判断线段之间的关系（D - Intersecting Lines POJ - 1269 ）

Posted 2021-02-07 letlifestop

题目链接：https://vjudge.net/contest/276358#problem/D

题目大意：每一次给你两条直线，然后问你这两条直线的关系（平行，共线，相交（输出交点））。

具体思路：先判断共线，再去判断平行，其次是相交，这些都能通过叉积来判断。

具体的证明过程晚会发吧。

AC代码：

 1 #include<iostream>
 2 #include<stack>
 3 #include<stdio.h>
 4 #include<iomanip>
 5 #include<cmath>
 6 using namespace std;
 7 # define ll long long 
 8 const int maxn = 300+100;
 9 const double eps = 1e-8;
10 int cal(int x1,int y1,int x2,int y2){
11 return x1*y2-x2*y1;
12 }
13 int main(  )  {
14     int T;
15     int x1,y1,x2,y2;
16     int x3,y3,x4,y4;
17     double  a1,a2,b1,b2,c1,c2;
18     scanf("%d",&T);
19     printf("INTERSECTING LINES OUTPUT
");
20     while(T--){
21     scanf("%d %d %d %d %d %d %d %d",&x1,&y1,&x2,&y2,&x3,&y3,&x4,&y4);
22     if(cal(x2-x1,y2-y1,x3-x1,y3-y1)==0&&cal(x2-x1,y2-y1,x4-x1,y4-y1)==0)  {
23           printf("LINE
");
24     }
25     else if(cal(x2-x1,y2-y1,x4-x3,y4-y3)==0){
26         printf("NONE
");
27     }
28     else {
29         a1=y1-y2;
30         a2=y3-y4;
31         b1=x2-x1;
32         b2=x4-x3;
33         c1=x1*y2-x2*y1;
34        c2=x3*y4-x4*y3;
35         printf("POINT %.2lf %.2lf
",(c1*b2-c2*b1)/(a2*b1-a1*b2),(c1*a2-c2*a1)/(b2*a1-b1*a2));
36     }
37     }  
38     printf("END OF OUTPUT
");
39     return 0;
40 }