A14377 | $Ezzat and Two Subsequences$

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题目描述

Ezzat has an array of $n$ integers (maybe negative). He wants to split it into two non-empty subsequences $a$ and $b$ , such that every element from the array belongs to exactly one subsequence, and the value of $f(a) + f(b)$ is the maximum possible value, where $f(x)$ is the average of the subsequence $x$ . A sequence $x$ is a subsequence of a sequence $y$ if $x$ can be obtained from $y$ by deletion of several (possibly, zero or all) elements. The average of a subsequence is the sum of the numbers of this subsequence divided by the size of the subsequence. For example, the average of $[1,5,6]$ is $(1+5+6)/3 = 12/3 = 4$ , so $f([1,5,6]) = 4$ .

The first line contains a single integer $t$ ( $1 \le t \le 10^3$ )— the number of test cases. Each test case consists of two lines. The first line contains a single integer $n$ ( $2 \le n \le 10^5$ ). The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $-10^9 \le a_i \le 10^9$ ). It is guaranteed that the sum of $n$ over all test cases does not exceed $3\cdot10^5$ .

For each test case, print a single value — the maximum value that Ezzat can achieve. Your answer is considered correct if its absolute or relative error does not exceed $10^{-6}$ . Formally, let your answer be $a$ , and the jury's answer be $b$ . Your answer is accepted if and only if $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$ .

输入 #1

输出 #1

4.500000000
-12.500000000
4.000000000
18.666666667

C++ 编辑器

输入

输出