POJ 1039 Pipe | 线段相交

题目:

给一个管子,有很多转弯处,问从管口的射线射进去最长能射到多远

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题解:

根据黑书,可以证明的是这条光线一定经过了一个上顶点和下顶点

所以我们枚举每对上下顶点就可以了

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#define eps 1e-5
using namespace std;
bool dcmp(double x,double y)
{
    if (fabs(x-y)>eps) return 1;
    return 0;
}
struct point
{
    double x,y;
    point () {};
    point (double _x,double _y)
	{
	    x=_x,y=_y;
	}
    point operator + (const point &a)const
	{
	    return point(x+a.x,y+a.y);
	}
    point operator - (const point &a) const
	{
	    return point(x-a.x,y-a.y);
	}
    double operator * (const point &a)const
	{
	    return x*a.y-a.x*y;
	}
    double dot (const point &a,const point &b)
	{
	    return a.x*b.x+a.y*b.y;
	}
    bool operator < (const point &a)const
	{
	    return x<a.x;
	}
    bool operator == (const point &a)const
	{
	    return dcmp(x,a.x) && dcmp(y,a.y);
	}
}up[105],down[105];
inline double Max(double a,double b)
{
    return a>b?a:b;
}
double Multi(point a,point b,point c)
{
    return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);
}
bool Across(point a,point b,point c,point d)
{
    double tmp=Multi(c,b,a)*Multi(d,b,a);
    if (tmp<0 || fabs(tmp)<eps) return 1;
    return 0;
}
double getIntersect(point a,point b,point c,point d)
{
    double A1=b.y-a.y,B1=a.x-b.x,C1=(b.x-a.x)*a.y-(b.y-a.y)*a.x;
    double A2=d.y-c.y,B2=c.x-d.x,C2=(d.x-c.x)*c.y-(d.y-c.y)*c.x;
    return (C2*B1-C1*B2)/(A1*B2-A2*B1);
}
int n,flag;
double ans;
int main()
{
    while (scanf("%d",&n) && n)
    {
	for (int i=0;i<n;i++)
	{
	    scanf("%lf%lf",&up[i].x,&up[i].y);
	    down[i].x=up[i].x;
	    down[i].y=up[i].y-1;
	}
	ans=up[0].x;
	flag=0;
	for (int i=0;i<n && !flag;i++)
	    for (int j=0;j<n && !flag;j++)
		if (i!=j)
		{
		    int k;
 		    for  (k=0;k<n;k++)
			if (!Across(up[i],down[j],up[k],down[k])) break;
		    if (k==n) flag=1;
		    else if (k>i && k>j)
		    {
			double tmp;
			tmp=getIntersect(up[i],down[j],up[k-1],up[k]);
			//	printf("%.2f\n",tmp);
			if (tmp>ans) ans=tmp;
			tmp=getIntersect(up[i],down[j],down[k-1],down[k]);
			//	printf("%.2f\n",tmp);
			if (tmp>ans) ans=tmp;
		    }
		}
  	if (flag) puts("Through all the pipe.");
	else printf("%.2f\n",ans);
    }
    return 0;
}