判断线段和直线相交 POJ 3304

Posted 2020-08-07 blues

 1 // 判断线段和直线相交 POJ 3304
 2 // 思路：
 3 // 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。
 4 
 5 #include <cstdio>
 6 #include <cstring>
 7 #include <iostream>
 8 #include <algorithm>
 9 #include <map>
10 #include <set>
11 #include <queue>
12 #include <stdlib.h>
13 #include <cmath>
14 using namespace std;
15 typedef long long LL;
16 const LL inf = 1e18;
17 const int N = 5000;
18 const double eps = 1e-8;
19 
20 int sgn(double x){
21     if(fabs(x)<eps) return  0;
22     if(x<0) return -1;
23     return 1;
24 }
25 
26 struct Point{
27     double x,y;
28     Point(){}
29     Point(double _x,double _y){
30         x=_x;y=_y;
31     }
32     Point operator -(const Point &b)const{
33         return Point(x-b.x,y-b.y);
34     }
35     double operator *(const Point &b)const{
36         return x*b.x+y*b.y;
37     }
38     double operator ^(const Point &b)const{
39         return x*b.y-y*b.x;
40     } 
41 };
42 
43 struct Line{
44     Point s,e;
45     Line(){}
46     Line(Point _s,Point _e){
47         s=_s,e=_e;
48     }
49 };
50 
51 double xmult(Point p0,Point p1,Point p2){
52     return (p1-p0)^(p2-p0);
53 }
54 
55 bool Seg_inter_line(Line l1,Line l2){
56     return sgn(xmult(l2.s,l1.s,l1.e))*sgn(xmult(l2.e,l1.s,l1.e))<=0;
57 }
58 
59 double dist(Point a,Point b){
60     return sqrt((a-b)*(a-b));
61 }
62 Line line[N];
63 bool work(Line l1,int n){
64     if(sgn(dist(l1.s,l1.e))==0) return false;
65     for(int i=0;i<n;i++){
66         if(Seg_inter_line(l1,line[i])==false) return false;
67     }
68     return true;
69 }
70 int main(){
71     int n,T;
72     scanf("%d",&T);
73     while(T--){
74         scanf("%d",&n);
75         double x1,y1,x2,y2;
76         for(int i=0;i<n;i++){
77             scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
78             line[i]=Line(Point(x1,y1),Point(x2,y2));
79         }
80         bool flag=false;
81         for(int i=0;i<n;i++){
82             for(int j=0;j<n;j++){
83                 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)){
84                     flag=true;
85                     break;
86                 }
87             }
88             if(flag) break;
89         }
90         if(flag) puts("Yes!");
91         else puts("No!");
92     }
93     return 0;
94 }