A14131. Pairs of Paths
编程题
普及/提高-
知识点
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 $v$ ).
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 #1
5 1 2 1 3 1 4 3 5 4 2 3 2 4 3 4 3 5
输出 #1
2
输入 #2
1 3 1 1 1 1 1 1
输出 #2
3
输入 #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 #3
7
说明/提示
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.
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.