Score : $475$ points

问题描述

给定一个包含 $N$ 个顶点和 $M$ 条边的无向图 $G$。对于 $i = 1, 2, \ldots, M$，第 $i$ 条边是一条连接顶点 $u_i$ 和 $v_i$ 的无向边。

若一个包含 $N$ 个顶点的图满足以下条件，则称其为 好 图：

• 对于所有 $i = 1, 2, \ldots, K$，在图 $G$ 中不存在一条连接顶点 $x_i$ 和 $y_i$ 的路径。

给定的图 $G$ 是一个好图。

你将收到 $Q$ 个独立的问题，请逐一回答。对于 $i = 1, 2, \ldots, Q$，第 $i$ 个问题是：

• 在给定的图 $G$ 中添加一条连接顶点 $p_i$ 和 $q_i$ 的无向边得到的新图 $G^{(i)}$ 是否仍是一个好图？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given an undirected graph $G$ with $N$ vertices and $M$ edges. For $i = 1, 2, \ldots, M$, the $i$-th edge is an undirected edge connecting vertices $u_i$ and $v_i$.

A graph with $N$ vertices is called good if the following condition holds for all $i = 1, 2, \ldots, K$:

• there is no path connecting vertices $x_i$ and $y_i$ in $G$.

The given graph $G$ is good.

You are given $Q$ independent questions. Answer all of them. For $i = 1, 2, \ldots, Q$, the $i$-th question is as follows.

• Is the graph $G^{(i)}$ obtained by adding an undirected edge connecting vertices $p_i$ and $q_i$ to the given graph $G$ good?

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq 2 \times10^5$
• $1 \leq u_i, v_i \leq N$
• $1 \leq K \leq 2 \times 10^5$
• $1 \leq x_i, y_i \leq N$
• $x_i \neq y_i$
• $i \neq j \implies \lbrace x_i, y_i \rbrace \neq \lbrace x_j, y_j \rbrace$
• For all $i = 1, 2, \ldots, K$, there is no path connecting vertices $x_i$ and $y_i$.
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq p_i, q_i \leq N$
• $p_i \neq q_i$
• All input values are integers.

Input

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

$N$ $M$

$u_1$ $v_1$

$u_2$ $v_2$

$\vdots$

$u_M$ $v_M$

$K$

$x_1$ $y_1$

$x_2$ $y_2$

$\vdots$

$x_K$ $y_K$

$Q$

$p_1$ $q_1$

$p_2$ $q_2$

$\vdots$

$p_Q$ $q_Q$

Output

Print $Q$ lines. For $i = 1, 2, \ldots, Q$, the $i$-th line should contain the answer to the $i$-th question: Yes if the graph $G^{(i)}$ is good, and No otherwise.

Sample Input 1

6 6
1 2
2 3
2 3
3 1
5 4
5 5
3
1 5
2 6
4 3
4
2 5
2 6
5 6
5 4

Sample Output 1

No
No
Yes
Yes

• For the first question, the graph $G^{(1)}$ is not good because it has a path $1 \rightarrow 2 \rightarrow 5$ connecting vertices $x_1 = 1$ and $y_1 = 5$. Therefore, print No.
• For the second question, the graph $G^{(2)}$ is not good because it has a path $2 \rightarrow 6$ connecting vertices $x_2 = 2$ and $y_2 = 6$. Therefore, print No.
• For the third question, the graph $G^{(3)}$ is good. Therefore, print Yes.
• For the fourth question, the graph $G^{(4)}$ is good. Therefore, print Yes.

As seen in this sample input, note that the given graph $G$ may have self-loops or multi-edges.

update @ 2024/3/10 08:34:18