MPI Maelstrom（East Central North America 1996）（poj1502）

MPI Maelstrom

總時間限制: 

1000ms

 

記憶體限制: 

65536kB

描述

BIT has recently taken delivery of their new supercomputer, a 32 processor Apollo Odyssey distributed shared memory machine with a hierarchical communication subsystem. Valentine McKee's research advisor, Jack Swigert, has asked her to benchmark the new system. 
``Since the Apollo is a distributed shared memory machine, memory access and communication times are not uniform,'' Valentine told Swigert. ``Communication is fast between processors that share the same memory subsystem, but it is slower between processors that are not on the same subsystem. Communication between the Apollo and machines in our lab is slower yet.'' 

``How is Apollo's port of the Message Passing Interface (MPI) working out?'' Swigert asked. 

``Not so well,'' Valentine replied. ``To do a broadcast of a message from one processor to all the other n-1 processors, they just do a sequence of n-1 sends. That really serializes things and kills the performance.'' 

``Is there anything you can do to fix that?'' 

``Yes,'' smiled Valentine. ``There is. Once the first processor has sent the message to another, those two can then send messages to two other hosts at the same time. Then there will be four hosts that can send, and so on.'' 

``Ah, so you can do the broadcast as a binary tree!'' 

``Not really a binary tree -- there are some particular features of our network that we should exploit. The interface cards we have allow each processor to simultaneously send messages to any number of the other processors connected to it. However, the messages don't necessarily arrive at the destinations at the same time -- there is a communication cost involved. In general, we need to take into account the communication costs for each link in our network topologies and plan accordingly to minimize the total time required to do a broadcast.''

輸入

The input will describe the topology of a network connecting n processors. The first line of the input will be n, the number of processors, such that 1 <= n <= 100. 

The rest of the input defines an adjacency matrix, A. The adjacency matrix is square and of size n x n. Each of its entries will be either an integer or the character x. The value of A(i,j) indicates the expense of sending a message directly from node i to node j. A value of x for A(i,j) indicates that a message cannot be sent directly from node i to node j. 

Note that for a node to send a message to itself does not require network communication, so A(i,i) = 0 for 1 <= i <= n. Also, you may assume that the network is undirected (messages can go in either direction with equal overhead), so that A(i,j) = A(j,i). Thus only the entries on the (strictly) lower triangular portion of A will be supplied. 

The input to your program will be the lower triangular section of A. That is, the second line of input will contain one entry, A(2,1). The next line will contain two entries, A(3,1) and A(3,2), and so on.

輸出

Your program should output the minimum communication time required to broadcast a message from the first processor to all the other processors.

樣例輸入

5
50
30 5
100 20 50
10 x x 10

樣例輸出

35

來源

East Central North America 1996

題意：有N個處理器要傳信息，處理器給自己傳信息不需要時間，兩個人互相傳信息花費時間相等。問：從第一個處理器傳信息到其他所有處理器所用的最短時間。用鄰接矩陣輸入處理器傳信息的時間，如果兩台處理器不能傳信息就輸入‘x’。

思路：裸的單元最短路徑，可以用SPFA、Dijkstra。因為數據很小，N最大才是100，所以甚至可以用Floyd做。（身為蒟蒻的我只能用Floyd大暴力QAQ）

註意: 輸入有點坑，要用讀入優化或algorithm里的一種神奇函數atoi（），將字元轉為整型。

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
int n,ans,i,j,k,e[1077][1077];
int read()
{
    int x=0;
    char ch=getchar();
    while(ch<'0'||ch>'9')   {if(ch=='x') return 1000000000;ch=getchar();}
    while(ch>='0'&&ch<='9') {x=x*10+ch-'0';ch=getchar();}
    return x;
}
int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        memset(e,1000000000,sizeof(e));
        char s[8];
        for(i=2;i<=n;i++)
          for(j=1;j<i;j++)
            e[i][j]=e[j][i]=read();
        ans=-1;
        for(k=1;k<=n;k++)
            for(i=1;i<=n;i++)
            for(j=1;j<=n;j++)
                if(e[i][k]+e[k][j]<e[i][j])
                e[i][j]=e[i][k]+e[k][j];
        for(i=2;i<=n;i++)
          if(e[1][i]>ans)
            ans=e[1][i];
        printf("%d\n",ans);
    }
    return 0;
}