# BZOJ 1038 ZJOI2008 瞭望塔 半平面交

#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define M 310
#define eps 1e-7
using namespace std;
struct point{
double x,y;
}points[M];
struct line{
point *p1,*p2;
double k,b;
void Get_Parameters()
{
k=(double)(p1->y-p2->y)/(p1->x-p2->x);
b=p1->y-k*p1->x;
}
bool operator < (const line &x) const
{
if( fabs(k-x.k)<eps )
return b < x.b;
return k < x.k;
}
}lines[M];
int n;
double ans=1e11;
line *stack[M];int top;
inline point Get_Intersection(const line &l1,const line &l2)
{
point re;
re.x=-(l1.b-l2.b)/(l1.k-l2.k);
re.y=l1.k*re.x+l1.b;
return re;
}
void Insert(line &l)
{
while(top>=2)
{
if( Get_Intersection(*stack[top],l).x < Get_Intersection(*stack[top-1],*stack[top]).x )
--top;
else
break;
}
stack[++top]=&l;
}
double F(double x)
{
int i;
double re=0;
for(i=1;i<=top;i++)
re=max(re,stack[i]->k*x+stack[i]->b);
return re;
}
double G(double x)
{
int i;
for(i=n;i;i--)
if(x>=points[i].x)
break;
return points[i].y+(x-points[i].x)/(points[i+1].x-points[i].x)*(points[i+1].y-points[i].y);
}
int main()
{
int i;
cin>>n;
for(i=1;i<=n;i++)
scanf("%lf",&points[i].x);
for(i=1;i<=n;i++)
scanf("%lf",&points[i].y);
for(i=1;i<n;i++)
lines[i].p1=points+i,lines[i].p2=points+i+1,lines[i].Get_Parameters();
sort(lines+1,lines+n);
for(i=1;i<n;i++)
if(i==n-1||fabs(lines[i].k-lines[i+1].k)>eps)
Insert(lines[i]);
for(i=1;i<=n;i++)
ans=min(ans,F(points[i].x)-points[i].y);
for(i=1;i<top;i++)
{
point p=Get_Intersection(*stack[i],*stack[i+1]);
ans=min(ans,p.y-G(p.x));
}
printf("%.3lf\n",ans);
}


posted @ 2016-01-23 09:25  mengfanrong  阅读(448)  评论(1编辑  收藏  举报