第13篇英语翻译

出处：https://acs.jxnu.edu.cn/contest/23/board/challenge/E；

重点单词：

Append the MEX of the first k numbers of the array a to the end of array b

将数组a的前k个数的MEX附加到数组b的末尾

the first k numbers   前k个数

 

Meximum Array

描述：

Mihai has just learned about the MEX concept and since he liked it so much, he decided to use it right away.

Mihai刚刚了解了MEX的概念，因为他非常喜欢它，所以他决定立即使用它。

Given an array aa of n non-negative integers, Mihai wants to create a new array b that is formed in the following way:

给定n个非负整数的数组a，Mihai希望创建一个新的数组b，其形式如下：

While a is not empty:

当a数组不为空：

• Choose an integer k (1≤k≤|a|1≤k≤|a|).
• Append the MEX of the first kk numbers of the array aa to the end of array bb and erase them from the array aa, shifting the positions of the remaining numbers in aa.

选择整数k

将数组a的前k个数的MEX附加到数组b的末尾，并将它们从数组a中删除，从而移动a中其余数的位置。

But, since Mihai loves big arrays as much as the MEX concept, he wants the new array bb to be the lexicographically maximum. So, Mihai asks you to tell him what the maximum array bb that can be created by constructing the array optimally is.

但是，由于Mihai和MEX概念一样喜欢大数组，他希望新的数组b在词典编纂上是最大的。所以，Mihai让你告诉他，通过优化构建数组可以创建的最大数组b是多少。

An array x is lexicographically greater than an array yy if in the first position where xx and yy differ xi>yixi>yi or if |x|>|y||x|>|y| and yy is a prefix of xx (where |x||x| denotes the size of the array xx).

The MEX of a set of non-negative integers is the minimal non-negative integer such that it is not in the set. For example, MEX({1,2,31,2,3}) =0=0 and MEX({0,1,2,4,50,1,2,4,5}) =3=3.

如果在第一个位置x和yy不同xi>yixi>yi，或者如果|x |>y | | x |>y |，并且yy是xx的前缀（其中| x | | x |表示数组xx的大小），那么数组xx在词典学上大于数组yy。

一组非负整数的MEX是最小的非负整数，因此它不在该集合中。例如，MEX（{1,2,3}）=0=0和MEX（{0,1,2,4,5）=3。

输入：

The first line of the input contains a single integer tt (1≤t≤1001≤t≤100) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer nn (1≤n≤2⋅1051≤n≤2⋅105) — the number of elements in the array aa.

The second line of each test case contains nn non-negative integers a1,…,ana1,…,an (0≤ai≤n0≤ai≤n), where aiai is the ii-th integer from the array aa.

It is guaranteed that the sum of nn over all test cases does not exceed 2⋅1052⋅105.

输出：

For each test case print mm — the length of the maximum array bb Mihai can create, followed by mm integers denoting the elements of the array bb.

样例输入：

6
5
1 0 2 0 3
8
2 2 3 4 0 1 2 0
1
1
5
0 1 2 3 4
4
0 1 1 0
10
0 0 2 1 1 1 0 0 1 1

复制

样例输出：

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

复制

注释：

In the first test case, the lexicographically maximum array bb is obtained by selecting k=5k=5, resulting in the MEXMEX of the whole array aa. It is lexicographically maximum because an array starting with a smaller number than 44 is lexicographically smaller, and choosing a k<5k<5 would result in an array starting with a number smaller than 44.

In the second test case, there are two ways to obtain the maximum array: first selecting k=6k=6, then k=2k=2, or first selecting k=7k=7 and then k=1k=1.