hdu 4273 Rescue（三维凸包重心）

#include<algorithm>  
#include<iostream>  
#include<cstring>  
#include<fstream>  
#include<sstream>  
#include<vector>  
#include<string>  
#include<cstdio>  
#include<bitset>  
#include<queue>  
#include<stack>  
#include<cmath>  
#include<map>  
#include<set>  
#define FF(i, a, b) for(int i=a; i<b; i++)  
#define FD(i, a, b) for(int i=a; i>=b; i--)  
#define REP(i, n) for(int i=0; i<n; i++)  
#define CLR(a, b) memset(a, b, sizeof(a))  
#define debug puts("**debug**")  
#define LL long long  
#define PB push_back  
#define MP make_pair  
#define eps 1e-8  
using namespace std;  
  
int dcmp(double x) { if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }  
  
struct Point3 {  
  double x, y, z;  
  Point3(double x=0, double y=0, double z=0):x(x),y(y),z(z) { }  
};  
  
typedef Point3 Vector3;  
  
Vector3 operator + (const Vector3& A, const Vector3& B) { return Vector3(A.x+B.x, A.y+B.y, A.z+B.z); }  
Vector3 operator - (const Point3& A, const Point3& B) { return Vector3(A.x-B.x, A.y-B.y, A.z-B.z); }  
Vector3 operator * (const Vector3& A, double p) { return Vector3(A.x*p, A.y*p, A.z*p); }  
Vector3 operator / (const Vector3& A, double p) { return Vector3(A.x/p, A.y/p, A.z/p); }  
  
bool operator == (const Point3& a, const Point3& b) {  
  return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0 && dcmp(a.z-b.z) == 0;  
}  
  
Point3 read_point3() {  
  Point3 p;  
  scanf("%lf%lf%lf", &p.x, &p.y, &p.z);  
  return p;  
}  
  
double Dot(const Vector3& A, const Vector3& B) { return A.x*B.x + A.y*B.y + A.z*B.z; }  
double Length(const Vector3& A) { return sqrt(Dot(A, A)); }  
double Angle(const Vector3& A, const Vector3& B) { return acos(Dot(A, B) / Length(A) / Length(B)); }  
Vector3 Cross(const Vector3& A, const Vector3& B) { return Vector3(A.y*B.z - A.z*B.y, A.z*B.x - A.x*B.z, A.x*B.y - A.y*B.x); }  
double Area2(const Point3& A, const Point3& B, const Point3& C) { return Length(Cross(B-A, C-A)); }  
double Volume6(const Point3& A, const Point3& B, const Point3& C, const Point3& D) { return Dot(D-A, Cross(B-A, C-A)); }  
Point3 Centroid(const Point3& A, const Point3& B, const Point3& C, const Point3& D) { return (A + B + C + D)/4.0; }  
  
double rand01() { return rand() / (double)RAND_MAX; }  
double randeps() { return (rand01() - 0.5) * eps; }  
  
Point3 add_noise(const Point3& p) {  
  return Point3(p.x + randeps(), p.y + randeps(), p.z + randeps());  
}  
  
struct Face {  
  int v[3];  
  Face(int a, int b, int c) { v[0] = a; v[1] = b; v[2] = c; }  
  Vector3 Normal(const vector<Point3>& P) const {  
    return Cross(P[v[1]]-P[v[0]], P[v[2]]-P[v[0]]);  
  }  
  // f是否能看见P[i]  
  int CanSee(const vector<Point3>& P, int i) const {  
    return Dot(P[i]-P[v[0]], Normal(P)) > 0;  
  }  
};  
  
// 增量法求三维凸包  
// 注意：没有考虑各种特殊情况（如四点共面）。实践中，请在调用前对输入点进行微小扰动  
vector<Face> CH3D(const vector<Point3>& P) {  
  int n = P.size();  
  vector<vector<int> > vis(n);  
  for(int i = 0; i < n; i++) vis[i].resize(n);  
  
  vector<Face> cur;  
  cur.push_back(Face(0, 1, 2)); // 由于已经进行扰动，前三个点不共线  
  cur.push_back(Face(2, 1, 0));  
  for(int i = 3; i < n; i++) {  
    vector<Face> next;  
    // 计算每条边的“左面”的可见性  
    for(int j = 0; j < cur.size(); j++) {  
      Face& f = cur[j];  
      int res = f.CanSee(P, i);  
      if(!res) next.push_back(f);  
      for(int k = 0; k < 3; k++) vis[f.v[k]][f.v[(k+1)%3]] = res;  
    }  
    for(int j = 0; j < cur.size(); j++)  
      for(int k = 0; k < 3; k++) {  
        int a = cur[j].v[k], b = cur[j].v[(k+1)%3];  
        if(vis[a][b] != vis[b][a] && vis[a][b]) // (a,b)是分界线，左边对P[i]可见  
          next.push_back(Face(a, b, i));  
      }  
    cur = next;  
  }  
  return cur;  
}  
  
struct ConvexPolyhedron {  
  int n;  
  vector<Point3> P, P2;  
  vector<Face> faces;  
  
  bool read() {  
    if(scanf("%d", &n) != 1) return false;  
    P.resize(n);  
    P2.resize(n);  
    for(int i = 0; i < n; i++) { P[i] = read_point3(); P2[i] = add_noise(P[i]); }  
    faces = CH3D(P2);  
    return true;  
  }  
  
  Point3 centroid() {  
    Point3 C = P[0];  
    double totv = 0;  
    Point3 tot(0,0,0);  
    for(int i = 0; i < faces.size(); i++) {  
      Point3 p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];  
      double v = -Volume6(p1, p2, p3, C);  
      totv += v;  
      tot = tot + Centroid(p1, p2, p3, C)*v;  
    }  
    return tot / totv;  
  }  
  
  double mindist(Point3 C) {  
    double ans = 1e30;  
    for(int i = 0; i < faces.size(); i++) {  
      Point3 p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];  
      ans = min(ans, fabs(-Volume6(p1, p2, p3, C) / Area2(p1, p2, p3)));  
    }  
    return ans;  
  }  
}P1;  
  
int main()  
{  
  int n, m;  
  ConvexPolyhedron P1, P2;  
  while(P1.read()) {  
    Point3 C1 = P1.centroid();  
    double d1 = P1.mindist(C1);  
    printf("%.3f\n", d1);  
  }  
  return 0;  
}