判断线段和直线相交 POJ 3304

 // 判断线段和直线相交 POJ 3304
 // 思路：
 // 如果存在一条直线和所有线段相交，那么平移该直线一定可以经过线段上任意两个点，并且和所有线段相交。

 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>
 #include <map>
 #include <set>
 #include <queue>
 #include <stdlib.h>
 #include <cmath>
 using namespace std;
 typedef long long LL;
 const LL inf = 1e18;
 const int N = ;
 const double eps = 1e-;

 int sgn(double x){
     if(fabs(x)<eps) return  ;
     if(x<) return -;
     return ;
 }

 struct Point{
     double x,y;
     Point(){}
     Point(double _x,double _y){
         x=_x;y=_y;
     }
     Point operator -(const Point &b)const{
         return Point(x-b.x,y-b.y);
     }
     double operator *(const Point &b)const{
         return x*b.x+y*b.y;
     }
     double operator ^(const Point &b)const{
         return x*b.y-y*b.x;
     }
 };

 struct Line{
     Point s,e;
     Line(){}
     Line(Point _s,Point _e){
         s=_s,e=_e;
     }
 };

 double xmult(Point p0,Point p1,Point p2){
     return (p1-p0)^(p2-p0);
 }

 bool Seg_inter_line(Line l1,Line l2){
     return sgn(xmult(l2.s,l1.s,l1.e))*sgn(xmult(l2.e,l1.s,l1.e))<=;
 }

 double dist(Point a,Point b){
     return sqrt((a-b)*(a-b));
 }
 Line line[N];
 bool work(Line l1,int n){
     if(sgn(dist(l1.s,l1.e))==) return false;
     for(int i=;i<n;i++){
         if(Seg_inter_line(l1,line[i])==false) return false;
     }
     return true;
 }
 int main(){
     int n,T;
     scanf("%d",&T);
     while(T--){
         scanf("%d",&n);
         double x1,y1,x2,y2;
         for(int i=;i<n;i++){
             scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
             line[i]=Line(Point(x1,y1),Point(x2,y2));
         }
         bool flag=false;
         for(int i=;i<n;i++){
             for(int j=;j<n;j++){
                 if(work(Line(line[i].s,line[j].e),n)||work(Line(line[i].s,line[j].s),n)||work(Line(line[i].e,line[j].e),n)||work(Line(line[i].e,line[j].s),n)){
                     flag=true;
                     break;
                 }
             }
             if(flag) break;
         }
         if(flag) puts("Yes!");
         else puts("No!");
     }
     return ;
 }