# P3132 [USACO16JAN]愤怒的奶牛Angry Cows

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• 题目提供者 FarmerJohn2
• 评测方式 云端评测
• 标签 Tarjan 概率论,统计 贪心 USACO 2016
• 难度 提高+/省选-
• 时空限制 1000ms / 128MB
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## 题目背景

【题目描述】

奶牛Bessie设计了一个游戏：“愤怒的奶牛”。游戏的原型是：有一些可爆炸的草堆分布在一条数轴的某些坐标上，玩家用弹弓把一头奶牛发射到数轴上。奶牛砸到数轴上的冲击波会引发附近的草堆爆炸，而被引爆的草堆可能会引爆其他草堆。游戏的目标是玩家用一只奶牛炸掉所有的草堆。

有N个草堆在数轴的不同位置，坐标为x1,x2,….,xn。如果玩家以能量R把奶牛发射到坐标x，就会引爆半径R及以内的的草堆，即坐标范围[x−R,x+R]的草堆都会燃爆，每个被奶牛引爆的草堆又会2次引爆半径R-1及以内的的草堆，2次引爆的草堆又会3次引爆半径R-2及以内的的草堆...直到一次引爆后没有其他草堆被波及或半径为0。

现在只有1头奶牛，能量为R，请计算如果要引爆所有的草堆，最小的R是多少？

【输入格式】

第一行：1个整数N(2≤N≤50,000)。

下面有N行,每行一个整数：x1,x2,…,xn，范围在[0…1,000,000,000]。

【输出格式】

输出最小的能量R，保留1位小数。

感谢wenyu0909和世界第一弱的翻译。

## 题目描述

Bessie the cow has designed what she thinks will be the next big hit video game: "Angry Cows". The premise, which she believes is completely original, is that the player shoots a cow with a slingshot into a one-dimensional scene consisting of a set of hay bales located at various points on a number line; the cow lands with sufficient force to detonate the hay bales in close proximity to her landing site, which in turn might set of a chain reaction that causes additional hay bales to explode. The goal is to use a single cow to start a chain reaction that detonates all the hay bales.

There are $N$ hay bales located at distinct integer positions $x_1, x_2, \ldots, x_N$ on the number line. If a cow is launched with power $R$ landing at position $x$, this will causes a blast of "radius $R$", engulfing all hay bales within the range $x-R \ldo s x+R$. These hay bales then themselves explode (all simultaneously), each with a blast radius of $R-1$. Any not-yet-exploded bales caught in these blasts then all explode (all simultaneously) with blast radius $R-2$, and so on.

Please determine the minimum amount of power $R$ with which a single cow may be launched so that, if it lands at an appropriate location, it will cause subsequent detonation of every single hay bale in the scene.

## 输入输出格式

输入格式：

The first line of input contains $N$ ($2 \leq N \leq 50,000$). The remaining

$N$ lines all contain integers $x_1 \ldots x_N$ (each in the range

$0 \ldots 1,000,000,000$).

输出格式：

Please output the minimum power $R$ with which a cow must be launched in order

to detonate all the hay bales. Answers should be rounded and printed to exactly

1 decimal point.

## 输入输出样例

输入样例#1： 复制
5
8
10
3
11
1
输出样例#1： 复制
3.0

## 说明

In this example, a cow launched with power 3 at, say, location 5, will cause

immediate detonation of hay bales at positions 3 and 8. These then explode

(simultaneously) each with blast radius 2, engulfing bales at positions 1 and

10, which next explode (simultaneously) with blast radius 1, engulfing the final

bale at position 11, which finally explodes with blast radius 0.

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