bzoj千题计划126：bzoj1038: [ZJOI2008]瞭望塔

#include<cmath>
#include<cstdio>
#include<algorithm>

using namespace std;

#define N 301

const double eps=1e-7;

int n;

struct POINT
{
    double x,y;
}e[N];

struct LINE
{
    double k,b;
    bool exit;
}l[N];

bool cmp(POINT p,POINT q)
{
    return p.x<q.x;
}

double cal(double x,double y)
{
    double tmp=0;
    for(int i=1;i<n;++i)
    {
        if(!l[i].exit) continue;
        tmp=fmax(tmp,l[i].k*x+l[i].b-y);
    }
    return tmp;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;++i) scanf("%lf",&e[i].x);
    for(int i=1;i<=n;++i) scanf("%lf",&e[i].y);
    sort(e+1,e+n+1,cmp);
    for(int i=1;i<n;++i)
    {
        if(fabs(e[i].x-e[i+1].x)<eps) continue;
        l[i].k=(e[i].y-e[i+1].y)/(e[i].x-e[i+1].x);
        l[i].b=e[i].y-e[i].x*l[i].k;
        l[i].exit=true;
    }
    double L,R,mid1,mid2;
    int T;
    double ans=1e20;
    for(int i=1;i<n;++i)
    {
        if(!l[i].exit) continue;
        T=100; L=e[i].x; R=e[i+1].x;
        while(T--)
        {
            mid1=L+(R-L)/3; mid2=R-(R-L)/3;
            if(cal(mid1,l[i].k*mid1+l[i].b)<cal(mid2,l[i].k*mid2+l[i].b)) R=mid2;
            else L=mid1;
        }
        ans=fmin(ans,cal(mid1,l[i].k*mid1+l[i].b));
    }
    printf("%.3lf",ans);
}