy*y+2*r*r*h*vz-2*r*r*z*vz; c=h*h*x*x+h*h*y*y-h*h*r*r-r*r*z*z+2*r*r*h*z; double ht=b*b-4*a*c; double t1=(sqrt(ht)-b)/(2.0*a); double t2=-1.0*(sqrt(ht)+b)/(2.0*a); double t=1e18; if(judge(t1)) t=min(t,t1); if(judge(t2)) t=min(t,t2); printf("Case %d: ",cas); printf("%.10f\n",t); } return 0; }
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