A15820 | A Wide, Wide Graph
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题目描述
You are given a tree (a connected graph without cycles) with $n$ vertices.
Consider a fixed integer $k$ . Then, the graph $G_k$ is an undirected graph with $n$ vertices, where an edge between vertices $u$ and $v$ exists if and only if the distance between vertices $u$ and $v$ in the given tree is at least $k$ .
For each $k$ from $1$ to $n$ , print the number of connected components in the graph $G_k$ .
Consider a fixed integer $k$ . Then, the graph $G_k$ is an undirected graph with $n$ vertices, where an edge between vertices $u$ and $v$ exists if and only if the distance between vertices $u$ and $v$ in the given tree is at least $k$ .
For each $k$ from $1$ to $n$ , print the number of connected components in the graph $G_k$ .
输入格式
The first line contains the integer $n$ ( $2 \le n \le 10^5$ ) — the number of vertices in the graph.
Each of the next $n-1$ lines contains two integers $u$ and $v$ ( $1 \le u, v \le n$ ), denoting an edge between vertices $u$ and $v$ in the tree. It is guaranteed that these edges form a valid tree.
Each of the next $n-1$ lines contains two integers $u$ and $v$ ( $1 \le u, v \le n$ ), denoting an edge between vertices $u$ and $v$ in the tree. It is guaranteed that these edges form a valid tree.
输出格式
Output $n$ integers: the number of connected components in the graph $G_k$ for each $k$ from $1$ to $n$ .
输入输出样例
输入 #1
6 1 2 1 3 2 4 2 5 3 6
输出 #1
1 1 2 4 6 6
输入 #2
5 1 2 2 3 3 4 3 5
输出 #2
1 1 3 5 5
In the first example: If $k=1$ , the graph has an edge between each pair of vertices, so it has one component. If $k=4$ , the graph has only edges $4 \leftrightarrow 6$ and $5 \leftrightarrow 6$ , so the graph has $4$ components.
In the second example: when $k=1$ or $k=2$ the graph has one component. When $k=3$ the graph $G_k$ splits into $3$ components: one component has vertices $1$ , $4$ and $5$ , and two more components contain one vertex each. When $k=4$ or $k=5$ each vertex is a separate component.
In the second example: when $k=1$ or $k=2$ the graph has one component. When $k=3$ the graph $G_k$ splits into $3$ components: one component has vertices $1$ , $4$ and $5$ , and two more components contain one vertex each. When $k=4$ or $k=5$ each vertex is a separate component.
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评测结果：Accepted