Highest Ratio

AtCoder

IDabc341_g

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
1 1 4 5 3

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 $\frac{10}{3}=3.333\ldots$, $\frac{9}{2}=4.5$, $\frac{5}{1}=5$, $\frac{3}{1}=3$.

Input #2

3
999999 1 1000000

Output #2

999999.00000000
500000.50000000
1000000.00000000

API Response (JSON)

{
  "problem": {
    "name": "Highest Ratio",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc341_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$.  \nFor each $k=1,2,\\ldots,N$, solve the following problem:\n\n*   Find the maximum possible average value of the $k$\\-th to $r$\\-th terms ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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