<span>BZOJ4509 Angry Cows（dp）</span>

/* ***********************************************
Author        :devil
************************************************ */
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <stdlib.h>
using namespace std;
typedef long long LL;
const int inf=0x3f3f3f3f;
const int mod=1e9+7;
const int N=5e4+10;
int ml[N],mr[N],a[N],n;
int main()
{
    //freopen("in.txt","r",stdin);
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]);
    sort(a+1,a+n+1);
    memset(ml,inf,sizeof(ml));
    memset(mr,inf,sizeof(mr));
    ml[1]=mr[n]=0;
    int k=1;
    for(int i=2;i<=n;i++)
    {
        while(k+1<i&&a[i]-a[k+1]>ml[k+1]+1) k++;
        ml[i]=min(a[i]-a[k],ml[k+1]+1);
    }
    k=n;
    for(int i=n-1;i>=1;i--)
    {
        while(k-1>i&&a[k-1]-a[i]>mr[k-1]+1) k--;
        mr[i]=min(a[k]-a[i],mr[k-1]+1);
    }
    double ans=inf;
    for(int i=1,j=n;i<j;)
    {
        ans=min(ans,(double)max((a[j]-a[i])/2.0,(double)max(ml[i],mr[j])+1));
        if(ml[i+1]<mr[j-1]) i++;
        else j--;
    }
    printf("%.1f\n",ans);
    return 0;
}