[USACO16JAN] Angry Cows G

【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。

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.

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

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.

5
8
10
3
11
1

3.0

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.