P2912 [USACO08OCT]牧场散步Pasture Walking

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  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 USACO 2008
  • 难度 普及+/提高
  • 时空限制 1000ms / 128MB

题解

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    题目描述

    The N cows (2 <= N <= 1,000) conveniently numbered 1..N are grazing among the N pastures also conveniently numbered 1..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 <= A_i <= N; 1 <= B_i <= N) and has a length of L_i (1 <= L_i <= 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 1 <= L_i <= 10,000 pairs of pastures (each pair given as a query p1,p2 (1 <= p1 <= N; 1 <= p2 <= N).

    POINTS: 200

    有N(2<=N<=1000)头奶牛,编号为1到W,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Ai个牧场和第Bi个牧场连了起来(1 <= A_i <= N; 1 <= B_i <= N),而它的长度 是 1 <= L_i <= 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p1,p2 (1 <= p1 <= N; 1 <= p2 <= N). 的形式给出.

    输入输出格式

    输入格式:

    * Line 1: Two space-separated integers: N and Q

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

    * Lines N+1..N+Q: Each line contains two space-separated integers representing two distinct pastures between which the cows wish to travel: p1 and p2

    输出格式:

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

    输入输出样例

    输入样例#1: 复制
    4 2 
    2 1 2 
    4 3 2 
    1 4 3 
    1 2 
    3 2 
    
    输出样例#1: 复制
    2 
    7 
    

    说明

    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.

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