102313: [AtCoder]ABC231 D - Neighbors

Problem Statement

Determine whether there is a way to line up $N$ people, numbered $1$ to $N$, in a row side by side to satisfy all of the $M$ conditions in the following format.

• Condition: Person $A_i$ and Person $B_i$ are adjacent.

Constraints

• $2 \leq N \leq 10^5$
• $0 \leq M \leq 10^5$
• $1\leq A_i < B_i \leq N$
• All pairs $(A_i,B_i)$ are distinct.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$

Output

If there is a way to line up people to satisfy the conditions, print Yes; if not, print No.

Sample Input 1

4 2
1 3
2 3

Sample Output 1

Yes

One way to satisfy all the conditions is to line them up in the order $4,1,3,2$.

Sample Input 2

4 3
1 4
2 4
3 4

Sample Output 2

No

There is no way to line them up to satisfy all the conditions.

问题描述

判断是否有一种方式将编号为1到N的N个人排成一行，相邻的方式满足以下M个条件。

• 条件：编号为A_i和B_i的人相邻。

限制条件

• $2 \leq N \leq 10^5$
• $0 \leq M \leq 10^5$
• $1\leq A_i < B_i \leq N$
• 所有对$(A_i,B_i)$都是不同的。

输入

输入将以以下格式从标准输入给出：

$N$ $M$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$

输出

如果有办法按照条件排列人，打印Yes；如果没有，打印No。

样例输入1

4 2
1 3
2 3

样例输出1

Yes

一种满足所有条件的排列方式是按顺序排列4、1、3、2。

样例输入2

4 3
1 4
2 4
3 4

样例输出2

No

没有一种方式可以按照条件排列他们。