等价于是否存在一条直线穿过所有线段
判断直线与线段是否相交:
首先用两点p1,p2确定了一条直线 在用p1,p2分别与计算线段两个端点计算叉乘即可 ,叉乘之积>0就说明线段两端点在直线的同侧,也就是直线不经过此线段
注意顺序不要搞反了
#include#include #include #include #include using namespace std;const double eps=1e-8;const int maxn=100004;int dcmp(double x) { if(fabs(x) < eps) return 0; return x < 0 ? -1 : 1;}#define Point Vectorstruct Vector{ double x,y; Vector(double x=0,double y=0):x(x),y(y){}; Vector operator + (const Vector &A) const{ return Vector(x+A.x,y+A.y); } Vector operator - (const Vector &A) const{ return Vector(x-A.x,y-A.y); } Vector operator * (const double &A) const{ return Vector(x*A,y*A); } Vector operator / (const double &A) const{ return Vector(x/A,y/A); } bool operator == (const Vector &A) const{ return dcmp(x-A.x)==0&&dcmp(y-A.y)==0; }};struct Line{ Point p1,p2; Line(){}; Line(Point p1,Point p2):p1(p1),p2(p2){}}li[maxn];bool operator < (Line l1,Line l2){ if(l1.p1.x==l2.p1.x) return l1.p1.y 0) return false; } return true;}int main(){ int T;scanf("%d",&T); while(T--){ scanf("%d",&n); for(int i=1;i<=n;i++){ Point p1,p2; scanf("%lf%lf%lf%lf",&p1.x,&p1.y,&p2.x,&p2.y); li[i]=Line(p1,p2); } if(n==1) {printf("Yes!\n");continue;} int flag=0; for(int i=1;i<=n;i++){ if(solve(li[i].p1,li[i].p2)) { //cout< <