Score : $300$ points

问题描述

高桥运营了一个名为“Twidai”的SNS社交网络，该网络拥有从用户1到用户$N$共$N$名用户。在Twidai中，用户可以关注或取消关注其他用户。

自Twidai上线以来，已经执行了$Q$次操作。第$i$次（$1\leq i\leq Q$）操作由三个整数$T_i$、$A_i$和$B_i$表示，它们的含义如下：

• 如果$T_i = 1$：表示用户$A_i$开始关注用户$B_i$。如果在此操作时用户$A_i$已经关注了用户$B_i$，则不会有任何改变。
• 如果$T_i = 2$：表示用户$A_i$取消关注用户$B_i$。如果在此操作时用户$A_i$并未关注用户$B_i$，则不会有任何改变。
• 如果$T_i = 3$：表示询问用户$A_i$和用户$B_i$是否互相关注。若用户$A_i$关注用户$B_i$且用户$B_i$也关注用户$A_i$，则输出Yes；否则，输出No。

当服务刚上线时，没有任何用户关注其他用户。

请按照$i$的升序依次打印出所有$T_i = 3$对应的操作所要求的答案。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi runs an SNS "Twidai," which has $N$ users from user $1$ through user $N$. In Twidai, users can follow or unfollow other users.

$Q$ operations have been performed since Twidai was launched. The $i$-th $(1\leq i\leq Q)$ operation is represented by three integers $T_i$, $A_i$, and $B_i$, whose meanings are as follows:

• If $T_i = 1$: it means that user $A_i$ follows user $B_i$. If user $A_i$ is already following user $B_i$ at the time of this operation, it does not make any change.
• If $T_i = 2$: it means that user $A_i$ unfollows user $B_i$. If user $A_i$ is not following user $B_i$ at the time of this operation, it does not make any change.
• If $T_i = 3$: it means that you are asked to determine if users $A_i$ and $B_i$ are following each other. You need to print Yes if user $A_i$ is following user $B_i$ and user $B_i$ is following user $A_i$, and No otherwise.

When the service was launched, no users were following any users.

Print the correct answers for all operations such that $T_i = 3$ in ascending order of $i$.

Constraints

• $2 \leq N \leq 10 ^ 9$
• $1 \leq Q \leq 2\times10 ^ 5$
• $T _ i=1,2,3\ (1\leq i\leq Q)$
• $1 \leq A _ i \leq N\ (1\leq i\leq Q)$
• $1 \leq B _ i \leq N\ (1\leq i\leq Q)$
• $A _ i\neq B _ i\ (1\leq i\leq Q)$
• There exists $i\ (1\leq i\leq Q)$ such that $T _ i=3$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $Q$

$T _ 1$ $A _ 1$ $B _ 1$

$T _ 2$ $A _ 2$ $B _ 2$

$\vdots$

$T _ Q$ $A _ Q$ $B _ Q$

Output

Print $X$ lines, where $X$ is the number of $i$'s $(1\leq i\leq Q)$ such that $T _ i=3$. The $j$-th $(1\leq j\leq X)$ line should contain the answer to the $j$-th operation such that $T _ i=3$.

Sample Input 1

3 9
1 1 2
3 1 2
1 2 1
3 1 2
1 2 3
1 3 2
3 1 3
2 1 2
3 1 2

Sample Output 1

No
Yes
No
No

Twidai has three users. The nine operations are as follows.

• User $1$ follows user $2$. No other users are following or followed by any users.
• Determine if users $1$ and $2$ are following each other. User $1$ is following user $2$, but user $2$ is not following user $1$, so No is the correct answer to this operation.
• User $2$ follows user $1$.
• Determine if users $1$ and $2$ are following each other. User $1$ is following user $2$, and user $2$ is following user $1$, so Yes is the correct answer to this operation.
• User $2$ follows user $3$.
• User $3$ follows user $2$.
• Determine if users $1$ and $3$ are following each other. User $1$ is not following user $3$, and user $3$ is not following user $1$, so No is the correct answer to this operation.
• User $1$ unfollows user $2$.
• Determine if users $1$ and $2$ are following each other. User $2$ is following user $1$, but user $1$ is not following user $2$, so No is the correct answer to this operation.

Sample Input 2

2 8
1 1 2
1 2 1
3 1 2
1 1 2
1 1 2
1 1 2
2 1 2
3 1 2

Sample Output 2

Yes
No

A user may follow the same user multiple times.

Sample Input 3

10 30
3 1 6
3 5 4
1 6 1
3 1 7
3 8 4
1 1 6
2 4 3
1 6 5
1 5 6
1 1 8
1 8 1
2 3 10
1 7 6
3 5 6
1 6 7
3 6 7
1 9 5
3 8 6
3 3 8
2 6 9
1 7 1
3 10 8
2 9 2
1 10 9
2 6 10
2 6 8
3 1 6
3 1 8
2 8 5
1 9 10

Sample Output 3

No
No
No
No
Yes
Yes
No
No
No
Yes
Yes

update @ 2024/3/10 11:42:15