#89. Cow Relays

Cow Relays

[USACO07NOV]Cow Relays G

题面翻译

给定一张 TT 条边的无向连通图,求从 SSEE 经过 NN 条边的最短路长度。

输入格式

第一行四个正整数 N,T,S,EN,T,S,E ,意义如题面所示。

接下来 TT 行每行三个正整数 w,u,vw,u,v ,分别表示路径的长度,起点和终点。

输出格式

一行一个整数表示图中从 SSEE 经过 NN 条边的最短路长度。

数据范围

对于所有的数据,保证 1N1061\le N\le 10^62T1002\le T\le 100

所有的边保证 1u,v10001\le u,v\le 10001w10001\le w\le 1000

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.

样例 #1

样例输入 #1

2 6 6 4
11 4 6
4 4 8
8 4 9
6 6 8
2 6 9
3 8 9

样例输出 #1

10