Pairs of Paths
题意翻译
给定一棵包含 $n$ 个节点(编号 $1$ 到 $n$),$n-1$ 条边(编号 $1$ 到 $n-1$)的树,我们同时选定该树上的 $m$ 条简单路径 $path_1,path_2,...,path_m$。第 $i$ 条边连接节点 $u_i,v_i$,第 $i$ 条简单路径 $path_i$ 为节点 $x_i,y_i$ 之间的最短路径。
你需要找出对于这棵树,有多少个二元组 $(i,j)$ 满足:
- $1\leq i,j\leq m$ 且 $i\ne j$。
- $path_i$ 和 $path_j$ 有且仅有一个交点。
第一行输入一个整数 $n$,接下来输入 $n-1$ 行,第 $i$ 行两个整数表示 $u_i,v_i$;然后输入一行一个整数 $m$,最后输入 $m$ 行,第 $i$ 行两个整数表示 $x_i,y_i$。
输出有多少满足要求的二元组。
$1\leq n,m\leq3\times10^5;1\leq u_i,v_i,x_i,y_i\leq n;$
样例解释:
对于样例一:
![](https://cdn.luogu.com.cn/upload/image_hosting/uvhwvz3s.png)
满足要求的二元组为 $(1,4),(3,4)$。
对于样例三:
![](https://cdn.luogu.com.cn/upload/image_hosting/prqo45wk.png)
满足要求的二元组为 $(1,4),(3,4),(1,5),(2,5),(3,5),(3,6),(5,6)$。
题目描述
You are given a tree consisting of $ n $ vertices, and $ m $ simple vertex paths. Your task is to find how many pairs of those paths intersect at exactly one vertex. More formally you have to find the number of pairs $ (i, j) $ $ (1 \leq i < j \leq m) $ such that $ path_i $ and $ path_j $ have exactly one vertex in common.
输入输出格式
输入格式
First line contains a single integer $ n $ $ (1 \leq n \leq 3 \cdot 10^5) $ .
Next $ n - 1 $ lines describe the tree. Each line contains two integers $ u $ and $ v $ $ (1 \leq u, v \leq n) $ describing an edge between vertices $ u $ and $ v $ .
Next line contains a single integer $ m $ $ (1 \leq m \leq 3 \cdot 10^5) $ .
Next $ m $ lines describe paths. Each line describes a path by it's two endpoints $ u $ and $ v $ $ (1 \leq u, v \leq n) $ . The given path is all the vertices on the shortest path from $ u $ to $ v $ (including $ u $ and $ v $ ).
输出格式
Output a single integer — the number of pairs of paths that intersect at exactly one vertex.
输入输出样例
输入样例 #1
5
1 2
1 3
1 4
3 5
4
2 3
2 4
3 4
3 5
输出样例 #1
2
输入样例 #2
1
3
1 1
1 1
1 1
输出样例 #2
3
输入样例 #3
5
1 2
1 3
1 4
3 5
6
2 3
2 4
3 4
3 5
1 1
1 2
输出样例 #3
7
说明
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1486F/a19cd21d095785ac889753153b27201ab276d741.png)
The tree in the first example and paths look like this. Pairs $ (1,4) $ and $ (3,4) $ intersect at one vertex.
In the second example all three paths contain the same single vertex, so all pairs $ (1, 2) $ , $ (1, 3) $ and $ (2, 3) $ intersect at one vertex.
The third example is the same as the first example with two additional paths. Pairs $ (1,4) $ , $ (1,5) $ , $ (2,5) $ , $ (3,4) $ , $ (3,5) $ , $ (3,6) $ and $ (5,6) $ intersect at one vertex.