poj3862 Asteroids【模板题】

题目链接：http://poj.org/problem?id=3862
题意：就是让你求两个多面体的质心到面的距离之和的最小值
解析：模板题，三维凸包质心，然后枚举每一个面算质心到面的距离取最小值

#include <iostream>#include <cstdio>#include <algorithm>#include <vector>#include <cstring>#include <queue>#include <cmath>#include <map>using namespace std;const int maxn = 1e6+100;const int inf = 0x7ffffff;const double eps = 1e-8;int n;struct point{    double x,y,z;    point() {}    point(double _x,double _y,double _z)    {        x = _x;        y = _y;        z = _z;    }    point operator - (const point &b)const    {        point ret;        ret.x = x-b.x;        ret.y = y-b.y;        ret.z = z-b.z;        return ret;    }    point operator + (const point &b)const    {        point ret;        ret.x = x+b.x;        ret.y = y+b.y;        ret.z = z+b.z;        return ret;    }    point operator * (const double &b)const    {        point ret;        ret.x = x*b;        ret.y = y*b;        ret.z = z*b;        return ret;    }    point operator / (const double &b)const    {        point ret;        ret.x = x/b;        ret.y = y/b;        ret.z = z/b;        return ret;    }};int dblcmp(double x){    if(fabs(x)<eps)        return 0;    return x>0?1:-1;}point x_mul(point u,point v){    point ret;    ret.x = u.y*v.z-u.z*v.y;    ret.y = u.z*v.x-u.x*v.z;    ret.z = u.x*v.y-u.y*v.x;    return ret;}double dot_mul(point u,point v){    return u.x*v.x+u.y*v.y+u.z*v.z;}double dis(point p1,point p2){    double t1 = (p1.x-p2.x)*(p1.x-p2.x);    double t2 = (p1.y-p2.y)*(p1.y-p2.y);    double t3 = (p1.z-p2.z)*(p1.z-p2.z);    return sqrt(t1+t2+t3);}double vlen(point p){    return sqrt(dot_mul(p,p));}double area(point a,point b,point c,point d){    point t1 = d-a;    point t2 = b-a;    point t3 = c-a;    point tmp = x_mul(b-a,c-a);    double ans = dot_mul(d-a,x_mul(b-a,c-a));    return dot_mul(d-a,x_mul(b-a,c-a));}double area2(point a,point b,point c){    return vlen(x_mul(b-a,c-a));}point slove(point a,point b,point c,point d){    return (a+b+c+d)/4.0;}struct plane{    int v[3];    plane(int a, int b, int c)    {        v[0] = a;        v[1] = b;        v[2] = c;    }    point Normal(const vector<point>& P) const    {        return x_mul(P[v[1]]-P[v[0]], P[v[2]]-P[v[0]]);    }    int CanSee(const vector<point>& P, int i) const    {        return dot_mul(P[i]-P[v[0]], Normal(P)) > 0;    }};vector<point> P;vector<plane> faces;int vis[100][100];vector<plane> CH3D(const vector<point>& P){    int n = P.size();    memset(vis,0,sizeof(vis));    vector<plane> cur;    cur.push_back(plane(0, 1, 2));    cur.push_back(plane(2, 1, 0));    for(int i = 3; i < n; i++)    {        vector<plane> nex;        for(int j = 0; j < cur.size(); j++)        {            plane& f = cur[j];            int res = f.CanSee(P, i);            if(!res)                nex.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])                    nex.push_back(plane(a, b, i));            }        }        cur = nex;    }    return cur;}double rand01(){    return rand() / (double)RAND_MAX;}double randeps(){    return (rand01() - 0.5) * eps;}point add_noise(const point& p){    return point(p.x + randeps(), p.y + randeps(), p.z + randeps());}point centroid(){    point c = P[0];    double totv = 0;    point tot(0,0,0);    for(int i=0;i<faces.size();i++)    {        point p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];        double v = -area(p1, p2, p3, c);        totv += v;        tot = tot + slove(p1, p2, p3, c)*v;    }    return tot/totv;}double mindis(point c){    double ans = 1e30;    for(int i=0;i<faces.size();i++)    {        point p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];        ans = min(ans,fabs(-area(p1,p2,p3,c))/area2(p1,p2,p3));    }    //printf("%.2f\n",ans);    return ans;}double ss(int n){    P.resize(n);    for(int i=0;i<n;i++)    {        scanf("%lf %lf %lf",&P[i].x,&P[i].y,&P[i].z);        P[i] = add_noise(P[i]);    }//    for(int i=0;i<n;i++)//        printf("%.2f %.2f %.2f\n",P[i].x,P[i].y,P[i].z);    faces = CH3D(P);    point tt = centroid();    //printf("%.2f %.2f %.2f\n",tt.x,tt.y,tt.z);    double ans = mindis(tt);    return ans;}int main(void){    freopen("asteroids.in","r",stdin);    freopen("asteroids.out","w",stdout);    scanf("%d",&n);    double ans = ss(n);    //printf("%.2f\n",ans);    scanf("%d",&n);    ans += ss(n);    printf("%.5f\n",ans);    return 0;}