Score: $575$ points

问题描述

你已知一个长度为 $N$ 的序列 $A=(A_1,A_2,\ldots,A_N)$。对于每个 $k=1,2,\ldots,N$，解决以下问题：

• 找出当选择满足 $k\leq r\leq N$ 的整数 $r$ 时，序列 $A$ 中从第 $k$ 项到第 $r$ 项可能的最大平均值。
  • 在这里，序列 $A$ 中从第 $k$ 项到第 $r$ 项的平均值定义为 $\frac{1}{r-k+1}\displaystyle\sum_{i=k}^r A_i$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given a sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$.
For each $k=1,2,\ldots,N$, solve the following problem:

• Find the maximum possible average value of the $k$-th to $r$-th terms of the sequence $A$ when choosing an integer $r$ such that $k\leq r\leq N$.
  Here, the average value of the $k$-th to $r$-th term of the sequence $A$ is defined as $\frac{1}{r-k+1}\displaystyle\sum_{i=k}^r A_i$.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq A_i\leq 10^6$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print $N$ lines.
The $i$-th line $(1\leq i\leq N)$ should contain the answer to the problem for $k=i$.
Your output will be considered correct if, for every line, the absolute or relative error of the printed value from the true value is at most $10^{-6}$.

Sample Input 1

5
1 1 4 5 3

Sample Output 1

2.80000000
3.33333333
4.50000000
5.00000000
3.00000000

For $k=1$, the possible choices for $r$ are $r=1,2,3,4,5$, and the average value for each of them is:

• $\frac{1}{1}=1$
• $\frac{1}{2}(1+1)=1$
• $\frac{1}{3}(1+1+4)=2$
• $\frac{1}{4}(1+1+4+5)=2.75$
• $\frac{1}{5}(1+1+4+5+3)=2.8$

Thus, the maximum is achieved when $r=5$, and the answer for $k=1$ is $2.8$.
Similarly, for $k=2,3,4,5$, the maximum is achieved when $r=4,4,4,5$, respectively, with the values of $\frac{10}{3}=3.333\ldots$, $\frac{9}{2}=4.5$, $\frac{5}{1}=5$, $\frac{3}{1}=3$.

Sample Input 2

3
999999 1 1000000

Sample Output 2

999999.00000000
500000.50000000
1000000.00000000

update @ 2024/3/10 01:35:37