poj1279 半平面交

题意：没看懂= =

sol：在纸上随便画两下就可以看出，答案即按逆时针方向建立line，求它们的半平面交的面积。

模板题。注意输出答案时输出ans+eps，否则可能会出现结果为-0.00的情况。

#include<vector>
#include<list>
#include<map>
#include<set>
#include<deque>
#include<queue>
#include<stack>
#include<bitset>
#include<algorithm>
#include<functional>
#include<numeric>
#include<utility>
#include<iostream>
#include<sstream>
#include<iomanip>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cctype>
#include<string>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<climits>
#include<complex>
#define mp make_pair
#define pb push_back
using namespace std;
const double eps=1e-6;
const double pi=acos(-1.0);
const double inf=1e20;
const int maxp=1111;
int dblcmp(double d)
{
    if (fabs(d)<eps)return 0;
    return d>eps?1:-1;
}
inline double sqr(double x){return x*x;}
struct point
{
    double x,y;
    point(){}
    point(double _x,double _y):
    x(_x),y(_y){};
    void input()
    {
        scanf("%lf%lf",&x,&y);
    }
    void output()
    {
        printf("%.2f %.2f
",x,y);
    }
    bool operator==(point a)const
    {
        return dblcmp(a.x-x)==0&&dblcmp(a.y-y)==0;
    }
    bool operator<(point a)const
    {
        return dblcmp(a.x-x)==0?dblcmp(y-a.y)<0:x<a.x;
    }
    double len()
    {
        return hypot(x,y);
    }
    double len2()
    {
        return x*x+y*y;
    }
    double distance(point p)
    {
        return hypot(x-p.x,y-p.y);
    }
    point add(point p)
    {
        return point(x+p.x,y+p.y);
    }
    point sub(point p)
    {
        return point(x-p.x,y-p.y);
    }
    point mul(double b)
    {
        return point(x*b,y*b);
    }
    point div(double b)
    {
        return point(x/b,y/b);
    }
    double dot(point p)
    {
        return x*p.x+y*p.y;
    }
    double det(point p)
    {
        return x*p.y-y*p.x;
    }
    double rad(point a,point b)
    {
        point p=*this;
        return fabs(atan2(fabs(a.sub(p).det(b.sub(p))),a.sub(p).dot(b.sub(p))));
    }
    point trunc(double r)
    {
        double l=len();
        if (!dblcmp(l))return *this;
        r/=l;
        return point(x*r,y*r);
    }
    point rotleft()
    {
        return point(-y,x);
    }
    point rotright()
    {
        return point(y,-x);
    }
    point rotate(point p,double angle)//绕点p逆时针旋转angle角度
    {
        point v=this->sub(p);
        double c=cos(angle),s=sin(angle);
        return point(p.x+v.x*c-v.y*s,p.y+v.x*s+v.y*c);
    }
};
struct line
{
    point a,b;
    line(){}
    line(point _a,point _b)
    {
        a=_a;
        b=_b;
    }
    bool operator==(line v)
    {
        return (a==v.a)&&(b==v.b);
    }
    //倾斜角angle
    line(point p,double angle)
    {
        a=p;
        if (dblcmp(angle-pi/2)==0)
        {
            b=a.add(point(0,1));
        }
        else
        {
            b=a.add(point(1,tan(angle)));
        }
    }
    //ax+by+c=0
    line(double _a,double _b,double _c)
    {
        if (dblcmp(_a)==0)
        {
            a=point(0,-_c/_b);
            b=point(1,-_c/_b);
        }
        else if (dblcmp(_b)==0)
        {
            a=point(-_c/_a,0);
            b=point(-_c/_a,1);
        }
        else
        {
            a=point(0,-_c/_b);
            b=point(1,(-_c-_a)/_b);
        }
    }
    void input()
    {
        a.input();
        b.input();
    }
    void adjust()
    {
        if (b<a)swap(a,b);
    }
    double length()
    {
        return a.distance(b);
    }
    double angle()//直线倾斜角 0<=angle<180
    {
        double k=atan2(b.y-a.y,b.x-a.x);
        if (dblcmp(k)<0)k+=pi;
        if (dblcmp(k-pi)==0)k-=pi;
        return k;
    }
    //点和线段关系
    //1 在逆时针
    //2 在顺时针
    //3 平行
    int relation(point p)
    {
        int c=dblcmp(p.sub(a).det(b.sub(a)));
        if (c<0)return 1;
        if (c>0)return 2;
        return 3;
    }
    bool pointonseg(point p)
    {
        return dblcmp(p.sub(a).det(b.sub(a)))==0&&dblcmp(p.sub(a).dot(p.sub(b)))<=0;
    }
    bool parallel(line v)
    {
        return dblcmp(b.sub(a).det(v.b.sub(v.a)))==0;
    }
    //2 规范相交
    //1 非规范相交
    //0 不相交
    int segcrossseg(line v)
    {
        int d1=dblcmp(b.sub(a).det(v.a.sub(a)));
        int d2=dblcmp(b.sub(a).det(v.b.sub(a)));
        int d3=dblcmp(v.b.sub(v.a).det(a.sub(v.a)));
        int d4=dblcmp(v.b.sub(v.a).det(b.sub(v.a)));
        if ((d1^d2)==-2&&(d3^d4)==-2)return 2;
        return (d1==0&&dblcmp(v.a.sub(a).dot(v.a.sub(b)))<=0||
                d2==0&&dblcmp(v.b.sub(a).dot(v.b.sub(b)))<=0||
                d3==0&&dblcmp(a.sub(v.a).dot(a.sub(v.b)))<=0||
                d4==0&&dblcmp(b.sub(v.a).dot(b.sub(v.b)))<=0);
    }
    int linecrossseg(line v)//*this seg v line
    {
        int d1=dblcmp(b.sub(a).det(v.a.sub(a)));
        int d2=dblcmp(b.sub(a).det(v.b.sub(a)));
        if ((d1^d2)==-2)return 2;
        return (d1==0||d2==0);
    }
    //0 平行
    //1 重合
    //2 相交
    int linecrossline(line v)
    {
        if ((*this).parallel(v))
        {
            return v.relation(a)==3;
        }
        return 2;
    }
    point crosspoint(line v)
    {
        double a1=v.b.sub(v.a).det(a.sub(v.a));
        double a2=v.b.sub(v.a).det(b.sub(v.a));
        return point((a.x*a2-b.x*a1)/(a2-a1),(a.y*a2-b.y*a1)/(a2-a1));
    }
    double dispointtoline(point p)
    {
        return fabs(p.sub(a).det(b.sub(a)))/length();
    }
    double dispointtoseg(point p)
    {
        if (dblcmp(p.sub(b).dot(a.sub(b)))<0||dblcmp(p.sub(a).dot(b.sub(a)))<0)
        {
            return min(p.distance(a),p.distance(b));
        }
        return dispointtoline(p);
    }
    point lineprog(point p)
    {
        return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a))/b.sub(a).len2()));
    }
    point symmetrypoint(point p)
    {
        point q=lineprog(p);
        return point(2*q.x-p.x,2*q.y-p.y);
    }
};

struct Vector:public point
{
    Vector(){}
    Vector(double a,double b)
    {
        x=a;    y=b;
    }
    Vector(point _a,point _b)   //a->b
    {
        double dx=_b.x-_a.x;
        double dy=_b.y-_a.y;
        x=dx;   y=dy;
    }
    Vector(line v)
    {
        double dx=v.b.x-v.a.x;
        double dy=v.b.y-v.a.y;
        x=dx;   y=dy;
    }
    double length()
    {
        return (sqrt(x*x+y*y));
    }
    Vector Normal()
    {
        double L=sqrt(x*x+y*y);
        Vector Vans=Vector(-y/L,x/L);
        return Vans;
    }
};

struct halfplane:public line    //半平面
{
    double angle;
    halfplane(){}
    //表示向量 a->b逆时针(左侧)的半平面
    halfplane(point _a,point _b)
    {
        a=_a;
        b=_b;
    }
    halfplane(line v)
    {
        a=v.a;
        b=v.b;
    }
    void calcangle()
    {
        angle=atan2(b.y-a.y,b.x-a.x);
    }
    bool operator<(const halfplane &b)const
    {
        return angle<b.angle;
    }
};

struct polygon
{
    int n;
    point p[maxp];
    line l[maxp];
    void input()
    {
        n=4;
        for (int i=0;i<n;i++)
        {
            p[i].input();
        }
    }
    void add(point q)
    {
        p[n++]=q;
    }
    void getline()
    {
        for (int i=0;i<n;i++)
        {
            l[i]=line(p[i],p[(i+1)%n]);
        }
    }
    struct cmp
    {
        point p;
        cmp(const point &p0){p=p0;}
        bool operator()(const point &aa,const point &bb)
        {
            point a=aa,b=bb;
            int d=dblcmp(a.sub(p).det(b.sub(p)));
            if (d==0)
            {
                return dblcmp(a.distance(p)-b.distance(p))<0;
            }
            return d>0;
        }
    };
    void norm()
    {
        point mi=p[0];
        for (int i=1;i<n;i++)mi=min(mi,p[i]);
        sort(p,p+n,cmp(mi));
    }
    void getconvex(polygon &convex)
    {
        int i,j,k;
        sort(p,p+n);
        convex.n=n;
        for (i=0;i<min(n,2);i++)
        {
            convex.p[i]=p[i];
        }
        if (n<=2)return;
        int &top=convex.n;
        top=1;
        for (i=2;i<n;i++)
        {
            while (top&&convex.p[top].sub(p[i]).det(convex.p[top-1].sub(p[i]))<=0)
                top--;
            convex.p[++top]=p[i];
        }
        int temp=top;
        convex.p[++top]=p[n-2];
        for (i=n-3;i>=0;i--)
        {
            while (top!=temp&&convex.p[top].sub(p[i]).det(convex.p[top-1].sub(p[i]))<=0)
                top--;
            convex.p[++top]=p[i];
        }
    }
    bool isconvex()
    {
        bool s[3];
        memset(s,0,sizeof(s));
        int i,j,k;
        for (i=0;i<n;i++)
        {
            j=(i+1)%n;
            k=(j+1)%n;
            s[dblcmp(p[j].sub(p[i]).det(p[k].sub(p[i])))+1]=1;
            if (s[0]&&s[2])return 0;
        }
        return 1;
    }
    //3 点上
    //2 边上
    //1 内部
    //0 外部
    int relationpoint(point q)
    {
        int i,j;
        for (i=0;i<n;i++)
        {
            if (p[i]==q)return 3;
        }
        getline();
        for (i=0;i<n;i++)
        {
            if (l[i].pointonseg(q))return 2;
        }
        int cnt=0;
        for (i=0;i<n;i++)
        {
            j=(i+1)%n;
            int k=dblcmp(q.sub(p[j]).det(p[i].sub(p[j])));
            int u=dblcmp(p[i].y-q.y);
            int v=dblcmp(p[j].y-q.y);
            if (k>0&&u<0&&v>=0)cnt++;
            if (k<0&&v<0&&u>=0)cnt--;
        }
        return cnt!=0;
    }
    //1 在多边形内长度为正
    //2 相交或与边平行
    //0 无任何交点
    int relationline(line u)
    {
        int i,j,k=0;
        getline();
        for (i=0;i<n;i++)
        {
            if (l[i].segcrossseg(u)==2)return 1;
            if (l[i].segcrossseg(u)==1)k=1;
        }
        if (!k)return 0;
        vector<point>vp;
        for (i=0;i<n;i++)
        {
            if (l[i].segcrossseg(u))
            {
                if (l[i].parallel(u))
                {
                    vp.pb(u.a);
                    vp.pb(u.b);
                    vp.pb(l[i].a);
                    vp.pb(l[i].b);
                    continue;
                }
                vp.pb(l[i].crosspoint(u));
            }
        }
        sort(vp.begin(),vp.end());
        int sz=vp.size();
        for (i=0;i<sz-1;i++)
        {
            point mid=vp[i].add(vp[i+1]).div(2);
            if (relationpoint(mid)==1)return 1;
        }
        return 2;
    }
    //直线u切割凸多边形左侧
    //注意直线方向
    void convexcut(line u,polygon &po)
    {
        int i,j,k;
        int &top=po.n;
        top=0;
        for (i=0;i<n;i++)
        {
            int d1=dblcmp(p[i].sub(u.a).det(u.b.sub(u.a)));
            int d2=dblcmp(p[(i+1)%n].sub(u.a).det(u.b.sub(u.a)));
            if (d1>=0)po.p[top++]=p[i];
            if (d1*d2<0)po.p[top++]=u.crosspoint(line(p[i],p[(i+1)%n]));
        }
    }
    double getcircumference()
    {
        double sum=0;
        int i;
        for (i=0;i<n;i++)
        {
            sum+=p[i].distance(p[(i+1)%n]);
        }
        return sum;
    }
    double getarea()
    {
        double sum=0;
        int i;
        for (i=0;i<n;i++)
        {
            sum+=p[i].det(p[(i+1)%n]);
        }
        return fabs(sum)/2;
    }
    bool getdir()//1代表逆时针 0代表顺时针
    {
        double sum=0;
        int i;
        for (i=0;i<n;i++)
        {
            sum+=p[i].det(p[(i+1)%n]);
        }
        if (dblcmp(sum)>0)return 1;
        return 0;
    }
    point getbarycentre()
    {
        point ret(0,0);
        double area=0;
        int i;
        for (i=1;i<n-1;i++)
        {
            double tmp=p[i].sub(p[0]).det(p[i+1].sub(p[0]));
            if (dblcmp(tmp)==0)continue;
            area+=tmp;
            ret.x+=(p[0].x+p[i].x+p[i+1].x)/3*tmp;
            ret.y+=(p[0].y+p[i].y+p[i+1].y)/3*tmp;
        }
        if (dblcmp(area))ret=ret.div(area);
        return ret;
    }
    double areaintersection(polygon po)
    {
    }
    double areaunion(polygon po)
    {
        return getarea()+po.getarea()-areaintersection(po);
    }
    /*
    double areacircle(circle c)
    {
        int i,j,k,l,m;
        double ans=0;
        for (i=0;i<n;i++)
        {
            int j=(i+1)%n;
            if (dblcmp(p[j].sub(c.p).det(p[i].sub(c.p)))>=0)
            {
                ans+=c.areatriangle(p[i],p[j]);
            }
            else
            {
                ans-=c.areatriangle(p[i],p[j]);
            }
        }
        return fabs(ans);
    }
    //多边形和圆关系
    //0 一部分在圆外
    //1 与圆某条边相切
    //2 完全在圆内
    int relationcircle(circle c)
    {
        getline();
        int i,x=2;
        if (relationpoint(c.p)!=1)return 0;
        for (i=0;i<n;i++)
        {
            if (c.relationseg(l[i])==2)return 0;
            if (c.relationseg(l[i])==1)x=1;
        }
        return x;
    }
    void find(int st,point tri[],circle &c)
    {
        if (!st)
        {
            c=circle(point(0,0),-2);
        }
        if (st==1)
        {
            c=circle(tri[0],0);
        }
        if (st==2)
        {
            c=circle(tri[0].add(tri[1]).div(2),tri[0].distance(tri[1])/2.0);
        }
        if (st==3)
        {
            c=circle(tri[0],tri[1],tri[2]);
        }
    }
    void solve(int cur,int st,point tri[],circle &c)
    {
        find(st,tri,c);
        if (st==3)return;
        int i;
        for (i=0;i<cur;i++)
        {
            if (dblcmp(p[i].distance(c.p)-c.r)>0)
            {
                tri[st]=p[i];
                solve(i,st+1,tri,c);
            }
        }
    }
    circle mincircle()//点集最小圆覆盖
    {
        random_shuffle(p,p+n);
        point tri[4];
        circle c;
        solve(n,0,tri,c);
        return c;
    }
    int circlecover(double r)//单位圆覆盖
    {
        int ans=0,i,j;
        vector<pair<double,int> >v;
        for (i=0;i<n;i++)
        {
            v.clear();
            for (j=0;j<n;j++)if (i!=j)
            {
                point q=p[i].sub(p[j]);
                double d=q.len();
                if (dblcmp(d-2*r)<=0)
                {
                    double arg=atan2(q.y,q.x);
                    if (dblcmp(arg)<0)arg+=2*pi;
                    double t=acos(d/(2*r));
                    v.push_back(make_pair(arg-t+2*pi,-1));
                    v.push_back(make_pair(arg+t+2*pi,1));
                }
            }
            sort(v.begin(),v.end());
            int cur=0;
            for (j=0;j<v.size();j++)
            {
                if (v[j].second==-1)++cur;
                else --cur;
                ans=max(ans,cur);
            }
        }
        return ans+1;
    }
    */
    int pointinpolygon(point q)//点在凸多边形内部的判定
    {
        if (getdir())reverse(p,p+n);
        if (dblcmp(q.sub(p[0]).det(p[n-1].sub(p[0])))==0)
        {
            if (line(p[n-1],p[0]).pointonseg(q))return n-1;
            return -1;
        }
        int low=1,high=n-2,mid;
        while (low<=high)
        {
            mid=(low+high)>>1;
            if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0])))>=0&&dblcmp(q.sub(p[0]).det(p[mid+1].sub(p[0])))<0)
            {
                polygon c;
                c.p[0]=p[mid];
                c.p[1]=p[mid+1];
                c.p[2]=p[0];
                c.n=3;
                if (c.relationpoint(q))return mid;
                return -1;
            }
            if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0])))>0)
            {
                low=mid+1;
            }
            else
            {
                high=mid-1;
            }
        }
        return -1;
    }
};

struct halfplanes   //半平面交
{
    int n;
    halfplane hp[maxp];
    point p[maxp];
    int que[maxp];
    int st,ed;
    void push(halfplane tmp)
    {
        hp[n++]=tmp;
    }
    void unique()
    {
        int m=1,i;
        for (i=1;i<n;i++)
        {
            if (dblcmp(hp[i].angle-hp[i-1].angle))hp[m++]=hp[i];
            else if (dblcmp(hp[m-1].b.sub(hp[m-1].a).det(hp[i].a.sub(hp[m-1].a))>0))hp[m-1]=hp[i];
        }
        n=m;
    }
    bool halfplaneinsert()
    {
        int i;
        for (i=0;i<n;i++)hp[i].calcangle();
        sort(hp,hp+n);
        unique();
        que[st=0]=0;
        que[ed=1]=1;
        p[1]=hp[0].crosspoint(hp[1]);
        for (i=2;i<n;i++)
        {
            while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a))))<0)ed--;
            while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[st+1].sub(hp[i].a))))<0)st++;
            que[++ed]=i;
            if (hp[i].parallel(hp[que[ed-1]]))return false;
            p[ed]=hp[i].crosspoint(hp[que[ed-1]]);
        }
        while (st<ed&&dblcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a)))<0)ed--;
        while (st<ed&&dblcmp(hp[que[ed]].b.sub(hp[que[ed]].a).det(p[st+1].sub(hp[que[ed]].a)))<0)st++;
        if (st+1>=ed)return false;
        return true;
    }
    void getconvex(polygon &con)
    {
        p[st]=hp[que[st]].crosspoint(hp[que[ed]]);
        con.n=ed-st+1;
        int j=st,i=0;
        for (;j<=ed;i++,j++)
        {
            con.p[i]=p[j];
        }
    }
};

point p[2000];
halfplanes TH;
int n,T;

int main()
{
    //freopen("in.txt","r",stdin);

    cin>>T;
    while (T--)
    {
        cin>>n;
        for (int i=n-1;i>=0;i--)
            p[i].input();
        //p[i]->p[i+1]

        TH.n=0;
        for (int i=0;i<=n-1;i++)
            TH.push(halfplane(p[i],p[(i+1)%n]));

        double ans=0.00;
        if (TH.halfplaneinsert())
        {
            polygon Gans;
            TH.getconvex(Gans);
            ans=Gans.getarea();
        }
        printf("%.2lf
",ans+eps);
    }

    return 0;
}