（关系幂运算->n长度的最短路）河南省第十届ACM省赛题目：问题 I: Transmit information

问题 I: Transmit information

时间限制: 3 Sec  内存限制: 128 MB
提交: 2  解决: 2
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题目描述

 The Chinese people threw themselves into an all-out war of resistance against Japanese aggression in 1937. The first line of  resistance against aggression was formed by spies and underground workers. 

They lurked  in every place of the city.

 

There's a piece of information that needs to be passed on to them.  Now there is a  traffic map, each road connects two different intersectionsXiand Yi, each of which is the termination for at least two road. The length of each road is known LENi,  no two intersections are directly connected by two different roads.

 

N spies lurk at every intersection , some intersections mignt have more than one spy. For security, they must position themselves properly ,each spy cannot accept information from localintersection ,  can only be transferred from elsewhere and end up at the finishing pace.

 

At first, the information is in the hands of a spy atS intersection. AfterN spies transmission, and finally arrived atE intersection .

 

Write a program to find the shortest path that connects the starting intersection(S) and the ending intersection(E) ang transmission exactly N spies.

 

输入

The first line of the input contains one integers T, which is the nember of  test cases (1<=T<=5).  Each test case specifies:

 

* Line 1:        Four space-separated integers:  N  M  S  E

* Lines 2..M+1:  Line i+1 describes road i with three space-separated integers:  LENi  Xi  Yi

 

          (  2<=N<=300,000  2<=M<=100,  1<= LENi, Xi, Yi ,S, E <=1000  i=1,…,m)

 

输出

For each test case generate a single line containing a single integer that is the shortest path from intersection S to intersection E thattransmits exactly N spies.

样例输入

12  6  6  411  4  64  4  88  4  96  6  82  6  93  8  9

样例输出

10

【体会】：这题在赛时连题意都没读懂。。。。。。。。

赛后百度到一篇题解，原来是求S到E点的长度为N的最短路。

竟然回到了离散知识。

对于邻接矩阵，进行关系的幂运算，就可以得到长度为指数的邻接矩阵。

比如邻接矩阵A，进行关系的幂运算，得到A的n次方，那得到的矩阵中的A[i][j]表示i到j的长度为n的路的权值

（我这里说的长度是走过的边的数目）

（关系的幂运算：利用关系的传递性，进行运算，跟矩阵乘法不一样。跟弗洛伊德算法相似）

转载一篇题解吧：http://blog.csdn.net/wyxeainn/article/details/72603049