OJ-Problems-Source/HDOJ/4273_autoAC.cpp

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#include<stdio.h>
#include<algorithm>
#include<string.h>
#include<math.h>
#include<stdlib.h>
using namespace std;
const int MAXN=550;
const double eps=1e-8;
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 +(const Point p1)
{
return Point(x+p1.x,y+p1.y,z+p1.z);
}
Point operator *(const Point p)
{
return Point(y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x);
}
Point operator *(double d)
{
return Point(x*d,y*d,z*d);
}
Point operator / (double d)
{
return Point(x/d,y/d,z/d);
}
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.z-a.z)*(c.x-a.x)-(b.x-a.x)*(c.z-a.z),
(b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x)
);
}
double area(Point a,Point b,Point c)
{
return vlen((b-a)*(c-a));
}
double volume(Point a,Point b,Point c,Point d)
{
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=true;
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 create()
{
int i,j,tmp;
face add;
num=0;
if(n<4)return;
bool 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(int 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;
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;
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 barycenter()
{
Point ans(0,0,0),o(0,0,0);
double all=0;
for(int i=0;i<num;i++)
{
double vol=volume(o,P[F[i].a],P[F[i].b],P[F[i].c]);
ans=ans+(o+P[F[i].a]+P[F[i].b]+P[F[i].c])/4.0*vol;
all+=vol;
}
ans=ans/all;
return ans;
}
double ptoface(Point p,int i)
{
return fabs(volume(P[F[i].a],P[F[i].b],P[F[i].c],p)/vlen((P[F[i].b]-P[F[i].a])*(P[F[i].c]-P[F[i].a])));
}
};
CH3D hull;
int main()
{
while(scanf("%d",&hull.n)==1)
{
for(int i=0;i<hull.n;i++)
{
scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);
}
hull.create();
Point p=hull.barycenter();
double minn=1e20;
for(int i=0;i<hull.num;i++)
{
minn=min(minn,hull.ptoface(p,i));
}
printf("%.3lf\n",minn);
}
return 0;
}