Score : $500$ points

问题陈述

给定一个含有 $N$ 个顶点和 $M$ 条边的无向图。

边 $i$ 连接顶点 $A_i$ 和 $B_i$。

我们将按照顺序逐一擦除顶点 $1, 2, \ldots, N$。
其中，擦除顶点 $i$ 意味着从图中删除顶点 $i$ 及其所有连接到顶点 $i$ 的边。

对于每个 $i=1, 2, \ldots, N$，在擦除了从顶点 $1$ 到顶点 $i$ 之后，图中会有多少个连通分量？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Given is an undirected graph with $N$ vertices and $M$ edges.
Edge $i$ connects Vertices $A_i$ and $B_i$.

We will erase Vertices $1, 2, \ldots, N$ one by one.
Here, erasing Vertex $i$ means deleting Vertex $i$ and all edges incident to Vertex $i$ from the graph.

For each $i=1, 2, \ldots, N$, how many connected components does the graph have when vertices up to Vertex $i$ are deleted?

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq \min(\frac{N(N-1)}{2} , 2 \times 10^5 )$
• $1 \leq A_i \lt B_i \leq N$
• $(A_i,B_i) \neq (A_j,B_j)$ if $i \neq j$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $B_1$

$A_2$ $B_2$

$\vdots$

$A_M$ $B_M$

Output

Print $N$ lines.
The $i$-th line should contain the number of connected components in the graph when vertices up to Vertex $i$ are deleted.

Sample Input 1

6 7
1 2
1 4
1 5
2 4
2 3
3 5
3 6

Sample Output 1

1
2
3
2
1
0

The figure above shows the transition of the graph.

Sample Input 2

8 7
7 8
3 4
5 6
5 7
5 8
6 7
6 8

Sample Output 2

3
2
2
1
1
1
1
0

The graph may be disconnected from the beginning.

update @ 2024/3/10 10:01:27