HDU 1086 You can Solve a Geometry Problem too

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

 

题解:

直接判断线段两端点是否分别在另一线段两端

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const int N=205;const double eps=1e-4;
struct P{
    double x,y;
    P(){};
    P(double _x,double _y){x=_x;y=_y;}
    P operator- (P a)const{
        return P(x-a.x,y-a.y);
    }
    double operator^ (const P a)const{
        return x*a.y-a.x*y;
    }
    P operator* (double k)const{
        return P(k*x,k*y);
    }
    P operator+ (const P a)const{
        return P(x+a.x,y+a.y);
    }
};
int n;
struct Line{
    P px,py;
}a[N];
double dot(P A,P B,P C){
    return ((A-C)^(B-C));
}
bool check(int i,int j){
    P pi1=a[i].px,pi2=a[i].py,pj1=a[j].px,pj2=a[j].py;
    double t1,t2;
    t1=dot(pi1,pi2,pj1)*dot(pi1,pi2,pj2);
   t2=dot(pj1,pj2,pi1)*dot(pj1,pj2,pi2);
    if(t1<eps && t2<eps)return true;
    return false;
}
void work(){
    for(int i=1;i<=n;i++){
        scanf("%lf%lf%lf%lf",&a[i].px.x,&a[i].px.y,&a[i].py.x,&a[i].py.y);
    }
    int ans=0;
    for(int i=1;i<=n;i++){
        for(int j=i+1;j<=n;j++){
            if(check(i,j))ans++;
        }
    }
    printf("%d
",ans);
}
int main()
{
    while(scanf("%d",&n)){
        if(!n)break;
        work();
    }
    return 0;
}