【hdu】 Intersection 线段相交 cross+quick

Intersection

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 20000/10000K (Java/Other)

Total Submission(s) : 6   Accepted Submission(s) : 6

Problem 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.

 

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.

 

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

14 9 11 2 1 5 7 1

 

Sample Output

F

 

Source

PKU

 
这么漂亮的代码搞了半天终于ac
1.point点一定不用int，需用double类型
2.线段判交：快速排斥（以P1P2为对角线的矩形S1是否和以P3P4为对角线的矩形S2相交），跨立实验（点P1，P2必然在线段P3P4的不同侧，点P3，P4必然在线段P1P2的不同侧，两者关系&&）

#include<cstdio>using namespace std;#define eps 1e-8double x1,y1,x2,y2,x3,y3,x4,y4;//x1,x2 denotes the line,x3,x4 denotes the rec.y etc...struct Point{double x,y;    Point(double a=0.0,double b=0.0){x=a,y=b;}};struct Line{Point p,q;Line(Point u,Point v):p(u),q(v){}Line(){}}s[5];inline double max(double a,double b) {return a>b?a:b;}inline double min(double a,double b) {return a<b?a:b;}void swap(double &a,double &b){double t=a;a=b;b=t;}//(p1-p0)*(p2-p0)double cross(Point p1,Point p2,Point p0){return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x);}bool quick(Line a,Line b){if(min(a.p.x,a.q.x)<=max(b.p.x,b.q.x)&&min(b.p.x,b.q.x)<=max(a.p.x,a.q.x)&&min(a.p.y,a.q.y)<=max(b.p.y,b.q.y)&&min(b.p.y,b.q.y)<=max(a.p.y,a.q.y)&&cross(a.p,a.q,b.p)*cross(a.p,a.q,b.q)<=0&&cross(b.p,b.q,a.p)*cross(b.p,b.q,a.q)<=0)  //由于算线段的端点和另一线段相交的情况。。。return true;return false;}bool check(Line k){if(k.p.x>=x3&&k.p.x<=x4&&k.p.y>=y4&&k.p.y<=y3||k.q.x>=x3&&k.q.x<=x4&&k.q.y>=y4&&k.q.y<=y3) return true;return false;}int main(){int T;scanf("%d",&T);while(T--){scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&x1,&y1,&x2,&y2,&x3,&y3,&x4,&y4);if(x3>x4) swap(x3,x4);if(y3<y4) swap(y3,y4);s[0]=Line(Point(x1,y1),Point(x2,y2));s[1]=Line(Point(x3,y3),Point(x4,y3));s[2]=Line(Point(x4,y3),Point(x4,y4));s[3]=Line(Point(x3,y4),Point(x4,y4));s[4]=Line(Point(x3,y3),Point(x3,y4));if(quick(s[0],s[1])||quick(s[0],s[2])||quick(s[0],s[3])||quick(s[0],s[4])||check(s[0]))        printf("T\n");else printf("F\n");}return 0;}

附上poj测试数据：

684 9 11 2 1 1 7 511 2 4 9 1 1 7 512 12 24 24 19 5 25 174 6 15 9 1 1 11 1119 5 25 17 12 12 24 240 18 8 12 1 1 11 112 4 4 2 1 1 11 11-4 9 -11 2 -1 1 -7 5-11 2 -4 9 -1 1 -7 5-12 12 -24 24 -19 5 -25 17-4 6 -15 9 -1 1 -11 11-19 5 -25 17 -12 12 -24 240 18 -8 12 -1 1 -11 11-2 4 -4 2 -1 1 -11 114 -9 11 -2 1 -1 7 -511 -2 4 -9 1 -1 7 -512 -12 24 -24 19 -5 25 -174 -6 15 -9 1 -1 11 -1119 -5 25 -17 12 -12 24 -240 -18 8 -12 1 -1 11 -112 -4 4 -2 1 -1 11 -11-4 -9 -11 -2 -1 -1 -7 -5-11 -2 -4 -9 -1 -1 -7 -5-12 -12 -24 -24 -19 -5 -25 -17-4 -6 -15 -9 -1 -1 -11 -11-19 -5 -25 -17 -12 -12 -24 -240 -18 -8 -12 -1 -1 -11 -11-2 -4 -4 -2 -1 -1 -11 -119 1 9 2 4 3 9 69 2 9 1 4 3 9 610 3 13 3 4 3 9 613 3 10 3 4 3 9 610 6 14 6 4 3 9 614 6 10 6 4 3 9 69 7 9 10 4 3 9 69 10 9 7 4 3 9 64 7 4 10 4 3 9 64 10 4 7 4 3 9 60 6 3 6 4 3 9 63 6 0 6 4 3 9 61 3 3 3 4 3 9 63 3 1 3 4 3 9 64 0 4 2 4 3 9 64 2 4 0 4 3 9 65 3 8 5 4 3 9 68 5 5 3 4 3 9 65 3 8 3 4 3 9 68 3 5 3 4 3 9 66 4 6 5 4 3 9 66 5 6 4 4 3 9 64 3 9 6 4 3 9 69 6 4 3 4 3 9 64 3 5 4 4 3 9 65 4 4 3 4 3 9 65 3 8 3 4 3 9 68 3 5 3 4 3 9 65 3 9 3 4 3 9 69 3 5 3 4 3 9 64 4 4 5 4 3 9 64 5 4 4 4 3 9 64 3 4 5 4 3 9 64 5 4 3 4 3 9 64 3 4 6 4 3 9 64 6 4 3 4 3 9 69 2 9 5 4 3 9 69 5 9 2 4 3 9 69 2 9 7 4 3 9 69 7 9 2 4 3 9 6