Transit Tree Path

题目描述

You are given a tree with $N$ vertices.
Here, a tree is a kind of graph, and more specifically, a connected undirected graph with $N-1$ edges, where $N$ is the number of its vertices.
The $i$-th edge $(1≤i≤N-1)$ connects Vertices $a_i$ and $b_i$, and has a length of $c_i$. You are also given $Q$ queries and an integer $K$. In the $j$-th query $(1≤j≤Q)$:

find the length of the shortest path from Vertex $x_j$ and Vertex $y_j$ via Vertex $K$.

输入格式

Input is given from Standard Input in the following format:
$N$
$a_1$ $b_1$ $c_1$
:
$a_{N-1}$ $b_{N-1}$ $c_{N-1}$ $Q$ $K$ $x_1$ $y_1$ :
$x_{Q}$ $y_{Q}$

输出格式

Print the responses to the queries in $Q$ lines.
In the $j$-th line $j(1≤j≤Q)$, print the response to the $j$-th query.

5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5

3
2
4

7
1 2 1
1 3 3
1 4 5
1 5 7
1 6 9
1 7 11
3 2
1 3
4 5
6 7

5
14
22

10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10

17000000000

提示

$3≤N≤10^5$ $1≤a_i,b_i≤N (1≤i≤N-1)$ $1≤c_i≤10^9 (1≤i≤N-1)$ The given graph is a tree. $1≤Q≤10^5$ $1≤K≤N$ $1≤x_j,y_j≤N (1≤j≤Q)$ $x_j≠y_j (1≤j≤Q)$ $x_j≠K,y_j≠K (1≤j≤Q)$以下为三个查询的最短路径：

查询 $1$：顶点 $2$ → 顶点 $1$ → 顶点 $2$ → 顶点 $4$ ：长度 $1+1+1=3$ 查询 $2$：顶点 $2$ → 顶点 $1$ → 顶点 $3$ ：长度 $1+1=2$ 查询 $3$：顶点 $4$ → 顶点 $2$ → 顶点 $1$ → 顶点 $3$ → 顶点 $5$ ：长度 $1+1+1+1=4$
每个查询的路径必须经过顶点 $K=2$。

标签: AtCoder|abc070D

来源

AtCoder|abc070D