hdu1086 You can Solve a Geometry Problem too （判断两线段是否相交）

You can Solve a Geometry Problem too

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 9195    Accepted Submission(s): 4498

Problem Description

Many geometry（几何）problems were designed in the ACM/ICPC. And now, I also prepare a geometry problem for this final exam. According to the experience of many ACMers, geometry problems are always much trouble, but this problem is very easy, after all we are now attending an exam, not a contest :)
Give you N (1<=N<=100) segments（线段）, please output the number of all intersections（交点）. You should count repeatedly if M (M>2) segments intersect at the same point.

Note:
You can assume that two segments would not intersect at more than one point. 

 

Input

Input contains multiple test cases. Each test case contains a integer N (1=N<=100) in a line first, and then N lines follow. Each line describes one segment with four float values x1, y1, x2, y2 which are coordinates of the segment’s ending. 
A test case starting with 0 terminates the input and this test case is not to be processed.

 

Output

For each case, print the number of intersections, and one line one case.

 

Sample Input

2 0.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 3 0.00 0.00 1.00 1.00 0.00 1.00 1.00 0.000 0.00 0.00 1.00 0.00 0

 

Sample Output

1 3

 

Author

lcy

 

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解析：http://dev.gameres.com/Program/Abstract/Geometry.htm#判断两线段是否相交
                 需要注意的是，在做跨立实验的时候，需要同时满足 L1的两个端点在L2两端，L2的两个端点在 L1 两端。
           比如这组数据：
           2
           -1.00 0.00 1.00 1.00
          1.0 0.0 2.0 0.0
代码：

#include
#include
using namespace std;

const int maxn=1e2;
struct tnode{
    double x,y;
}a[maxn*2+10];

bool ok(int i,int j)
{
  if(min(a[i].x,a[i+1].x)>max(a[j].x,a[j+1].x))return 0;
  if(max(a[i].x,a[i+1].x)max(a[j].y,a[j+1].y))return 0;
  if(max(a[i].y,a[i+1].y)0)return 0; 

  x1=a[i+1].x-a[i].x,y1=a[i+1].y-a[i].y;
  x3=a[j+1].x-a[i].x,y3=a[j+1].y-a[i].y;
  x2=a[j].x-a[i].x,y2=a[j].y-a[i].y;
  return (x1*y2-x2*y1)*(x1*y3-x3*y1)<=0;
}

int main()
{
  //freopen("1.in","r",stdin);
  
  int n,i,j,ans;
  while(scanf("%d",&n),n)
    {
      for(n*=2,i=1;i<=n;i++)
        scanf("%lf%lf",&a[i].x,&a[i].y);
      for(ans=0,i=1;i<=n;i+=2)
        for(j=i+2;j<=n;j+=2)ans+=ok(i,j);
      printf("%d\n",ans);
    }
  return 0;
}