P3515 [POI2011]Lightning Conductor

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  • 题目提供者 洛谷
  • 评测方式 云端评测
  • 标签 动态规划,动规,dp 斜率优化 POI 2011 高性能
  • 难度 省选/NOI-
  • 时空限制 1000ms / 128MB

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    题目描述

    Progressive climate change has forced the Byteburg authorities to build a huge lightning conductor that would protect all the buildings within the city.

    These buildings form a row along a single street, and are numbered from to .

    The heights of the buildings and the lightning conductor are non-negative integers.

    Byteburg's limited funds allow construction of only a single lightning conductor.

    Moreover, as you would expect, the higher it will be, the more expensive.

    The lightning conductor of height located on the roof of the building (of height ) protects the building (of height ) if the following inequality holds:

    where denotes the absolute value of the difference between and .

    Byteasar, the mayor of Byteburg, asks your help.

    Write a program that, for every building , determines the minimum height of a lightning conductor that would protect all the buildings if it were put on top of the building .

    已知一个长度为n的序列a1,a2,...,an。

    对于每个1<=i<=n,找到最小的非负整数p满足 对于任意的j, aj < = ai + p - sqrt(abs(i-j))

    输入输出格式

    输入格式:

    In the first line of the standard input there is a single integer () that denotes the number of buildings in Byteburg.

    Each of the following lines holds a single integer () that denotes the height of the -th building.

    输出格式:

    Your program should print out exactly lines to the standard output.

    The -th line should give a non-negative integer denoting the minimum height of the lightning conductor on the -th building.

    输入输出样例

    输入样例#1: 复制
    6
    5
    3
    2
    4
    2
    4
    输出样例#1: 复制
    2
    3
    5
    3
    5
    4

    说明

    已知一个长度为n的序列a1,a2,...,an。

    对于每个1<=i<=n,找到最小的非负整数p满足 对于任意的j, aj < = ai + p - sqrt(abs(i-j))

    提示
    标程仅供做题后或实在无思路时参考。
    请自觉、自律地使用该功能并请对自己的学习负责。
    如果发现恶意抄袭标程,将按照I类违反进行处理。