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HDU/HDOJ 1086 You can Solve a Geometry Problem too

26 Apr 2011
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题目传送门:http://acm.hdu.edu.cn/showproblem.php?pid=1086

判断两条直线是否相交,感觉这是一道非常不错的题,高中学的向量积,数量积都还给老师了(其实在高数上册最后也讲过),悲催啊~~~

这里有一篇非常给力的讲解:

http://dev.gameres.com/Program/Abstract/Geometry.htm

AC代码:

#include   
using namespace std;  

typedef struct line 
{  
    double x1,y1,x2,y2;  
}line;  

int n;
line ln[105];

int mul(double a, double b, double c, double d)  
{  
    return a * d - b * c;  
}

bool judge(int i, int j)
{
    double a = mul(ln[i].x1-ln[j].x1, ln[i].y1-ln[j].y1, ln[j].x2-ln[j].x1, ln[j].y2-ln[j].y1);
    double b = mul(ln[i].x2-ln[j].x1, ln[i].y2-ln[j].y1, ln[j].x2-ln[j].x1, ln[j].y2-ln[j].y1);
    double c = a * b;

    double d = mul(ln[j].x1-ln[i].x1, ln[j].y1-ln[i].y1, ln[i].x2-ln[i].x1, ln[i].y2-ln[i].y1);
    double e = mul(ln[j].x2-ln[i].x1, ln[j].y2-ln[i].y1, ln[i].x2-ln[i].x1, ln[i].y2-ln[i].y1);
    double f = d * e;

    if(c <= 0 && f <= 0)
        return 1;
    else
        return 0;
}


int main()  
{  
    //freopen("input.txt", "r", stdin);  
    while(scanf("%d", &n;) && n)  
    {  
        for(int i=1; i<=n; ++i)  
            scanf("%lf %lf %lf %lf", &ln;[i].x1, &ln;[i].y1, &ln;[i].x2, &ln;[i].y2);  
        int count=0;  
        for(int i=1; i
using namespace std;

double p[100][2],q[100][2];

// 判断点与直线的关系
double direction(double p[],double q[] ,double r[]){
    return ((r[0]-p[0])*(q[1]-p[1])-(r[1]-p[1])*(q[0]-p[0]));
}

// 判断是否在线段构成的矩形内
bool onsegment(double p[],double q[], double r[]){
    if(((r[0]-p[0])*(r[0]-q[0])<=0)&&((r[1]-p[1])*(r[1]-q[1])<=0))
        return true;
    else return false;
}

bool judge(int i, int j){
    double d1,d2,d3,d4;
    d1=direction(p[i],q[i],p[j]);
    d2=direction(p[i],q[i],q[j]);
    d3=direction(p[j],q[j],p[i]);
    d4=direction(p[j],q[j],q[i]);
    if((d1*d2<0)&&(d3*d4<0))
        return true;
    else if(d1==0&& onsegment(p[i],q[i],p[j])==1)
        return true;
    else if(d2==0&& onsegment(p[i],q[i],q[j])==1)
        return true;
    else if(d3==0&& onsegment(p[j],q[j],p[i])==1)
        return true;
    else if(d4==0&& onsegment(p[j],q[j],q[i])==1)
        return true;
    else return false;
}

int main(){
    int n,i,j,count;
    while(scanf("%d",&n;)){
        if(n==0)    break;
        for(i=0;i<n;++i){
            scanf("%lf %lf %lf %lf",&p[i][0],&p[i][1],&q[i][0],&q[i][1]);
        }
        for(i=0,count=0;i<n;i++)
            for(j=i+1;j<n;j++)
                if(judge(i,j)==1)
                    ++count;
        printf("%d\n",count);
    }
    return 0;
}