Stockbroker Grapevine

墨蓝 2022-06-17 13:58 108阅读 0赞

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

题目大意是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"。不用考虑这种情况一样能AC

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

#include <cstring>
    #include <string>
    #include <cstdio>
    #include <algorithm>
    #include <iostream>
    using namespace std;
    const int inf=(1<<20);
    struct A
    {
        int x,time;
    };
    int main()
    {
        int n,m,a,b,dis[101][101];
        while(~scanf("%d",&n),n)
        {
            for(int i=0; i<101; i++)
            {
                for(int j=0; j<101; j++)
                {
                    if(i==j)
                        dis[i][j]=0;
                    else
                        dis[i][j]=inf;
                }
            }
            for(int j=1; j<=n; j++)
            {
                scanf("%d",&m);
                for(int i=1; i<=m; i++)
                {
                    scanf("%d %d",&a,&b);
                    dis[j][a]=b;
                }
            }
            //Floyd算法找出从i点到j点的最短时间,注意这里的最短时间不仅仅
            //指的是之间到达所用时间最短，还可以是间接到达所用的时间最短
            for(int i=1;i<=n;i++)
            {
                for(int j=1;j<=n;j++)
                {
                    for(int l=1;l<=n;l++)
                    {
                        if(dis[j][l]>dis[j][i]+dis[i][l])
                            dis[j][l]=dis[j][i]+dis[i][l];
                    }
                }
            }
            A q,p;
            q.time=inf;
            for(int i=1;i<=n;i++)
            {
                p.time=-1;
                //因为只有当 把传递消息耗时最久的那个传完，
                //才算所有人都传完了,(即所有人都知道了谣言)
                for(int j=1;j<=n;j++)
                {
                    if(p.time<dis[i][j])
                    {
                        p.time=dis[i][j];
                        p.x=i;
                    }
                }
                //上一步只是从其中某一个起点（或者说某一个人）那里传出，还可以从另外的传出啊
                //遍历就是了，找出最短的那个
                if(q.time>p.time)
                {
                    q.time=p.time;
                    q.x=p.x;
                }
            }
            printf("%d %d\n",q.x,q.time);
        }
        return 0;
    }