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POJ 1502 MPI Maelstrom （Dijkstra算法）

2024-11-04 00:04:40   204人阅读

MPI Maelstrom
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 5712 Accepted: 3553

Description

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.‘‘

Input

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.

Output

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

Sample Input

5
50
30 5
100 20 50
10 x x 10

Sample Output

35

Source

East Central North America 1996



题意：信息传输，总共有n个传输机，先要从1号传输机向其余n-1个传输机传输数据，传输需要时间，给出一个严格的下三角（其实就是对角线之下的不包括对角线的部分）时间矩阵，a[i][j]代表从i向j传输数据需要的时间，并规定数据传输之间并无影响，即第一个传输机可以同时向其余传输机传输数据。求所有传输任务所需的最短时间。


解析：一个很裸的单元最短路，并且按题意可知边不可能为负值，那么直接用Dijkstra即可。求编号为1的传输机到所有传输机的最短传输时间之后，那么所有最短时间中的最大值即为完成传输任务的最短时间。

PS：这题的读入还是很恶心的，因为有x的存在，所以我们就需要把数字当成字符串去读，然后再将其转成int。




AC代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <stack>
using namespace std;
#define INF 0x7fffffff
#define LL long long
#define MID(a, b)  a+(b-a)/2
const int maxn = 1000 + 10;

#pragma comment(linker, "/STACK:1024000000,1024000000")       //手动扩栈

//适用于正负整数
template <class T>
inline bool scan_d(T &ret) {
 char c; int sgn;
 if(c=getchar(),c==EOF) return 0; //EOF
 while(c!='-' &&(c<'0' ||c>'9' )) c=getchar();
 sgn=(c=='-' )?-1:1;
 ret=(c=='-' )?0:(c-'0' );
 while(c=getchar(),c>='0' &&c<='9' ) ret=ret*10+(c-'0' );
 ret*=sgn;
 return 1;
}
inline void out(int x) {
 if(x>9) out(x/10);
 putchar(x%10+'0' );
}

int w[102][102];             //时间矩阵
int v[102], d[102];          //v[]是否访问过，d[]最短距离

int input(){                 //读入数据
    char str[10];
    scanf("%s", &str);
    if(!strcmp(str, "x")) return 123456789;     //如果是x，代表无穷大，两点之间无路径
    else{                                       //如果不是，转成int
        int ans = 0;
        int len = strlen(str);
        for(int i=0; i<len; i++){
            ans = ans*10 + str[i] - '0';
        }
        return ans;
    }
}

int main(){
    #ifdef sxk
        freopen("in.txt", "r", stdin);
    #endif // sxk

    std::ios::sync_with_stdio(false);         //cin加速
    std::cin.tie(0);

    int n;
    while(scanf("%d", &n)!=EOF){
        for(int i=1; i<=n; i++)         //读入数据
            for(int j=1; j<=i; j++){
                if(i == j) w[i][j] = 0;
                else  w[j][i] = w[i][j] = input();
            }

        memset(v, 0, sizeof(v));         //预处理
        for(int i=1; i<=n; i++) d[i] = (i == 1 ? 0 : 123456789);
        for(int i=1; i<=n; i++){         //dijestral
            int x, m = 123456789;
            for(int y=1; y<=n; y++)
                if(!v[y] && d[y] <= m){
                x = y;
                m = d[x];
            }
            v[x] = 1;
            for(int y=1; y<=n ;y++) d[y] = min(d[y], d[x] + w[x][y]);
        }
        int ans = -123456789;
        for(int i=1; i<=n; i++){
            if(ans < d[i]) ans = d[i];
        }
        printf("%d\n", ans);
    }
    return 0;
}





POJ 1502 MPI Maelstrom （Dijkstra算法）


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