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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