【计算几何】 Codeforces Beta Round #67 (Div. 2) E. Ship's Shortest Path

读懂题意其实是模板题。就是细节略多。

#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
#define EPS 0.00000001
struct Point
{
	double x,y;
	Point(){}
	Point(const double &X,const double &Y){x=X;y=Y;}
	double Length()
	  {
	  	return sqrt(x*x+y*y);
	  }
}p[3],a[31];
struct data
{
	Point p;
	int I,J;
	data(){}
	data(const Point &P,const int &II,const int &JJ)
	  {
	  	p=P;
	  	I=II;
	  	J=JJ;
	  }
}b[31];
int e;
typedef Point Vector;
Vector operator - (const Point &a,const Point &b)
{
    return Vector(a.x-b.x,a.y-b.y);
}
Vector operator + (const Vector &a,const Vector &b)
{
    return Vector(a.x+b.x,a.y+b.y);
}
double Cross(Vector a,Vector b)
{
    return a.x*b.y-a.y*b.x;
}
Vector operator * (const double &K,const Vector &v)
{
    return Vector(K*v.x,K*v.y);
}
Point GetIntersection(Point P,Vector v,Point Q,Vector w)
{
    return P+(Cross(w,P-Q)/Cross(v,w))*v;
}
double dot(Vector a,Vector b)
{
	return a.x*b.x+a.y*b.y;
}
bool InLine(Point a,Point P,Point Q)
{
	if(fabs(Cross(a-P,Q-P))>=EPS)
	  return 0;
	return dot(a-P,a-Q)<EPS;
}
int n;
int main()
{
//	freopen("s.in","r",stdin);
	double sum=0;
	for(int i=0;i<2;++i)
	  scanf("%lf%lf",&p[i].x,&p[i].y);
	scanf("%d",&n);
	for(int i=0;i<n;++i)
	  scanf("%lf%lf",&a[i].x,&a[i].y);
	for(int i=0;i<n;++i)
	  if(fabs(Cross(p[1]-a[(i+1)%n],a[i]-p[0]))<EPS)
	    {
	      printf("%.9lf\n",(p[1]-p[0]).Length());
	      return 0;
	    }
	for(int i=0;i<n;++i)
	  sum+=(a[(i+1)%n]-a[i]).Length();
					/*double sum2=0;
	  	  	  	  	for(int k=i+1;k<j;++k)
	  	  	  	  	  sum2+=(a[(k+1)%n]-a[k]).Length();
	  	  	  	  	sum2+=(a[i+1]-tp).Length();
	  	  	  	  	sum2+=(tp2-a[j]).Length();
	  	  	  	  	double td=min((tp-p[0]).Length()+(tp2-p[1]).Length(),
							(tp2-p[0]).Length()+(tp-p[1]).Length());
	  	  	  	  	printf("%.9lf\n",td+min(sum-sum2,min(sum2,(tp2-tp).Length()*2.0)));*/
	for(int i=0;i<n;++i)
	  {
	  	Point tp=GetIntersection(p[1],p[1]-p[0],a[i],a[(i+1)%n]-a[i]);
	  	if(InLine(tp,a[i],a[(i+1)%n]) && InLine(tp,p[0],p[1]))
	  	  {
	  	  	for(int j=i+1;j<n;++j)
	  	  	  {
	  	  	  	Point tp2=GetIntersection(p[1],p[1]-p[0],a[j],a[(j+1)%n]-a[j]);
	  	  	  	if(InLine(tp2,a[j],a[(j+1)%n]) && InLine(tp2,p[0],p[1]))
	  	  	  	  b[++e]=data(tp2,i,j);
	  	  	  }
	  	  	for(int j=1;j<=e;++j)
	  	  	  if(fabs(b[j].p.x-tp.x)>=EPS || fabs(b[j].p.y-tp.y)>=EPS)
	  	  	    {
	  	  	      int I=b[j].I,J=b[j].J;
	  	  	      Point tp2=b[j].p;
	  	  	      double sum2=0;
	  	  	  	  for(int k=I+1;k<J;++k)
	  	  	  	  	sum2+=(a[(k+1)%n]-a[k]).Length();
	  	  	  	  sum2+=(a[I+1]-tp).Length();
	  	  	  	  sum2+=(tp2-a[J]).Length();
	  	  	  	  double td=min((tp-p[0]).Length()+(tp2-p[1]).Length(),
					(tp2-p[0]).Length()+(tp-p[1]).Length());
	  	  	  	  printf("%.9lf\n",td+min(sum-sum2,min(sum2,(tp2-tp).Length()*2.0)));
	  	  	  	  return 0;
	  	  	    }
	  	  		  int I=b[1].I,J=b[1].J;
	  	  	      Point tp2=b[1].p;
	  	  	      double sum2=0;
	  	  	  	  for(int k=I+1;k<J;++k)
	  	  	  	  	sum2+=(a[(k+1)%n]-a[k]).Length();
	  	  	  	  sum2+=(a[I+1]-tp).Length();
	  	  	  	  sum2+=(tp2-a[J]).Length();
	  	  	  	  double td=min((tp-p[0]).Length()+(tp2-p[1]).Length(),
					(tp2-p[0]).Length()+(tp-p[1]).Length());
	  	  	  	  printf("%.9lf\n",td+min(sum-sum2,min(sum2,(tp2-tp).Length()*2.0)));
	  	  	  	  return 0;
	  	  }
	  }
	printf("%.9lf\n",(p[1]-p[0]).Length());
	return 0;
}