hdu 5017 Ellipsoid

Ellipsoid

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1028    Accepted Submission(s): 364
Special Judge

Problem Description

Given a 3-dimension ellipsoid(椭球面)

your task is to find the minimal distance between the original point (0,0,0) and points on the ellipsoid. The distance between two points (x₁,y₁,z₁) and (x₂,y₂,z₂) is defined as 

 

Input

There are multiple test cases. Please process till EOF.

For each testcase, one line contains 6 real number a,b,c(0 < a,b,c,< 1),d,e,f(0 ≤ d,e,f < 1), as described above. It is guaranteed that the input data forms a ellipsoid. All numbers are fit in double.

 

Output

For each test contains one line. Describes the minimal distance. Answer will be considered as correct if their absolute error is less than 10^-5.

 

Sample Input

1 0.04 0.01 0 0 0

 

Sample Output

1.0000000

 

这道题目就相对来说更接近模拟退火的算法了，每次像八个方向试探，初始温度设置在（0.8，1)左右，不然AC不了。很奇怪吧，一般来说初始温度越高越好，但这题却不是。之后就是逐渐降温了。

代码：

#include<cstdio>#include<iostream>#include<cmath>#include<stdlib.h>#include<ctime>#define eps 1e-8using namespace std;double a,b,c,d,e,f;const double inf=1LL<<60;int dx[]={-1,-1,-1,0,0,1,1,1};int dy[]={-1,0,1,-1,1,-1,0,1};double dis(double x,double y,double z){    return sqrt(x*x+y*y+z*z);}double getz(double x,double y){    double ta=c,tb=d*y+e*x,tc=a*x*x+b*y*y+f*x*y-1;    double delta=tb*tb-4*ta*tc;    if(delta<0) return inf;    double z1=(-tb+sqrt(delta))/(2*ta);    double z2=(-tb-sqrt(delta))/(2*ta);    return z1*z1<z2*z2?z1:z2;}void solve(){    double x=0,y=0,z=getz(x,y),delta=0.8;    while(delta>eps){        for(int i=0;i<8;i++){            double tx=x+dx[i]*delta,                ty=y+dy[i]*delta,                tz=getz(tx,ty);            if(tz>inf/10) continue;            if(dis(tx,ty,tz)-dis(x,y,z)<0)                x=tx,y=ty,z=tz;        }        delta*=0.99;    }    printf("%.7f\n",dis(x,y,z));}int main(){    srand((unsigned)time(NULL));    while(~scanf("%lf%lf%lf%lf%lf%lf",&a,&b,&c,&d,&e,&f)){        solve();    }return 0;}