Poj 1125 Stockbroker Grapevine(Floyd算法求结点对的最短路径问题)

一、Description

Stockbrokers are known to overreact to rumours. You have been contracted to develop a method of spreading disinformation amongst the stockbrokers to give your employer the tactical edge in the stock market. For maximum effect,
you have to spread the rumours in the fastest possible way.

Unfortunately for you, stockbrokers only trust information coming from their "Trusted sources" This means you have to take into account the structure of their contacts when starting a rumour. It takes a certain amount of time for a specific stockbroker to pass
the rumour on to each of his colleagues. Your task will be to write a program that tells you which stockbroker to choose as your starting point for the rumour, as well as the time it will take for the rumour to spread throughout the stockbroker community.
This duration is measured as the time needed for the last person to receive the information.

Input

Your program will input data for different sets of stockbrokers. Each set starts with a line with the number of stockbrokers. Following this is a line for each stockbroker which contains the number of people who they have contact
with, who these people are, and the time taken for them to pass the message to each person. The format of each stockbroker line is as follows: The line starts with the number of contacts (n), followed by n pairs of integers, one pair for each contact. Each
pair lists first a number referring to the contact (e.g. a '1' means person number one in the set), followed by the time in minutes taken to pass a message to that person. There are no special punctuation symbols or spacing rules.

Each person is numbered 1 through to the number of stockbrokers. The time taken to pass the message on will be between 1 and 10 minutes (inclusive), and the number of contacts will range between 0 and one less than the number of stockbrokers. The number of
stockbrokers will range from 1 to 100. The input is terminated by a set of stockbrokers containing 0 (zero) people.

Output

For each set of data, your program must output a single line containing the person who results in the fastest message transmission, and how long before the last person will receive any given message after you give it to this person,
measured in integer minutes.

It is possible that your program will receive a network of connections that excludes some persons, i.e. some people may be unreachable. If your program detects such a broken network, simply output the message "disjoint". Note that the time taken to pass the
message from person A to person B is not necessarily the same as the time taken to pass it from B to A, if such transmission is possible at all.

二、题解

        该题的英文比题目更难懂啊，幸好BBS上有大神的翻译和解释，下面就是引用：

        首先，题目可能有多组测试数据，每个测试数据的第一行为经纪人数量N（当N=0时，输入数据结束），然后接下来N行描述第i（1<=i<=N）个经纪人与其他经纪人的关系 。每行开头数字M为该行对应的经纪人有多少个经纪人朋友（该节点的出度，可以为0），然后紧接着M对整数，每对整数表示成a,b,则表明该经纪人向第a个经纪人传递信息需要b单位时间（即第i号结点到第a号结点的孤长为b），整张图为有向图，即弧Vij 可能不等于弧Vji。当构图完毕后，求当从该图中某点出发，将“消息”传播到整个经纪人网络的最小时间，输出这个经纪人号和最小时间。最小时间的判定方式为——从这个经纪人（结点）出发，整个经纪人网络中最后一个人接到消息的时间。如果有一个或一个以上经纪人无论如何无法收到消息，输出“disjoint”（有关图的连通性，你们懂得，但据其他同学说，POJ测试数据中不会有，就是说，你不判定，一样能过，题目数据够水的）。

       解决这个问题的方法有本文所用的Floyd-Warshall算法，也可以用迪杰斯特拉最短路径算法。Floyd-Warshall算法详见算法，我已经在前篇文章中简单介绍了一下。

三、Java代码

import java.util.Scanner;

public class Main {
	static int[][] map;
	static int[][][] dist;
	static int n;
	static int INF=Integer.MAX_VALUE;
	public static void floyd(){
		  int i,j,k;
	      for(k=1;k<=n;k++){
	          for(i=1;i<=n;i++){
	             for(j=1;j<=n;j++){
	            	 if (i!=j && map[i][k]!=INF && map[k][j]!=INF && map[i][k] + map[k][j] < map[i][j]) {
	            		 map[i][j] = map[i][k] + map[k][j];
                     }
	              }
	          }
	      }
	}
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int i,j,temp,temp2,temp3;
		while((n=sc.nextInt())!=0){
			map=new int[n+1][n+1];
			for(i=0;i<=n;i++){
				for(j=0;j<=n;j++){
					map[i][j]= (i==j)? 0:INF;
				}
			}
			for(i=1;i<=n;i++){
				temp=sc.nextInt();
				for(j=1;j<=temp;j++){
					temp2=sc.nextInt();
					temp3=sc.nextInt();
					map[i][temp2]=temp3;
				}
			}
			 floyd();
			 int min=INF;
			 int max;
			 int number = 0;
			 for(i=1;i<=n;i++){
				  max=Integer.MIN_VALUE;
		          for(j=1;j<=n;j++){
		            	if(map[i][j]>max)
		            	  	max=map[i][j];
		          }
		          if(max!= INF && max!=0 && max<min){
		        	  min=max;
		        	  number=i;
		          }
			 }
			 if(min==INF)
				 System.out.println("disjoint");
			 else
				 System.out.println(number+" "+min);
		}
	}
}

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