Intersection
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 12162 | Accepted: 3157 |
Description
You are to write a program that has to decide whether a given line segment intersects a given rectangle.
An example:
line: start point: (4,9)
end point: (11,2)
rectangle: left-top: (1,5)
right-bottom: (7,1)
Figure 1: Line segment does not intersect rectangle
The line is said to intersect the rectangle if the line and the rectangle have at least one point in common. The rectangle consists of four straight lines and the area in between. Although all input values are integer numbers, valid intersection points do not have to lay on the integer grid.
An example:
line: start point: (4,9)
end point: (11,2)
rectangle: left-top: (1,5)
right-bottom: (7,1)
Figure 1: Line segment does not intersect rectangle
The line is said to intersect the rectangle if the line and the rectangle have at least one point in common. The rectangle consists of four straight lines and the area in between. Although all input values are integer numbers, valid intersection points do not have to lay on the integer grid.
Input
The input consists of n test cases. The first line of the input file contains the number n. Each following line contains one test case of the format:
xstart ystart xend yend xleft ytop xright ybottom
where (xstart, ystart) is the start and (xend, yend) the end point of the line and (xleft, ytop) the top left and (xright, ybottom) the bottom right corner of the rectangle. The eight numbers are separated by a blank. The terms top left and bottom right do not imply any ordering of coordinates.
xstart ystart xend yend xleft ytop xright ybottom
where (xstart, ystart) is the start and (xend, yend) the end point of the line and (xleft, ytop) the top left and (xright, ybottom) the bottom right corner of the rectangle. The eight numbers are separated by a blank. The terms top left and bottom right do not imply any ordering of coordinates.
Output
For each test case in the input file, the output file should contain a line consisting either of the letter "T" if the line segment intersects the rectangle or the letter "F" if the line segment does not intersect the rectangle.
Sample Input
1 4 9 11 2 1 5 7 1
Sample Output
F
Source
分析：
1 #include <cstdio> 2 #include<algorithm> 3 #include<iostream> 4 #include<string> 5 #include<cstring> 6 #include<vector> 7 using namespace std; 8 struct point{ 9 double x,y; 10 }; 11 double det(point a,point b,point c){ 12 return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y); 13 } 14 point a,b,c,d,e,f; 15 bool check(point e){ 16 if(e.x>=a.x&&e.y<=a.y&&e.x<=c.x&&e.y>=c.y){ 17 return true; 18 } 19 return false; 20 } 21 double max(double a,double b){ 22 if(a>b){ 23 return a; 24 } 25 return b; 26 } 27 double min(double a,double b){ 28 if(a>b){ 29 return b; 30 } 31 return a; 32 } 33 int main(){ 34 int n; 35 cin>>n; 36 while(n--){ 37 double xl,yt,xr,yb; 38 cin>>e.x>>e.y>>f.x>>f.y>>xl>>yt>>xr>>yb; 39 if(xl>xr){ 40 double x=xl; 41 xl=xr; 42 xr=x; 43 } 44 if(yt<yb){ 45 double y=yt; 46 yt=yb; 47 yb=y; 48 } 49 a.x=xl; 50 a.y=yt; 51 b.x=xr; 52 b.y=yt; 53 c.x=xr; 54 c.y=yb; 55 d.x=xl; 56 d.y=yb; 57 if(check(e)||check(f)){//线段有至少一个端点在矩形内部或边界上 58 cout<<"T"<<endl; 59 continue; 60 } 61 double aa,bb,cc,dd; 62 aa=det(e,a,b)*det(f,a,b),bb=det(a,e,f)*det(b,e,f); 63 if(aa==0&&bb==0&&(max(e.x,f.x)<min(b.x,a.x)||max(e.y,f.y)<min(b.y,a.y)||max(b.x,a.x)<min(e.x,f.x)||max(b.y,a.y)<min(e.y,f.y))){//特殊情况：线段与矩形四条边界中的任一条共线，但满足次条件表示没有公共交点 64 cout<<"F"<<endl; 65 continue; 66 } 67 if(aa<=0&&bb<=0){//除去前面的特殊情况，满足次条件表示两线段相交 68 cout<<"T"<<endl; 69 continue; 70 } 71 /*if(det(e,b,c)*det(f,b,c)<=0&&det(b,e,f)*det(c,e,f)<=0){ 72 cout<<"det(e,b,c): "<<det(e,b,c)<<endl; 73 cout<<"det(f,b,c): "<<det(f,b,c)<<endl; 74 cout<<"det(b,e,f): "<<det(b,e,f)<<endl; 75 cout<<"det(c,e,f): "<<det(c,e,f)<<endl; 76 cout<<"T"<<endl; 77 continue; 78 }*/ 79 aa=det(e,b,c)*det(f,b,c),bb=det(b,e,f)*det(c,e,f); 80 if(aa==0&&bb==0&&(max(e.x,f.x)<min(b.x,c.x)||max(e.y,f.y)<min(b.y,c.y)||max(b.x,c.x)<min(e.x,f.x)||max(b.y,c.y)<min(e.y,f.y))){ 81 cout<<"F"<<endl; 82 continue; 83 } 84 if(aa<=0&&bb<=0){ 85 cout<<"T"<<endl; 86 continue; 87 } 88 89 aa=det(e,c,d)*det(f,c,d),bb=det(c,e,f)*det(d,e,f); 90 if(aa==0&&bb==0&&(max(e.x,f.x)<min(c.x,d.x)||max(e.y,f.y)<min(c.y,d.y)||max(c.x,d.x)<min(e.x,f.x)||max(c.y,d.y)<min(e.y,f.y))){ 91 cout<<"F"<<endl; 92 continue; 93 } 94 if(aa<=0&&bb<=0){ 95 cout<<"T"<<endl; 96 continue; 97 } 98 99 aa=det(e,d,a)*det(f,d,a),bb=det(d,e,f)*det(a,e,f); 100 if(aa==0&&bb==0&&(max(e.x,f.x)<min(a.x,d.x)||max(e.y,f.y)<min(a.y,d.y)||max(a.x,d.x)<min(e.x,f.x)||max(a.y,d.y)<min(e.y,f.y))){ 101 cout<<"F"<<endl; 102 continue; 103 } 104 if(aa<=0&&bb<=0){ 105 cout<<"T"<<endl; 106 continue; 107 } 108 109 cout<<"F"<<endl; 110 } 111 return 0; 112 }