A12108. Detect Robots
编程题
普及/提高-
知识点
题目描述
You successfully found poor Arkady near the exit of the station you've perfectly predicted. You sent him home on a taxi and suddenly came up with a question.
There are $n$ crossroads in your city and several bidirectional roads connecting some of them. A taxi ride is a path from some crossroads to another one without passing the same crossroads twice. You have a collection of rides made by one driver and now you wonder if this driver can be a robot or they are definitely a human.
You think that the driver can be a robot if for every two crossroads $a$ and $b$ the driver always chooses the same path whenever he drives from $a$ to $b$ . Note that $a$ and $b$ here do not have to be the endpoints of a ride and that the path from $b$ to $a$ can be different. On the contrary, if the driver ever has driven two different paths from $a$ to $b$ , they are definitely a human.
Given the system of roads and the description of all rides available to you, determine if the driver can be a robot or not.
There are $n$ crossroads in your city and several bidirectional roads connecting some of them. A taxi ride is a path from some crossroads to another one without passing the same crossroads twice. You have a collection of rides made by one driver and now you wonder if this driver can be a robot or they are definitely a human.
You think that the driver can be a robot if for every two crossroads $a$ and $b$ the driver always chooses the same path whenever he drives from $a$ to $b$ . Note that $a$ and $b$ here do not have to be the endpoints of a ride and that the path from $b$ to $a$ can be different. On the contrary, if the driver ever has driven two different paths from $a$ to $b$ , they are definitely a human.
Given the system of roads and the description of all rides available to you, determine if the driver can be a robot or not.
输入格式
Each test contains one or more test cases. The first line contains a single integer $t$ ( $1 \le t \le 3 \cdot 10^5$ ) — the number of test cases.
The first line of each test case contains a single integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ) — the number of crossroads in the city.
The next line contains a single integer $q$ ( $1 \le q \le 3 \cdot 10^5$ ) — the number of rides available to you.
Each of the following $q$ lines starts with a single integer $k$ ( $2 \le k \le n$ ) — the number of crossroads visited by the driver on this ride. It is followed by $k$ integers $c_1$ , $c_2$ , ..., $c_k$ ( $1 \le c_i \le n$ ) — the crossroads in the order the driver visited them. It is guaranteed that all crossroads in one ride are distinct.
It is guaranteed that the sum of values $k$ among all rides of all test cases does not exceed $3 \cdot 10^5$ .
It is guaranteed that the sum of values $n$ and the sum of values $q$ doesn't exceed $3 \cdot 10^5$ among all test cases.
The first line of each test case contains a single integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ) — the number of crossroads in the city.
The next line contains a single integer $q$ ( $1 \le q \le 3 \cdot 10^5$ ) — the number of rides available to you.
Each of the following $q$ lines starts with a single integer $k$ ( $2 \le k \le n$ ) — the number of crossroads visited by the driver on this ride. It is followed by $k$ integers $c_1$ , $c_2$ , ..., $c_k$ ( $1 \le c_i \le n$ ) — the crossroads in the order the driver visited them. It is guaranteed that all crossroads in one ride are distinct.
It is guaranteed that the sum of values $k$ among all rides of all test cases does not exceed $3 \cdot 10^5$ .
It is guaranteed that the sum of values $n$ and the sum of values $q$ doesn't exceed $3 \cdot 10^5$ among all test cases.
输出格式
Output a single line for each test case.
If the driver can be a robot, output "Robot" in a single line. Otherwise, output "Human".
You can print each letter in any case (upper or lower).
If the driver can be a robot, output "Robot" in a single line. Otherwise, output "Human".
You can print each letter in any case (upper or lower).
输入输出样例
输入 #1
1 5 2 4 1 2 3 5 3 1 4 3
输出 #1
Human
输入 #2
1 4 4 3 1 2 3 3 2 3 4 3 3 4 1 3 4 1 2
输出 #2
Robot
说明/提示
In the first example it is clear that the driver used two different ways to get from crossroads $1$ to crossroads $3$ . It must be a human.
In the second example the driver always drives the cycle $1 \to 2 \to 3 \to 4 \to 1$ until he reaches destination.
In the second example the driver always drives the cycle $1 \to 2 \to 3 \to 4 \to 1$ until he reaches destination.