4thweek contest problem_B 灯笼半径问题

题目描述如下：

Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point a_i. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.

Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?

 

Input：

The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 10⁹) — the number of lanterns and the length of the street respectively.

The next line contains n integers a_i (0 ≤ a_i ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.

Output：

Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10^- 9.

Sample Input

Input：

7 15 15 5 3 7 9 14 0

Output：

2.5000000000

Input：

2 5 2 5

Output：

2.0000000000

Hint：

Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment[3, 5]. Thus, the whole street will be lit。

代码及分析：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int m=1005;
int point[m],len[m];

int main()
{
    int n,l,i;
    double r;
    scanf("%d%d",&n,&l);
    point[0]=0;     //先设置一个point[0]=0,目的仅仅是为了求len[1]，后面可以忽略point[0];
    for(i=1;i<=n;i++)   //注意：从point[1]开始输入
        scanf("%d",&point[i]);
    sort(point+1,point+n+1);   //从point[1]到point[n]排序！！
    //for(i=1;i<=n;i++)
    // printf("%d /",point[i]);
    //memset(point,0,sizeof(point));
    
    for(i=1;i<=n;i++)
        len[i]=point[i]-point[i-1];
    
    sort(len+1,len+n+1);
    //for(i=1;i<=n;i++)
    // printf("%d  ",len[i]);
    double maxn=len[n];
    r=maxn/2.0;
    //printf("%llf\n",r);
    double back=l-point[n];      //设置front记录第一个灯笼和街道首的距离
    double front=point[1]-0;     //设置back记录最后一个灯笼和街道尾的距离
    if(r<front||r<back)          // 特别注意此处分类
    {  
        double ans;
        ans=front>back?front:back;
        printf("%.10llf",ans);
    }
    else
        printf("%.10llf",r);
    return 0;
    
}