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-;
 const double pi=acos(-1.0);
 const double inf=1e20;
 const int maxp=;
 int dblcmp(double d)
 {
     if (fabs(d)<eps)return ;
     return d>eps?:-;
 }
 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\n",x,y);
     }
     bool operator==(point a)const
     {
         return dblcmp(a.x-x)==&&dblcmp(a.y-y)==;
     }
     bool operator<(point a)const
     {
         return dblcmp(a.x-x)==?dblcmp(y-a.y)<: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/)==)
         {
             b=a.add(point(,));
         }
         else
         {
             b=a.add(point(,tan(angle)));
         }
     }
     //ax+by+c=0
     line(double _a,double _b,double _c)
     {
         if (dblcmp(_a)==)
         {
             a=point(,-_c/_b);
             b=point(,-_c/_b);
         }
         else if (dblcmp(_b)==)
         {
             a=point(-_c/_a,);
             b=point(-_c/_a,);
         }
         else
         {
             a=point(,-_c/_b);
             b=point(,(-_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)<)k+=pi;
         if (dblcmp(k-pi)==)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<)return ;
         if (c>)return ;
         return ;
     }
     bool pointonseg(point p)
     {
         return dblcmp(p.sub(a).det(b.sub(a)))==&&dblcmp(p.sub(a).dot(p.sub(b)))<=;
     }
     bool parallel(line v)
     {
         return dblcmp(b.sub(a).det(v.b.sub(v.a)))==;
     }
     //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)==-&&(d3^d4)==-)return ;
         return (d1==&&dblcmp(v.a.sub(a).dot(v.a.sub(b)))<=||
                 d2==&&dblcmp(v.b.sub(a).dot(v.b.sub(b)))<=||
                 d3==&&dblcmp(a.sub(v.a).dot(a.sub(v.b)))<=||
                 d4==&&dblcmp(b.sub(v.a).dot(b.sub(v.b)))<=);
     }
     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)==-)return ;
         return (d1==||d2==);
     }
     //0 平行
     //1 重合
     //2 相交
     int linecrossline(line v)
     {
         if ((*this).parallel(v))
         {
             return v.relation(a)==;
         }
         return ;
     }
     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)))<||dblcmp(p.sub(a).dot(b.sub(a)))<)
         {
             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(*q.x-p.x,*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=;
         for (int i=;i<n;i++)
         {
             p[i].input();
         }
     }
     void add(point q)
     {
         p[n++]=q;
     }
     void getline()
     {
         for (int i=;i<n;i++)
         {
             l[i]=line(p[i],p[(i+)%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==)
             {
                 return dblcmp(a.distance(p)-b.distance(p))<;
             }
             return d>;
         }
     };
     void norm()
     {
         point mi=p[];
         for (int i=;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=;i<min(n,);i++)
         {
             convex.p[i]=p[i];
         }
         if (n<=)return;
         int &top=convex.n;
         top=;
         for (i=;i<n;i++)
         {
             while (top&&convex.p[top].sub(p[i]).det(convex.p[top-].sub(p[i]))<=)
                 top--;
             convex.p[++top]=p[i];
         }
         int temp=top;
         convex.p[++top]=p[n-];
         for (i=n-;i>=;i--)
         {
             while (top!=temp&&convex.p[top].sub(p[i]).det(convex.p[top-].sub(p[i]))<=)
                 top--;
             convex.p[++top]=p[i];
         }
     }
     bool isconvex()
     {
         bool s[];
         memset(s,,sizeof(s));
         int i,j,k;
         for (i=;i<n;i++)
         {
             j=(i+)%n;
             k=(j+)%n;
             s[dblcmp(p[j].sub(p[i]).det(p[k].sub(p[i])))+]=;
             if (s[]&&s[])return ;
         }
         return ;
     }
     //3 点上
     //2 边上
     //1 内部
     //0 外部
     int relationpoint(point q)
     {
         int i,j;
         for (i=;i<n;i++)
         {
             if (p[i]==q)return ;
         }
         getline();
         for (i=;i<n;i++)
         {
             if (l[i].pointonseg(q))return ;
         }
         int cnt=;
         for (i=;i<n;i++)
         {
             j=(i+)%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>&&u<&&v>=)cnt++;
             if (k<&&v<&&u>=)cnt--;
         }
         return cnt!=;
     }
     //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=;
         getline();
         for (i=;i<n;i++)
         {
             if (l[i].segcrossseg(u)==)return ;
             if (l[i].segcrossseg(u)==)k=;
         }
         if (!k)return ;
         vector<point>vp;
         for (i=;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=;i<sz-;i++)
         {
             point mid=vp[i].add(vp[i+]).div();
             if (relationpoint(mid)==)return ;
         }
         return ;
     }
     //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=;
         for (i=;i<n;i++)
         {
             int d1=dblcmp(p[i].sub(u.a).det(u.b.sub(u.a)));
             int d2=dblcmp(p[(i+)%n].sub(u.a).det(u.b.sub(u.a)));
             if (d1>=)po.p[top++]=p[i];
             if (d1*d2<)po.p[top++]=u.crosspoint(line(p[i],p[(i+)%n]));
         }
     }
     double getcircumference()
     {
         double sum=;
         int i;
         for (i=;i<n;i++)
         {
             sum+=p[i].distance(p[(i+)%n]);
         }
         return sum;
     }
     double getarea()
     {
         double sum=;
         int i;
         for (i=;i<n;i++)
         {
             sum+=p[i].det(p[(i+)%n]);
         }
         return fabs(sum)/;
     }
     bool getdir()//1代表逆时针 0代表顺时针
     {
         double sum=;
         int i;
         for (i=;i<n;i++)
         {
             sum+=p[i].det(p[(i+)%n]);
         }
         if (dblcmp(sum)>)return ;
         return ;
     }
     point getbarycentre()
     {
         point ret(,);
         double area=;
         int i;
         for (i=;i<n-;i++)
         {
             double tmp=p[i].sub(p[]).det(p[i+].sub(p[]));
             if (dblcmp(tmp)==)continue;
             area+=tmp;
             ret.x+=(p[].x+p[i].x+p[i+].x)/*tmp;
             ret.y+=(p[].y+p[i].y+p[i+].y)/*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[]).det(p[n-].sub(p[])))==)
         {
             if (line(p[n-],p[]).pointonseg(q))return n-;
             return -;
         }
         int low=,high=n-,mid;
         while (low<=high)
         {
             mid=(low+high)>>;
             if (dblcmp(q.sub(p[]).det(p[mid].sub(p[])))>=&&dblcmp(q.sub(p[]).det(p[mid+].sub(p[])))<)
             {
                 polygon c;
                 c.p[]=p[mid];
                 c.p[]=p[mid+];
                 c.p[]=p[];
                 c.n=;
                 if (c.relationpoint(q))return mid;
                 return -;
             }
             if (dblcmp(q.sub(p[]).det(p[mid].sub(p[])))>)
             {
                 low=mid+;
             }
             else
             {
                 high=mid-;
             }
         }
         return -;
     }
 };

 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=,i;
         for (i=;i<n;i++)
         {
             if (dblcmp(hp[i].angle-hp[i-].angle))hp[m++]=hp[i];
             else if (dblcmp(hp[m-].b.sub(hp[m-].a).det(hp[i].a.sub(hp[m-].a))>))hp[m-]=hp[i];
         }
         n=m;
     }
     bool halfplaneinsert()
     {
         int i;
         for (i=;i<n;i++)hp[i].calcangle();
         sort(hp,hp+n);
         unique();
         que[st=]=;
         que[ed=]=;
         p[]=hp[].crosspoint(hp[]);
         for (i=;i<n;i++)
         {
             while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a))))<)ed--;
             while (st<ed&&dblcmp((hp[i].b.sub(hp[i].a).det(p[st+].sub(hp[i].a))))<)st++;
             que[++ed]=i;
             if (hp[i].parallel(hp[que[ed-]]))return false;
             p[ed]=hp[i].crosspoint(hp[que[ed-]]);
         }
         while (st<ed&&dblcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a)))<)ed--;
         while (st<ed&&dblcmp(hp[que[ed]].b.sub(hp[que[ed]].a).det(p[st+].sub(hp[que[ed]].a)))<)st++;
         if (st+>=ed)return false;
         return true;
     }
     void getconvex(polygon &con)
     {
         p[st]=hp[que[st]].crosspoint(hp[que[ed]]);
         con.n=ed-st+;
         int j=st,i=;
         for (;j<=ed;i++,j++)
         {
             con.p[i]=p[j];
         }
     }
 };

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

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

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

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

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

     return ;
 }