Subset Mex
题意翻译
给出一个数列,你需要将这个数列划分成两个集合$A$和$B$,并最大化$\operatorname{mex}(A)+\operatorname{mex}(B)$。
$\operatorname{mex}$的定义:$\operatorname{mex}(A)$为最小的没有在集合$A$中出现过的非负整数的值。
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 $ .
输入输出格式
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
输入样例 #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
输出样例 #1
5
3
4
0
说明
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.