POJ 2451 Uyuw's Concert(半平面交nlgn)
//#pragma comment(linker, "/STACK:16777216") //for c++ Compiler #include <stdio.h> #include <iostream> #include <cstring> #include <cmath> #include <stack> #include <queue> #include <vector> #include <algorithm> #define ll long long #define Max(a,b) (((a) > (b)) ? (a) : (b)) #define Min(a,b) (((a) < (b)) ? (a) : (b)) #define Abs(x) (((x) > 0) ? (x) : (-(x))) #define eps 1e-11 #define zero(a) fabs(a)<eps using namespace std; const int INF = 0x3f3f3f3f; const int N = 20005; struct Point{ double x,y; }p[N*2]; struct Segment{ Point s,e; double angle; void get_angle(){angle=atan2(e.y-s.y,e.x-s.x);} }seg[N]; int m; //叉积为正说明,p2在p0-p1的左侧 double xmul(Point p0,Point p1,Point p2){ return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y); } Point Get_Intersect(Segment s1,Segment s2){ double u=xmul(s1.s,s1.e,s2.s),v=xmul(s1.e,s1.s,s2.e); Point t; t.x=(s2.s.x*v+s2.e.x*u)/(u+v);t.y=(s2.s.y*v+s2.e.y*u)/(u+v); return t; } bool cmp(Segment s1,Segment s2){ //先按极角排序 if(s1.angle>s2.angle) return true; //极角相等,内侧的在前 else if(zero(s1.angle-s2.angle)&&xmul(s2.s,s2.e,s1.e)>-eps) return true; return false; } void HalfPlaneIntersect(Segment seg[],int n){ sort(seg,seg+n,cmp); int tmp=1; for(int i=1;i<n;i++) if(!zero(seg[i].angle-seg[tmp-1].angle)) seg[tmp++]=seg[i]; n=tmp; Segment deq[N]; deq[0]=seg[0];deq[1]=seg[1]; int head=0,tail=1; for(int i=2;i<n;i++){ while(head<tail&&xmul(seg[i].s,seg[i].e,Get_Intersect(deq[tail],deq[tail-1]))<-eps) tail--; while(head<tail&&xmul(seg[i].s,seg[i].e,Get_Intersect(deq[head],deq[head+1]))<-eps) head++; deq[++tail]=seg[i]; } while(head<tail&&xmul(deq[head].s,deq[head].e,Get_Intersect(deq[tail],deq[tail-1]))<-eps) tail--; while(head<tail&&xmul(deq[tail].s,deq[tail].e,Get_Intersect(deq[head],deq[head+1]))<-eps) head++; if(head==tail) return; m=0; for(int i=head;i<tail;i++) p[m++]=Get_Intersect(deq[i],deq[i+1]); if(tail>head+1) p[m++]=Get_Intersect(deq[head],deq[tail]); } double Get_area(Point p[],int &n){ double area=0; for(int i=1;i<n-1;i++) area+=xmul(p[0],p[i],p[i+1]); return fabs(area)/2.0; } int main(){ int n; while(scanf("%d",&n)!=EOF){ seg[0].s.x=0;seg[0].s.y=0;seg[0].e.x=10000;seg[0].e.y=0;seg[0].get_angle(); seg[1].s.x=10000;seg[1].s.y=0;seg[1].e.x=10000;seg[1].e.y=10000;seg[1].get_angle(); seg[2].s.x=10000;seg[2].s.y=10000;seg[2].e.x=0;seg[2].e.y=10000;seg[2].get_angle(); seg[3].s.x=0;seg[3].s.y=10000;seg[3].e.x=0;seg[3].e.y=0;seg[3].get_angle(); for(int i=0;i<n;i++){ scanf("%lf%lf%lf%lf",&seg[i+4].s.x,&seg[i+4].s.y,&seg[i+4].e.x,&seg[i+4].e.y); seg[i+4].get_angle(); } HalfPlaneIntersect(seg,n+4); printf("%.1f\n",Get_area(p,m)); } return 0; }