计算几何专项：UVa 811

枚举砍掉的树的集合，然后对未砍树做一次凸包，求出凸包的周长与砍掉树所能做出的fence长度进行比较即可。

#include <iostream>#include <cstdio>#include <algorithm>#include <cmath>#include <vector>using namespace std;const double eps=1e-6;int dcmp(double x){    if(fabs(x)<eps) return 0;    else return x<0?-1:1;}struct point{    double x,y;    point(double x=0,double y=0):x(x),y(y){}} p[20];point operator-(point a,point b){return point(a.x-b.x,a.y-b.y);}double cross(point a,point b){return a.x*b.y-a.y*b.x;}double dot(point a,point b){return a.x*b.x+a.y*b.y;}double length(point a){return sqrt(dot(a,a));}bool operator<(const point& a,const point& b){    return a.x<b.x||(a.x==b.x&&a.y<b.y);}double convex(int poly,int N){    vector<point> P;    for(int i=0;i<N;i++) if(poly&(1<<i)) P.push_back(p[i]);    int n=P.size();    vector<point> ch(n+1);    sort(P.begin(),P.end());    int m=0;    for(int i=0;i<n;i++)    {        while(m>1&&cross(ch[m-1]-ch[m-2],P[i]-ch[m-2])<=0) m--;        ch[m++]=P[i];    }    int k=m;    for(int i=n-2;i>=0;i--)    {        while(m>k&&cross(ch[m-1]-ch[m-2],P[i]-ch[m-2])<=0) m--;        ch[m++]=P[i];    }    if(n>1) m--;    ch.resize(m);    double ans=0;    for(int i=0;i<ch.size();i++)    {        point p1=ch[i],p2=ch[(i+1)%ch.size()];        ans+=length(p1-p2);    }    return ans;}int n;int v[20],l[20];int bitcount(int x){return x==0?0:bitcount(x/2)+(x&1);}int main(){    freopen("in.txt","r",stdin);    int kase=1;    while(cin>>n&&n)    {        for(int i=0;i<n;i++)        {            cin>>p[i].x>>p[i].y>>v[i]>>l[i];        }        int ans=1<<30,st;        double extra;        for(int s=1;s<(1<<n);s++)        {            double e=0;            int val=0;            for(int i=0;i<n;i++) if(!(s&(1<<i)))            {                e+=l[i];val+=v[i];            }            double len=convex(s,n);            if(dcmp(len-e)<=0)            {                if(ans>val)                {                    ans=val;                    st=s;                    extra=e-len;                }                else if(ans==val&&bitcount(st)>bitcount(s))                {                    st=s;extra=e-len;                }            }        }        if(kase!=1) puts("");        printf("Forest %d\n",kase++);        printf("Cut these trees:");        for(int i=0;i<n;i++) if(!(st&(1<<i))) printf(" %d",i+1);        puts("");        printf("Extra wood: %.2f\n",extra);    }    return 0;}