Vanya and Lanterns
题意翻译
### 题意简述
⼀个⻓为$ L$ 的街道（左端点是 $0$，右端点是$ L$）上有 $n $个相
同的灯，第$ i$ 个灯放置的位置是 $a_i$。
- 问灯的半径⾄少要是多少，才能使得整个街道都有灯光。
### 数据范围
- $ n \le 1000$，$L \le 10^9$
题目描述
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?
输入输出格式
输入格式
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?
输出格式
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} $ .
输入输出样例
输入样例 #1
7 15
15 5 3 7 9 14 0
输出样例 #1
2.5000000000
输入样例 #2
2 5
2 5
输出样例 #2
2.0000000000
说明
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?