[日常摸鱼]bzoj1038[ZJOI2008]瞭望塔-半平面交

#include<cstdio>
#include<iostream>
#include<algorithm>
#define rep(i,n) for(register int i=1;i<=n;i++)
#define REP(i,a,b) for(register int i=a;i<=b;i++)
#define debug(x) cout<<#x<<" = "<<x<<endl
typedef double dl;
using namespace std;
const int N=305;
const dl INF=~0u>>1;
struct P
{
    dl x,y;
    P(dl x=0,dl y=0):x(x),y(y){}
}p[N],ps[N];
struct L
{
    dl k,b;
}l[N];
inline bool operator < (L a,L b){return a.k<b.k||(a.k==b.k&&a.b>b.b);}
inline bool operator==(L a,L b){return a.k==b.k;}
inline dl get_x(L a,L b){return -(b.b-a.b)/(b.k-a.k);}
inline dl get_val(L a,dl x){return a.k*x+a.b;}
inline L get_line(P a,P b)
{
    L res;res.k=(a.y-b.y)/(a.x-b.x);
    res.b=a.y-res.k*a.x;return res;
}
inline double calc(dl x,L a,L b)
{
    return get_val(a,x)-get_val(b,x);
}
int r,m,n;
inline void input()
{
    scanf("%d",&n);
    rep(i,n)scanf("%lf",&p[i].x);
    rep(i,n)scanf("%lf",&p[i].y);
}
inline void work()
{
    rep(i,n-1)l[i]=get_line(p[i],p[i+1]);
    m=n-1;sort(l+1,l+m+1);m=unique(l+1,l+m+1)-l-1;
    rep(i,m)
    {
        while(r>1&&get_x(l[r],l[r-1])-get_x(l[r-1],l[i])>=0)r--;l[++r]=l[i];
    }m=r;
    int i=1,j=1;dl ans=1e30; 
    #define updata(x) ans=min(ans,calc(x,l[j],get_line(p[i],p[i+1])))
    while(i<n&&j<=m)
    {
        dl L=(j>1?get_x(l[j-1],l[j]):-INF);
        dl R=(j<m?get_x(l[j],l[j+1]):INF);
        if(L>p[i+1].x){i++;continue;}
        if(R<p[i].x){j++;continue;}
        updata(max(L,p[i].x));updata(min(R,p[i+1].x));
        if(R<p[i+1].x)j++;
        else i++;
    }
    if(n<=2)ans=0;
    printf("%.3lf",ans);
}
int main()
{
    //freopen("input.in","r",stdin);
    input();
    work();
    return 0;
}