POJ 1125 Stockbroker Grapevine（Floyd多源最短路）

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.

Sample Input

3
2 2 4 3 5
2 1 2 3 6
2 1 2 2 2
5
3 4 4 2 8 5 3
1 5 8
4 1 6 4 10 2 7 5 2
0
2 2 5 1 5
0

Sample Output

3 2
3 10

题目大意：股票经纪人要在一群人中散布一个谣言，而谣言只能在亲密的人中传递，题目各处了人与人之间的关系及传递谣言所用的时间，要求程序给出应以那个人为起点，可以在最短的时间内让所有的人都得知这个谣言。

要注意从a到b传递的时间不一定等于从b到a的时间，如果没有方案能够让每一个人都知道谣言，则输出"disjoint"。（有关图的连通性，你懂得！但好像不用考虑这种情况一样能AC，只能说测试数据有点小水！）

题目数据的输入第一行为n，代表总人数，当n=0时结束程序，接着n行，第i+1行的第一个是一个整数t，表示第i个人与t个人的关系要好，接着有t对整数，每对的第一个数是j，表示i与j要好，第二个数是从i直接传递谣言到j所用的时间。

数据的输出是两个整数，第一个为选点的散布谣言的起点，第二个整数时所有人得知谣言的最短时间例如，对于数据1，可知如果从3开始播，则1，2得知谣言的时间都是2，所用的时间比从1，2开始传播所用的时间要短，故程序的输出时3 2；

解题思路：多源最短路Floyd()算法，详解见代码中的标注

具体代码:
#include <stdio.h>
#include <string.h>
#define INF 0x3f3f3f3f
#define Min(a,b) a>b?b:a
int map[200][200];
int dist[200][200];
int N;
void Floyd()
{
	int i,j,k;
	for(k=1;k<=N;k++)
		for(i=1;i<=N;i++)
			for(j=1;j<=N;j++)
				dist[i][j]=Min(dist[i][j],dist[i][k]+dist[k][j]);
}
int main()
{
	int n,i,j,v1,w;
	while(scanf("%d",&N) && N!=0)
	{
		memset(dist,INF,sizeof(dist));
		for(i=0;i<=N;i++)
			dist[i][i]=0;
		for(i=1;i<=N;i++)
		{ 
			scanf("%d",&n);
			for(j=1;j<=n;j++)
			{
				scanf("%d%d",&v1,&w);
				dist[i][v1]=w;//单向传递，有向图 
			}
		}
		Floyd();//弗洛伊德多源最短路 
		int begin1,begin,time,tmin=INF;
		for(i=1;i<=N;i++)
		{
			time=0;//每次从i点开始传递时，时间初始化为 0 
			for(j=1;j<=N;j++)//从起点i开始查找i能够到达点的所需最长时间
				if(dist[i][j]>time)
				{
					time=dist[i][j];//更新每次的从i作为起点得到的最大时间 
					begin1=i;//记录此时的起点 
				}
			if(time<tmin)//通过以上循环产生N个time，再求N个time中的最小值，并记录最小time时的begin 
			{
				tmin=time; begin=begin1;
			}
		}
		if(tmin>=INF)//不能全部传达到 
			printf("disjoint\n");
		else
			printf("%d %d\n",begin,tmin);	
	}
	return 0;
}