P2886 [USACO07NOV]牛继电器Cow Relays

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  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 动态规划,动规,dp 最短路 矩阵乘法 USACO 2007 高性能
  • 难度 提高+/省选-
  • 时空限制 1000ms / 128MB

题解

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    题目描述

    For their physical fitness program, N (2 ≤ N ≤ 1,000,000) cows have decided to run a relay race using the T (2 ≤ T ≤ 100) cow trails throughout the pasture.

    Each trail connects two different intersections (1 ≤ I1i ≤ 1,000; 1 ≤ I2i ≤ 1,000), each of which is the termination for at least two trails. The cows know the lengthi of each trail (1 ≤ lengthi  ≤ 1,000), the two intersections the trail connects, and they know that no two intersections are directly connected by two different trails. The trails form a structure known mathematically as a graph.

    To run the relay, the N cows position themselves at various intersections (some intersections might have more than one cow). They must position themselves properly so that they can hand off the baton cow-by-cow and end up at the proper finishing place.

    Write a program to help position the cows. Find the shortest path that connects the starting intersection (S) and the ending intersection (E) and traverses exactly N cow trails.

    给出一张无向连通图,求S到E经过k条边的最短路。

    输入输出格式

    输入格式:

    * Line 1: Four space-separated integers: N, T, S, and E

    * Lines 2..T+1: Line i+1 describes trail i with three space-separated integers: lengthi , I1i , and I2i

    输出格式:

    * Line 1: A single integer that is the shortest distance from intersection S to intersection E that traverses exactly N cow trails.

    输入输出样例

    输入样例#1: 复制
    2 6 6 4
    11 4 6
    4 4 8
    8 4 9
    6 6 8
    2 6 9
    3 8 9
    输出样例#1: 复制
    10
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