Good Graph

AtCoder

IDabc304_e

Time3000ms

Memory256MB

Difficulty—

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: $N$ $M$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_M$ $v_M$ $K$ $x_1$ $y_1$ $x_2$ $y_2$ $\vdots$ $x_K$ $y_K$ $Q$ $p_1$ $q_1$ $p_2$ $q_2$ $\vdots$ $p_Q$ $q_Q$ [samples]

Samples

Input #1

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.

API Response (JSON)

{
  "problem": {
    "name": "Good Graph",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc304_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 $v_i$.\nA graph with $N$ vertices ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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