POJ 1502 MPI Maelstrom / UVA 432 MPI Maelstrom / SCU 1068 MPI Maelstrom / UVALive 5398 MPI Maelstrom /ZOJ 1291 MPI Maelstrom （最短路径）

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

Http

POJ:https://vjudge.net/problem/POJ-1502

UVA:https://vjudge.net/problem/UVA-423

SCU:https://vjudge.net/problem/SCU-1068

UVALive:https://vjudge.net/problem/UVALive-5398

ZOJ:https://vjudge.net/problem/ZOJ-1291

Source

图论，最短路径

题目大意

在一个无向图中有n个点，现在从1号点开始传递信息，每传递到一个点，这个点也可以开始传递信息。一个点可以同时向多个方向传递。问使所有点收到信息的最短时间

解决思路

一开始看到这道题以为是最小生成树，但如果手动模拟一下，发现就是Dijkstra算法的过程，即：

寻找当前已经确定的点的集合相连的点中路径最小的，加入已确定集合，并用其修改其他点的最短路径。

这就是求最短路径的算法

关键要理解题意。

注意：ZOJ有多组数据

代码

#include<iostream>

#include<cstdio>

#include<cstdlib>

#include<cstring>

#include<algorithm>

using namespace std;

const int maxN=100;

const int inf=147483647;

int n;

int M[maxN][maxN];

int Dist[maxN];

bool solve[maxN];

int read();

int main()

{

	int T;

	//cin>>T;//ZOJ有多组数据

	//for (int ti=1;ti<=T;ti++)

	//{

	cin>>n;

	for (int i=1;i<=n;i++)

	{

		M[i][i]=0;

		for (int j=1;j<i;j++)

		{

			M[i][j]=M[j][i]=read();

		}

	}

	for (int i=1;i<=n;i++)

	    Dist[i]=M[1][i];

	memset(solve,0,sizeof(solve));

	for (int i=1;i<n;i++)

	{

		int id,mi=inf;

		for (int j=1;j<=n;j++)

		    if ((solve[j]==0)&&(Dist[j]<mi))

		    {

		    	mi=Dist[j];

		    	id=j;

			}

		solve[id]=1;

		for (int j=1;j<=n;j++)

		    if ((solve[j]==0)&&(Dist[id]+M[id][j]<Dist[j]))

		    {

		    	Dist[j]=Dist[id]+M[id][j];

			}

	}

	int Ans=0;

	for (int i=1;i<=n;i++)

	    Ans=max(Ans,Dist[i]);

	cout<<Ans<<endl;

	//if (ti!=T)

	//    cout<<endl;//ZOJ还要调格式

//}

	return 0;

}

int read()

{

	int x=0;

	int k=1;

	char ch=getchar();

	while (((ch>'9')||(ch<'0'))&&(ch!='-')&&(ch!='x'))

	    ch=getchar();

	if (ch=='x')//快速读入修改一下，如果是x就返回无穷大

	    return inf;

	if (ch=='-')

	{

		k=-1;

		ch=getchar();

	}

	while ((ch>='0')&&(ch<='9'))

	{

		x=x*10+ch-48;

		ch=getchar();

	}

	return x*k;

}