Snow Walking Robot

题意翻译

有一个机器人，站在一个平面直角坐标系上，开始时他的坐标为$(0,0)$ 给出一个指令序列$s$，它只由`L`,`R`,`U`,`D` 四个大写字母组成 若机器人当前坐标为$(x,y)$ - 如果当前字母为 `L`，那么机器人就会向左移动到$x-1,y$ - 如果当前字母为 `R`，那么机器人就会向右移动到$x+1,y$ - 如果当前字母为 `U`，那么机器人就会向上移动到$x,y+1$ - 如果当前字母为 `D`，那么机器人就会向下移动到$x,y-1$ 如果一个坐标的点被走过了两次（除$(0,0)$外），那么机器人就会爆炸 一个操作序列合法，当且仅当中途机器人不会爆炸，并且满足指令序列结束时，机器人的坐标为$(0,0)$（也就是最后回到原点） 当然，空指令序列也是合法的 我们发现，所有的指令序列不一定都合法 给出一个指令序列$s$，你的任务是通过删除指令和重排序列，让指令序列合法，并且满足删除的指令数最小 ## 输入格式 第一行一个整数$q$，表示有$q$组数据 接下来$q$行，每行一个字符串，代表一个指令串 ## 输出格式 对于每组数据： 第一行一个整数，表示最多剩下多少条指令，使得指令序列合法，如果无论如何都不合法，输出$0$ 第二行表示合法的指令序列，如果有多个合法序列，输出任意一个 如果无论如何都不合法，输出空的一行（注意那一行要空出来，详情见样例） ### 数据范围 $1 \le q \le 2\cdot 10^4$，$\sum|s| \le 10^5$ 其中$|s|$为字符串$s$的长度 感谢 @_Wolverine 提供的翻译

题目描述

Recently you have bought a snow walking robot and brought it home. Suppose your home is a cell $ (0, 0) $ on an infinite grid. You also have the sequence of instructions of this robot. It is written as the string $ s $ consisting of characters 'L', 'R', 'U' and 'D'. If the robot is in the cell $ (x, y) $ right now, he can move to one of the adjacent cells (depending on the current instruction). - If the current instruction is 'L', then the robot can move to the left to $ (x - 1, y) $ ; - if the current instruction is 'R', then the robot can move to the right to $ (x + 1, y) $ ; - if the current instruction is 'U', then the robot can move to the top to $ (x, y + 1) $ ; - if the current instruction is 'D', then the robot can move to the bottom to $ (x, y - 1) $ . You've noticed the warning on the last page of the manual: if the robot visits some cell (except $ (0, 0) $ ) twice then it breaks. So the sequence of instructions is valid if the robot starts in the cell $ (0, 0) $ , performs the given instructions, visits no cell other than $ (0, 0) $ two or more times and ends the path in the cell $ (0, 0) $ . Also cell $ (0, 0) $ should be visited at most two times: at the beginning and at the end (if the path is empty then it is visited only once). For example, the following sequences of instructions are considered valid: "UD", "RL", "UUURULLDDDDLDDRRUU", and the following are considered invalid: "U" (the endpoint is not $ (0, 0) $ ) and "UUDD" (the cell $ (0, 1) $ is visited twice). The initial sequence of instructions, however, might be not valid. You don't want your robot to break so you decided to reprogram it in the following way: you will remove some (possibly, all or none) instructions from the initial sequence of instructions, then rearrange the remaining instructions as you wish and turn on your robot to move. Your task is to remove as few instructions from the initial sequence as possible and rearrange the remaining ones so that the sequence is valid. Report the valid sequence of the maximum length you can obtain. Note that you can choose any order of remaining instructions (you don't need to minimize the number of swaps or any other similar metric). You have to answer $ q $ independent test cases.

输入输出格式

输入格式

The first line of the input contains one integer $ q $ ( $ 1 \le q \le 2 \cdot 10^4 $ ) — the number of test cases. The next $ q $ lines contain test cases. The $ i $ -th test case is given as the string $ s $ consisting of at least $ 1 $ and no more than $ 10^5 $ characters 'L', 'R', 'U' and 'D' — the initial sequence of instructions. It is guaranteed that the sum of $ |s| $ (where $ |s| $ is the length of $ s $ ) does not exceed $ 10^5 $ over all test cases ( $ \sum |s| \le 10^5 $ ).

输出格式

For each test case print the answer on it. In the first line print the maximum number of remaining instructions. In the second line print the valid sequence of remaining instructions $ t $ the robot has to perform. The moves are performed from left to right in the order of the printed sequence. If there are several answers, you can print any. If the answer is $ 0 $ , you are allowed to print an empty line (but you can don't print it).

输入输出样例

输入样例 #1

6
LRU
DURLDRUDRULRDURDDL
LRUDDLRUDRUL
LLLLRRRR
URDUR
LLL

输出样例 #1

2
LR
14
RUURDDDDLLLUUR
12
ULDDDRRRUULL
2
LR
2
UD
0

说明

There are only two possible answers in the first test case: "LR" and "RL". The picture corresponding to the second test case:  Note that the direction of traverse does not matter Another correct answer to the third test case: "URDDLLLUURDR".