CF1406A.Subset Mex

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

Given a set of integers (it can contain equal elements).

You have to split it into two subsets $A$ and $B$ (both of them can contain equal elements or be empty). You have to maximize the value of $mex(A)+mex(B)$ .

Here $mex$ of a set denotes the smallest non-negative integer that doesn't exist in the set. For example:

$mex(\{1,4,0,2,2,1\})=3$
$mex(\{3,3,2,1,3,0,0\})=4$
$mex(\varnothing)=0$ ( $mex$ for empty set)

The set is splitted into two subsets $A$ and $B$ if for any integer number $x$ the number of occurrences of $x$ into this set is equal to the sum of the number of occurrences of $x$ into $A$ and the number of occurrences of $x$ into $B$ .

输入格式

The input consists of multiple test cases. The first line contains an integer $t$ ( $1\leq t\leq 100$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ( $1\leq n\leq 100$ ) — the size of the set.

The second line of each testcase contains $n$ integers $a_1,a_2,\dots a_n$ ( $0\leq a_i\leq 100$ ) — the numbers in the set.

输出格式

For each test case, print the maximum value of $mex(A)+mex(B)$ .

输入输出样例

输入#1

4
6
0 2 1 5 0 1
3
0 1 2
4
0 2 0 1
6
1 2 3 4 5 6

输出#1

说明/提示

In the first test case, $A=\left\{0,1,2\right\},B=\left\{0,1,5\right\}$ is a possible choice.

In the second test case, $A=\left\{0,1,2\right\},B=\varnothing$ is a possible choice.

In the third test case, $A=\left\{0,1,2\right\},B=\left\{0\right\}$ is a possible choice.

In the fourth test case, $A=\left\{1,3,5\right\},B=\left\{2,4,6\right\}$ is a possible choice.

首页