Three Paths on a Tree
题意翻译
给定一棵含 $n\ (3\leq n\leq2\cdot 10^5)$ 个结点的无权树,试找出三个结点 $u$、$v$、$w$,$\operatorname{s.t.}$
$$\operatorname{card}(\{u,v\text{ 间的路径}\}\cup\{v,w\text{ 间的路径}\}\cup\{w,u\text{ 间的路径}\})$$
最大。
你需要输出两行:
第一行为 $\max\operatorname{card}(\{u,v\text{ 间的路径}\}\cup\{v,w\text{ 间的路径}\}\cup\{w,u\text{ 间的路径}\})$
第二行三个整数,即 $u$、$v$、$w$,如有多种答案,输出一种即可。
题目描述
You are given an unweighted tree with $ n $ vertices. Recall that a tree is a connected undirected graph without cycles.
Your task is to choose three distinct vertices $ a, b, c $ on this tree such that the number of edges which belong to at least one of the simple paths between $ a $ and $ b $ , $ b $ and $ c $ , or $ a $ and $ c $ is the maximum possible. See the notes section for a better understanding.
The simple path is the path that visits each vertex at most once.
输入输出格式
输入格式
The first line contains one integer number $ n $ ( $ 3 \le n \le 2 \cdot 10^5 $ ) — the number of vertices in the tree.
Next $ n - 1 $ lines describe the edges of the tree in form $ a_i, b_i $ ( $ 1 \le a_i $ , $ b_i \le n $ , $ a_i \ne b_i $ ). It is guaranteed that given graph is a tree.
输出格式
In the first line print one integer $ res $ — the maximum number of edges which belong to at least one of the simple paths between $ a $ and $ b $ , $ b $ and $ c $ , or $ a $ and $ c $ .
In the second line print three integers $ a, b, c $ such that $ 1 \le a, b, c \le n $ and $ a \ne, b \ne c, a \ne c $ .
If there are several answers, you can print any.
输入输出样例
输入样例 #1
8
1 2
2 3
3 4
4 5
4 6
3 7
3 8
输出样例 #1
5
1 8 6
说明
The picture corresponding to the first example (and another one correct answer):
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1294F/77ac761e87577c88357c329d0c2cba3e83446e14.png)
If you choose vertices $ 1, 5, 6 $ then the path between $ 1 $ and $ 5 $ consists of edges $ (1, 2), (2, 3), (3, 4), (4, 5) $ , the path between $ 1 $ and $ 6 $ consists of edges $ (1, 2), (2, 3), (3, 4), (4, 6) $ and the path between $ 5 $ and $ 6 $ consists of edges $ (4, 5), (4, 6) $ . The union of these paths is $ (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) $ so the answer is $ 5 $ . It can be shown that there is no better answer.