A13152 | Almost Same Distance
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内存限制256MB
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题目描述
Let $G$ be a simple graph. Let $W$ be a non-empty subset of vertices. Then $W$ is almost- $k$ -uniform if for each pair of distinct vertices $u,v \in W$ the distance between $u$ and $v$ is either $k$ or $k+1$ .
You are given a tree on $n$ vertices. For each $i$ between $1$ and $n$ , find the maximum size of an almost- $i$ -uniform set.
You are given a tree on $n$ vertices. For each $i$ between $1$ and $n$ , find the maximum size of an almost- $i$ -uniform set.
输入格式
The first line contains a single integer $n$ ( $2 \leq n \leq 5 \cdot 10^5$ ) – the number of vertices of the tree.
Then $n-1$ lines follows, the $i$ -th of which consisting of two space separated integers $u_i$ , $v_i$ ( $1 \leq u_i, v_i \leq n$ ) meaning that there is an edge between vertices $u_i$ and $v_i$ .
It is guaranteed that the given graph is tree.
Then $n-1$ lines follows, the $i$ -th of which consisting of two space separated integers $u_i$ , $v_i$ ( $1 \leq u_i, v_i \leq n$ ) meaning that there is an edge between vertices $u_i$ and $v_i$ .
It is guaranteed that the given graph is tree.
输出格式
Output a single line containing $n$ space separated integers $a_i$ , where $a_i$ is the maximum size of an almost- $i$ -uniform set.
输入输出样例
输入 #1
5 1 2 1 3 1 4 4 5
输出 #1
4 3 2 1 1
输入 #2
6 1 2 1 3 1 4 4 5 4 6
输出 #2
4 4 2 1 1 1
Consider the first example.
- The only maximum almost- $1$ -uniform set is $\{1, 2, 3, 4\}$ .
- One of the maximum almost- $2$ -uniform sets is or $\{2, 3, 5\}$ , another one is $\{2, 3, 4\}$ .
- A maximum almost- $3$ -uniform set is any pair of vertices on distance $3$ .
- Any single vertex is an almost- $k$ -uniform set for $k \geq 1$ .
In the second sample there is an almost- $2$ -uniform set of size $4$ , and that is $\{2, 3, 5, 6\}$ .
- The only maximum almost- $1$ -uniform set is $\{1, 2, 3, 4\}$ .
- One of the maximum almost- $2$ -uniform sets is or $\{2, 3, 5\}$ , another one is $\{2, 3, 4\}$ .
- A maximum almost- $3$ -uniform set is any pair of vertices on distance $3$ .
- Any single vertex is an almost- $k$ -uniform set for $k \geq 1$ .
In the second sample there is an almost- $2$ -uniform set of size $4$ , and that is $\{2, 3, 5, 6\}$ .
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评测结果：Accepted