poj1502_最短路径

 poj1502

MPI Maelstrom

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 13350		Accepted: 8210

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

 分析：

1.迪杰斯特拉算法要点

1. 进行初始化
2. 找最短路径的下一个节点
3. 更新集合以外的其他节点到初始节点的距离

2.输入错误的抛出

 Integer.parseInt()和这个Integer.valueOf()的详解【转】

利用抛出错误，通过捕获来个目标赋值

 

/**
*@author yangyvting
*@date 2019年5月5日
*/
package 图论;

import java.util.Scanner;

public class Main {
	public static int n ; 	 
	public static boolean vis[];
	public static int graph[][];
	public static int min[] ;
	public static int NOTTO = 1000000000;

	public static void main(String[] args) {
		Scanner sca = new Scanner(System.in);
		n = sca.nextInt();
		graph = new int[n][n];
		vis = new boolean[n];
		min = new int[n];
		
		//输入数据
		for(int i = 1; i < n; i ++) {
			for(int j = 0; j < i; j ++) {
				try {
					int x = Integer.parseInt(sca.next());
					graph[j][i] = graph[i][j] = x;
				}catch (NumberFormatException e) {
					graph[j][i] = graph[i][j] = NOTTO;
				}
				
			}
		}
		long st = System.currentTimeMillis();
		Dijstra();
		long end = System.currentTimeMillis();
		
		
		int max = 0;
		for(int i = 0; i < n; i ++) {
			 if(max < min[i]) {
				 max = min[i];
			 }
	
		}
		System.out.println(max);
		System.out.println("Running Time :" + (end - st));
	}
	
 /**
  * Dijstra算法
  */
	private static void Dijstra() {
		//1.初始化
		for(int i = 1; i < n ; i ++) {		 
			min[i] = graph[0][i];		
		}
		vis[0] = true; //先将起始点归并大集合中
		
		//2.依次归并下一个节点
		int mn = 0 , mint = NOTTO;
		for(int i = 1; i < n ; i ++) {
			//找出最短边
			mint = NOTTO;
			for(int j = 0; j < n; j ++) {
				if(!vis[j]) {  //在集合外选一点
					if(min[j] < mint && !vis[j]  ) { 
						mint = min[j];
						mn = j;				 
					}
				}
			}
			if(mint == NOTTO)return;
			
			vis[mn] = true;
			 		
			//3.并更新最短路径
			for(int j = 0; j < n; j ++) {
				if( !vis[j] && graph[mn][j] != NOTTO) {         //在集合外选择有通过mn间接到达的点
					int dis = min[mn] + graph[mn][j];          //该点通过mn间接到达的距离				 
					if(dis < min[j]) {				 
						min[j] = dis;
					}
				}
			}
		}
			
		 
	}
	
 }

运行结果1

5
23 
3 23 
3 322 1
23 4 x 3
10
Running Time :0

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