HDU4273 Rescue(2012 ACM/ICPC Asia Regional Changchun Online)

#include<iostream>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
using namespace std;

const int MAXN=1001;
const int N = 500;
const double EPS=1e-8;

int g[MAXN][MAXN];

struct Point{
    double x,y,z;
    Point(){}
    Point(double xx,double yy,double zz):x(xx),y(yy),z(zz){}
    
    Point operator -(const Point p1){//     
		return Point(x-p1.x,y-p1.y,z-p1.z);
	}
    Point operator *(Point p){//  
		return Point(y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x);
	}
    double operator ^(Point p){//  
		return (x*p.x+y*p.y+z*p.z);
	}
};

struct CH3D{

    struct face{
        int a,b,c;//              
        bool ok;//               
    };

    int n;//      
    Point P[MAXN];//    

    int num; //         
    face F[8*MAXN];  
    
    //int g[MAXN][MAXN];//        
    
    double vlen(Point a){//    
		return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);
	}
    
    Point cross(const Point &a, const Point &b, const Point &c){//  
		return Point((b.y-a.y)*(c.z-a.z)-(b.z-a.z)*(c.y-a.y),-((b.x-a.x)*(c.z-a.z)-(b.z-a.z)*(c.x-a.x)),(b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x));
    }
    
    double area(Point a,Point b,Point c){//     *2
		return vlen((b-a)*(c-a));
    }
    
    double volume(Point a,Point b,Point c,Point d){//       *6
		return (b-a)*(c-a)^(d-a);
    }
    
    double dblcmp(Point &p,face &f){// :     
		Point m=P[f.b]-P[f.a];
        Point n=P[f.c]-P[f.a];
        Point t=p-P[f.a];
        return (m*n)^t;
    }
    
    void deal(int p,int a,int b){
		int f=g[a][b];
        face add;
        if(F[f].ok){
            if(dblcmp(P[p],F[f])>EPS){
                dfs(p,f);
			}
            else {
                add.a=b;    
                add.b=a;
                add.c=p;
                add.ok=1;
                g[p][b]=g[a][p]=g[b][a]=num;
                F[num++]=add;
            }
        }
    }
    
    void dfs(int p,int now){
        F[now].ok=0;
        deal(p,F[now].b,F[now].a);
        deal(p,F[now].c,F[now].b);
        deal(p,F[now].a,F[now].c);
    }
    
    bool same(int s,int t){
        Point &a=P[F[s].a];
        Point &b=P[F[s].b];
        Point &c=P[F[s].c];
        return fabs(volume(a,b,c,P[F[t].a]))<EPS && fabs(volume(a,b,c,P[F[t].b]))<EPS
            && fabs(volume(a,b,c,P[F[t].c]))<EPS;
    }
    
    void pretreat(){//      
		int i,j,tmp;
        face add;
        bool flag;
        num=0;
        if(n<4) return;

		flag=true;
        for(i=1;i<n;i++){//              ,    ,    
			if(vlen(P[0]-P[i])>EPS){
                swap(P[1],P[i]);
                flag=false; break;
            }
        }
        if(flag) return;

        flag=true;
        for(i=2;i<n;i++){//       
			if(vlen((P[0]-P[1])*(P[1]-P[i]))>EPS){
                swap(P[2],P[i]);
                flag=false; break;
            }
        }
        if(flag) return;

        flag=true;
        for(i=3;i<n;i++){//       
			if(fabs((P[0]-P[1])*(P[1]-P[2])^(P[0]-P[i]))>EPS){
                swap(P[3],P[i]);
                flag=false;
                break;
            }
        }
        if(flag) return;

        for(i=0;i<4;i++){
            add.a=(i+1)%4;
            add.b=(i+2)%4;
            add.c=(i+3)%4;
            add.ok=true;
            if(dblcmp(P[i],add)>0)
                swap(add.b,add.c);
            g[add.a][add.b]=g[add.b][add.c]=g[add.c][add.a]=num;
            F[num++]=add;
        }
        for(i=4;i<n;i++){
            for(j=0;j<num;j++){
                if(F[j].ok && dblcmp(P[i],F[j])>EPS){
                    dfs(i,j);
					break;
                }
            }
        }
        tmp=num;
        for(i=num=0;i<tmp;i++){
			if(F[i].ok) F[num++]=F[i];
		}
    }
    
    double area(){//   
		double res=0.0;
        if(n==3){
            Point p=cross(P[0],P[1],P[2]);
            res=vlen(p)/2.0;
            return res;
        }        
        for(int i=0;i<num;i++)
            res+=area(P[F[i].a],P[F[i].b],P[F[i].c]);
        return res/2.0;
    }
    
    double volume(){//  
		double res=0.0;
        Point tmp(0,0,0);
        for(int i=0;i<num;i++)
            res+=volume(tmp,P[F[i].a],P[F[i].b],P[F[i].c]);
        return fabs(res/6.0);
    }
    
    int triangle(){//       
		return num;
    }
    
    int polygon(){//       
		int i,j,res,flag;
        for(i=res=0;i<num;i++){
            flag=1;
            for(j=0;j<i;j++){
                if(same(i,j)){
                    flag=0; break;
                }
                res+=flag;
			}
        }
        return res;
    }
    
	Point getcent(){//     
        Point ans(0,0,0),temp=P[F[0].a];
        double v = 0.0,t2;
        for(int i=0;i<num;i++){
            if(F[i].ok == true){
                Point p1=P[F[i].a],p2=P[F[i].b],p3=P[F[i].c];
                t2 = volume(temp,p1,p2,p3)/6.0;//    0，    ，  temp       
                if(t2>0){
                    ans.x += (p1.x+p2.x+p3.x+temp.x)*t2;
                    ans.y += (p1.y+p2.y+p3.y+temp.y)*t2;
                    ans.z += (p1.z+p2.z+p3.z+temp.z)*t2;
                    v += t2;
                }
            }
        }
        ans.x /= (4*v); ans.y /= (4*v); ans.z /= (4*v);
        return ans;
    }

    double function(Point fuck){//          （            ）

        double min=99999999;
        for(int i=0;i<num;i++){
            if(F[i].ok==true){
                Point p1=P[F[i].a] , p2=P[F[i].b] , p3=P[F[i].c];

                double a = ( (p2.y-p1.y)*(p3.z-p1.z)-(p2.z-p1.z)*(p3.y-p1.y) );
                double b = ( (p2.z-p1.z)*(p3.x-p1.x)-(p2.x-p1.x)*(p3.z-p1.z) );
                double c = ( (p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x) );
                double d = ( 0-(a*p1.x+b*p1.y+c*p1.z) );
                double temp = fabs(a*fuck.x+b*fuck.y+c*fuck.z+d)/sqrt(a*a+b*b+c*c);

                if(temp<min)min = temp;
            }
        }return min;
    }
    
};

//CH3D hull;

int main()
{
    int i,n;
    while(~scanf("%d",&n)){
        CH3D hull;
        memset(g,0,sizeof(g));
        memset(hull.P,0,sizeof(hull.P));
        hull.n = n;
        for(i=0;i<hull.n;i++){
            scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);
        }
        hull.pretreat();

        Point temp=hull.getcent();
        printf("%.3lf
",hull.function(temp));
    }
    return 0;
}