pku 3613 Cow Relays

题意：给一个无向图，求从起点s到终点e尽力n条边的路径最小值。



边的数量2<=t<=100(每条边可以重复遍历)



算法：利用dp求出 path[ l ] [ i ] [ k ]=MIN(path[ l ][ i ] [ k ] , path[ l ][ i ] [ j ] + path[ l ][ j ] [ k ])



l 表示的是2的指数，假设 i 到 k 要途径 2^l 条边，那么他可以被分为两段 途径2^（l - 1）的路径。



利用开始的输入，然后递推，就可以推出所有的状态。



当需要找途经N条边的路径最小值时.将上面的值有效的组合起来.



上面求出了 1 2 4 8 16 …… 时的任意两条边的代价



对应的二进制是 1 10 100 1000 10000 ……



N可以拆成相应的二进制，然后用类似矩阵相乘的方法，往下推，就得到答案



m表示节点个数，(aXb)表示a行b列的矩阵一个 ，那么（1Xm）* path[ l ](mXm) 。



最终复杂度为O（t^3logn）

-Cow Relays

Time Limit: 1000MS　Memory Limit: 65536K

Total Submissions: 1163　Accepted: 433



Descr iption



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