Miaomiao's Geometry

　　HDU 4932  Bestcoder

Problem Description

There are N point on X-axis . Miaomiao would like to cover them ALL by using segments with same length.

There are 2 limits:

1.A point is convered if there is a segments T , the point is the left end or the right end of T.
2.The length of the intersection of any two segments equals zero.

For example , point 2 is convered by [2 , 4] and not convered by [1 , 3]. [1 , 2] and [2 , 3] are legal segments , [1 , 2] and [3 , 4] are legal segments , but [1 , 3] and [2 , 4] are not (the length of intersection doesn't equals zero), [1 , 3] and [3 , 4] are not(not the same length).

Miaomiao wants to maximum the length of segements , please tell her the maximum length of segments.

For your information , the point can't coincidently at the same position.

 

Input

There are several test cases.
There is a number T ( T <= 50 ) on the first line which shows the number of test cases.
For each test cases , there is a number N ( 3 <= N <= 50 ) on the first line.
On the second line , there are N integers Ai (-1e9 <= Ai <= 1e9) shows the position of each point.

 

Output

For each test cases , output a real number shows the answser. Please output three digit after the decimal point.

Sample Input

3

3

1 2 3

3

1 2 4

4

1 9 100 10

Sample Output

1.000

2.000

8.000

Hint

For the first sample , a legal answer is [1,2] [2,3] so the length is 1. For the second sample , a legal answer is [-1,1] [2,4] so the answer is 2. For the thired sample , a legal answer is [-7,1] , [1,9] , [10,18] , [100,108] so the answer is 8.

 

 

注意本题的答案可能是某个相邻两点的距离差的一半。会有很多人考虑 不全面，所以适合作为cf和bf题目。

初次通过部分的数据的答案不会出现距离差的 一半，不然就不好hack了。

付一组数据

6

1 5 15 18 24

答案应该为5，而不是4

#include <stdio.h>
#include <string.h>
#include <algorithm>
#include<iostream>
#include<math.h>

using namespace std;

int main()
{
    int cas,i,n,right,left;
    double res,a[55],b[120];
    cin>>cas;
    while(cas--)
    {
        cin>>n;
        int j=0;
        for(i=0;i<n;i++)
        {
            cin>>a[i];
        }
        sort(a,a+n);
        for(i=1;i<n;i++)
        {
            b[j++]=a[i]-a[i-1];
            b[j++]=(a[i]-a[i-1]) /2 ;
        }
        sort(b,b+j);
        int flag=0;
        j=j-1;
        res=(double)b[j];

        while(1)
        {
            right =0; left=0;
            flag=0;
            for(i=1;i<n;i++)
            {
                if(i==n-1) continue;
                if(a[i]-res<a[i-1] && a[i]+res>a[i+1])
                {
                    flag=1;
                    break;
                }
                if(a[i]-res>=a[i-1]) 
                {
                    if(right==1)
                    {
                        if(a[i]-a[i-1]==res) {left=1; right=0; }
                        else if(a[i]-a[i-1]>=2*res) { left=1; right=0; }
                        else if(a[i]+res<=a[i+1]) { left=0; right=1; }
                        else flag=1;
                    }
                    else { left=1; right=0; }
                }
                else if(a[i]+res<=a[i+1]) {
                    right=1;
                    left=0;
                }
                
            }
            if(flag==1) {
                j--;
                res=b[j];
            }
            else 
            {
                printf("%.3lf
",res);
                break;
            }
        }
    }
    return 0;
}