半平面交的板子
//By SiriusRen #include <bits/stdc++.h> #define double long double using namespace std; const int N=100050; const double eps=1e-10; int n,m,xx,yy,tot; double Ans; vector<int>vec[N]; struct Point{double x,y;}point[N]; struct Line{Point a,b;double angle;}line[N],q[N]; void addline(Line &l,Point a,Point b){l.a=a,l.b=b,l.angle=atan2(b.y-a.y,b.x-a.x); } Point operator-(Point a,Point b){Point c;c.x=a.x-b.x,c.y=a.y-b.y;return c; } double operator*(Point a,Point b){return a.x*b.y-a.y*b.x; } bool operator<(Line a,Line b){if(a.angle==b.angle)return (b.b-a.a)*(b.a-a.a)>0;return a.angle<b.angle; } Point inter(Line a,Line b){double k1,k2,t;k1=(a.b-b.a)*(b.b-b.a);k2=(b.b-b.a)*(a.a-b.a);t=k1/(k1+k2);Point ans;ans.x=a.b.x+(a.a.x-a.b.x)*t;ans.y=a.b.y+(a.a.y-a.b.y)*t;return ans; } double dis(Point x,Point y){x=y-x;return sqrt(x.x*x.x+x.y*x.y); } bool judge(Line a,Line b,Line t){Point p=inter(a,b);return (t.a-p)*(t.b-p)<0; } void bpmj(){sort(line+1,line+1+tot);n=0;for(int i=1;i<=tot;i++){if(abs(line[i].angle-line[i-1].angle)>eps)n++;line[n]=line[i];}int r=1,l=0;q[0]=line[1],q[1]=line[2];for(int i=3;i<=n;i++){while(l<r&&judge(q[r],q[r-1],line[i]))r--;while(l<r&&judge(q[l],q[l+1],line[i]))l++;q[++r]=line[i];}while(l<r&&judge(q[r],q[r-1],q[l]))r--;while(l<r&&judge(q[l],q[l+1],q[r]))l++;q[r+1]=q[l],tot=0;for(int i=l;i<=r;i++)point[++tot]=inter(q[i],q[i+1]);point[++tot]=point[1];for(int i=1;i<tot;i++)Ans+=dis(point[i],point[i+1]); } int main(){scanf("%d%d",&n,&m);for(int i=1;i<=n;i++)scanf("%Lf%Lf",&point[i].x,&point[i].y);Ans=-dis(point[1],point[n]);for(int i=1;i<=m;i++){scanf("%d%d",&xx,&yy);if(xx>yy)swap(xx,yy);vec[xx].push_back(yy);}for(int i=1,j,k;i<=n;i++){sort(vec[i].begin(),vec[i].end());for(j=n,k=vec[i].size()-1;j>i&&~k;j--,k--)if(vec[i][k]!=j)break;if(i==1&&j==n){printf("%.10Lf\n",dis(point[1],point[n]));return 0;}if(j>i)addline(line[++tot],point[j],point[i]);}addline(line[++tot],point[1],point[n]);bpmj();printf("%.10Lf\n",Ans); }
