hdu 4573 Throw the Stones

求三维凸包，其中求体积的部分值得借鉴

#include<cstdio>#include<algorithm>#include<cmath>using namespace std;#define MAXN 10005const double eps = 1e-9;int n, fc_cnt, leg[MAXN][MAXN];double mx_ff, dis_ff;inline int sig(double x){    return (x>eps) - (x<-eps);}struct node{    double x, y, z;    node(double a = 0.0, double b = 0.0, double c = 0.0):x(a),y(b),z(c) {}        node operator - (node& a) const    {        return node(x-a.x, y-a.y, z-a.z);    }    node operator + (node& a) const    {        return node(x+a.x, y+a.y, z+a.z);    }    node operator ^ (node a) const // this * a * sin($)    {        return node(y*a.z-a.y*z, z*a.x-a.z*x, x*a.y-a.x*y);    }    double operator * (node a) const // this * a * cin($)    {        return x*a.x + y*a.y + z*a.z;    }    node cross(node a, node b)    {        return a - *this^b - *this;    }    double L()    {        return sqrt(x*x + y*y + z*z);    }    double vv6(node a, node b)    {        return (a^b)*(*this);    }} P[MAXN];struct FACE{    int a, b, c;    int isOK;    FACE(int x = 0, int y = 0, int z = 0, int ik = 0):a(x),b(y),c(z), isOK(ik){}    int visit(node mm)    {        return sig(P[a].cross(P[b], P[c])*(mm - P[a])) > 0;    }}facc[MAXN*8];void deal(int o, int a, int b);void dfs(int f, int o){    facc[f].isOK = 0;    dis_ff -= P[facc[f].a].vv6(P[facc[f].b], P[facc[f].c]);    deal(o, facc[f].b, facc[f].a);    deal(o, facc[f].a, facc[f].c);    deal(o, facc[f].c, facc[f].b);}void deal(int o, int a, int b){    int i = leg[a][b];    if (facc[i].isOK)    {        if (facc[i].visit(P[o]))            dfs(i, o);        else        {            dis_ff += P[b].vv6(P[a], P[o]);            FACE add(b, a, o, 1);            leg[b][a] = leg[a][o] = leg[o][b] = fc_cnt;            facc[fc_cnt++] = add;        }    }}void _update(int idx){    for (int i = 0; i< fc_cnt; i++)    {        if (facc[i].isOK && facc[i].visit(P[idx]))        {            dfs(i, idx);            break;        }    }}double getV(){    double v = 0;    for (int i = 0; i<fc_cnt; i++)    {        if (facc[i].isOK)        {            v += P[facc[i].a].vv6(P[facc[i].b], P[facc[i].c]);        }    }    return v/6;}void solve(){    mx_ff = dis_ff = 0;    int kg = 1, flg = 1;    int i, j;    for (i = 1; i< n; i++)    {        if (flg == 1)        {            flg += sig((P[0]-P[i]).L());            if (flg > 1)                swap(P[1], P[i]);        }        else if (flg == 2)        {            flg += sig((P[0].cross(P[1], P[i])).L());            if (flg > 2)                swap(P[i], P[2]);        }        else if (flg == 3)        {            flg += sig(P[0].cross(P[1], P[2]) * (P[i]-P[0])) != 0;            if (flg > 3)            {                swap(P[3], P[i]);                fc_cnt = 0;                for (j = 0; j< 4; j++)                {                    FACE add((j+1)%4, (j+2)%4, (j+3)%4, 1);                    if (add.visit(P[j]))                        swap(add.b, add.c);                    leg[add.a][add.b] = leg[add.b][add.c] = leg[add.c][add.a] = fc_cnt;                    facc[fc_cnt++] = add;                }                for (j = 4; j<= i; j++)                {                    _update(j);                }                kg = i+1;                mx_ff = getV();            }        }        else        {            dis_ff = 0;            _update(i);            dis_ff /= 6;            if (sig(dis_ff - mx_ff) > 0)            {                mx_ff = dis_ff;                kg = i+1;            }        }    }    printf("%d %.2lf\n", kg, mx_ff);}int main(){#ifndef ONLINE_JUDGE    freopen("in.txt", "r", stdin);#endif    int cs = 0;    while (scanf("%d", &n) != EOF)    {        for (int i = 0; i< n; ++i)        {            scanf("%lf%lf%lf", &P[i].x, &P[i].y, &P[i].z);        }        printf("Case #%d:\n", ++cs);        solve();    }    return 0;}