[USACO08OCT] Pasture Walking G

题目描述

The $N$ cows $(2 \leq N \leq 1,000)$ conveniently numbered $1\cdots N$ are grazing among the $N$ pastures also conveniently numbered $1\cdots N$. Most conveniently of all, cow $i$ is grazing in pasture $i$.

Some pairs of pastures are connected by one of $N-1$ bidirectional walkways that the cows can traverse. Walkway $i$ connects pastures $A_i$ and $B_i (1 \leq A_i \leq N; 1 \leq B_i \leq N)$ and has a length of $L_i (1 \leq L_i \leq 10,000)$.

The walkways are set up in such a way that between any two distinct pastures, there is exactly one path of walkways that travels between them. Thus, the walkways form a tree.

The cows are very social and wish to visit each other often. Ever in a hurry, they want you to help them schedule their visits by computing the lengths of the paths between $Q$ pairs of pastures (each pair given as a query $p_1,p_2 (1 \leq p_1 \leq N; 1 \leq p_2 \leq N)$.

有 $N(2\leq N\leq 1000)$ 头奶牛，编号为 $1$ 到 $N$，它们正在同样编号为 $1$ 到 $N$ 的牧场上行走.为了方便，我们假设编号为 $i$ 的牛恰好在第 $i$ 号牧场上.

有一些牧场间每两个牧场用一条双向道路相连，道路总共有 $N - 1$ 条，奶牛可以在这些道路上行走.第 $i$ 条道路把第 $A_i$ 个牧场和第 $B_i$ 个牧场连了起来 $(1 \leq A_i \leq N; 1 \leq B_i \leq N)$，而它的长度是 $1 \leq L_i \leq 10,000$.在任意两个牧场间，有且仅有一条由若干道路组成的路径相连.也就是说，所有的道路构成了一棵树.

奶牛们十分希望经常互相见面.它们十分着急，所以希望你帮助它们计划它们的行程，你只需要计算出 $Q(1 < Q < 1000)$ 对点之间的路径长度•每对点以一个询问 $p_1,p_2 (1 \leq p_1 \leq N; 1 \leq p_2 \leq N)$. 的形式给出.

输入格式

Line $1$: Two space-separated integers: $N$ and $Q$.

Lines $2\cdots N$: Line i+1 contains three space-separated integers: $A_i, B_i$, and $L_i$.

Lines $N+1\cdots N+Q$: Each line contains two space-separated integers representing two distinct pastures between which the cows wish to travel: $p_1$ and $p_2$

输出格式

Lines $1\cdots Q$: Line $i$ contains the length of the path between the two pastures in query $i$.

样例 #1

样例输入 #1

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

样例输出 #1

2 
7

提示

Query 1: The walkway between pastures 1 and 2 has length 2.

Query 2: Travel through the walkway between pastures 3 and 4, then the one between 4 and 1, and finally the one between 1 and 2, for a total length of 7.

Source

资格赛